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+[
+    {
+        "url": "http://arxiv.org/abs/2404.17943v1",
+        "title": "Interaction Event Forecasting in Multi-Relational Recursive HyperGraphs: A Temporal Point Process Approach",
+        "abstract": "Modeling the dynamics of interacting entities using an evolving graph is an\nessential problem in fields such as financial networks and e-commerce.\nTraditional approaches focus primarily on pairwise interactions, limiting their\nability to capture the complexity of real-world interactions involving multiple\nentities and their intricate relationship structures. This work addresses the\nproblem of forecasting higher-order interaction events in multi-relational\nrecursive hypergraphs. This is done using a dynamic graph representation\nlearning framework that can capture complex relationships involving multiple\nentities. The proposed model, \\textit{Relational Recursive Hyperedge Temporal\nPoint Process} (RRHyperTPP) uses an encoder that learns a dynamic node\nrepresentation based on the historical interaction patterns and then a\nhyperedge link prediction based decoder to model the event's occurrence. These\nlearned representations are then used for downstream tasks involving\nforecasting the type and time of interactions. The main challenge in learning\nfrom hyperedge events is that the number of possible hyperedges grows\nexponentially with the number of nodes in the network. This will make the\ncomputation of negative log-likelihood of the temporal point process expensive,\nas the calculation of survival function requires a summation over all possible\nhyperedges. In our work, we use noise contrastive estimation to learn the\nparameters of our model, and we have experimentally shown that our models\nperform better than previous state-of-the-art methods for interaction\nforecasting.",
+        "authors": "Tony Gracious, Ambedkar Dukkipati",
+        "published": "2024-04-27",
+        "updated": "2024-04-27",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI",
+            "cs.SI"
+        ],
+        "label": "Original Paper",
+        "paper_cat": "Temporal AND Graph",
+        "gt": "The current works on interaction forecasting on networks are of two kinds, the ones that are trained using TPP loss and the ones that are using link prediction. The models in the first category parameterize the probability density function of a Neural Temporal Point Process with edges as the mark associated with events [28]. These involve models DeepCoevolve [10], DyReP [30], DSPP [5], and GNPP [33] that uses neural networks to parameterize the conditional intensity function of a TPP based on the nodes involved in the edges. These works mostly focus on interaction forecasting on bipartite and homogeneous networks. More recently, GHNN [17] defined TPPs on Temporal Knowledge Graphs where entities of different kinds and interactions are associated with relation type. However, all these models are developed for pair-wise interaction forecasting and cannot accurately model the higher-order interactions. Recent work [15] modeled higher-order interactions as hyperedge event formation in a network. Although this model can capture interactions between any number of nodes, it does not consider the internal groupings of nodes or their relationships with other nodes, such as in email exchanges or co-authorship networks. The works in the second category use graph representation learning to learn continuous-time representations for the nodes that are then used to predict links using a binary scoring function. This involves models like JODIE [21], TGAT [9], and TGN [27]. These models can only predict the presence of an interaction at a given time and cannot answer temporal queries like when two nodes will interact or the time of the next interaction.",
+        "pre_questions": [],
+        "main_content": "INTRODUCTION With the rise in the field of geometric deep learning, there is a new interest in learning representations from higher-order relations in networks [3, 4]. These works mostly focused on hypergraphs where relations are represented as hyperedges that represent interactions of groups of entities/nodes [1, 14, 22]. With the availability of richer datasets and better computational facilities one can go beyond hypergraphs by incorporating a wide variety of information associated with the interaction. These ideas are being explored in recent works of topology-aware deep learning where higher-order network structures such as simplicial complexes, cell complexes, and multi-scale topological information are used for improving graph neural networks [16, 18]. Recent works have shown that n-ary facts or multi-relational hyperedges are the natural data representations for Knowledge graphs, and models based on those perform better than that use pairwise multi-relation models [12, 32]. Most of these works ignore the temporal aspects of the network, where entities interact and evolve. This has been addressed using dynamic network models based on temporal point processes (TPP) and link prediction. The existing works model interactions as instantaneous edges [5, 10, 21, 30]/hyperedges [15] forming between a pair of nodes or a group of nodes, and a generative model is parameterized to model the formation of edges given the history. However, real-world interactions can be much more complex than just a group of entities interacting. These interactions can exhibit group structure within themselves. For example, a directed hyperedge involves interaction between two groups of entities in the source and destination. Here, one can represent the source and destination as hyperedges which act as nodes to the interaction hyperedge. In our work, we generalize this recursive group structure property of real-world interactions to incorporate a variable number of groupings. Examples of these types of interaction can be seen in email exchanges, where there are sender, recipients, and carbon-copied recipients (CCed) addresses. Each group except the sender can have a variable number of addresses, and CCed group is not always present in an email exchange. Similarly, in citation networks, the authors of a scientific article are ordered according to their contributions to the work. Here, the author\u2019s position is the grouping, and multiple authors can be in the same position. We use a multi-relational recursive hyperedges structure to incorporate these complex higher-order interactions. Here, hyperedges can act as nodes in other hyperedges (like CCed or receiver groups in email interactions) and contain relation types indicating their role in the interactions. Then a TPP is defined with these hyperedges as event types with conditional intensity function parameterized using representations/embeddings of the nodes and relations involved in the interactions. Furthermore, the previous approaches in TPP based interaction forecasting use negative sampling to approximate the loss associated with survival function, which is intractable to calculate due to the huge number of possible event types in the TPP. arXiv:2404.17943v1  [cs.LG]  27 Apr 2024 Tony Gracious and Ambedkar Dukkipati This can introduce biases in training, especially in these complex interactions. To address these challenges, we propose the model Relational Recursive Hyperedge Temporal Point Process (RRHyperTPP), and the following are the contributions of our work, (i) A contrastive learning strategy for higher-order interaction for hyperedge events in networks. This provides a more principled way of training our model without maximum likelihood estimation, thereby avoiding the computationally expensive survival function calculation. Our model performs better than the previous models that use negative sampling; (ii) New deep learning architecture for learning node representation from higher-order interaction. This involves two stages: interaction update and temporal drift. Interaction update is used to revise the node representation when an event involving it occurs by using the features of the type of interaction. Temporal drift is used to model the evolution of node representation during the interevent period using time projection based on JODIE [21] or Neural ODE [6] or time embeddings based on Fourier time features [9]; (iii) A new method for hyperedge link prediction for multi-relational recursive hypergraphs; (iv) Curated eight datasets for temporal multi-relational recursive hypergraphs; (v) Extensive experiments are done to show the advantage of our model over existing state-of-the-art models. Hypergraph. A Hypergraph is denoted by the tuple G = (V, H), where V = {\ud835\udc631, \ud835\udc632, . . . , \ud835\udc63|V|} is the set of nodes, H is the set of hyperedges with H \u2282C(V) and C(V) is the powerset of V. Sender Recievers CCed v1 v2 v3 v4 v5 v6 Figure 1: Email exchange between a group of people is represented as a Relational Recursive Hyperedges depth. Here, the sender involves a single person and multiple persons are in CCed and Receiver groups. Recursive Hypergraph. A Recursive Hypergraph G = (V, H) is a generalization of Hypergraph, where hyperedges can contain nodes and other hyperedges. Let, H\ud835\udc59= C(\u222a\ud835\udc59\u22121 \ud835\udc56=0 H\ud835\udc56) if \ud835\udc59\u22651, where H0 = C(V). A recursive hypergraph is of depth \ud835\udc59if H \u2282H\ud835\udc59. This work focuses on recursive hypergraphs of depth one and two. The following is the experimental setting followed in this paper. Temporal Multi-relational Recursive Hypergraphs. A Temporal Multi-relational Recursive hypergraph is denoted by tuple G(\ud835\udc61) = (V, H, R, E(\ud835\udc61)), where E(\ud835\udc61) = {(\ud835\udc521,\ud835\udc611), . . . , (\ud835\udc52\ud835\udc41,\ud835\udc61\ud835\udc41)} is the ordered set of historical events till time \ud835\udc61with \ud835\udc52\ud835\udc5b\u2208H and \ud835\udc5bis number events occurred and R is the set of relation. Here, each hyperedge \u210e\u2208H is formed of a set of recursive hyperedges, \u210e= \u210e\ud835\udc59= {(\u210e\ud835\udc59\u22121 1 ,\ud835\udc5f\ud835\udc59\u22121 1 ), . . . , (\u210e\ud835\udc59\u22121 \ud835\udc58\ud835\udc59\u22121,\ud835\udc5f\ud835\udc59\u22121 \ud835\udc58\ud835\udc59\u22121)} of depth \ud835\udc59. Here, \ud835\udc5f\ud835\udc59\u22121 \ud835\udc56 \u2208R is the relation of hyperedge \u210e\ud835\udc59\u22121 with respect to hyperedge \u210e\ud835\udc59, and {(\u2212 1 \u2212 1 ) (\u2212 \ud835\udc58\ud835\udc59\u22121\u2212 \ud835\udc58\ud835\udc59\u22121)}\u2212 \ud835\udc56 \u2208R is the relation of hyperedge \u210e\ud835\udc59\u22121 \ud835\udc56 with respect to hyperedge \u210e\ud835\udc59, and \u210e\ud835\udc59\u22121 \ud835\udc56 \u2208H\ud835\udc59\u22121. Here, \ud835\udc58\ud835\udc59\u22121 is the number of relational groups, or depth zero hyperedges in hyperedge \u210e, and E(\ud835\udc61\ud835\udc4e,\ud835\udc61\ud835\udc4f) is the ordered set of events observed during the interval [\ud835\udc61\ud835\udc4e,\ud835\udc61\ud835\udc4f]. Using the above definition, we can represent a Directed temporal hypergraph by using relations indicating the source and destination groups, here |R| = 2. Furthermore, including the node type attribute, we can extend this definition to a Bipartite Temporal Hypergraph where the nodes set is a union of two types, V = U\ud835\udc5f\u222aU\ud835\udc59. Here, U\ud835\udc5f and U\ud835\udc59are the two sets of nodes, and all interactions are between where the nodes set is a union of two types, V = U\u222aU. Here, U and U\ud835\udc59are the two sets of nodes, and all interactions are between them. To use this framework for Temporal Knowledge Graph (TKGs) where interactions are represented as a triplet of the subject entity \ud835\udc63\ud835\udc60, object entity \ud835\udc63\ud835\udc5c, and relation \ud835\udc5fbetween them, \u210e= (\ud835\udc63\ud835\udc60,\ud835\udc5f, \ud835\udc63\ud835\udc5c)). Here, \ud835\udc63\ud835\udc60, \ud835\udc63\ud835\udc5c\u2208V. This can be framed as a Multi-relational Recursive Hypergraph with \u210e= {(\u210e0 0,\ud835\udc5f0 1), (\u210e0 1,\ud835\udc5f0 2)}. Here, \ud835\udc5f0 1 = \ud835\udc5f,\ud835\udc5f0 2 = \ud835\udc5f\u22121 is the inverse relation, \u210e0 0 = {\ud835\udc63\ud835\udc60}, and \u210e0 1 = {\ud835\udc63\ud835\udc5c}.  Given historical interac{}  {} Problem. Given E(\ud835\udc61) = {(\ud835\udc521,\ud835\udc611), . . . , (\ud835\udc52\ud835\udc5b,\ud835\udc61\ud835\udc5b)} historical interactions until time \ud835\udc61> \ud835\udc61\ud835\udc5b, we aim to forecast the next interaction (\ud835\udc61\ud835\udc5b+1,\ud835\udc52\ud835\udc5b+1) where \ud835\udc61\ud835\udc5b+1 > \ud835\udc61> \ud835\udc61\ud835\udc5b. Here, we want to estimate the time \ud835\udc61\ud835\udc5b+1 and the type of interaction \ud835\udc52\ud835\udc5b+1. This work mainly focuses on higher-order interactions in communications networks and real-world events stored in source and target entities. The higher-order interaction in communications networks is represented using a recursive hyperedge graph of Intereaction Event Forecasting in Multi-Relational Recursive HyperGraphs Actor Sector Country Putin Russia Government Politics Actor Sector Country EU Belgium Organisation Politics Federation SpokedIn InverseSpokedIn Figure 2: Real world events represented as Relational Recursive Hyperedges. Here, there are source and target hyperedges with three relations inside them and a relation type indicating the nature of the interaction. depth one \u210e= {(\u210e0 \ud835\udc56,\ud835\udc5f0 \ud835\udc56))}\ud835\udc580 \ud835\udc56=0. Here, relations are used to represent {\ud835\udc5f0 \ud835\udc56}3 \ud835\udc56=0 the sender, recipients, and carbon-copied recipients\u2019 addresses in case of email exchange and {\ud835\udc5f0 \ud835\udc56}4 \ud835\udc56=0 represents the sender, receiver, retweeter, and retweeted nodes in Twitter network. Figure 1 shows an email exchange as a higher-order interaction of depth one. The e higher-order interaction in real-world events is represented using depth two hypergraphs \u210e= {(\u210e1 0,\ud835\udc5f1 0), (\u210e1 1,\ud835\udc5f1 1)} and \u210e1 0/1 = {(\u210e0 \ud835\udc56,\ud835\udc5f0 \ud835\udc56)}3 \ud835\udc56=0. Here, \u210e1 0,\u210e1 1 are the two entities involved in the interactions, \ud835\udc5f1 0 and \ud835\udc5f1 1 are the inverse relation pair indicating the type of interactions, {\ud835\udc5f0 \ud835\udc56}3 \ud835\udc56=0 is relation indicating the actor, sector, country of the entity. Figure 2 shows an example of this type of higher-order interaction. 4 RRHYPERTPP MODEL The probability of the occurrence of hyperedge event \u210eat time \ud835\udc61is defined as follows, P\u210e(\ud835\udc61) = \ud835\udf06\u210e(\ud835\udc61)S\u210e(\ud835\udc61\ud835\udc5d \u210e,\ud835\udc61). (1) Here, \ud835\udf06\u210e(\ud835\udc61) is the conditional intensity function of the temporal point process, S\u210e(\ud835\udc61\ud835\udc5d \u210e,\ud835\udc61) is the survival function that denotes the probability that the event does not occur during the interval [\ud835\udc61\ud835\udc5d \u210e,\ud835\udc61], S\u210e(\ud835\udc61\ud835\udc5d \u210e,\ud835\udc61) = exp   \u2212 \u222b\ud835\udc61 \ud835\udc61\ud835\udc5d \u210e \ud835\udf06\u210e(\ud835\udf0f)d\ud835\udf0f ! . (2) In this, \ud835\udc61\ud835\udc5d \u210e< \ud835\udc61is the time of the last occurrence of hyperedge \u210e before time \ud835\udc61, and it is initialized to zero for all the hyperedges at the beginning. The complete likelihood for observing E(\ud835\udc47) = {(\ud835\udc521,\ud835\udc612), . . . , (\ud835\udc52\ud835\udc41,\ud835\udc61\ud835\udc41)} in the interval [0,\ud835\udc47] can be written as, P(E(\ud835\udc47)) = \ud835\udc41 \u00d6 \ud835\udc5b=1 P\ud835\udc52\ud835\udc5b(\ud835\udc61\ud835\udc5b) \u00d6 \u210e\u2208H S\u210e(\ud835\udc61\u2113 \u210e,\ud835\udc47). (3) Here, \ud835\udc61\u2113 \u210eis the last occurrence of hyperedge \u210ewith \ud835\udc61\u2113= 0 for \u210e\u2208H that is not observed in the training data. P(E(\ud835\udc47)) = \ud835\udc41 \u00d6 \ud835\udc5b=1 \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61\ud835\udc5b)S\ud835\udc52\ud835\udc5b(\ud835\udc61\ud835\udc5d \ud835\udc52\ud835\udc5b,\ud835\udc61\ud835\udc5b) \u00d6 \u210e\u2208H S\u210e(\ud835\udc61\u2113 \u210e,\ud835\udc47), P(E(\ud835\udc47)) = \ud835\udc41 \u00d6 \ud835\udc5b=1 \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61\ud835\udc5b) \u00d6 \u210e\u2208H S\u210e(0,\ud835\udc47). (4) For learning the parameters of conditional intensity \ud835\udf06\u210e(\ud835\udc61), we calculate the loss by taking a negative log-likelihood as shown below, NLL = \u2212 \ud835\udc41 \u2211\ufe01 \ud835\udc5b=1 log \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61\ud835\udc5b) + \u2211\ufe01 \u210e\u2208H \u222b\ud835\udc47 0 \ud835\udf06\u210e(\ud835\udc61)d\ud835\udc61. (5) However, direct minimization of the above loss function is computationally expensive due to the summation over all possible hyperedges in the survival function, which have an exponential number of possibilities, and also due to the integral over the entire duration of observation \u222b\ud835\udc47 0 (.). So, to avoid these difficulties in computing the likelihood, we use the noise contrastive estimation technique of learning multivariate temporal point process [24] as explained in Section 4.1. Furthermore, defining separate conditional intensity functions for each hyperedge will lead to difficulty in learning, as the number of parameters will increase linearly to the number of hyperedges, which is exponential on the order of the number of nodes, as explained earlier. It leads to overfitting while training and poor generalization in the test set. Hence, we define the conditional function as a positive function of dynamic embeddings nodes involved in it, \ud835\udf06\u210e(\ud835\udc61) = \ud835\udc53(\u210e; V(\ud835\udc61), R). Here, V(\ud835\udc61) is the dynamic node embedding of nodes at time \ud835\udc61, and R is the relation embeddings. In this model, the number of parameters will be linear to the number of nodes, as hyperedges that share nodes will share the respective parameters. 4.1 Learning and Inference An alternate approach to MLE for learning parameters is to use noise contrastive estimation (NCE). To achieve this, we discretize the training period [0,\ud835\udc47] into intervals of size \u0394\ud835\udc61and simulate \ud835\udc41\ud835\udc5enoise streams {E\ud835\udc56(\ud835\udc61,\ud835\udc61+ \u0394\ud835\udc61)}\ud835\udc41\ud835\udc5e \ud835\udc56=1 from the noise distribution Q(.|E(\ud835\udc61)) in addition to observed data E0(\ud835\udc61,\ud835\udc61+\u0394\ud835\udc61) = E(\ud835\udc61,\ud835\udc61+\u0394\ud835\udc61). In the following section, we will also use the zeroth index to denote the observed events for ease of depiction. Then the model parameters are trained to discriminate true and noise events from the candidate set {E\ud835\udc56(\ud835\udc61,\ud835\udc61+ \u0394\ud835\udc61)}\ud835\udc41\ud835\udc5e \ud835\udc56=0. This can be written as follows, log   P\u2217\u0010 E0(\ud835\udc61,\ud835\udc61+ \u0394\ud835\udc61) \u0011 \ud835\udc41\ud835\udc5e \u00d6 \ud835\udc56=1 Q\u2217(E\ud835\udc56(\ud835\udc61,\ud835\udc61+ \u0394\ud835\udc61)) ! \u2212 log \u00a9 \u00ad \u00ab \ud835\udc41\ud835\udc5e \u2211\ufe01 \ud835\udc56=0 P\u2217(E\ud835\udc56(\ud835\udc61,\ud835\udc61+ \u0394\ud835\udc61)) \ud835\udc41\ud835\udc5e \u00d6 \ud835\udc57\u2260\ud835\udc56,\ud835\udc57=1 Q\u2217(E \ud835\udc57(\ud835\udc61,\ud835\udc61+ \u0394\ud835\udc61))\u00aa \u00ae \u00ac . Here, P\u2217(\u00b7) = P(\u00b7|E(\ud835\udc61)) and Q\u2217(\u00b7) = Q(\u00b7|E(\ud835\udc61)). However, we still need to calculate the integral \u00cd \u210e\u2208H \u222b\ud835\udc61+\u0394\ud835\udc61 \ud835\udc61 in the probability density function, which is still computationally expensive. The solution is to shrink the interval to an infinitesimal width of d\ud835\udc61when lim d\ud835\udc61\u21920. Then we can rewrite the above equation as, log   P\u2217\u0010 E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) \u0011 \ud835\udc41\ud835\udc5e \u00d6 \ud835\udc56=1 Q\u2217(E\ud835\udc56(\ud835\udc61,\ud835\udc61+ d\ud835\udc61)) ! \u2212 log \u00a9 \u00ad \u00ab \ud835\udc41\ud835\udc5e \u2211\ufe01 \ud835\udc56=0 P\u2217(E\ud835\udc56(\ud835\udc61,\ud835\udc61+ d\ud835\udc61)) \ud835\udc41\ud835\udc5e \u00d6 \ud835\udc57\u2260\ud835\udc56,\ud835\udc57=1 Q\u2217(E \ud835\udc57(\ud835\udc61,\ud835\udc61+ d\ud835\udc61))\u00aa \u00ae \u00ac . Here, in the interval [\ud835\udc61,\ud835\udc61+ d\ud835\udc61], an event will be observed E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = {(\u210e,\ud835\udc61)} or a null event will be observed E0(\ud835\udc61,\ud835\udc61+d\ud835\udc61) = {(\u2205,\ud835\udc61)} Tony Gracious and Ambedkar Dukkipati with respect to the distribution P\u2217\u0000E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61)\u0001. So, the probability distribution should satisfy the following inequality at the interval [\ud835\udc61,\ud835\udc61+ d\ud835\udc61], \u2211\ufe01 \u210e\u2208H P\u2217\u0010 E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = (\u210e\ud835\udc56,\ud835\udc61) \u0011 + P\u2217\u0010 E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = (\u2205,\ud835\udc61) \u0011 =1, \u2211\ufe01 \u210e\u2208H \ud835\udf06\u210e(\ud835\udc61)d\ud835\udc61+ P\u2217\u0010 E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = (\u2205,\ud835\udc61) \u0011 =1. (6) Here, P\u2217\u0000E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = {(\u210e,\ud835\udc61)}\u0001 = \ud835\udf06\u210ed\ud835\udc61from the temporal point process conditional intensity function definition, and P\u2217\u0010 E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = (\u2205, 1) \u0011 = 1, when d\ud835\udc61\u21920. Similarly, we can define Q\u2217\u0000E\ud835\udc56(\ud835\udc61,\ud835\udc61+ d\ud835\udc61)\u0001 using its definition of conditional intensity function. As a result of this, our objective function when there are no events in the observed stream E0(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = (\u2205,\ud835\udc61) and in the \ud835\udc41\ud835\udc5enoise streams {E\ud835\udc56(\ud835\udc61,\ud835\udc61+d\ud835\udc61) = {(\u2205,\ud835\udc61)}}\ud835\udc41\ud835\udc5e \ud835\udc56=1 becomes log 1 \ud835\udc41\ud835\udc5e+1. However, when event \u210eoccurs in the true data stream or the noise data stream. The loss could be written as follows, log \ud835\udf06\u210e(\ud835\udc61) \ud835\udf06\u210e(\ud835\udc61) + \ud835\udf06\ud835\udc5e \u210e(\ud835\udc61)\ud835\udc41\ud835\udc5eif E(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = {(\u210e,\ud835\udc61)} else, for \ud835\udc56= 1 to \ud835\udc41\ud835\udc5e, log \ud835\udf06\ud835\udc5e \u210e(\ud835\udc61) \ud835\udf06\u210e(\ud835\udc61) + \ud835\udf06\ud835\udc5e \u210e(\ud835\udc61)\ud835\udc41\ud835\udc5eif \u2203E\ud835\udc56(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = {(\u210e,\ud835\udc61)} . (7) The complete loss function for the noise contrastive estimation can be written as follows, L\ud835\udc41\ud835\udc36\ud835\udc38= \u2212EE(\ud835\udc47)\u223cP(.),{E\ud835\udc56(\ud835\udc47)}\ud835\udc41\ud835\udc5e \ud835\udc56=1 \u223cQ(.) h \u2211\ufe01 E(\ud835\udc61,\ud835\udc61+d\ud835\udc61)={(\u210e,\ud835\udc61)} log \ud835\udf06\u210e(\ud835\udc61) \ud835\udf06\u210e(\ud835\udc61) + \ud835\udc41\ud835\udc5e \u2211\ufe01 \ud835\udc56=1 \u2211\ufe01 E\ud835\udc56(\ud835\udc61,\ud835\udc61+d\ud835\udc61)={(\u210e,\ud835\udc61)} log \ud835\udf06\ud835\udc5e \u210e(\ud835\udc61) \ud835\udf06\u210e(\ud835\udc61) i . (8) Here, \ud835\udf06\u210e(\ud835\udc61) = \ud835\udf06\u210e(\ud835\udc61) + \ud835\udf06\ud835\udc5e \u210e(\ud835\udc61)\ud835\udc41\ud835\udc5e. In the above equation, we contrast the samples from the true distribution, the observed data, to the \ud835\udc41\ud835\udc5e independently sampled noise stream conditioned on the observed true historical data. A more detailed explanation of this contrastive loss function and the optimality of this technique can be found in the work of Mei et al. [24]. Additionally, to direct the gradients towards better model parameters, we add a classification-based noise contrastive loss at the time of the event as follows, L\ud835\udc60 \ud835\udc41\ud835\udc36\ud835\udc38= \u2211\ufe01 (\ud835\udc52\ud835\udc5b,\ud835\udc61\ud835\udc5b)\u2208E(\ud835\udc47) log \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61) \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61) + \u00cd \u210e\u2208H\ud835\udc5b\ud835\udc52\ud835\udc54 \ud835\udc52\ud835\udc5b\ud835\udf06\u210e(\ud835\udc61) . (9) Here, H\ud835\udc5b\ud835\udc52\ud835\udc54 \ud835\udc52\ud835\udc5b are the negative samples generated by negative sampling for the hyperedge \ud835\udc52\ud835\udc5b. Then the combined loss can be written as follows, Loss = L\ud835\udc41\ud835\udc36\ud835\udc38+ \ud835\udefcL\ud835\udc60 \ud835\udc41\ud835\udc36\ud835\udc38. (10) Here, \ud835\udefcis a hyperparameter. Algorithm 1 Training procedure of RRHyperTPP Input: G(\ud835\udc47). while not convergence do H\ud835\udc5b\ud835\udc52\ud835\udc54\u223cCorruptionModel(H). H\ud835\udc50= H \u222aH\ud835\udc5b\ud835\udc52\ud835\udc54. Set \ud835\udc61= \ud835\udc610 = 0, \ud835\udc5b= 1, L\ud835\udc41\ud835\udc36\ud835\udc38= 0. for \ud835\udc5b\u2264\ud835\udc41do while \ud835\udc61< \ud835\udc61\ud835\udc5bdo Sample \ud835\udf06\ud835\udc5e(\ud835\udc61) \u223c 1 \ud835\udc41\ud835\udc64 \u00cd\ud835\udc41 \ud835\udc56=1 K(\ud835\udf06\ud835\udc5e\u2212 1 \ud835\udc61\ud835\udc56\u2212\ud835\udc61\ud835\udc56\u22121 ;\ud835\udc64). Sample \u0394\ud835\udc61\u223cexponenetial(\ud835\udc41\ud835\udc5e\ud835\udf06\ud835\udc5e(\ud835\udc61)). Sample \u210e\u223cUniform(H\ud835\udc50). Next event time \ud835\udc61= \ud835\udc61+ \u0394\ud835\udc61. Loss = Loss \u2212log \ud835\udf06\ud835\udc5e \u210e(\ud835\udc61) \ud835\udf06\u210e(\ud835\udc61) end while H\ud835\udc5b\ud835\udc52\ud835\udc54 \ud835\udc52\ud835\udc5b \u223cCorruptionModel(\ud835\udc52\ud835\udc5b) Loss = Loss \u2212log \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61) \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61) Loss = Loss \u2212\ud835\udefclog \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61) \ud835\udf06\ud835\udc52\ud835\udc5b(\ud835\udc61)+\u00cd \u210e\u2208H\ud835\udc5b\ud835\udc52\ud835\udc54 \ud835\udc52\ud835\udc5b \ud835\udf06\u210e(\ud835\udc61) \ud835\udc5b= \ud835\udc5b+ 1. If \ud835\udc5bmod \ud835\udc35= 0, Update the model parameters by AdamW Optimizer and set Loss = 0. end for end while 4.2 Noise Distribution Here, we propose a method for simulating noise sequences by modeling the conditional distribution Q\u2217(E\ud835\udc56(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = {(\u210e,\ud835\udc61)}). The thinning algorithm is a popular method for simulating a nonhomogeneous Poisson process [7]. This way of sampling is computationally expensive if the acceptance probability is low. Moreover, modeling each hyperedge as a non-homogeneous Poisson process does not avoid the computational complexity of having many event types. To overcome these limitations and accelerate training, we model the rate of events \ud835\udf06\ud835\udc5eusing a stochastic process independent of the event type and time. The probability density function of this process is learned from the observed event times in the training data E(\ud835\udc47) using kernel density estimation [29], \ud835\udf06\ud835\udc5e\u223c 1 \ud835\udc41\ud835\udc64 \u00cd\ud835\udc41 \ud835\udc56=1 K(\ud835\udf06\ud835\udc5e\u2212 1 \ud835\udc61\ud835\udc56\u2212\ud835\udc61\ud835\udc56\u22121 ;\ud835\udc64). Here, K is the kernel, and \ud835\udc64is the bandwidth of the kernel. We use the Gaussian kernel, and bandwidth is learned from the dataset. This will allow for a closed-form sampling of noise event times. Then we generate the type of event by uniformly sampling from a set of candidate hyperedges H\ud835\udc50. Then \ud835\udf06\ud835\udc5e \u210e= 1 |H\ud835\udc50| \ud835\udf06\ud835\udc5eand Q(E\ud835\udc56(\ud835\udc61,\ud835\udc61+ d\ud835\udc61) = {(\u210e,\ud835\udc61)}) = 1 |H\ud835\udc50| \ud835\udf06\ud835\udc5eexp (\u2212\ud835\udf06\ud835\udc5e(\ud835\udc61\u2212\ud835\udc61\ud835\udc5b)). The set of candidate hyperedges, denoted as H\ud835\udc50, is formed by combining the true hyperedges observed in the training data with the negative hyperedges generated through the corruption of observed hyperedges. For depth one hyperedge datasets, we expand the hyperedge as a tuple of node and relation pairs in ascending order. Then we learn the categorical distribution of each position condition on all the previous relations, along with an end state. Then for each positive hyperedge, we first sample the relations till the end state is observed. Subsequently, we randomly populate each Intereaction Event Forecasting in Multi-Relational Recursive HyperGraphs position in the negative hyperedge with nodes. This is done by filling each position with nodes from the true hyperedge or randomly sampled nodes without repeating if they have the same relation value. This is done in such a way that at most half of the nodes of negative hyperedges are nodes from true hyperedge, and the rest is filled in randomly, thereby ensuring diversity in negative samples. For depth two hyperedge datasets, we randomly corrupt any one of the depth one hyperedge within them by the above procedure to generate negative hyperedges. Here, for each observed hyperedge \u210e\u2208H, we generate \ud835\udc41\ud835\udc52= |H\ud835\udc5b\ud835\udc52\ud835\udc54 \u210e | negative hyperedges. For generating \ud835\udc41\ud835\udc5enoise streams, we multiply the noise distribution intensity function by \ud835\udc41\ud835\udc5e, \ud835\udf06\ud835\udc5e(\ud835\udc61)\ud835\udc41\ud835\udc5e, and simulated samples. This scaling will not affect NCE loss Equation 8, as all the noise streams have the same intensity values. Algorithm 1 summarizes the entire training procedure of the model. The CorruptionModel(.) is the negative hyperedge generation function, and Uniform(H\ud835\udc50) uniformly samples a hyperedge from the candidate hyperedges, H\ud835\udc50. In the following section, we explain the dynamic node representation learning used to parameterize the conditional intensity function of the model. In our implementation, we use the same negative samples to generate the noise stream and in the supervised noise contrastive loss in Equation 9, H\ud835\udc5b= \u222a\u210e\u2208HH\ud835\udc5b\ud835\udc52\ud835\udc54 \u210e . 5 DYNAMIC NODE REPRESENTATION The dynamic node representation of the nodes V \u2208R|V|\u00d7\ud835\udc51in the networks are learned using a continuous time recurrent-neural network model using two stages, i) Node Update and ii) Drift, for node evolution. 5.1 Node Update This stage is used to update the representation of a node \ud835\udc63when it is involved in an interaction \u210e= {(\u210e\ud835\udc59\u22121 1 ,\ud835\udc5f\ud835\udc59\u22121 1 ), . . . , (\u210e\ud835\udc59\u22121 \ud835\udc58\ud835\udc59\u22121,\ud835\udc5f\ud835\udc58\ud835\udc59\u22121)} at time \ud835\udc61. The update equation uses a recurrent neural network-based architecture that updates the node\u2019s previously stored embedding based on the features of interaction calculated as follows, i\u210e \ud835\udc63= MLP( h d\u210e \ud835\udc63; v(\ud835\udc61\u2212); \ud835\udebf(\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63) i ) v(\ud835\udc61+) = RNN(v(\ud835\udc61\ud835\udc5d \ud835\udc63), i\u210e \ud835\udc63). (11) Here, \ud835\udc63\u2208\u210e0, (\u210e0,\ud835\udc5f0) \u2208. . . \u2208\u210eand MLP is a two-layer multi-layer perceptron as shown below, i\u210e \ud835\udc63= W\ud835\udc56 1tanh \u0010 W\ud835\udc56 0 h d\u210e \ud835\udc63; v(\ud835\udc61\u2212); \ud835\udebf(\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63) i\u0011 . Here, W\ud835\udc56 0 \u2208R\ud835\udc51\u2217(\ud835\udc59+3)\u00d7\ud835\udc51\u2217(\ud835\udc59+3)/2, W\ud835\udc56 1 \u2208R\ud835\udc51\u2217(\ud835\udc59+3)/2\u00d7\ud835\udc51are learnable parameters and d\u210e \ud835\udc63\u2208R\ud835\udc51is the dynamic embedding calculated as a function of embeddings of other nodes involved in the interaction, d\u210e \ud835\udc63= \ud835\udc53\ud835\udc51\ud835\udc66\ud835\udc5b(\u210e; V(\ud835\udc61), R). The architecture of \ud835\udc53\ud835\udc51\ud835\udc66\ud835\udc5b(\u00b7) is shared with hyperedge link prediction as explained in Section 6. The second term \ud835\udebf(\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63) \u2208R\ud835\udc51is the Fourier features for a time calculated based on the duration since an event was observed on \ud835\udc63, (\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63). Here, \ud835\udc61\ud835\udc5d \ud835\udc63is the recent time node \ud835\udc63is involved in an interaction, and Fourier time features [9] are defined as \ud835\udebf(\ud835\udc61) = [cos(\ud835\udf141\ud835\udc61+ \ud835\udf191), . . . , cos(\ud835\udf14\ud835\udc51\ud835\udc61+ \ud835\udf19\ud835\udc51)] ,where {\ud835\udf14\ud835\udc56}\ud835\udc51 \ud835\udc56=1, and {\ud835\udf19\ud835\udc56}\ud835\udc51 \ud835\udc56=1 are learnable parameters. When \ud835\udc63is involved in multiple positions in hyperedge \u210e, an average of i\u210e \ud835\udc63is taken to update the node embedding. 5.2 Drift This stage is used for modeling the evolution of the nodes during the inter-event period. This helps to avoid the staleness of node embeddings due to not observing any event for a long duration [19]. Time Projection. In this technique, we project the node embeddings from the node update stage based on the elapsed time since the last update as follows, v(\ud835\udc61) = (1 + W\ud835\udc61(\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63)) \u25e6v(\ud835\udc61\ud835\udc5d \ud835\udc63). (12) Here, W\ud835\udc61\u2208R\ud835\udc51\u00d71 is a learnable parameter, and \u25e6denotes the Hadamard product. This version of the embedding projection was introduced in the work JODIE [21]. Time Embeddings. Here, we use Fourier time features to model the evolution of the nodes during the interevent time as follows, v(\ud835\udc61) = tanh(W\ud835\udc60v(\ud835\udc61\ud835\udc5d \ud835\udc63) + W\ud835\udc61\ud835\udebf(\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63)). (13) Here, W\ud835\udc60, W\ud835\udc61\u2208R\ud835\udc51\u00d7\ud835\udc51are learnable parameters. This form of drift stage is followed in previous work [15]. Neural ODE.. The node embedding evolution is modeled using a neural Ordinary Differential Equation (ODE) as follows, v(\ud835\udc61) = v(\ud835\udc61\ud835\udc5d \ud835\udc63) + \u222b\ud835\udc61 \ud835\udc61\ud835\udc5d \ud835\udc63 \ud835\udc53\u2207v \u0010 v(\ud835\udc61),\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63 \u0011 d\ud835\udc61. (14) Here, \ud835\udc53\u2207v is the gradient of the node embedding v(\ud835\udc61). We implement it using a multi-layer neural network that takes current node embedding and time elapsed since the last update as inputs to the network as shown below, \ud835\udc53\u2207v \u0010 v(\ud835\udc61),\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63 \u0011 = W\ud835\udc61 1tanh \u0010 W\ud835\udc61 0 h v(\ud835\udc61); W\ud835\udc61(\ud835\udc61\u2212\ud835\udc61\ud835\udc5d \ud835\udc63) i\u0011 . Here, W\ud835\udc61\u2208R1\u00d7\ud835\udc51, W\ud835\udc61 0 \u2208R2\ud835\udc51\u00d7\ud835\udc51, W\ud835\udc61 1 \u2208R\ud835\udc51\u00d7\ud835\udc51are learnable parameters. Neural ordinary differential equations are infinite-depth deep learning models that are suited for modeling continuous dynamical systems. For training the models, we use the adjoint sensitivity method for reducing memory cost during back-propagation [6]. 6 HYPEREDGE LINK PREDICTION Given the node embeddings and relation embeddings of a hyperedge, we use the quey-key-value attention mechanism used in transformer models [31] for hyperedge link prediction. For this, we first expand hyperedges at depth 0 as a tuple of node and relation pair and create an expanded depth one hyperedge \u00af \u210e0 = {(\ud835\udc63,\ud835\udc5f0)}\ud835\udc63\u2208\u210e0,(\u210e0,\ud835\udc5f0)\u2208\u210e1. Here, the relation is repeated for each node in the hyperedges. Then we create embeddings for query, key, and value, {vq \ud835\udc56(\ud835\udc61) = vv \ud835\udc56(\ud835\udc61) = [v\ud835\udc56(\ud835\udc61); r0 \ud835\udc56]}\u2200(\ud835\udc63\ud835\udc56,\ud835\udc5f0 \ud835\udc56) \u2208\u00af \u210e0, then we calculate the dynamic hyperedge embedding (here, dynamic is used to indicate the hyperedge dependent embeddings d\u2217 \u2217\u2019s) for each node as follows, d\u00af \u210e0 \ud835\udc63= MHAtt({vq(\ud835\udc61)}, {vk \ud835\udc57(\ud835\udc61)}\u00af \ud835\udc580 \ud835\udc57=1, {vv \ud835\udc57(\ud835\udc61)}\u00af \ud835\udc580 \ud835\udc57=1). (15) Here, MHAtt(\u00b7) is the MultiHeadAttention architecture proposed by Vaswani et al. [31]. Based on these, we create the depth one hyperedge embeddings by averaging out all the above node embeddings h1 \ud835\udc56= \u00cd \ud835\udc63\u2208\u00af \u210e0 \ud835\udc56 d \u00af \u210e0 \ud835\udc56 \ud835\udc63 | \u00af \u210e0 \ud835\udc56| . Then for the hyperedge at depths 2 \u2264\u2113\u2264\ud835\udc59, Tony Gracious and Ambedkar Dukkipati Figure 3: Deep Neural Network Architecture of RRHyperTPP: We calculate the dynamic node representation V(\ud835\udc61) by using Node Update (Section 5.1) and Drift (Section 5.2) stages. The node Update stage is used to update the node embeddings after an interaction involving that node occurs, and the Drift stage is used to model the evolution of node embedding during the interevent period. The dynamic node representation is used by the hyperedge link prediction-based decoder to infer the conditional intensity function \ud835\udf06\u210e(\ud835\udc61). we apply the following self-attention layer with query, key, and value as {vq \ud835\udc56(\ud835\udc61) = vk \ud835\udc56(\ud835\udc61) = [h\u2113\u22121 \ud835\udc56 (\ud835\udc61); r\u2113\u22121 \ud835\udc56 ]}\u2200(\u210e\u2113\u22121 \ud835\udc56 ,\ud835\udc5f\u2113\u22121 \ud835\udc56 ) \u2208\u210e\u2113, d\u210e\u2113 \u210e\u2113\u22121 \ud835\udc56 = MHAtt({vq \ud835\udc56(\ud835\udc61)}, {vk \ud835\udc57(\ud835\udc61)}\ud835\udc58\u2113\u22121 \ud835\udc57=1 , {vv \ud835\udc57(\ud835\udc61)}\ud835\udc58\u2113\u22121 \ud835\udc57=1 ), h\u2113= \u2211\ufe01 (\u210e\u2113\u22121 \ud835\udc56 ,\ud835\udc5f\u2113\u22121 \ud835\udc56 )\u2208\u210e\u2113 d\u210e\u2113 \u210e\u2113\u22121 \ud835\udc56 |\u210e\u2113| . (16) Then conditional density is parameterized by the difference between the hyperedge embedding and dynamic hyperedge embedding of the \ud835\udc59\u22121th layer as follows, \ud835\udc5c\u210e \ud835\udc56= W\ud835\udc5c(h\ud835\udc59\u22121 \ud835\udc56 \u2212d\u210e\ud835\udc59 \u210e\ud835\udc59\u22121 \ud835\udc56 )2 + \ud835\udc4f\ud835\udc5c \ud835\udf06\u210e(\ud835\udc61) = Softplus( \u2211\ufe01 (\u210e\ud835\udc59\u22121 \ud835\udc56 ,\ud835\udc5f\ud835\udc59\u22121 \ud835\udc56 )\u2208\u210e \ud835\udc5c\u210e \ud835\udc56). (17) The dynamic hyperedge embedding used in the interaction update is defined as follows, d\u210e \ud835\udc63= [d\u210e0 \ud835\udc63; d\u210e1 \u210e0; . . . ; d\u210e\ud835\udc59 \u210e\ud835\udc59\u22121; h\ud835\udc59], here \ud835\udc63\u2208\u210e0,\u210e0 \u2208\u210e1, . . . ,\u210e\ud835\udc59\u22121 \u2208\u210e. 7 EXPERIMENTAL SETTINGS AND RESULTS 7.1 Datasets Table 1 shows the vital statistics of the datasets used in this work. In this, Enron is an email exchange dataset, and all the others, except the last two, are based on Twitter exchange. These datasets contain depth one hyperedges and are created from the works of Chodrow and Mellor [8], Domenico and Altmann [11], Omodei et al. [25]. ICEWS-India and ICEWS-Nigeria contain depth two hyperedges created from events stored in Integrated Crisis Early Warning System data for countries India and Nigeria [2]. For preprocessing, we have filtered out the nodes based on frequency, and all the timestamps start from zero and are scaled down so that the mean interevent time is around one. Here, \u0394\ud835\udc61(\ud835\udc5a\ud835\udc52\ud835\udc4e\ud835\udc5b), \u0394\ud835\udc61(\ud835\udc5a\ud835\udc4e\ud835\udc65), and \u0394\ud835\udc61(\ud835\udc5a\ud835\udc56\ud835\udc5b) are the mean, maximum, and minimum interevent time. 7.2 Baselines We use TGN [27] to compare our model\u2019s performance against stateof-the-art pairwise interaction prediction models. Additionally, we use HGDHE [15] to get a comparison against state-of-the-art higherorder interaction forecasting model that uses hyperedges to forecast interactions. Further, we created the model RRHyperTPP-N to show the advantage of our training strategy over negative sampling explored in previous work [15]. Here, we use time embeddings for drift to make the model closer to the one proposed in their work. Additionally, to show the advantage of the recursive hyperedge link prediction in Section 6, we created baseline model HyperTPP to forecast hyperedges created from the nodes involved in the interactions, \u210e= {\ud835\udc63\ud835\udc56;\ud835\udc63\ud835\udc56\u2208\u210e0, (\u210e0,\ud835\udc5f0) \u2208. . . \u2208\u210e}, and this model is trained using the same loss as RRHyperTPP. 7.3 Forecasting Tasks And Evaluation Metrics We use two tasks, (i) Interaction Type Prediction and (ii) Interaction duration Prediction, to evaluate our models\u2019 performance. In the first task, we are trying to predict which type of hyperedge occurs at time \ud835\udc61given the history. This can be estimated by finding the hyperedge that has the maximum probability P(E(\ud835\udc61,\ud835\udc61+d\ud835\udc61) = (\u210e,\ud835\udc61))|E(\ud835\udc61)), which is equal to finding the hyperedge with maximum conditional intensity function as per definition of TPP, \u02c6 \u210e= arg max\u210e\ud835\udf06\u210e(\ud835\udc61). For evaluation, we calculate the Area Under the Curve (AUC) metric [13] by using the CorruptionModel to create \ud835\udc41\ud835\udc52false positive samples for each true positive sample and then calculate the area under the curve. Here, better performance is indicated by values close to one. For the second task, we are trying to predict the time at which interaction \u210eoccurs from the last interaction duration of nodes in the hyperedge \ud835\udc61\ud835\udc5d \u210e. This is be estimated using the condition probability density as \u02c6 \ud835\udc61\ud835\udc56= \u222b\u221e \ud835\udc61\ud835\udc5d \u210e\ud835\udc61P\u210e(\ud835\udc61|E(\ud835\udc61\ud835\udc5d \u210e))d\ud835\udc61. Here, P\u210e(\ud835\udc61|E(\ud835\udc61\ud835\udc5d \u210e)) is defined as in Equation 1, and all the integration involved are Intereaction Event Forecasting in Multi-Relational Recursive HyperGraphs Table 1: Temporal Multi-Relational Recursive Hypergraphs datasets and their vital statistics. Datasets |V| |E(\ud835\udc47) | |R| \ud835\udc47 \u0394\ud835\udc61(\ud835\udc5a\ud835\udc52\ud835\udc4e\ud835\udc5b) \u0394\ud835\udc61(\ud835\udc5a\ud835\udc4e\ud835\udc65) \u0394\ud835\udc61(\ud835\udc5a\ud835\udc56\ud835\udc5b) Enron 98 10,355 3 10,443.0 1.02 893.45 0.006 Twitter 2,714 52,383 4 54,028 1.54 25.64 0.625 Boston 2,400 20,070 4 20,069 1.03 37.13 0.044 Obama 1,721 22,690 4 22,689 1.02 1628.61 0.021 Pope 6,648 67,779 4 67,778 1.07 68.97 0.047 Cannes 672 9,078 4 9,077 1.00 58.02 0.007 ICEWS-India 1,066 86,609 201 364 1.00 1.0 1.0 ICEWS-Nigeria 894 6,95,433 181 715 1.00 2.94 0.98 Table 2: Performance on forecasting in interaction type and interaction duration prediction tasks on depth one hyperedges. Here, interaction type prediction is evaluated using AUC in %, and interaction duration prediction is evaluated using MAE. The proposed model RRHyperTPP beats baseline models in almost in settings. Here, -j, -f, and -o indicate the drift stage used. Methods Enron Twitter Boston Obama Pope Cannes AUC MAE AUC MAE AUC MAE AUC MAE AUC MAE AUC MAE TGN [27] 85.8 \u00b1 2.9 NA 97.0 \u00b1 0.5 NA 89.3 \u00b1 1.5 NA 93.0 \u00b1 1.0 NA 92.5 \u00b1 1.2 NA 87.6 \u00b1 2.4 NA HGDHE [15] 87.6 \u00b1 0.8 3.6 \u00b1 0.1 88.0 \u00b1 1.1 26.26 \u00b1 0.5 75.3 \u00b1 1.3 49.16 \u00b1 5.2 82.0 \u00b1 0.1 29.8 \u00b1 0.8 79.1 \u00b1 0.3 33.6 \u00b1 1.2 79.1 \u00b1 1.0 27.9 \u00b1 2.0 RRHyperTPP-N 91.0 \u00b1 0.9 3.5 \u00b1 0.0 94.2 \u00b1 0.6 21.9 \u00b1 0.4 80.8 \u00b1 0.2 39.9 \u00b1 0.1 85.2 \u00b1 0.4 27.6 \u00b1 0.6 82.5 \u00b1 0.5 31.9 \u00b1 0.3 81.9 \u00b1 1.0 25.4 \u00b1 1.8 HyperTPP-j 91.6 \u00b1 0.7 3.3 \u00b1 0.7 97.2 \u00b1 0.0 30.0 \u00b1 0.6 85.4 \u00b1 0.8 46.5 \u00b1 0.7 90.7 \u00b1 0.3 35.5 \u00b1 1.1 85.2 \u00b1 6.0 40.1 \u00b1 1.2 90.7 \u00b1 1.04 24.0 \u00b1 2.7 HyperTPP-f 90.8 \u00b1 1.0 3.7 \u00b1 0.3 97.3 \u00b1 0.1 33.4 \u00b1 0.5 83.4 \u00b1 0.2 49.6 \u00b1 2.1 86.6 \u00b1 0.2 37.4 \u00b1 1.5 91.8 \u00b1 0.8 37.6 \u00b1 0.2 86.4 \u00b1 0.5 28.2 \u00b1 2.1 HyperTPP-o 91.6 \u00b1 0.5 3.7 \u00b1 0.3 96.8 \u00b1 0.3 30.8 \u00b1 0.6 84.6 \u00b1 1.2 51.8 \u00b1 2.9 89.2 \u00b1 0.5 38.6 \u00b1 1.5 88.9 \u00b1 1.4 37.3 \u00b1 2.1 89.1 \u00b1 1.6 26.8 \u00b1 2.4 RRHyperTPP-j 93.3 \u00b1 0.7 3.3 \u00b1 0.2 98.5 \u00b1 0.1 30.6 \u00b11.8 89.2 \u00b1 0.1 45.7 \u00b1 0.4 93.5 \u00b1 0.5 32.5 \u00b1 0.4 94.2 \u00b1 0.4 36.2 \u00b1 1.0 92.1 \u00b1 0.4 25.6 \u00b1 1.5 RRHyperTPP-f 93.4 \u00b1 0.3 3.5 \u00b1 0.2 98.4 \u00b1 0.1 32.3 \u00b1 0.5 89.2 \u00b1 0.2 45.1 \u00b1 0.4 92.9 \u00b1 0.3 31.8 \u00b1 0.3 93.9 \u00b1 0.3 37.6 \u00b1 0.2 89.3 \u00b1 0.4 25.2 \u00b1 0.9 RRHyperTPP-o 93.5 \u00b1 0.2 3.7 \u00b1 0.1 98.3 \u00b1 0.1 30.1 \u00b1 0.9 88.0 \u00b1 1.7 46.3 \u00b1 3.1 92.3 \u00b1 1.0 35.6 \u00b1 2.0 94.0 \u00b1 0.7 35.4 \u00b1 1.2 91.2 \u00b1 0.7 28.6 \u00b1 0.6 computed using Monte-Carlo integration. Then, for evaluation, we use Mean Absolute Error (MAE) metric, MAE = 1 \ud835\udc41 \u00cd\ud835\udc41 \ud835\udc56=1 | \u02c6 \ud835\udc61\ud835\udc56\u2212\ud835\udc61\ud835\udc56| for all the samples in the test. 7.4 Parameter Settings In all our experiments, we fixed the embedding dimension at \ud835\udc51= 64, hidden and input dimension for the RNN at 64, batch size \ud835\udc35= 128, number of noise streams \ud835\udc41\ud835\udc5e= 20, number of corrupted hyperedges per true hyperedge is \ud835\udc41\ud835\udc52= 20, and number heads of MHAtt to four. The training is done for 200 epochs, and the model parameters that gave the least validation score L\ud835\udc41\ud835\udc36\ud835\udc38+ \ud835\udefcL\ud835\udc60 \ud835\udc41\ud835\udc36\ud835\udc38are used for testing. For all the training, we use the AdamW optimizer [23, 26] of PyTorch [20] with learning rate set to 0.0005. The first 50% of interactions is used for training, the next 25% for validation, and the rest for testing. 7.5 Results Table 2 shows the performance of our models RRHyperTPP against baseline models. Here, the models that use time projection, ODEs, and time embeddings for Drift stage are denoted by -j, -o, and -f at the end, respectively. In this, models that use ODE for the drift stage perform slightly less than ones that use other techniques. This is due to numerical issues involved with Neural ODE training, which involves computing integral in the gradient backpropagation. However, theoretically, Neural ODEs should perform better than others as they have fewer assumptions when compared to Fourier Table 3: Performance on forecasting in interaction type and interaction duration prediction tasks on depth two hyperedges. Methods ICEWS-India ICEWS-Nigeria AUC MAE AUC MAE RRHyperTPP-j 58.7 \u00b1 0.7 0.99 \u00b1 0.0 61.0 \u00b1 0.3 0.98 \u00b1 0.0 RRHyperTPP-f 58.9 \u00b1 0.2 0.75 \u00b1 0.2 60.5 \u00b1 0.5 0.81 \u00b1 0.1 RRHyperTPP-o 58.2 \u00b1 1.4 0.99 \u00b1 0.0 58.7 \u00b1 0.3 0.97 \u00b1 0.0 and time projection-based methods. We have also done experiments on depth two hyperedges, and the results are shown in Table 3. Here, we can also observe that no single model outperforms the rest in all the tasks. Further, there is an average increment of 3.6% in the AUC metric for RRHyperTPP models when compared to HyperTPP based models in interaction type prediction tasks. For the interaction duration prediction task, we observed a reduction of 4.6% MAE when compared to HyperTPP models. Hence, we can conclude that modeling the recursive group structure of interaction resulted in performance improvement. Hence, more exploration is needed to find a better noise generation strategy to achieve better performance simultaneously in both tasks. Moreover, we compare our model against TGN, a state-of-the-art pairwise interaction forecasting model. For the task of interaction type prediction, we can observe an increment of 2.9%, 2.3%, and 2.2% Tony Gracious and Ambedkar Dukkipati Enron Twitter Boston Obama Pope Cannes 86 88 90 92 94 96 98 100 AUC \u03b1 = 0 \u03b1 = 1 \u03b1 = 2 Figure 4: The performance gain obtained due to the addition of classification based noise contrastive loss mentioned Equation 10. Here, we can observe that models trained with supervised noise contrastive loss \ud835\udefc> 0 have more AUC scores for interaction type prediction than models that do not (\ud835\udefc= 0). for models RRHyperTPP-j, RRHyperTPP-f, and RRHyperTPP-o, respectively. Hence, we can conclude that recursive hyperedge-based models perform better than pairwise link prediction models. Similarly, we compared our model RRHyperTPP-f against the HGDHE state-of-the-art hyperedge forecasting model, as both use time embeddings for the drift stage. Here, we can observe a gain of 13.6% in AUC for interaction type prediction. We can observe similar improvements for other types of drift when compared to HGDHE model. To show the advantage of our training strategy over negative sampling-based loglikelihood approximation followed in the previous work by [15], we compare models RRHyperTPP-f against RRHyperTPP-N. Here, both models use the same architecture, but the former uses the noise-contrastive loss for training, and the latter uses negative sampling based on approximate negative loglikelihood. There is an average improvement of 8.2% in AUC for RRHyperTPP-f models compared to RRHyperTPP-N. However, there is an average increase of 15.3% in MAE for RRHyperTPP-f compared to RRHyperTPP-N. Hence, more exploration is needed to find a better noise generation strategy to achieve better performance simultaneously in both tasks. Further, RRHyperTPP-N has an improvement of 4.9% in AUC and 9.8% reduction in MAE over previous work HGDHE, which uses hyperedge to represent higher-order interaction. Hence, we can conclude that multi-relational recursive provides better representation for higher-order interactions than hyperedges. Performance gain due to supervised NCE . Figure 4 illustrates the performance improvement in AUC of RRHyperTPP-f with different weights of the supervised noise contrastive loss in Equation 10 for the interaction type prediction task. Here, it can be observed that when \ud835\udefc= 1, there is a 1.7% increase in AUC compared to \ud835\udefc= 0. Therefore, we infer that the supervised noise contrastive loss enhances performance. Additionally, it can be noted that when \ud835\udefcis increased to two, there are no significant improvements, and a performance decrement is observed for the Cannes dataset. Consequently, we can conclude that increasing \ud835\udefcwill not yield better performance. Furthermore, we observed no significant improvement for the interaction duration prediction task by changing \ud835\udefc. 8 CONCLUSION In this work, we have shown the significance of using the multirelational recursive hyperedges for interaction modeling as it is a more natural approximation of real-world events. Here, we created a dynamic node representation and link predictor framework that can use this intricate relationship of interactions to forecast future events. In addition, we also created a noise contrastive learning framework that avoids the integration calculation in the survival function and can train when the number of types of events is of exponential order. To evaluate the model, we curated six datasets of depth one and two datasets of depth two hyperedges. We observed that our model RRHyperTPP is performing better previous state-of-the-art graph link prediction model TGN, and the negative sampling-based training strategy followed in previous work by Gracious and Dukkipati [15]. As a future direction, we plan to explore new domains of application of these models and new architecture that uses higher-order information to learn efficient node representations. In addition to this, we also plan on improving the noise generation strategy by using historical data, so the noise-generated samples will look more closely to actual data, thereby reducing the training iterations.",
+        "additional_info": [
+            [
+                {
+                    "url": "http://arxiv.org/abs/2309.03616v2",
+                    "title": "Filtration Surfaces for Dynamic Graph Classification",
+                    "abstract": "Existing approaches for classifying dynamic graphs either lift graph kernels\nto the temporal domain, or use graph neural networks (GNNs). However, current\nbaselines have scalability issues, cannot handle a changing node set, or do not\ntake edge weight information into account. We propose filtration surfaces, a\nnovel method that is scalable and flexible, to alleviate said restrictions. We\nexperimentally validate the efficacy of our model and show that filtration\nsurfaces outperform previous state-of-the-art baselines on datasets that rely\non edge weight information. Our method does so while being either completely\nparameter-free or having at most one parameter, and yielding the lowest overall\nstandard deviation among similarly scalable methods.",
+                    "authors": "Franz Srambical, Bastian Rieck",
+                    "published": "2023-09-07",
+                    "updated": "2023-10-21",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Temporal AND Graph",
+                    "gt": "The popularity of methods analysing dynamic graphs has seen a notable surge in the last few years [7\u20139]. Among these methods, a significant portion of research efforts has been dedicated to dynamic graph neural networks (DyGNNs), which are specifically designed to excel in link prediction and node classification tasks [10]. Although DyGNNs can handle dynamic graph classification via global readout functions, their performance on such tasks remains largely unexplored in the literature, with only a few isolated exceptions noted [11\u201313]. One such exception, GDGESN [14], works by combining a Dynamical Graph Echo State Network (DynGESN) [15] with snapshot merging, resulting in accuracies that surpass those of the vanilla DynGESN, albeit falling short of the performance achieved by temporal graph kernels. Another exception, STAGIN [16], addresses the issue of the limited expressivity of vanilla readout functions by introducing spatial-attentionbased readout functions. Nevertheless, a big drawback of such methods is the need for extensive hyperparameter tuning to attain optimal performance. Wang et al. [17] try to solve the classification problem by first transforming a dynamic graph into a univariate or multivariate time series, and subsequently extracting time-series shapelets [18]. Shapelets are short time series subsequences that are maximally discriminative between classes. Ye et al. [19] employ a dynamic Dowker filtration to 1Our code and instructions to reproduce our experiments are available at https://github.com/ aidos-lab/filtration_surfaces. Preprint. Preliminary work. arXiv:2309.03616v2  [cs.LG]  21 Oct 2023 Filtration Surfaces for Dynamic Graph Representation Table 1: Comparison of the capabilities of different methods. FS-EW stands for filtration surfaces with the native edge weights as the filter function. Method Classification Edge weights Changing node set Scalable DL-WL (SE-WL) [20] yes no no no GDGESN [14] yes no no yes STAGIN [16] yes yes no yes TGN [21] no yes yes yes FS-EW (ours) yes yes yes yes compute persistence diagrams, which are vectorized to kernels and subsequently input to a support vector machine for classification. As such, their method inherits the scalability issues of kernel approaches. Finally, temporal graph kernels [20] present an entirely different approach to dynamic graph classification by lifting standard graph kernels to the temporal domain. While they achieve state-of-the-art accuracies, it is important to note that (i) the transformation to the static graph (the lifting) can lead to a blow-up of the size of the graph and (ii) their computational complexity is lower-bounded by that of standard graph kernels. As a consequence, the use of this method also becomes impractical for larger graphs. By contrast, our filtration surfaces offer a compromise that balances computational efficiency and predictive performance.",
+                    "pre_questions": [],
+                    "main_content": "Introduction Recent years have seen a plethora of works dealing with the analysis of graph-structured data [1\u20134]. While the analysis of static graphs is a well-studied field, the analysis of dynamic graphs is still nascent. In this work, we will focus on the task of dynamic graph classification, where the goal is to predict the class of a process, which cannot be observed from a single snapshot of the graph, but only from the way the graph evolves over time. Although various methods exist for dynamic graph classification, none, to our knowledge, concurrently offers (i) scalability, (ii) accommodates a changing node set, and (iii) considers edge weight information (Table 1). In this work, we explore an approach based on filtrations, a concept from topological data analysis typically associated with persistent homology [5]. Specifically, we extend prior work from O\u2019Bray et al. [6] on filtration curves to a dynamic setting. We refer to our method as filtration surfaces1 and find that it remedies the aforementioned shortcomings of existing methods. Before we introduce our proposed method, we will first provide some background on filtrations and filtration curves. This will equip us with the necessary tools to find a natural extension to the dynamic setting. While filtrations are a general topological method, we restrict ourselves to filtrations on graphs and refer the reader to Edelsbrunner and Harer [5] for a more general introduction. A filtration FG on a graph G = (V, E) is a sequence of subgraphs (G1, . . . , Gm) such that \u2205\u2286G1 \u2286. . . \u2286Gm = G. A filtration can be obtained by iteratively adding edges to the starting graph G1. More specifically, a filtration can be obtained using an edge weight function w: E \u2192R such that Gi is induced by all edges with weights less than or equal to wi, where wi is the ith smallest weight. This means that creating a filtration is equivalent to sorting the edges by weight and progressively adding them to the graph in order of increasing weight, yielding a time complexity of O(n log n) [6]. 3.1 Filtration Curves Filtration curves [6] are expressive, computationally efficient representations of static graphs. Unlike methods based on subgraph matching or neighbourhood comparison, filtration curves take both edge weights as well as the graph topology into account. The fundamental postulate behind filtration curves is that two graphs generated by a similar process have similar substructures emerging at similar filtration timesteps. To build a filtration curve, we need to choose (i) an edge weight function w: E \u2192R that assigns a weight to every edge, and (ii) a graph descriptor function f : G \u2192Rd that takes a (sub)graph and returns a value in Rd. By building the graph filtration FG in order of increasing edge weight and evaluating the graph descriptor function on every subgraph Gi of the filtration, one obtains a sequence of vectors which can be modeled as a matrix PG := \ufffdm i=1 f(Gi) \u2208Rm\u00d7d, the structure that O\u2019Bray et al. [6] termed filtration curve. In this definition, m denotes the number of thresholding edge weights in the filtration FG, and \ufffddenotes the concatenation operator. The filtration curve PG is a compact representation of the graph G that can be used for downstream tasks such as graph classification. Another way of looking at filtration curves is as a type of (topological) feature extraction method. The graph descriptor function f can be thought of as a feature extractor, which, when evaluated alongside a filtration, yields a multi-scale representation of the graph. Notice that the weight thresholds of PG are not necessarily equal among all graphs in the dataset. However, it is possible to standardize the representations by creating a shared sorted index of all weight thresholds of the dataset and forward-filling the missing values. O\u2019Bray et al. [6] propose the following edge weight functions to define a filtration over the graph: (i) the native edge weights, (ii) the max degree function wxy = max{degree(x), degree(y)}, (iii) the Ollivier\u2013Ricci curvature [22] with \u03b1 = 0.5, 2 Filtration Surfaces for Dynamic Graph Representation and (iv) the maximum of the heat kernel signatures [23] of the adjacent nodes. The Ollivier\u2013Ricci curvature is defined as \u03ba\u03b1(x, y) = 1\u2212 W (m\u03b1 x ,m\u03b1 y ) d(x,y) for all x, y \u2208V , where W denotes the Wasserstein distance [24] between two probability measures, d is some distance of a metric space (O\u2019Bray et al. [6] use the shortest path distance), and m\u03b1 x(v) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 \u03b1 if v = x 1\u2212\u03b1 degree(x) if v \u2208N(x) 0 otherwise, , where N(x) denotes the set of neighbours of x. The heat kernel signature is a highly expressive, but computationally costly summary due to needing a full eigendecomposition of a matrix. Carri\u00e8re et al. [25] define it as hks(G, t, v) = Pn i=1 exp(\u2212t\u03bbi)\u03c8i(v)2, where t is the diffusion parameter, \u03bbi is the ith eigenvalue of the Laplacian matrix of G, and \u03c8i(v) is the ith eigenfunction of the graph Laplacian. Besides defining a filtration over the graph, we need to choose a graph descriptor function f. O\u2019Bray et al. [6] propose two graph descriptor functions: (i) counting the number of nodes with a given label, and (ii) counting the number of connected components in the graph. Latter number only changes at thresholds at which a connected component is either created or destroyed. Therefore, it suffices to only store the count at these thresholds, leading to an even sparser representation of the graph. 3.2 Filtration Surfaces Now that we have introduced filtration curves, we propose a natural way of extending them to the dynamic setting. Specifically, we propose a method for classifying discrete-time dynamic graphs (DTDGs) G. Intuitively, we calculate filtration curves PGi for all dynamic graph timesteps Gi \u2208G and therefore extend the curve to another dimension, yielding a surface. Formally, we model the sequence of filtration curves as a tensor RG := Ln i=1 PGi \u2208Rn\u00d7m\u00d7d, where n is the length of the dynamic graph, m is the number of weight thresholds in the filtration, and d is the dimensionality of the graph descriptor function. The careful reader will note that the filtration curves PGi do not necessarily share the same weight thresholds. Therefore, it is necessary to compute a shared weight index as described in section 3.1. Just like filtration curves are step functions because the graph descriptor function does not change in-between thresholding weights, filtration surfaces can be thought of as step-like surfaces when assuming that the filtration curve does not change in-between timestamps of the dynamic graph. Latter assumption is reasonable when the dynamic graph is the \u201cground truth\u201d and the direct result of some generation process. However, in the case of real-world data, it is likely that the dynamic graph was obtained by sampling a streaming graph at discrete time intervals. In such cases, forwardfilling filtration curves until the next timestamp might not be the optimal approach. Instead, our representation permits the use of any interpolation function to fill the gaps between timestamps, which can even be learned from data. In contrast to existing approaches, filtration surfaces can handle a changing node set, since the filtration curves are computed independently for each graph and the shared weight index guarantees interoperability between graphs. Furthermore, our method is suitable for the online temporal graph setting, since a new timestamp can be added to the filtration surface by simply appending a new filtration curve to the tensor. To update the shared weight matrix, it suffices to insert the new weight thresholds into the existing matrices and forward-fill the missing values, which permits the use of online classifiers such as online random forests [26]. Classification. To classify filtration surfaces, we vectorize them by flattening the tensor along the time dimension, and flattening the resulting matrix along the weight dimension. The resulting vector is then input to a random forest classifier. This means that each dimension of the input vector corresponds to a specific weight threshold at a specific timestamp. Since we standardized all filtration curves of a dataset to have the same weight thresholds, all vectors have the same length and all vector dimensions are comparable. Limitations. On datasets without edge weight information, filtration surfaces do not yet obtain state-of-the-art accuracies (Tables 7 and 8). We posit that this is largely due to the choice of the filter and graph descriptor functions. Since this choice is dataset-dependent, learning these functions from data, as described in e.g. Hofer et al. [27], constitutes an interesting avenue for future work. 3 Filtration Surfaces for Dynamic Graph Representation Table 2: Gram matrix size compared to the cumulative filtration surface size in datasets of varying size. OOM means that the method ran out of memory while having 256GB RAM allocated. Notice that the Gram matrix size scales quadratically with the number of dynamic graphs n, whereas the cumulative filtration surface size scales linearly. n Gram Matrix Size (SE-WL) Cumulative Filtration Surface Size (FS-EW) 100 0.11 MiB 0.50 MiB 1000 12.17 MiB 4.64 MiB 10000 1312.64 MiB 49.05 MiB 100000 OOM 491.37 MiB Table 3: Accuracies (in %) and their standard deviations on the synthetic dataset (n = 1000). WL (k=0) FS-EW (ours) SE-WL DL-WL 100.00 \u00b10.00 50.80 \u00b14.51 50.80 \u00b14.51 4 Experiments & Conclusion We now empirically evaluate the scalability and performance of our method in comparison to current state-of-the-art approaches. Our investigation aims to address two pivotal questions: (i) How does the scalability of filtration surfaces compare against state-of-the-art methods? (ii) How do filtration surfaces perform in relation to baselines on datasets that rely on edge weight information? To answer the former question, we create multiple synthetic datasets of varying sizes and compare the runtime as well as the representation size of filtration surfaces against those of the current stateof-the-art: temporal graph kernels. We generate the datasets by constructing a starting graph via the Barab\u00e1si\u2013Albert model [28] and subsequently adding nodes and edges according to the preferential attachment mechanism [29]. Edge weights are assigned randomly from a uniform distribution, either in the range [1, 5] or [6, 10] depending on the class of the dynamic graph. Node labels are assigned randomly to class 0 or 1. The results show that the Gram matrices of temporal kernels scale quadratically with the number of dynamic graphs n, while the corresponding filtration surface representations scale linearly, as can be seen in Tables 2, 5 and 6. To answer the latter question, we compare the classification accuracies of filtration surfaces against those of temporal graph kernels on our synthetic datasets. We use the Weisfeiler\u2013Leman kernel with the directed line graph expansion (DL-WL) and the static expansion (SE-WL) techniques as baselines. We use the kernel implementations from Oettershagen et al. [20] and tune the hyperparameter k during an inner cross-validation loop. We evaluate the performance of all methods in a 10-fold cross-validation setting and report the mean and standard deviation of the accuracies (Table 3). Filtration surfaces are able to classify the synthetic datasets perfectly, while SE-WL and DL-WL only achieve chance accuracy. This is due to the fact that neither method can take edge weight information into account. We also evaluate the performance of filtration surfaces on real-world datasets [30] without edge weight information (Tables 7 and 8). Our method (filtration surfaces with the Ollivier-Ricci curvature as the edge weight function) achieves the lowest overall standard deviation and competitive\u2014albeit not state-of-the-art\u2014accuracies compared to similarly scalable methods. However, in contrast to our method, none of the comparison partners can handle a changing node set or take edge weight information into account. We can thus conclude that filtration surfaces constitute a robust method with desirable scalability properties, competitive performance and the ability to alleviate restrictions of existing approaches, making it a novel approach in the space of dynamic graph classification methods. 4 Filtration Surfaces for Dynamic Graph Representation"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.01237v1",
+                    "title": "Dynamical Graph Echo State Networks with Snapshot Merging for Dissemination Process Classification",
+                    "abstract": "The Dissemination Process Classification (DPC) is a popular application of\ntemporal graph classification. The aim of DPC is to classify different\nspreading patterns of information or pestilence within a community represented\nby discrete-time temporal graphs. Recently, a reservoir computing-based model\nnamed Dynamical Graph Echo State Network (DynGESN) has been proposed for\nprocessing temporal graphs with relatively high effectiveness and low\ncomputational costs. In this study, we propose a novel model which combines a\nnovel data augmentation strategy called snapshot merging with the DynGESN for\ndealing with DPC tasks. In our model, the snapshot merging strategy is designed\nfor forming new snapshots by merging neighboring snapshots over time, and then\nmultiple reservoir encoders are set for capturing spatiotemporal features from\nmerged snapshots. After those, the logistic regression is adopted for decoding\nthe sum-pooled embeddings into the classification results. Experimental results\non six benchmark DPC datasets show that our proposed model has better\nclassification performances than the DynGESN and several kernel-based models.",
+                    "authors": "Ziqiang Li, Kantaro Fujiwara, Gouhei Tanaka",
+                    "published": "2023-07-03",
+                    "updated": "2023-07-03",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04350v2",
+                    "title": "Time-Variant Graph Classification",
+                    "abstract": "Graphs are commonly used to represent objects, such as images and text, for\npattern classification. In a dynamic world, an object may continuously evolve\nover time, and so does the graph extracted from the underlying object. These\nchanges in graph structure with respect to the temporal order present a new\nrepresentation of the graph, in which an object corresponds to a set of\ntime-variant graphs. In this paper, we formulate a novel time-variant graph\nclassification task and propose a new graph feature, called a graph-shapelet\npattern, for learning and classifying time-variant graphs. Graph-shapelet\npatterns are compact and discriminative graph transformation subsequences. A\ngraph-shapelet pattern can be regarded as a graphical extension of a shapelet\n-- a class of discriminative features designed for vector-based temporal data\nclassification. To discover graph-shapelet patterns, we propose to convert a\ntime-variant graph sequence into time-series data and use the discovered\nshapelets to find graph transformation subsequences as graph-shapelet patterns.\nBy converting each graph-shapelet pattern into a unique tokenized graph\ntransformation sequence, we can measure the similarity between two\ngraph-shapelet patterns and therefore classify time-variant graphs. Experiments\non both synthetic and real-world data demonstrate the superior performance of\nthe proposed algorithms.",
+                    "authors": "Haishuai Wang",
+                    "published": "2016-09-14",
+                    "updated": "2017-06-12",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.10637v3",
+                    "title": "Temporal Graph Networks for Deep Learning on Dynamic Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) have recently become increasingly popular due to\ntheir ability to learn complex systems of relations or interactions arising in\na broad spectrum of problems ranging from biology and particle physics to\nsocial networks and recommendation systems. Despite the plethora of different\nmodels for deep learning on graphs, few approaches have been proposed thus far\nfor dealing with graphs that present some sort of dynamic nature (e.g. evolving\nfeatures or connectivity over time). In this paper, we present Temporal Graph\nNetworks (TGNs), a generic, efficient framework for deep learning on dynamic\ngraphs represented as sequences of timed events. Thanks to a novel combination\nof memory modules and graph-based operators, TGNs are able to significantly\noutperform previous approaches being at the same time more computationally\nefficient. We furthermore show that several previous models for learning on\ndynamic graphs can be cast as specific instances of our framework. We perform a\ndetailed ablation study of different components of our framework and devise the\nbest configuration that achieves state-of-the-art performance on several\ntransductive and inductive prediction tasks for dynamic graphs.",
+                    "authors": "Emanuele Rossi, Ben Chamberlain, Fabrizio Frasca, Davide Eynard, Federico Monti, Michael Bronstein",
+                    "published": "2020-06-18",
+                    "updated": "2020-10-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.08565v2",
+                    "title": "Dynamic Graph Echo State Networks",
+                    "abstract": "Dynamic temporal graphs represent evolving relations between entities, e.g.\ninteractions between social network users or infection spreading. We propose an\nextension of graph echo state networks for the efficient processing of dynamic\ntemporal graphs, with a sufficient condition for their echo state property, and\nan experimental analysis of reservoir layout impact. Compared to temporal graph\nkernels that need to hold the entire history of vertex interactions, our model\nprovides a vector encoding for the dynamic graph that is updated at each\ntime-step without requiring training. Experiments show accuracy comparable to\napproximate temporal graph kernels on twelve dissemination process\nclassification tasks.",
+                    "authors": "Domenico Tortorella, Alessio Micheli",
+                    "published": "2021-10-16",
+                    "updated": "2022-10-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.13495v2",
+                    "title": "Learning Dynamic Graph Representation of Brain Connectome with Spatio-Temporal Attention",
+                    "abstract": "Functional connectivity (FC) between regions of the brain can be assessed by\nthe degree of temporal correlation measured with functional neuroimaging\nmodalities. Based on the fact that these connectivities build a network,\ngraph-based approaches for analyzing the brain connectome have provided\ninsights into the functions of the human brain. The development of graph neural\nnetworks (GNNs) capable of learning representation from graph structured data\nhas led to increased interest in learning the graph representation of the brain\nconnectome. Although recent attempts to apply GNN to the FC network have shown\npromising results, there is still a common limitation that they usually do not\nincorporate the dynamic characteristics of the FC network which fluctuates over\ntime. In addition, a few studies that have attempted to use dynamic FC as an\ninput for the GNN reported a reduction in performance compared to static FC\nmethods, and did not provide temporal explainability. Here, we propose STAGIN,\na method for learning dynamic graph representation of the brain connectome with\nspatio-temporal attention. Specifically, a temporal sequence of brain graphs is\ninput to the STAGIN to obtain the dynamic graph representation, while novel\nREADOUT functions and the Transformer encoder provide spatial and temporal\nexplainability with attention, respectively. Experiments on the HCP-Rest and\nthe HCP-Task datasets demonstrate exceptional performance of our proposed\nmethod. Analysis of the spatio-temporal attention also provide concurrent\ninterpretation with the neuroscientific knowledge, which further validates our\nmethod. Code is available at https://github.com/egyptdj/stagin",
+                    "authors": "Byung-Hoon Kim, Jong Chul Ye, Jae-Jin Kim",
+                    "published": "2021-05-27",
+                    "updated": "2021-10-21",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "q-bio.NC"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.07496v2",
+                    "title": "Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey",
+                    "abstract": "Dynamic networks are used in a wide range of fields, including social network\nanalysis, recommender systems, and epidemiology. Representing complex networks\nas structures changing over time allow network models to leverage not only\nstructural but also temporal patterns. However, as dynamic network literature\nstems from diverse fields and makes use of inconsistent terminology, it is\nchallenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a\nlot of attention in recent years for their ability to perform well on a range\nof network science tasks, such as link prediction and node classification.\nDespite the popularity of graph neural networks and the proven benefits of\ndynamic network models, there has been little focus on graph neural networks\nfor dynamic networks. To address the challenges resulting from the fact that\nthis research crosses diverse fields as well as to survey dynamic graph neural\nnetworks, this work is split into two main parts. First, to address the\nambiguity of the dynamic network terminology we establish a foundation of\ndynamic networks with consistent, detailed terminology and notation. Second, we\npresent a comprehensive survey of dynamic graph neural network models using the\nproposed terminology",
+                    "authors": "Joakim Skarding, Bogdan Gabrys, Katarzyna Musial",
+                    "published": "2020-05-13",
+                    "updated": "2021-06-13",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.05496v2",
+                    "title": "Temporal Graph Kernels for Classifying Dissemination Processes",
+                    "abstract": "Many real-world graphs or networks are temporal, e.g., in a social network\npersons only interact at specific points in time. This information directs\ndissemination processes on the network, such as the spread of rumors, fake\nnews, or diseases. However, the current state-of-the-art methods for supervised\ngraph classification are designed mainly for static graphs and may not be able\nto capture temporal information. Hence, they are not powerful enough to\ndistinguish between graphs modeling different dissemination processes. To\naddress this, we introduce a framework to lift standard graph kernels to the\ntemporal domain. Specifically, we explore three different approaches and\ninvestigate the trade-offs between loss of temporal information and efficiency.\nMoreover, to handle large-scale graphs, we propose stochastic variants of our\nkernels with provable approximation guarantees. We evaluate our methods on a\nwide range of real-world social networks. Our methods beat static kernels by a\nlarge margin in terms of accuracy while still being scalable to large graphs\nand data sets. Hence, we confirm that taking temporal information into account\nis crucial for the successful classification of dissemination processes.",
+                    "authors": "Lutz Oettershagen, Nils M. Kriege, Christopher Morris, Petra Mutzel",
+                    "published": "2019-10-14",
+                    "updated": "2021-08-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.12003v1",
+                    "title": "On Finding Separators in Temporal Split and Permutation Graphs",
+                    "abstract": "Removing all connections between two vertices s and z in a graph by removing\na minimum number of vertices is a fundamental problem in algorithmic graph\ntheory. This (s,z)-separation problem is well-known to be polynomial solvable\nand serves as an important primitive in many applications related to network\nconnectivity. We study the NP-hard temporal (s,z)-separation problem on\ntemporal graphs, which are graphs with fixed vertex sets but edge sets that\nchange over discrete time steps. We tackle this problem by restricting the\nlayers (i.e., graphs characterized by edges that are present at a certain point\nin time) to specific graph classes. We restrict the layers of the temporal\ngraphs to be either all split graphs or all permutation graphs (both being\nperfect graph classes) and provide both intractability and tractability\nresults. In particular, we show that in general the problem remains NP-hard\nboth on temporal split and temporal permutation graphs, but we also spot\npromising islands of fixed-parameter tractability particularly based on\nparameterizations that measure the amount of \"change over time\".",
+                    "authors": "Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken",
+                    "published": "2021-05-25",
+                    "updated": "2021-05-25",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.06411v1",
+                    "title": "On the Size and the Approximability of Minimum Temporally Connected Subgraphs",
+                    "abstract": "We consider temporal graphs with discrete time labels and investigate the\nsize and the approximability of minimum temporally connected spanning\nsubgraphs. We present a family of minimally connected temporal graphs with $n$\nvertices and $\\Omega(n^2)$ edges, thus resolving an open question of (Kempe,\nKleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal\nconnectivity certificates. Next, we consider the problem of computing a minimum\nweight subset of temporal edges that preserve connectivity of a given temporal\ngraph either from a given vertex r (r-MTC problem) or among all vertex pairs\n(MTC problem). We show that the approximability of r-MTC is closely related to\nthe approximability of Directed Steiner Tree and that r-MTC can be solved in\npolynomial time if the underlying graph has bounded treewidth. We also show\nthat the best approximation ratio for MTC is at least $O(2^{\\log^{1-\\epsilon}\nn})$ and at most $O(\\min\\{n^{1+\\epsilon}, (\\Delta M)^{2/3+\\epsilon}\\})$, for\nany constant $\\epsilon > 0$, where $M$ is the number of temporal edges and\n$\\Delta$ is the maximum degree of the underlying graph. Furthermore, we prove\nthat the unweighted version of MTC is APX-hard and that MTC is efficiently\nsolvable in trees and $2$-approximable in cycles.",
+                    "authors": "Kyriakos Axiotis, Dimitris Fotakis",
+                    "published": "2016-02-20",
+                    "updated": "2016-02-20",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2008.08282v2",
+                    "title": "Multiscale Snapshots: Visual Analysis of Temporal Summaries in Dynamic Graphs",
+                    "abstract": "The overview-driven visual analysis of large-scale dynamic graphs poses a\nmajor challenge. We propose Multiscale Snapshots, a visual analytics approach\nto analyze temporal summaries of dynamic graphs at multiple temporal scales.\nFirst, we recursively generate temporal summaries to abstract overlapping\nsequences of graphs into compact snapshots. Second, we apply graph embeddings\nto the snapshots to learn low-dimensional representations of each sequence of\ngraphs to speed up specific analytical tasks (e.g., similarity search). Third,\nwe visualize the evolving data from a coarse to fine-granular snapshots to\nsemi-automatically analyze temporal states, trends, and outliers. The approach\nenables to discover similar temporal summaries (e.g., recurring states),\nreduces the temporal data to speed up automatic analysis, and to explore both\nstructural and temporal properties of a dynamic graph. We demonstrate the\nusefulness of our approach by a quantitative evaluation and the application to\na real-world dataset.",
+                    "authors": "Eren Cakmak, Udo Schlegel, Dominik J\u00e4ckle, Daniel Keim, Tobias Schreck",
+                    "published": "2020-08-19",
+                    "updated": "2020-09-15",
+                    "primary_cat": "cs.HC",
+                    "cats": [
+                        "cs.HC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.12931v1",
+                    "title": "Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal forecasting has attracted tremendous attention in a wide\nrange of applications, and traffic flow prediction is a canonical and typical\nexample. The complex and long-range spatial-temporal correlations of traffic\nflow bring it to a most intractable challenge. Existing works typically utilize\nshallow graph convolution networks (GNNs) and temporal extracting modules to\nmodel spatial and temporal dependencies respectively. However, the\nrepresentation ability of such models is limited due to: (1) shallow GNNs are\nincapable to capture long-range spatial correlations, (2) only spatial\nconnections are considered and a mass of semantic connections are ignored,\nwhich are of great importance for a comprehensive understanding of traffic\nnetworks. To this end, we propose Spatial-Temporal Graph Ordinary Differential\nEquation Networks (STGODE). Specifically, we capture spatial-temporal dynamics\nthrough a tensor-based ordinary differential equation (ODE), as a result,\ndeeper networks can be constructed and spatial-temporal features are utilized\nsynchronously. To understand the network more comprehensively, semantical\nadjacency matrix is considered in our model, and a well-design temporal\ndialated convolution structure is used to capture long term temporal\ndependencies. We evaluate our model on multiple real-world traffic datasets and\nsuperior performance is achieved over state-of-the-art baselines.",
+                    "authors": "Zheng Fang, Qingqing Long, Guojie Song, Kunqing Xie",
+                    "published": "2021-06-24",
+                    "updated": "2021-06-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1912.03904v1",
+                    "title": "Weighted temporal event graphs",
+                    "abstract": "The times of temporal-network events and their correlations contain\ninformation on the function of the network and they influence dynamical\nprocesses taking place on it. To extract information out of correlated event\ntimes, techniques such as the analysis of temporal motifs have been developed.\nWe discuss a recently-introduced, more general framework that maps\ntemporal-network structure into static graphs while retaining information on\ntime-respecting paths and the time differences between their consequent events.\nThis framework builds on weighted temporal event graphs: directed, acyclic\ngraphs (DAGs) that contain a superposition of all temporal paths. We introduce\nthe reader to the temporal event-graph mapping and associated computational\nmethods and illustrate its use by applying the framework to temporal-network\npercolation.",
+                    "authors": "Jari Saram\u00e4ki, Mikko Kivel\u00e4, M\u00e1rton Karsai",
+                    "published": "2019-12-09",
+                    "updated": "2019-12-09",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.03651v1",
+                    "title": "Temporal Graph Analysis with TGX",
+                    "abstract": "Real-world networks, with their evolving relations, are best captured as\ntemporal graphs. However, existing software libraries are largely designed for\nstatic graphs where the dynamic nature of temporal graphs is ignored. Bridging\nthis gap, we introduce TGX, a Python package specially designed for analysis of\ntemporal networks that encompasses an automated pipeline for data loading, data\nprocessing, and analysis of evolving graphs. TGX provides access to eleven\nbuilt-in datasets and eight external Temporal Graph Benchmark (TGB) datasets as\nwell as any novel datasets in the .csv format. Beyond data loading, TGX\nfacilitates data processing functionalities such as discretization of temporal\ngraphs and node subsampling to accelerate working with larger datasets. For\ncomprehensive investigation, TGX offers network analysis by providing a diverse\nset of measures, including average node degree and the evolving number of nodes\nand edges per timestamp. Additionally, the package consolidates meaningful\nvisualization plots indicating the evolution of temporal patterns, such as\nTemporal Edge Appearance (TEA) and Temporal Edge Trafficc (TET) plots. The TGX\npackage is a robust tool for examining the features of temporal graphs and can\nbe used in various areas like studying social networks, citation networks, and\ntracking user interactions. We plan to continuously support and update TGX\nbased on community feedback. TGX is publicly available on:\nhttps://github.com/ComplexData-MILA/TGX.",
+                    "authors": "Razieh Shirzadkhani, Shenyang Huang, Elahe Kooshafar, Reihaneh Rabbany, Farimah Poursafaei",
+                    "published": "2024-02-06",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.04434v1",
+                    "title": "Frequency Analysis of Temporal Graph Signals",
+                    "abstract": "This letter extends the concept of graph-frequency to graph signals that\nevolve with time. Our goal is to generalize and, in fact, unify the familiar\nconcepts from time- and graph-frequency analysis. To this end, we study a joint\ntemporal and graph Fourier transform (JFT) and demonstrate its attractive\nproperties. We build on our results to create filters which act on the joint\n(temporal and graph) frequency domain, and show how these can be used to\nperform interference cancellation. The proposed algorithms are distributed,\nhave linear complexity, and can approximate any desired joint filtering\nobjective.",
+                    "authors": "Andreas Loukas, Damien Foucard",
+                    "published": "2016-02-14",
+                    "updated": "2016-02-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SY",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.09677v1",
+                    "title": "A Simple Temporal Information Matching Mechanism for Entity Alignment Between Temporal Knowledge Graphs",
+                    "abstract": "Entity alignment (EA) aims to find entities in different knowledge graphs\n(KGs) that refer to the same object in the real world. Recent studies\nincorporate temporal information to augment the representations of KGs. The\nexisting methods for EA between temporal KGs (TKGs) utilize a time-aware\nattention mechanism to incorporate relational and temporal information into\nentity embeddings. The approaches outperform the previous methods by using\ntemporal information. However, we believe that it is not necessary to learn the\nembeddings of temporal information in KGs since most TKGs have uniform temporal\nrepresentations. Therefore, we propose a simple graph neural network (GNN)\nmodel combined with a temporal information matching mechanism, which achieves\nbetter performance with less time and fewer parameters. Furthermore, since\nalignment seeds are difficult to label in real-world applications, we also\npropose a method to generate unsupervised alignment seeds via the temporal\ninformation of TKG. Extensive experiments on public datasets indicate that our\nsupervised method significantly outperforms the previous methods and the\nunsupervised one has competitive performance.",
+                    "authors": "Li Cai, Xin Mao, Meirong Ma, Hao Yuan, Jianchao Zhu, Man Lan",
+                    "published": "2022-09-20",
+                    "updated": "2022-09-20",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.08733v1",
+                    "title": "Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast",
+                    "abstract": "Self-supervised learning on graphs has recently drawn a lot of attention due\nto its independence from labels and its robustness in representation. Current\nstudies on this topic mainly use static information such as graph structures\nbut cannot well capture dynamic information such as timestamps of edges.\nRealistic graphs are often dynamic, which means the interaction between nodes\noccurs at a specific time. This paper proposes a self-supervised dynamic graph\nrepresentation learning framework (DySubC), which defines a temporal subgraph\ncontrastive learning task to simultaneously learn the structural and\nevolutional features of a dynamic graph. Specifically, a novel temporal\nsubgraph sampling strategy is firstly proposed, which takes each node of the\ndynamic graph as the central node and uses both neighborhood structures and\nedge timestamps to sample the corresponding temporal subgraph. The subgraph\nrepresentation function is then designed according to the influence of\nneighborhood nodes on the central node after encoding the nodes in each\nsubgraph. Finally, the structural and temporal contrastive loss are defined to\nmaximize the mutual information between node representation and temporal\nsubgraph representation. Experiments on five real-world datasets demonstrate\nthat (1) DySubC performs better than the related baselines including two graph\ncontrastive learning models and four dynamic graph representation learning\nmodels in the downstream link prediction task, and (2) the use of temporal\ninformation can not only sample more effective subgraphs, but also learn better\nrepresentation by temporal contrastive loss.",
+                    "authors": "Linpu Jiang, Ke-Jia Chen, Jingqiang Chen",
+                    "published": "2021-12-16",
+                    "updated": "2021-12-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1601.05909v2",
+                    "title": "Efficient Processing of Reachability and Time-Based Path Queries in a Temporal Graph",
+                    "abstract": "A temporal graph is a graph in which vertices communicate with each other at\nspecific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is\nmodeled by an edge from $A$ to $B$ with starting time \"11 a.m.\" and duration \"7\nmins\". Temporal graphs can be used to model many networks with time-related\nactivities, but efficient algorithms for analyzing temporal graphs are severely\ninadequate. We study fundamental problems such as answering reachability and\ntime-based path queries in a temporal graph, and propose an efficient indexing\ntechnique specifically designed for processing these queries in a temporal\ngraph. Our results show that our method is efficient and scalable in both index\nconstruction and query processing.",
+                    "authors": "Huanhuan Wu, Yuzhen Huang, James Cheng, Jinfeng Li, Yiping Ke",
+                    "published": "2016-01-22",
+                    "updated": "2016-01-25",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.19292v1",
+                    "title": "Fusing Temporal Graphs into Transformers for Time-Sensitive Question Answering",
+                    "abstract": "Answering time-sensitive questions from long documents requires temporal\nreasoning over the times in questions and documents. An important open question\nis whether large language models can perform such reasoning solely using a\nprovided text document, or whether they can benefit from additional temporal\ninformation extracted using other systems. We address this research question by\napplying existing temporal information extraction systems to construct temporal\ngraphs of events, times, and temporal relations in questions and documents. We\nthen investigate different approaches for fusing these graphs into Transformer\nmodels. Experimental results show that our proposed approach for fusing\ntemporal graphs into input text substantially enhances the temporal reasoning\ncapabilities of Transformer models with or without fine-tuning. Additionally,\nour proposed method outperforms various graph convolution-based approaches and\nestablishes a new state-of-the-art performance on SituatedQA and three splits\nof TimeQA.",
+                    "authors": "Xin Su, Phillip Howard, Nagib Hakim, Steven Bethard",
+                    "published": "2023-10-30",
+                    "updated": "2023-10-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.15862v1",
+                    "title": "Restless Temporal Path Parameterized Above Lower Bounds",
+                    "abstract": "Reachability questions are one of the most fundamental algorithmic primitives\nin temporal graphs -- graphs whose edge set changes over discrete time steps. A\ncore problem here is the NP-hard Short Restless Temporal Path: given a temporal\ngraph $\\mathcal G$, two distinct vertices $s$ and $z$, and two numbers $\\delta$\nand $k$, is there a $\\delta$-restless temporal $s$-$z$ path of length at most\n$k$? A temporal path is a path whose edges appear in chronological order and a\ntemporal path is $\\delta$-restless if two consecutive path edges appear at most\n$\\delta$ time steps apart from each other. Among others, this problem has\napplications in neuroscience and epidemiology. While Short Restless Temporal\nPath is known to be computationally hard, e.g., it is NP-hard for only three\ntime steps and W[1]-hard when parameterized by the feedback vertex number of\nthe underlying graph, it is fixed-parameter tractable when parameterized by the\npath length $k$. We improve on this by showing that Short Restless Temporal\nPath can be solved in (randomized) $4^{k-d}|\\mathcal G|^{O(1)}$ time, where $d$\nis the minimum length of a temporal $s$-$z$ path.",
+                    "authors": "Philipp Zschoche",
+                    "published": "2022-03-29",
+                    "updated": "2022-03-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02212v1",
+                    "title": "Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by\nattaching the time scope. Existing temporal knowledge graph question answering\n(TKGQA) models solely approach simple questions, owing to the prior assumption\nthat each question only contains a single temporal fact with explicit/implicit\ntemporal constraints. Hence, they perform poorly on questions which own\nmultiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint\n\\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts\n\\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly\nreasoning multiple temporal facts for accurately answering \\emph{complex}\ntemporal questions. Specifically, JMFRN first retrieves question-related\ntemporal facts from TKG for each entity of the given complex question. For\njoint reasoning, we design two different attention (\\ie entity-aware and\ntime-aware) modules, which are suitable for universal settings, to aggregate\nentities and timestamps information of retrieved facts. Moreover, to filter\nincorrect type answers, we introduce an additional answer type discrimination\ntask. Extensive experiments demonstrate our proposed method significantly\noutperforms the state-of-art on the well-known complex temporal question\nbenchmark TimeQuestions.",
+                    "authors": "Rikui Huang, Wei Wei, Xiaoye Qu, Wenfeng Xie, Xianling Mao, Dangyang Chen",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08514v2",
+                    "title": "Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction",
+                    "abstract": "Understanding crowd motion dynamics is critical to real-world applications,\ne.g., surveillance systems and autonomous driving. This is challenging because\nit requires effectively modeling the socially aware crowd spatial interaction\nand complex temporal dependencies. We believe attention is the most important\nfactor for trajectory prediction. In this paper, we present STAR, a\nSpatio-Temporal grAph tRansformer framework, which tackles trajectory\nprediction by only attention mechanisms. STAR models intra-graph crowd\ninteraction by TGConv, a novel Transformer-based graph convolution mechanism.\nThe inter-graph temporal dependencies are modeled by separate temporal\nTransformers. STAR captures complex spatio-temporal interactions by\ninterleaving between spatial and temporal Transformers. To calibrate the\ntemporal prediction for the long-lasting effect of disappeared pedestrians, we\nintroduce a read-writable external memory module, consistently being updated by\nthe temporal Transformer. We show that with only attention mechanism, STAR\nachieves state-of-the-art performance on 5 commonly used real-world pedestrian\nprediction datasets.",
+                    "authors": "Cunjun Yu, Xiao Ma, Jiawei Ren, Haiyu Zhao, Shuai Yi",
+                    "published": "2020-05-18",
+                    "updated": "2020-07-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.RO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1810.06240v4",
+                    "title": "Comparing Temporal Graphs Using Dynamic Time Warping",
+                    "abstract": "Within many real-world networks the links between pairs of nodes change over\ntime. Thus, there has been a recent boom in studying temporal graphs.\nRecognizing patterns in temporal graphs requires a proximity measure to compare\ndifferent temporal graphs. To this end, we propose to study dynamic time\nwarping on temporal graphs. We define the dynamic temporal graph warping\ndistance (dtgw) to determine the dissimilarity of two temporal graphs. Our\nnovel measure is flexible and can be applied in various application domains. We\nshow that computing the dtgw-distance is a challenging (in general) NP-hard\noptimization problem and identify some polynomial-time solvable special cases.\nMoreover, we develop a quadratic programming formulation and an efficient\nheuristic. In experiments on real-word data we show that the heuristic performs\nvery well and that our dtgw-distance performs favorably in de-anonymizing\nnetworks compared to other approaches.",
+                    "authors": "Vincent Froese, Brijnesh Jain, Rolf Niedermeier, Malte Renken",
+                    "published": "2018-10-15",
+                    "updated": "2020-07-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.13517v1",
+                    "title": "Temporal Graph Signal Decomposition",
+                    "abstract": "Temporal graph signals are multivariate time series with individual\ncomponents associated with nodes of a fixed graph structure. Data of this kind\narises in many domains including activity of social network users, sensor\nnetwork readings over time, and time course gene expression within the\ninteraction network of a model organism. Traditional matrix decomposition\nmethods applied to such data fall short of exploiting structural regularities\nencoded in the underlying graph and also in the temporal patterns of the\nsignal. How can we take into account such structure to obtain a succinct and\ninterpretable representation of temporal graph signals?\n  We propose a general, dictionary-based framework for temporal graph signal\ndecomposition (TGSD). The key idea is to learn a low-rank, joint encoding of\nthe data via a combination of graph and time dictionaries. We propose a highly\nscalable decomposition algorithm for both complete and incomplete data, and\ndemonstrate its advantage for matrix decomposition, imputation of missing\nvalues, temporal interpolation, clustering, period estimation, and rank\nestimation in synthetic and real-world data ranging from traffic patterns to\nsocial media activity. Our framework achieves 28% reduction in RMSE compared to\nbaselines for temporal interpolation when as many as 75% of the observations\nare missing. It scales best among baselines taking under 20 seconds on 3.5\nmillion data points and produces the most parsimonious models. To the best of\nour knowledge, TGSD is the first framework to jointly model graph signals by\ntemporal and graph dictionaries.",
+                    "authors": "Maxwell McNeil, Lin Zhang, Petko Bogdanov",
+                    "published": "2021-06-25",
+                    "updated": "2021-06-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0807.2357v1",
+                    "title": "Temporal Graphs",
+                    "abstract": "We introduce the idea of temporal graphs, a representation that encodes\ntemporal data into graphs while fully retaining the temporal information of the\noriginal data. This representation lets us explore the dynamic temporal\nproperties of data by using existing graph algorithms (such as shortest-path),\nwith no need for data-driven simulations. We also present a number of metrics\nthat can be used to study and explore temporal graphs. Finally, we use temporal\ngraphs to analyse real-world data and present the results of our analysis.",
+                    "authors": "Vassilis Kostakos",
+                    "published": "2008-07-15",
+                    "updated": "2008-07-15",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08909v2",
+                    "title": "Maximum 0-1 Timed Matching on Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs where the topology and/or other properties of the\ngraph change with time. They have been used to model applications with temporal\ninformation in various domains. Problems on static graphs become more\nchallenging to solve in temporal graphs because of dynamically changing\ntopology, and many recent works have explored graph problems on temporal\ngraphs. In this paper, we define a type of matching called {\\em 0-1 timed\nmatching} for temporal graphs, and investigate the problem of finding a {\\em\nmaximum 0-1 timed matching} for different classes of temporal graphs. We first\nprove that the problem is NP-Complete for rooted temporal trees when each edge\nis associated with two or more time intervals. We then propose an $O(n \\log n)$\ntime algorithm for the problem on a rooted temporal tree with $n$ nodes when\neach edge is associated with exactly one time interval. The problem is then\nshown to be NP-Complete also for bipartite temporal graphs even when each edge\nis associated with a single time interval and degree of each node is bounded by\na constant $k \\geq 3$. We next investigate approximation algorithms for the\nproblem for temporal graphs where each edge is associated with more than one\ntime intervals. It is first shown that there is no\n$\\frac{1}{n^{1-\\epsilon}}$-factor approximation algorithm for the problem for\nany $\\epsilon > 0$ even on a rooted temporal tree with $n$ nodes unless NP =\nZPP. We then present a $\\frac{5}{2\\mathcal{N}^* + 3}$-factor approximation\nalgorithm for the problem for general temporal graphs where $\\mathcal{N^*}$ is\nthe average number of edges overlapping in time with each edge in the temporal\ngraph. The same algorithm is also a constant-factor approximation algorithm for\ndegree bounded temporal graphs.",
+                    "authors": "Subhrangsu Mandal, Arobinda Gupta",
+                    "published": "2020-12-16",
+                    "updated": "2022-02-01",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.10379v1",
+                    "title": "ChronoR: Rotation Based Temporal Knowledge Graph Embedding",
+                    "abstract": "Despite the importance and abundance of temporal knowledge graphs, most of\nthe current research has been focused on reasoning on static graphs. In this\npaper, we study the challenging problem of inference over temporal knowledge\ngraphs. In particular, the task of temporal link prediction. In general, this\nis a difficult task due to data non-stationarity, data heterogeneity, and its\ncomplex temporal dependencies. We propose Chronological Rotation embedding\n(ChronoR), a novel model for learning representations for entities, relations,\nand time. Learning dense representations is frequently used as an efficient and\nversatile method to perform reasoning on knowledge graphs. The proposed model\nlearns a k-dimensional rotation transformation parametrized by relation and\ntime, such that after each fact's head entity is transformed using the\nrotation, it falls near its corresponding tail entity. By using high\ndimensional rotation as its transformation operator, ChronoR captures rich\ninteraction between the temporal and multi-relational characteristics of a\nTemporal Knowledge Graph. Experimentally, we show that ChronoR is able to\noutperform many of the state-of-the-art methods on the benchmark datasets for\ntemporal knowledge graph link prediction.",
+                    "authors": "Ali Sadeghian, Mohammadreza Armandpour, Anthony Colas, Daisy Zhe Wang",
+                    "published": "2021-03-18",
+                    "updated": "2021-03-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.00963v5",
+                    "title": "The Complexity of Finding Small Separators in Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs with time-stamped edges. We study the problem of\nfinding a small vertex set (the separator) with respect to two designated\nterminal vertices such that the removal of the set eliminates all temporal\npaths connecting one terminal to the other. Herein, we consider two models of\ntemporal paths: paths that pass through arbitrarily many edges per time step\n(non-strict) and paths that pass through at most one edge per time step\n(strict). Regarding the number of time steps of a temporal graph, we show a\ncomplexity dichotomy (NP-hardness versus polynomial-time solvability) for both\nproblem variants. Moreover we prove both problem variants to be NP-complete\neven on temporal graphs whose underlying graph is planar. We further show that,\non temporal graphs with planar underlying graph, if additionally the number of\ntime steps is constant, then the problem variant for strict paths is solvable\nin quasi-linear time. Finally, we introduce and motivate the notion of a\ntemporal core (vertices whose incident edges change over time). We prove that\nthe non-strict variant is fixed-parameter tractable when parameterized by the\nsize of the temporal core, while the strict variant remains NP-complete, even\nfor constant-size temporal cores.",
+                    "authors": "Philipp Zschoche, Till Fluschnik, Hendrik Molter, Rolf Niedermeier",
+                    "published": "2017-11-02",
+                    "updated": "2018-07-25",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.17110v2",
+                    "title": "LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?",
+                    "abstract": "In an era marked by the increasing adoption of Large Language Models (LLMs)\nfor various tasks, there is a growing focus on exploring LLMs' capabilities in\nhandling web data, particularly graph data. Dynamic graphs, which capture\ntemporal network evolution patterns, are ubiquitous in real-world web data.\nEvaluating LLMs' competence in understanding spatial-temporal information on\ndynamic graphs is essential for their adoption in web applications, which\nremains unexplored in the literature. In this paper, we bridge the gap via\nproposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic\ngraphs, to the best of our knowledge, for the first time. Specifically, we\npropose the LLM4DyG benchmark, which includes nine specially designed tasks\nconsidering the capability evaluation of LLMs from both temporal and spatial\ndimensions. Then, we conduct extensive experiments to analyze the impacts of\ndifferent data generators, data statistics, prompting techniques, and LLMs on\nthe model performance. Finally, we propose Disentangled Spatial-Temporal\nThoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal\nunderstanding abilities. Our main observations are: 1) LLMs have preliminary\nspatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph\ntasks show increasing difficulties for LLMs as the graph size and density\nincrease, while not sensitive to the time span and data generation mechanism,\n3) the proposed DST2 prompting method can help to improve LLMs'\nspatial-temporal understanding abilities on dynamic graphs for most tasks. The\ndata and codes will be open-sourced at publication time.",
+                    "authors": "Zeyang Zhang, Xin Wang, Ziwei Zhang, Haoyang Li, Yijian Qin, Wenwu Zhu",
+                    "published": "2023-10-26",
+                    "updated": "2024-03-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08804v1",
+                    "title": "Temporal Graph Modeling for Skeleton-based Action Recognition",
+                    "abstract": "Graph Convolutional Networks (GCNs), which model skeleton data as graphs,\nhave obtained remarkable performance for skeleton-based action recognition.\nParticularly, the temporal dynamic of skeleton sequence conveys significant\ninformation in the recognition task. For temporal dynamic modeling, GCN-based\nmethods only stack multi-layer 1D local convolutions to extract temporal\nrelations between adjacent time steps. With the repeat of a lot of local\nconvolutions, the key temporal information with non-adjacent temporal distance\nmay be ignored due to the information dilution. Therefore, these methods still\nremain unclear how to fully explore temporal dynamic of skeleton sequence. In\nthis paper, we propose a Temporal Enhanced Graph Convolutional Network (TE-GCN)\nto tackle this limitation. The proposed TE-GCN constructs temporal relation\ngraph to capture complex temporal dynamic. Specifically, the constructed\ntemporal relation graph explicitly builds connections between semantically\nrelated temporal features to model temporal relations between both adjacent and\nnon-adjacent time steps. Meanwhile, to further explore the sufficient temporal\ndynamic, multi-head mechanism is designed to investigate multi-kinds of\ntemporal relations. Extensive experiments are performed on two widely used\nlarge-scale datasets, NTU-60 RGB+D and NTU-120 RGB+D. And experimental results\nshow that the proposed model achieves the state-of-the-art performance by\nmaking contribution to temporal modeling for action recognition.",
+                    "authors": "Jianan Li, Xuemei Xie, Zhifu Zhao, Yuhan Cao, Qingzhe Pan, Guangming Shi",
+                    "published": "2020-12-16",
+                    "updated": "2020-12-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.03897v1",
+                    "title": "Temporal Graph Representation Learning with Adaptive Augmentation Contrastive",
+                    "abstract": "Temporal graph representation learning aims to generate low-dimensional\ndynamic node embeddings to capture temporal information as well as structural\nand property information. Current representation learning methods for temporal\nnetworks often focus on capturing fine-grained information, which may lead to\nthe model capturing random noise instead of essential semantic information.\nWhile graph contrastive learning has shown promise in dealing with noise, it\nonly applies to static graphs or snapshots and may not be suitable for handling\ntime-dependent noise. To alleviate the above challenge, we propose a novel\nTemporal Graph representation learning with Adaptive augmentation Contrastive\n(TGAC) model. The adaptive augmentation on the temporal graph is made by\ncombining prior knowledge with temporal information, and the contrastive\nobjective function is constructed by defining the augmented inter-view contrast\nand intra-view contrast. To complement TGAC, we propose three adaptive\naugmentation strategies that modify topological features to reduce noise from\nthe network. Our extensive experiments on various real networks demonstrate\nthat the proposed model outperforms other temporal graph representation\nlearning methods.",
+                    "authors": "Hongjiang Chen, Pengfei Jiao, Huijun Tang, Huaming Wu",
+                    "published": "2023-11-07",
+                    "updated": "2023-11-07",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.05018v2",
+                    "title": "Time-varying Graph Learning Under Structured Temporal Priors",
+                    "abstract": "This paper endeavors to learn time-varying graphs by using structured\ntemporal priors that assume underlying relations between arbitrary two graphs\nin the graph sequence. Different from many existing chain structure based\nmethods in which the priors like temporal homogeneity can only describe the\nvariations of two consecutive graphs, we propose a structure named\n\\emph{temporal graph} to characterize the underlying real temporal relations.\nUnder this framework, the chain structure is actually a special case of our\ntemporal graph. We further proposed Alternating Direction Method of Multipliers\n(ADMM), a distributed algorithm, to solve the induced optimization problem.\nNumerical experiments demonstrate the superiorities of our method.",
+                    "authors": "Xiang Zhang, Qiao Wang",
+                    "published": "2021-10-11",
+                    "updated": "2022-02-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.SP"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1805.06836v2",
+                    "title": "Deleting edges to restrict the size of an epidemic in temporal networks",
+                    "abstract": "Spreading processes on graphs are a natural model for a wide variety of\nreal-world phenomena, including information spread over social networks and\nbiological diseases spreading over contact networks. Often, the networks over\nwhich these processes spread are dynamic in nature, and can be modeled with\ntemporal graphs. Here, we study the problem of deleting edges from a given\ntemporal graph in order to reduce the number of vertices (temporally) reachable\nfrom a given starting point. This could be used to control the spread of a\ndisease, rumour, etc. in a temporal graph. In particular, our aim is to find a\ntemporal subgraph in which a process starting at any single vertex can be\ntransferred to only a limited number of other vertices using a\ntemporally-feasible path. We introduce a natural edge-deletion problem for\ntemporal graphs and provide positive and negative results on its computational\ncomplexity and approximability.",
+                    "authors": "Jessica Enright, Kitty Meeks, George B. Mertzios, Viktor Zamaraev",
+                    "published": "2018-05-17",
+                    "updated": "2021-02-11",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.05064v1",
+                    "title": "Adaptive Graph Spatial-Temporal Transformer Network for Traffic Flow Forecasting",
+                    "abstract": "Traffic flow forecasting on graphs has real-world applications in many\nfields, such as transportation system and computer networks. Traffic\nforecasting can be highly challenging due to complex spatial-temporal\ncorrelations and non-linear traffic patterns. Existing works mostly model such\nspatial-temporal dependencies by considering spatial correlations and temporal\ncorrelations separately and fail to model the direct spatial-temporal\ncorrelations. Inspired by the recent success of transformers in the graph\ndomain, in this paper, we propose to directly model the cross-spatial-temporal\ncorrelations on the spatial-temporal graph using local multi-head\nself-attentions. To reduce the time complexity, we set the attention receptive\nfield to the spatially neighboring nodes, and we also introduce an adaptive\ngraph to capture the hidden spatial-temporal dependencies. Based on these\nattention mechanisms, we propose a novel Adaptive Graph Spatial-Temporal\nTransformer Network (ASTTN), which stacks multiple spatial-temporal attention\nlayers to apply self-attention on the input graph, followed by linear layers\nfor predictions. Experimental results on public traffic network datasets,\nMETR-LA PEMS-BAY, PeMSD4, and PeMSD7, demonstrate the superior performance of\nour model.",
+                    "authors": "Aosong Feng, Leandros Tassiulas",
+                    "published": "2022-07-09",
+                    "updated": "2022-07-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2204.09236v1",
+                    "title": "Scalable Motif Counting for Large-scale Temporal Graphs",
+                    "abstract": "One fundamental problem in temporal graph analysis is to count the\noccurrences of small connected subgraph patterns (i.e., motifs), which benefits\na broad range of real-world applications, such as anomaly detection, structure\nprediction, and network representation learning. However, existing works\nfocused on exacting temporal motif are not scalable to large-scale temporal\ngraph data, due to their heavy computational costs or inherent inadequacy of\nparallelism. In this work, we propose a scalable parallel framework for exactly\ncounting temporal motifs in large-scale temporal graphs. We first categorize\nthe temporal motifs based on their distinct properties, and then design\ncustomized algorithms that offer efficient strategies to exactly count the\nmotif instances of each category. Moreover, our compact data structures, namely\ntriple and quadruple counters, enable our algorithms to directly identify the\ntemporal motif instances of each category, according to edge information and\nthe relationship between edges, therefore significantly improving the counting\nefficiency. Based on the proposed counting algorithms, we design a hierarchical\nparallel framework that features both inter- and intra-node parallel\nstrategies, and fully leverages the multi-threading capacity of modern CPU to\nconcurrently count all temporal motifs. Extensive experiments on sixteen\nreal-world temporal graph datasets demonstrate the superiority and capability\nof our proposed framework for temporal motif counting, achieving up to 538*\nspeedup compared to the state-of-the-art methods. The source code of our method\nis available at: https://github.com/steven-ccq/FAST-temporal-motif.",
+                    "authors": "Zhongqiang Gao, Chuanqi Cheng, Yanwei Yu, Lei Cao, Chao Huang, Junyu Dong",
+                    "published": "2022-04-20",
+                    "updated": "2022-04-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1706.09480v1",
+                    "title": "A Temporal Tree Decomposition for Generating Temporal Graphs",
+                    "abstract": "Discovering the underlying structures present in large real world graphs is a\nfundamental scientific problem. Recent work at the intersection of formal\nlanguage theory and graph theory has found that a Hyperedge Replacement Grammar\n(HRG) can be extracted from a tree decomposition of any graph. This HRG can be\nused to generate new graphs that share properties that are similar to the\noriginal graph. Because the extracted HRG is directly dependent on the shape\nand contents of the of tree decomposition, it is unlikely that informative\ngraph-processes are actually being captured with the extraction algorithm. To\naddress this problem, the current work presents a new extraction algorithm\ncalled temporal HRG (tHRG) that learns HRG production rules from a temporal\ntree decomposition of the graph. We observe problems with the assumptions that\nare made in a temporal HRG model. In experiments on large real world networks,\nwe show and provide reasoning as to why tHRG does not perform as well as HRG\nand other graph generators.",
+                    "authors": "Corey Pennycuff, Salvador Aguinaga, Tim Weninger",
+                    "published": "2017-06-28",
+                    "updated": "2017-06-28",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.07117v1",
+                    "title": "On inefficiently connecting temporal networks",
+                    "abstract": "A temporal graph can be represented by a graph with an edge labelling, such\nthat an edge is present in the network if and only if the edge is assigned the\ncorresponding time label. A journey is a labelled path in a temporal graph such\nthat labels on successive edges of the path are increasing, and if all vertices\nadmit journeys to all other vertices, the temporal graph is temporally\nconnected. A temporal spanner is a sublabelling of the temporal graph such that\ntemporal connectivity is maintained. The study of temporal spanners has raised\ninterest since the early 2000's. Essentially two types of studies have been\nconducted: the positive side where families of temporal graphs are shown to\n(deterministically or stochastically) admit sparse temporal spanners, and the\nnegative side where constructions of temporal graphs with no sparse spanners\nare of importance. Often such studies considered temporal graphs with happy or\nsimple labellings, which associate exactly one label per edge. In this paper,\nwe focus on the negative side and consider proper labellings, where multiple\nlabels per edge are allowed. More precisely, we aim to construct dense\ntemporally connected graphs such that all labels are necessary for temporal\nconnectivity. Our contributions are multiple: we present the first labellings\nmaximizing a local density measure; exact or asymptotically tight results for\nbasic graph families, which are then extended to larger graph families; an\nextension of an efficient temporal graph labelling generator; and overall\ndenser labellings than previous work even when restricted to happy labellings.",
+                    "authors": "Esteban Christiann, Eric Sanlaville, Jason Schoeters",
+                    "published": "2023-12-12",
+                    "updated": "2023-12-12",
+                    "primary_cat": "cs.CC",
+                    "cats": [
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.02852v1",
+                    "title": "Introduction to a Temporal Graph Benchmark",
+                    "abstract": "A temporal graph is a data structure, consisting of nodes and edges in which\nthe edges are associated with time labels. To analyze the temporal graph, the\nfirst step is to find a proper graph dataset/benchmark. While many temporal\ngraph datasets exist online, none could be found that used the interval labels\nin which each edge is associated with a starting and ending time. Therefore we\ncreate a temporal graph data based on Wikipedia reference graph for temporal\nanalysis. This report aims to provide more details of this graph benchmark to\nthose who are interested in using it.",
+                    "authors": "Wouter Ligtenberg, Yulong Pei",
+                    "published": "2017-02-20",
+                    "updated": "2017-02-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1306.0493v1",
+                    "title": "Graph Metrics for Temporal Networks",
+                    "abstract": "Temporal networks, i.e., networks in which the interactions among a set of\nelementary units change over time, can be modelled in terms of time-varying\ngraphs, which are time-ordered sequences of graphs over a set of nodes. In such\ngraphs, the concepts of node adjacency and reachability crucially depend on the\nexact temporal ordering of the links. Consequently, all the concepts and\nmetrics proposed and used for the characterisation of static complex networks\nhave to be redefined or appropriately extended to time-varying graphs, in order\nto take into account the effects of time ordering on causality. In this chapter\nwe discuss how to represent temporal networks and we review the definitions of\nwalks, paths, connectedness and connected components valid for graphs in which\nthe links fluctuate over time. We then focus on temporal node-node distance,\nand we discuss how to characterise link persistence and the temporal\nsmall-world behaviour in this class of networks. Finally, we discuss the\nextension of classic centrality measures, including closeness, betweenness and\nspectral centrality, to the case of time-varying graphs, and we review the work\non temporal motifs analysis and the definition of modularity for temporal\ngraphs.",
+                    "authors": "Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, Vito Latora",
+                    "published": "2013-06-03",
+                    "updated": "2013-06-03",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.11244v1",
+                    "title": "Using Compressed Suffix-Arrays for a Compact Representation of Temporal-Graphs",
+                    "abstract": "Temporal graphs represent binary relationships that change along time. They\ncan model the dynamism of, for example, social and communication networks.\nTemporal graphs are defined as sets of contacts that are edges tagged with the\ntemporal intervals when they are active. This work explores the use of the\nCompressed Suffix Array (CSA), a well-known compact and self-indexed data\nstructure in the area of text indexing, to represent large temporal graphs. The\nnew structure, called Temporal Graph CSA (TGCSA), is experimentally compared\nwith the most competitive compact data structures in the state-of-the-art,\nnamely, EDGELOG and CET. The experimental results show that TGCSA obtains a\ngood space-time trade-off. It uses a reasonable space and is efficient for\nsolving complex temporal queries. Furthermore, TGCSA has wider expressive\ncapabilities than EDGELOG and CET, because it is able to represent temporal\ngraphs where contacts on an edge can temporally overlap.",
+                    "authors": "Nieves R. Brisaboa, Diego Caro, Antonio Fari\u00f1a, M. Andrea Rodriguez",
+                    "published": "2018-12-28",
+                    "updated": "2018-12-28",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.15894v1",
+                    "title": "A Gated MLP Architecture for Learning Topological Dependencies in Spatio-Temporal Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) and Transformer have been increasingly adopted\nto learn the complex vector representations of spatio-temporal graphs,\ncapturing intricate spatio-temporal dependencies crucial for applications such\nas traffic datasets. Although many existing methods utilize multi-head\nattention mechanisms and message-passing neural networks (MPNNs) to capture\nboth spatial and temporal relations, these approaches encode temporal and\nspatial relations independently, and reflect the graph's topological\ncharacteristics in a limited manner. In this work, we introduce the Cycle to\nMixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial\ninvariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP).\nThe Cy2Mixer is composed of three blocks based on MLPs: A message-passing block\nfor encapsulating spatial information, a cycle message-passing block for\nenriching topological information through cyclic subgraphs, and a temporal\nblock for capturing temporal properties. We bolster the effectiveness of\nCy2Mixer with mathematical evidence emphasizing that our cycle message-passing\nblock is capable of offering differentiated information to the deep learning\nmodel compared to the message-passing block. Furthermore, empirical evaluations\nsubstantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art\nperformances across various traffic benchmark datasets.",
+                    "authors": "Yun Young Choi, Minho Lee, Sun Woo Park, Seunghwan Lee, Joohwan Ko",
+                    "published": "2024-01-29",
+                    "updated": "2024-01-29",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2108.08719v5",
+                    "title": "Temporal Graph Functional Dependencies [Extended Version]",
+                    "abstract": "Data dependencies have been extended to graphs to characterize topological\nand value constraints. Existing data dependencies are defined to capture\ninconsistencies in static graphs. Nevertheless, inconsistencies may occur over\nevolving graphs and only for certain time periods. The need for capturing such\ninconsistencies in temporal graphs is evident in anomaly detection and\npredictive dynamic network analysis. This paper introduces a class of data\ndependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs\ngeneralize functional dependencies to temporal graphs as a sequence of graph\nsnapshots that are induced by time intervals, and enforce both topological\nconstraints and attribute value dependencies that must be satisfied by these\nsnapshots. (1) We establish the complexity results for the satisfiability and\nimplication problems of TGFDs. (2) We propose a sound and complete\naxiomatization system for TGFDs. (3) We also present efficient parallel\nalgorithms to detect inconsistencies in temporal graphs as violations of TGFDs.\nThe algorithm exploits data and temporal locality induced by time intervals,\nand uses incremental pattern matching and load balancing strategies to enable\nfeasible error detection in large temporal graphs. Using real datasets, we\nexperimentally verify that our algorithms achieve lower runtimes compared to\nexisting baselines, while improving the accuracy over error detection using\nexisting graph data constraints, e.g., GFDs and GTARs with 55% and 74% gain in\nF1-score, respectively.",
+                    "authors": "Morteza Alipourlangouri, Adam Mansfield, Fei Chiang, Yinghui Wu",
+                    "published": "2021-08-19",
+                    "updated": "2022-07-26",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.10364v3",
+                    "title": "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks",
+                    "abstract": "Recent years have seen a surge in research on dynamic graph representation\nlearning, which aims to model temporal graphs that are dynamic and evolving\nconstantly over time. However, current work typically models graph dynamics\nwith recurrent neural networks (RNNs), making them suffer seriously from\ncomputation and memory overheads on large temporal graphs. So far, scalability\nof dynamic graph representation learning on large temporal graphs remains one\nof the major challenges. In this paper, we present a scalable framework, namely\nSpikeNet, to efficiently capture the temporal and structural patterns of\ntemporal graphs. We explore a new direction in that we can capture the evolving\ndynamics of temporal graphs with spiking neural networks (SNNs) instead of\nRNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics\nas spike trains of neuron populations and enable spike-based propagation in an\nefficient way. Experiments on three large real-world temporal graph datasets\ndemonstrate that SpikeNet outperforms strong baselines on the temporal node\nclassification task with lower computational costs. Particularly, SpikeNet\ngeneralizes to a large temporal graph (2.7M nodes and 13.9M edges) with\nsignificantly fewer parameters and computation overheads.Our code is publicly\navailable at \\url{https://github.com/EdisonLeeeee/SpikeNet}.",
+                    "authors": "Jintang Li, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, Changhua Meng",
+                    "published": "2022-08-15",
+                    "updated": "2023-05-18",
+                    "primary_cat": "cs.NE",
+                    "cats": [
+                        "cs.NE",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.12587v1",
+                    "title": "TGLib: An Open-Source Library for Temporal Graph Analysis",
+                    "abstract": "We initiate an open-source library for the efficient analysis of temporal\ngraphs. We consider one of the standard models of dynamic networks in which\neach edge has a discrete timestamp and transition time. Recently there has been\na massive interest in analyzing such temporal graphs. Common computational data\nmining and analysis tasks include the computation of temporal distances,\ncentrality measures, and network statistics like topological overlap,\nburstiness, or temporal diameter. To fulfill the increasing demand for\nefficient and easy-to-use implementations of temporal graph algorithms, we\nintroduce the open-source library TGLib, which integrates efficient data\nstructures and algorithms for temporal graph analysis. TGLib is highly\nefficient and versatile, providing simple and convenient C++ and Python\ninterfaces, targeting computer scientists, practitioners, students, and the\n(temporal) network research community.",
+                    "authors": "Lutz Oettershagen, Petra Mutzel",
+                    "published": "2022-09-26",
+                    "updated": "2022-09-26",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.09610v2",
+                    "title": "Storing and Querying Large-Scale Spatio-Temporal Graphs with High-Throughput Edge Insertions",
+                    "abstract": "Real-world graphs often contain spatio-temporal information and evolve over\ntime. Compared with static graphs, spatio-temporal graphs have very different\ncharacteristics, presenting more significant challenges in data volume, data\nvelocity, and query processing. In this paper, we describe three representative\napplications to understand the features of spatio-temporal graphs. Based on the\ncommonalities of the applications, we define a formal spatio-temporal graph\nmodel, where a graph consists of location vertices, object vertices, and event\nedges. Then we discuss a set of design goals to meet the requirements of the\napplications: (i) supporting up to 10 billion object vertices, 10 million\nlocation vertices, and 100 trillion edges in the graph, (ii) supporting up to 1\ntrillion new edges that are streamed in daily, and (iii) minimizing\ncross-machine communication for query processing. We propose and evaluate PAST,\na framework for efficient PArtitioning and query processing of Spatio-Temporal\ngraphs. Experimental results show that PAST successfully achieves the above\ngoals. It improves query performance by orders of magnitude compared with\nstate-of-the-art solutions, including JanusGraph, Greenplum, Spark and\nST-Hadoop.",
+                    "authors": "Mengsu Ding, Muqiao Yang, Shimin Chen",
+                    "published": "2019-04-21",
+                    "updated": "2020-10-20",
+                    "primary_cat": "cs.DC",
+                    "cats": [
+                        "cs.DC",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.14303v1",
+                    "title": "TREND: TempoRal Event and Node Dynamics for Graph Representation Learning",
+                    "abstract": "Temporal graph representation learning has drawn significant attention for\nthe prevalence of temporal graphs in the real world. However, most existing\nworks resort to taking discrete snapshots of the temporal graph, or are not\ninductive to deal with new nodes, or do not model the exciting effects which is\nthe ability of events to influence the occurrence of another event. In this\nwork, We propose TREND, a novel framework for temporal graph representation\nlearning, driven by TempoRal Event and Node Dynamics and built upon a Hawkes\nprocess-based graph neural network (GNN). TREND presents a few major\nadvantages: (1) it is inductive due to its GNN architecture; (2) it captures\nthe exciting effects between events by the adoption of the Hawkes process; (3)\nas our main novelty, it captures the individual and collective characteristics\nof events by integrating both event and node dynamics, driving a more precise\nmodeling of the temporal process. Extensive experiments on four real-world\ndatasets demonstrate the effectiveness of our proposed model.",
+                    "authors": "Zhihao Wen, Yuan Fang",
+                    "published": "2022-03-27",
+                    "updated": "2022-03-27",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.07503v1",
+                    "title": "Temporal Aggregation and Propagation Graph Neural Networks for Dynamic Representation",
+                    "abstract": "Temporal graphs exhibit dynamic interactions between nodes over continuous\ntime, whose topologies evolve with time elapsing.\n  The whole temporal neighborhood of nodes reveals the varying preferences of\nnodes.\n  However, previous works usually generate dynamic representation with limited\nneighbors for simplicity, which results in both inferior performance and high\nlatency of online inference.\n  Therefore, in this paper, we propose a novel method of temporal graph\nconvolution with the whole neighborhood, namely Temporal Aggregation and\nPropagation Graph Neural Networks (TAP-GNN).\n  Specifically, we firstly analyze the computational complexity of the dynamic\nrepresentation problem by unfolding the temporal graph in a message-passing\nparadigm.\n  The expensive complexity motivates us to design the AP (aggregation and\npropagation) block, which significantly reduces the repeated computation of\nhistorical neighbors.\n  The final TAP-GNN supports online inference in the graph stream scenario,\nwhich incorporates the temporal information into node embeddings with a\ntemporal activation function and a projection layer besides several AP blocks.\n  Experimental results on various real-life temporal networks show that our\nproposed TAP-GNN outperforms existing temporal graph methods by a large margin\nin terms of both predictive performance and online inference latency.\n  Our code is available at \\url{https://github.com/doujiang-zheng/TAP-GNN}.",
+                    "authors": "Tongya Zheng, Xinchao Wang, Zunlei Feng, Jie Song, Yunzhi Hao, Mingli Song, Xingen Wang, Xinyu Wang, Chun Chen",
+                    "published": "2023-04-15",
+                    "updated": "2023-04-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.05631v2",
+                    "title": "ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling",
+                    "abstract": "The spatio-temporal graph learning is becoming an increasingly important\nobject of graph study. Many application domains involve highly dynamic graphs\nwhere temporal information is crucial, e.g. traffic networks and financial\ntransaction graphs. Despite the constant progress made on learning structured\ndata, there is still a lack of effective means to extract dynamic complex\nfeatures from spatio-temporal structures. Particularly, conventional models\nsuch as convolutional networks or recurrent neural networks are incapable of\nrevealing the temporal patterns in short or long terms and exploring the\nspatial properties in local or global scope from spatio-temporal graphs\nsimultaneously. To tackle this problem, we design a novel multi-scale\narchitecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series\nmodeling. In this U-shaped network, a paired sampling operation is proposed in\nspacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in\nspatial from its deterministic partition while abstracts multi-resolution\ntemporal dependencies through dilated recurrent skip connections; based on\nprevious settings in the downsampling, the unpooling (ST-Unpool) restores the\noriginal structure of spatio-temporal graphs and resumes regular intervals\nwithin graph sequences. Experiments on spatio-temporal prediction tasks\ndemonstrate that our model effectively captures comprehensive features in\nmultiple scales and achieves substantial improvements over mainstream methods\non several real-world datasets.",
+                    "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+                    "published": "2019-03-13",
+                    "updated": "2021-06-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.13177v1",
+                    "title": "It is all Connected: A New Graph Formulation for Spatio-Temporal Forecasting",
+                    "abstract": "With an ever-increasing number of sensors in modern society, spatio-temporal\ntime series forecasting has become a de facto tool to make informed decisions\nabout the future. Most spatio-temporal forecasting models typically comprise\ndistinct components that learn spatial and temporal dependencies. A common\nmethodology employs some Graph Neural Network (GNN) to capture relations\nbetween spatial locations, while another network, such as a recurrent neural\nnetwork (RNN), learns temporal correlations. By representing every recorded\nsample as its own node in a graph, rather than all measurements for a\nparticular location as a single node, temporal and spatial information is\nencoded in a similar manner. In this setting, GNNs can now directly learn both\ntemporal and spatial dependencies, jointly, while also alleviating the need for\nadditional temporal networks. Furthermore, the framework does not require\naligned measurements along the temporal dimension, meaning that it also\nnaturally facilitates irregular time series, different sampling frequencies or\nmissing data, without the need for data imputation. To evaluate the proposed\nmethodology, we consider wind speed forecasting as a case study, where our\nproposed framework outperformed other spatio-temporal models using GNNs with\neither Transformer or LSTM networks as temporal update functions.",
+                    "authors": "Lars \u00d8degaard Bentsen, Narada Dilp Warakagoda, Roy Stenbro, Paal Engelstad",
+                    "published": "2023-03-23",
+                    "updated": "2023-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1401.1919v1",
+                    "title": "Temporal Graph Traversals: Definitions, Algorithms, and Applications",
+                    "abstract": "A temporal graph is a graph in which connections between vertices are active\nat specific times, and such temporal information leads to completely new\npatterns and knowledge that are not present in a non-temporal graph. In this\npaper, we study traversal problems in a temporal graph. Graph traversals, such\nas DFS and BFS, are basic operations for processing and studying a graph. While\nboth DFS and BFS are well-known simple concepts, it is non-trivial to adopt the\nsame notions from a non-temporal graph to a temporal graph. We analyze the\ndifficulties of defining temporal graph traversals and propose new definitions\nof DFS and BFS for a temporal graph. We investigate the properties of temporal\nDFS and BFS, and propose efficient algorithms with optimal complexity. In\nparticular, we also study important applications of temporal DFS and BFS. We\nverify the efficiency and importance of our graph traversal algorithms in real\nworld temporal graphs.",
+                    "authors": "Silu Huang, James Cheng, Huanhuan Wu",
+                    "published": "2014-01-09",
+                    "updated": "2014-01-09",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.11074v1",
+                    "title": "On The Temporal Domain of Differential Equation Inspired Graph Neural Networks",
+                    "abstract": "Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling\ncomplex relationships in graph-structured data. A recent innovation in this\nfield is the family of Differential Equation-Inspired Graph Neural Networks\n(DE-GNNs), which leverage principles from continuous dynamical systems to model\ninformation flow on graphs with built-in properties such as feature smoothing\nor preservation. However, existing DE-GNNs rely on first or second-order\ntemporal dependencies. In this paper, we propose a neural extension to those\npre-defined temporal dependencies. We show that our model, called TDE-GNN, can\ncapture a wide range of temporal dynamics that go beyond typical first or\nsecond-order methods, and provide use cases where existing temporal models are\nchallenged. We demonstrate the benefit of learning the temporal dependencies\nusing our method rather than using pre-defined temporal dynamics on several\ngraph benchmarks.",
+                    "authors": "Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane Sch\u00f6nlieb",
+                    "published": "2024-01-20",
+                    "updated": "2024-01-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.09641v2",
+                    "title": "Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal data forecasting of traffic flow is a challenging task\nbecause of complicated spatial dependencies and dynamical trends of temporal\npattern between different roads. Existing frameworks typically utilize given\nspatial adjacency graph and sophisticated mechanisms for modeling spatial and\ntemporal correlations. However, limited representations of given spatial graph\nstructure with incomplete adjacent connections may restrict effective\nspatial-temporal dependencies learning of those models. To overcome those\nlimitations, our paper proposes Spatial-Temporal Fusion Graph Neural Networks\n(STFGNN) for traffic flow forecasting. SFTGNN could effectively learn hidden\nspatial-temporal dependencies by a novel fusion operation of various spatial\nand temporal graphs, which is generated by a data-driven method. Meanwhile, by\nintegrating this fusion graph module and a novel gated convolution module into\na unified layer, SFTGNN could handle long sequences. Experimental results on\nseveral public traffic datasets demonstrate that our method achieves\nstate-of-the-art performance consistently than other baselines.",
+                    "authors": "Mengzhang Li, Zhanxing Zhu",
+                    "published": "2020-12-15",
+                    "updated": "2021-03-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.04816v1",
+                    "title": "MTGER: Multi-view Temporal Graph Enhanced Temporal Reasoning over Time-Involved Document",
+                    "abstract": "The facts and time in the document are intricately intertwined, making\ntemporal reasoning over documents challenging. Previous work models time\nimplicitly, making it difficult to handle such complex relationships. To\naddress this issue, we propose MTGER, a novel Multi-view Temporal Graph\nEnhanced Temporal Reasoning framework for temporal reasoning over time-involved\ndocuments. Concretely, MTGER explicitly models the temporal relationships among\nfacts by multi-view temporal graphs. On the one hand, the heterogeneous\ntemporal graphs explicitly model the temporal and discourse relationships among\nfacts; on the other hand, the multi-view mechanism captures both time-focused\nand fact-focused information, allowing the two views to complement each other\nthrough adaptive fusion. To further improve the implicit reasoning capability\nof the model, we design a self-supervised time-comparing objective. Extensive\nexperimental results demonstrate the effectiveness of our method on the TimeQA\nand SituatedQA datasets. Furthermore, MTGER gives more consistent answers under\nquestion perturbations.",
+                    "authors": "Zheng Chu, Zekun Wang, Jiafeng Liang, Ming Liu, Bing Qin",
+                    "published": "2023-11-08",
+                    "updated": "2023-11-08",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10738v3",
+                    "title": "Deep Temporal Graph Clustering",
+                    "abstract": "Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.",
+                    "authors": "Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-05-18",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.11190v1",
+                    "title": "Using Motif Transitions for Temporal Graph Generation",
+                    "abstract": "Graph generative models are highly important for sharing surrogate data and\nbenchmarking purposes. Real-world complex systems often exhibit dynamic nature,\nwhere the interactions among nodes change over time in the form of a temporal\nnetwork. Most temporal network generation models extend the static graph\ngeneration models by incorporating temporality in the generation process. More\nrecently, temporal motifs are used to generate temporal networks with better\nsuccess. However, existing models are often restricted to a small set of\npredefined motif patterns due to the high computational cost of counting\ntemporal motifs. In this work, we develop a practical temporal graph generator,\nMotif Transition Model (MTM), to generate synthetic temporal networks with\nrealistic global and local features. Our key idea is modeling the arrival of\nnew events as temporal motif transition processes. We first calculate the\ntransition properties from the input graph and then simulate the motif\ntransition processes based on the transition probabilities and transition\nrates. We demonstrate that our model consistently outperforms the baselines\nwith respect to preserving various global and local temporal graph statistics\nand runtime performance.",
+                    "authors": "Penghang Liu, A. Erdem Sar\u0131y\u00fcce",
+                    "published": "2023-06-19",
+                    "updated": "2023-06-19",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.12973v1",
+                    "title": "Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is one of the most fundamental problems in transportation\nscience and artificial intelligence. The key challenge is to effectively model\ncomplex spatial-temporal dependencies and correlations in modern traffic data.\nExisting methods, however, cannot accurately model both long-term and\nshort-term temporal correlations simultaneously, limiting their expressive\npower on complex spatial-temporal patterns. In this paper, we propose a novel\nspatial-temporal neural network framework: Attention-based Spatial-Temporal\nGraph Convolutional Recurrent Network (ASTGCRN), which consists of a graph\nconvolutional recurrent module (GCRN) and a global attention module. In\nparticular, GCRN integrates gated recurrent units and adaptive graph\nconvolutional networks for dynamically learning graph structures and capturing\nspatial dependencies and local temporal relationships. To effectively extract\nglobal temporal dependencies, we design a temporal attention layer and\nimplement it as three independent modules based on multi-head self-attention,\ntransformer, and informer respectively. Extensive experiments on five real\ntraffic datasets have demonstrated the excellent predictive performance of all\nour three models with all their average MAE, RMSE and MAPE across the test\ndatasets lower than the baseline methods.",
+                    "authors": "Haiyang Liu, Chunjiang Zhu, Detian Zhang, Qing Li",
+                    "published": "2023-02-25",
+                    "updated": "2023-02-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1310.7898v1",
+                    "title": "Moving in temporal graphs with very sparse random availability of edges",
+                    "abstract": "In this work we consider temporal graphs, i.e. graphs, each edge of which is\nassigned a set of discrete time-labels drawn from a set of integers. The labels\nof an edge indicate the discrete moments in time at which the edge is\navailable. We also consider temporal paths in a temporal graph, i.e. paths\nwhose edges are assigned a strictly increasing sequence of labels. Furthermore,\nwe assume the uniform case (UNI-CASE), in which every edge of a graph is\nassigned exactly one time label from a set of integers and the time labels\nassigned to the edges of the graph are chosen randomly and independently, with\nthe selection following the uniform distribution. We call uniform random\ntemporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the\nexpected number of temporal paths of a given length in the uniform random\ntemporal clique. We define the term temporal distance of two vertices, which is\nthe arrival time, i.e. the time-label of the last edge, of the temporal path\nthat connects those vertices, which has the smallest arrival time amongst all\ntemporal paths that connect those vertices. We then propose and study two\nstatistical properties of temporal graphs. One is the maximum expected temporal\ndistance which is, as the term indicates, the maximum of all expected temporal\ndistances in the graph. The other one is the temporal diameter which, loosely\nspeaking, is the expectation of the maximum temporal distance in the graph. We\nderive the maximum expected temporal distance of a uniform random temporal star\ngraph as well as an upper bound on both the maximum expected temporal distance\nand the temporal diameter of the normalized version of the uniform random\ntemporal clique, in which the largest time-label available equals the number of\nvertices. Finally, we provide an algorithm that solves an optimization problem\non a specific type of temporal (multi)graphs of two vertices.",
+                    "authors": "Paul G. Spirakis, Eleni Ch. Akrida",
+                    "published": "2013-10-29",
+                    "updated": "2013-10-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1811.08366v1",
+                    "title": "Temporal Graph Offset Reconstruction: Towards Temporally Robust Graph Representation Learning",
+                    "abstract": "Graphs are a commonly used construct for representing relationships between\nelements in complex high dimensional datasets. Many real-world phenomenon are\ndynamic in nature, meaning that any graph used to represent them is inherently\ntemporal. However, many of the machine learning models designed to capture\nknowledge about the structure of these graphs ignore this rich temporal\ninformation when creating representations of the graph. This results in models\nwhich do not perform well when used to make predictions about the future state\nof the graph -- especially when the delta between time stamps is not small. In\nthis work, we explore a novel training procedure and an associated unsupervised\nmodel which creates graph representations optimised to predict the future state\nof the graph. We make use of graph convolutional neural networks to encode the\ngraph into a latent representation, which we then use to train our temporal\noffset reconstruction method, inspired by auto-encoders, to predict a later\ntime point -- multiple time steps into the future. Using our method, we\ndemonstrate superior performance for the task of future link prediction\ncompared with none-temporal state-of-the-art baselines. We show our approach to\nbe capable of outperforming non-temporal baselines by 38% on a real world\ndataset.",
+                    "authors": "Stephen Bonner, John Brennan, Ibad Kureshi, Georgios Theodoropoulos, Andrew Stephen McGough, Boguslaw Obara",
+                    "published": "2018-11-20",
+                    "updated": "2018-11-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08323v2",
+                    "title": "TG-GAN: Continuous-time Temporal Graph Generation with Deep Generative Models",
+                    "abstract": "The recent deep generative models for static graphs that are now being\nactively developed have achieved significant success in areas such as molecule\ndesign. However, many real-world problems involve temporal graphs whose\ntopology and attribute values evolve dynamically over time, including important\napplications such as protein folding, human mobility networks, and social\nnetwork growth. As yet, deep generative models for temporal graphs are not yet\nwell understood and existing techniques for static graphs are not adequate for\ntemporal graphs since they cannot 1) encode and decode continuously-varying\ngraph topology chronologically, 2) enforce validity via temporal constraints,\nor 3) ensure efficiency for information-lossless temporal resolution. To\naddress these challenges, we propose a new model, called ``Temporal Graph\nGenerative Adversarial Network'' (TG-GAN) for continuous-time temporal graph\ngeneration, by modeling the deep generative process for truncated temporal\nrandom walks and their compositions. Specifically, we first propose a novel\ntemporal graph generator that jointly model truncated edge sequences, time\nbudgets, and node attributes, with novel activation functions that enforce\ntemporal validity constraints under recurrent architecture. In addition, a new\ntemporal graph discriminator is proposed, which combines time and node encoding\noperations over a recurrent architecture to distinguish the generated sequences\nfrom the real ones sampled by a newly-developed truncated temporal random walk\nsampler. Extensive experiments on both synthetic and real-world datasets\ndemonstrate TG-GAN significantly outperforms the comparison methods in\nefficiency and effectiveness.",
+                    "authors": "Liming Zhang, Liang Zhao, Shan Qin, Dieter Pfoser",
+                    "published": "2020-05-17",
+                    "updated": "2020-06-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.00278v1",
+                    "title": "An Introduction to Temporal Graphs: An Algorithmic Perspective",
+                    "abstract": "A \\emph{temporal graph} is, informally speaking, a graph that changes with\ntime. When time is discrete and only the relationships between the\nparticipating entities may change and not the entities themselves, a temporal\ngraph may be viewed as a sequence $G_1,G_2\\ldots,G_l$ of static graphs over the\nsame (static) set of nodes $V$. Though static graphs have been extensively\nstudied, for their temporal generalization we are still far from having a\nconcrete set of structural and algorithmic principles. Recent research shows\nthat many graph properties and problems become radically different and usually\nsubstantially more difficult when an extra time dimension in added to them.\nMoreover, there is already a rich and rapidly growing set of modern systems and\napplications that can be naturally modeled and studied via temporal graphs.\nThis, further motivates the need for the development of a temporal extension of\ngraph theory. We survey here recent results on temporal graphs and temporal\ngraph problems that have appeared in the Computer Science community.",
+                    "authors": "Othon Michail",
+                    "published": "2015-03-01",
+                    "updated": "2015-03-01",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS",
+                        "05C85, 05C40, 05C38, 05C78, 05C80, 68R10, 68M14, 68M10, 68W25"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.02128v1",
+                    "title": "Interaction Order Prediction for Temporal Graphs",
+                    "abstract": "Link prediction in graphs is a task that has been widely investigated. It has\nbeen applied in various domains such as knowledge graph completion,\ncontent/item recommendation, social network recommendations and so on. The\ninitial focus of most research was on link prediction in static graphs.\nHowever, there has recently been abundant work on modeling temporal graphs, and\nconsequently one of the tasks that has been researched is link prediction in\ntemporal graphs. However, most of the existing work does not focus on the order\nof link formation, and only predicts the existence of links. In this study, we\naim to predict the order of node interactions.",
+                    "authors": "Nayana Bannur, Mashrin Srivastava, Harsha Vardhan",
+                    "published": "2023-02-04",
+                    "updated": "2023-02-04",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.00518v1",
+                    "title": "DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is essential to intelligent transportation systems, which\nis challenging due to the complicated spatial and temporal dependencies within\na road network. Existing works usually learn spatial and temporal dependencies\nseparately, ignoring the dependencies crossing spatial and temporal dimensions.\nIn this paper, we propose DSTCGCN, a dynamic spatial-temporal cross graph\nconvolution network to learn dynamic spatial and temporal dependencies jointly\nvia graphs for traffic forecasting. Specifically, we introduce a fast Fourier\ntransform (FFT) based attentive selector to choose relevant time steps for each\ntime step based on time-varying traffic data. Given the selected time steps, we\nintroduce a dynamic cross graph construction module, consisting of the spatial\ngraph construction, temporal connection graph construction, and fusion modules,\nto learn dynamic spatial-temporal cross dependencies without pre-defined\npriors. Extensive experiments on six real-world datasets demonstrate that\nDSTCGCN achieves the state-of-the-art performance.",
+                    "authors": "Binqing Wu, Ling Chen",
+                    "published": "2023-07-02",
+                    "updated": "2023-07-02",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.16078v2",
+                    "title": "Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs",
+                    "abstract": "We present the Evolving Graph Fourier Transform (EFT), the first invertible\nspectral transform that captures evolving representations on temporal graphs.\nWe motivate our work by the inadequacy of existing methods for capturing the\nevolving graph spectra, which are also computationally expensive due to the\ntemporal aspect along with the graph vertex domain. We view the problem as an\noptimization over the Laplacian of the continuous time dynamic graph.\nAdditionally, we propose pseudo-spectrum relaxations that decompose the\ntransformation process, making it highly computationally efficient. The EFT\nmethod adeptly captures the evolving graph's structural and positional\nproperties, making it effective for downstream tasks on evolving graphs. Hence,\nas a reference implementation, we develop a simple neural model induced with\nEFT for capturing evolving graph spectra. We empirically validate our\ntheoretical findings on a number of large-scale and standard temporal graph\nbenchmarks and demonstrate that our model achieves state-of-the-art\nperformance.",
+                    "authors": "Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Manish Singh, Toyotaro Suzumura",
+                    "published": "2024-02-25",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.09791v2",
+                    "title": "Temporal Betweenness Centrality on Shortest Paths",
+                    "abstract": "Betweenness centrality measure assesses the importance of nodes in a graph\nand has been used in a variety of contexts. Betweenness centrality has also\nbeen extended to temporal graphs. Temporal graphs have edges that bear labels\naccording to the time of the interactions between the nodes. Betweenness\ncentrality has been extended to the temporal graph settings, and the notion of\npaths has been extended to temporal paths. Recent results by Bu{\\ss} et al. and\nRymar et al. showed that the betweenness centrality of all nodes in a temporal\ngraph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of\ntime units, m the number of temporal edges and n the number of nodes. In this\npaper, we improve the running time analysis of these previous approaches to\ncompute the betweenness centrality of all nodes in a temporal graph. We give an\nalgorithm that runs in O(n m T + n^2 T ).",
+                    "authors": "Mehdi Naima, Matthieu Latapy, Cl\u00e9mence Magnien",
+                    "published": "2023-04-19",
+                    "updated": "2023-06-06",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.14199v2",
+                    "title": "MTRGL:Effective Temporal Correlation Discerning through Multi-modal Temporal Relational Graph Learning",
+                    "abstract": "In this study, we explore the synergy of deep learning and financial market\napplications, focusing on pair trading. This market-neutral strategy is\nintegral to quantitative finance and is apt for advanced deep-learning\ntechniques. A pivotal challenge in pair trading is discerning temporal\ncorrelations among entities, necessitating the integration of diverse data\nmodalities. Addressing this, we introduce a novel framework, Multi-modal\nTemporal Relation Graph Learning (MTRGL). MTRGL combines time series data and\ndiscrete features into a temporal graph and employs a memory-based temporal\ngraph neural network. This approach reframes temporal correlation\nidentification as a temporal graph link prediction task, which has shown\nempirical success. Our experiments on real-world datasets confirm the superior\nperformance of MTRGL, emphasizing its promise in refining automated pair\ntrading strategies.",
+                    "authors": "Junwei Su, Shan Wu, Jinhui Li",
+                    "published": "2024-01-25",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "econ.GN",
+                        "q-fin.EC",
+                        "q-fin.TR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.11979v1",
+                    "title": "MTGA: Multi-view Temporal Granularity aligned Aggregation for Event-based Lip-reading",
+                    "abstract": "Lip-reading is to utilize the visual information of the speaker's lip\nmovements to recognize words and sentences. Existing event-based lip-reading\nsolutions integrate different frame rate branches to learn spatio-temporal\nfeatures of varying granularities. However, aggregating events into event\nframes inevitably leads to the loss of fine-grained temporal information within\nframes. To remedy this drawback, we propose a novel framework termed Multi-view\nTemporal Granularity aligned Aggregation (MTGA). Specifically, we first present\na novel event representation method, namely time-segmented voxel graph list,\nwhere the most significant local voxels are temporally connected into a graph\nlist. Then we design a spatio-temporal fusion module based on temporal\ngranularity alignment, where the global spatial features extracted from event\nframes, together with the local relative spatial and temporal features\ncontained in voxel graph list are effectively aligned and integrated. Finally,\nwe design a temporal aggregation module that incorporates positional encoding,\nwhich enables the capture of local absolute spatial and global temporal\ninformation. Experiments demonstrate that our method outperforms both the\nevent-based and video-based lip-reading counterparts. Our code will be publicly\navailable.",
+                    "authors": "Wenhao Zhang, Jun Wang, Yong Luo, Lei Yu, Wei Yu, Zheng He",
+                    "published": "2024-04-18",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.05653v1",
+                    "title": "Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition",
+                    "abstract": "Accurate spatial-temporal traffic flow forecasting is essential for helping\ntraffic managers to take control measures and drivers to choose the optimal\ntravel routes. Recently, graph convolutional networks (GCNs) have been widely\nused in traffic flow prediction owing to their powerful ability to capture\nspatial-temporal dependencies. The design of the spatial-temporal graph\nadjacency matrix is a key to the success of GCNs, and it is still an open\nquestion. This paper proposes reconstructing the binary adjacency matrix via\ntensor decomposition, and a traffic flow forecasting method is proposed. First,\nwe reformulate the spatial-temporal fusion graph adjacency matrix into a\nthree-way adjacency tensor. Then, we reconstructed the adjacency tensor via\nTucker decomposition, wherein more informative and global spatial-temporal\ndependencies are encoded. Finally, a Spatial-temporal Synchronous Graph\nConvolutional module for localized spatial-temporal correlations learning and a\nDilated Convolution module for global correlations learning are assembled to\naggregate and learn the comprehensive spatial-temporal dependencies of the road\nnetwork. Experimental results on four open-access datasets demonstrate that the\nproposed model outperforms state-of-the-art approaches in terms of the\nprediction performance and computational cost.",
+                    "authors": "Qin Li, Xuan Yang, Yong Wang, Yuankai Wu, Deqiang He",
+                    "published": "2022-12-12",
+                    "updated": "2022-12-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.03251v3",
+                    "title": "Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of traditional Knowledge Graph\n(KG) that incorporates the dimension of time. Reasoning on TKGs is a crucial\ntask that aims to predict future facts based on historical occurrences. The key\nchallenge lies in uncovering structural dependencies within historical\nsubgraphs and temporal patterns. Most existing approaches model TKGs relying on\nentity modeling, as nodes in the graph play a crucial role in knowledge\nrepresentation. However, the real-world scenario often involves an extensive\nnumber of entities, with new entities emerging over time. This makes it\nchallenging for entity-dependent methods to cope with extensive volumes of\nentities, and effectively handling newly emerging entities also becomes a\nsignificant challenge. Therefore, we propose Temporal Inductive Path Neural\nNetwork (TiPNN), which models historical information in an entity-independent\nperspective. Specifically, TiPNN adopts a unified graph, namely history\ntemporal graph, to comprehensively capture and encapsulate information from\nhistory. Subsequently, we utilize the defined query-aware temporal paths on a\nhistory temporal graph to model historical path information related to queries\nfor reasoning. Extensive experiments illustrate that the proposed model not\nonly attains significant performance enhancements but also handles inductive\nsettings, while additionally facilitating the provision of reasoning evidence\nthrough history temporal graphs.",
+                    "authors": "Hao Dong, Pengyang Wang, Meng Xiao, Zhiyuan Ning, Pengfei Wang, Yuanchun Zhou",
+                    "published": "2023-09-06",
+                    "updated": "2024-01-25",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.04782v1",
+                    "title": "A Survey on Temporal Knowledge Graph: Representation Learning and Applications",
+                    "abstract": "Knowledge graphs have garnered significant research attention and are widely\nused to enhance downstream applications. However, most current studies mainly\nfocus on static knowledge graphs, whose facts do not change with time, and\ndisregard their dynamic evolution over time. As a result, temporal knowledge\ngraphs have attracted more attention because a large amount of structured\nknowledge exists only within a specific period. Knowledge graph representation\nlearning aims to learn low-dimensional vector embeddings for entities and\nrelations in a knowledge graph. The representation learning of temporal\nknowledge graphs incorporates time information into the standard knowledge\ngraph framework and can model the dynamics of entities and relations over time.\nIn this paper, we conduct a comprehensive survey of temporal knowledge graph\nrepresentation learning and its applications. We begin with an introduction to\nthe definitions, datasets, and evaluation metrics for temporal knowledge graph\nrepresentation learning. Next, we propose a taxonomy based on the core\ntechnologies of temporal knowledge graph representation learning methods, and\nprovide an in-depth analysis of different methods in each category. Finally, we\npresent various downstream applications related to the temporal knowledge\ngraphs. In the end, we conclude the paper and have an outlook on the future\nresearch directions in this area.",
+                    "authors": "Li Cai, Xin Mao, Yuhao Zhou, Zhaoguang Long, Changxu Wu, Man Lan",
+                    "published": "2024-03-02",
+                    "updated": "2024-03-02",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.11886v1",
+                    "title": "Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs",
+                    "abstract": "Temporal bipartite graphs are widely used to denote time-evolving\nrelationships between two disjoint sets of nodes, such as customer-product\ninteractions in E-commerce and user-group memberships in social networks.\nTemporal butterflies, $(2,2)$-bicliques that occur within a short period and in\na prescribed order, are essential in modeling the structural and sequential\npatterns of such graphs. Counting the number of temporal butterflies is thus a\nfundamental task in analyzing temporal bipartite graphs. However, existing\nalgorithms for butterfly counting on static bipartite graphs and motif counting\non temporal unipartite graphs are inefficient for this purpose. In this paper,\nwe present a general framework with three sampling strategies for temporal\nbutterfly counting. Since exact counting can be time-consuming on large graphs,\nour approach alternatively computes approximate estimates accurately and\nefficiently. We also provide analytical bounds on the number of samples each\nstrategy requires to obtain estimates with small relative errors and high\nprobability. We finally evaluate our framework on six real-world datasets and\ndemonstrate its superior accuracy and efficiency compared to several baselines.\nOverall, our proposed framework and sampling strategies provide efficient and\naccurate approaches to approximating temporal butterfly counts on large-scale\ntemporal bipartite graphs.",
+                    "authors": "Jiaxi Pu, Yanhao Wang, Yuchen Li, Xuan Zhou",
+                    "published": "2023-10-18",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.DB",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13624v1",
+                    "title": "Towards Linear Spanners in All Temporal Cliques",
+                    "abstract": "Many real-world networks, like transportation networks and social networks,\nare dynamic in the sense that the edge set may change over time, but these\nchanges are known in advance. This behavior is captured by the temporal graphs\nmodel, which has recently become a trending topic in theoretical computer\nscience. A core open problem in the field is to prove the existence of\nlinear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of\ncomplete temporal graphs that ensure all-pairs reachability via temporal paths.\nSo far, the best known result is the existence of temporal spanners with\n$\\mathcal{O}(n\\log n)$ many edges. We present significant progress towards\nproving that linear-size temporal spanners exist in all temporal cliques.\n  We adapt techniques used in previous works and heavily expand and generalize\nthem to provide a simpler and more intuitive proof of the $\\mathcal{O}(n\\log\nn)$ bound. Moreover, we use our novel approach to show that a large class of\ntemporal cliques, called edge-pivot graphs, admit linear-size temporal\nspanners. To contrast this, we investigate other classes of temporal cliques\nthat do not belong to the class of edge-pivot graphs. We introduce two such\ngraph classes and we develop novel techniques for establishing the existence of\nlinear temporal spanners in these graph classes as well.",
+                    "authors": "Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, Armin Wells",
+                    "published": "2024-02-21",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.06260v1",
+                    "title": "In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs",
+                    "abstract": "A graph whose edges only appear at certain points in time is called a\ntemporal graph (among other names). These graphs are temporally connected if\nall ordered pairs of vertices are connected by a path that traverses edges in\nchronological order (a temporal path). Reachability in temporal graphs departs\nsignificantly from standard reachability; in particular, it is not transitive,\nwith structural and algorithmic consequences. For instance, temporally\nconnected graphs do not always admit spanning trees, i.e., subsets of edges\nthat form a tree and preserve temporal connectivity among the nodes.\n  In this paper, we revisit fundamental questions about the loss of\nuniversality of spanning trees. To start, we show that deciding if a spanning\ntree exists in a given temporal graph is NP-complete. What could be appropriate\nreplacement for the concept? Beyond having minimum size, spanning trees enjoy\nthe feature of enabling reachability along the same underlying paths in both\ndirections, a pretty uncommon feature in temporal graphs. We explore\nrelaxations in this direction and show that testing the existence of\nbidirectional spanning structures (bi-spanners) is tractable in general. On the\ndown side, finding \\emph{minimum} such structures is NP-hard even in simple\ntemporal graphs. Still, the fact that bidirectionality can be tested\nefficiently may find applications, e.g. for routing and security, and the\ncorresponding primitive that we introduce in the algorithm may be of\nindependent interest.",
+                    "authors": "Arnaud Casteigts, Timoth\u00e9e Corsini",
+                    "published": "2023-12-11",
+                    "updated": "2023-12-11",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DC",
+                        "68R10, 68W15",
+                        "G.2.2; C.2.4"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.12843v1",
+                    "title": "An embedding-based distance for temporal graphs",
+                    "abstract": "We define a distance between temporal graphs based on graph embeddings built\nusing time-respecting random walks. We study both the case of matched graphs,\nwhen there exists a known relation between the nodes, and the unmatched case,\nwhen such a relation is unavailable and the graphs may be of different sizes.\nWe illustrate the interest of our distance definition, using both real and\nsynthetic temporal network data, by showing its ability to discriminate between\ngraphs with different structural and temporal properties. Leveraging\nstate-of-the-art machine learning techniques, we propose an efficient\nimplementation of distance computation that is viable for large-scale temporal\ngraphs.",
+                    "authors": "Lorenzo Dall'Amico, Alain Barrat, Ciro Cattuto",
+                    "published": "2024-01-23",
+                    "updated": "2024-01-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.08311v1",
+                    "title": "De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs",
+                    "abstract": "We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware\ngraph neural network architecture for time-resolved data on dynamic graphs. Our\napproach accounts for temporal-topological patterns that unfold in the causal\ntopology of dynamic graphs, which is determined by causal walks, i.e.\ntemporally ordered sequences of links by which nodes can influence each other\nover time. Our architecture builds on multiple layers of higher-order De Bruijn\ngraphs, an iterative line graph construction where nodes in a De Bruijn graph\nof order k represent walks of length k-1, while edges represent walks of length\nk. We develop a graph neural network architecture that utilizes De Bruijn\ngraphs to implement a message passing scheme that follows a non-Markovian\ndynamics, which enables us to learn patterns in the causal topology of a\ndynamic graph. Addressing the issue that De Bruijn graphs with different orders\nk can be used to model the same data set, we further apply statistical model\nselection to determine the optimal graph topology to be used for message\npassing. An evaluation in synthetic and empirical data sets suggests that\nDBGNNs can leverage temporal patterns in dynamic graphs, which substantially\nimproves the performance in a supervised node classification task.",
+                    "authors": "Lisi Qarkaxhija, Vincenzo Perri, Ingo Scholtes",
+                    "published": "2022-09-17",
+                    "updated": "2022-09-17",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.09114v1",
+                    "title": "Relational Temporal Graph Reasoning for Dual-task Dialogue Language Understanding",
+                    "abstract": "Dual-task dialog language understanding aims to tackle two correlative dialog\nlanguage understanding tasks simultaneously via leveraging their inherent\ncorrelations. In this paper, we put forward a new framework, whose core is\nrelational temporal graph reasoning.We propose a speaker-aware temporal graph\n(SATG) and a dual-task relational temporal graph (DRTG) to facilitate\nrelational temporal modeling in dialog understanding and dual-task reasoning.\nBesides, different from previous works that only achieve implicit\nsemantics-level interactions, we propose to model the explicit dependencies via\nintegrating prediction-level interactions. To implement our framework, we first\npropose a novel model Dual-tAsk temporal Relational rEcurrent Reasoning network\n(DARER), which first generates the context-, speaker- and temporal-sensitive\nutterance representations through relational temporal modeling of SATG, then\nconducts recurrent dual-task relational temporal graph reasoning on DRTG, in\nwhich process the estimated label distributions act as key clues in\nprediction-level interactions. And the relational temporal modeling in DARER is\nachieved by relational convolutional networks (RGCNs). Then we further propose\nRelational Temporal Transformer (ReTeFormer), which achieves fine-grained\nrelational temporal modeling via Relation- and Structure-aware Disentangled\nMulti-head Attention. Accordingly, we propose DARER with ReTeFormer (DARER2),\nwhich adopts two variants of ReTeFormer to achieve the relational temporal\nmodeling of SATG and DTRG, respectively. The extensive experiments on different\nscenarios verify that our models outperform state-of-the-art models by a large\nmargin. Remarkably, on the dialog sentiment classification task in the Mastodon\ndataset, DARER and DARER2 gain relative improvements of about 28% and 34% over\nthe previous best model in terms of F1.",
+                    "authors": "Bowen Xing, Ivor W. Tsang",
+                    "published": "2023-06-15",
+                    "updated": "2023-06-15",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.01727v2",
+                    "title": "Skeleton-Based Action Segmentation with Multi-Stage Spatial-Temporal Graph Convolutional Neural Networks",
+                    "abstract": "The ability to identify and temporally segment fine-grained actions in motion\ncapture sequences is crucial for applications in human movement analysis.\nMotion capture is typically performed with optical or inertial measurement\nsystems, which encode human movement as a time series of human joint locations\nand orientations or their higher-order representations. State-of-the-art action\nsegmentation approaches use multiple stages of temporal convolutions. The main\nidea is to generate an initial prediction with several layers of temporal\nconvolutions and refine these predictions over multiple stages, also with\ntemporal convolutions. Although these approaches capture long-term temporal\npatterns, the initial predictions do not adequately consider the spatial\nhierarchy among the human joints. To address this limitation, we recently\nintroduced multi-stage spatial-temporal graph convolutional neural networks\n(MS-GCN). Our framework replaces the initial stage of temporal convolutions\nwith spatial graph convolutions and dilated temporal convolutions, which better\nexploit the spatial configuration of the joints and their long-term temporal\ndynamics. Our framework was compared to four strong baselines on five tasks.\nExperimental results demonstrate that our framework is a strong baseline for\nskeleton-based action segmentation.",
+                    "authors": "Benjamin Filtjens, Bart Vanrumste, Peter Slaets",
+                    "published": "2022-02-03",
+                    "updated": "2022-10-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.02606v1",
+                    "title": "Learning adjacency matrix for dynamic graph neural network",
+                    "abstract": "In recent work, [1] introduced the concept of using a Block Adjacency Matrix\n(BA) for the representation of spatio-temporal data. While their method\nsuccessfully concatenated adjacency matrices to encapsulate spatio-temporal\nrelationships in a single graph, it formed a disconnected graph. This\nlimitation hampered the ability of Graph Convolutional Networks (GCNs) to\nperform message passing across nodes belonging to different time steps, as no\ntemporal links were present. To overcome this challenge, we introduce an\nencoder block specifically designed to learn these missing temporal links. The\nencoder block processes the BA and predicts connections between previously\nunconnected subgraphs, resulting in a Spatio-Temporal Block Adjacency Matrix\n(STBAM). This enriched matrix is then fed into a Graph Neural Network (GNN) to\ncapture the complex spatio-temporal topology of the network. Our evaluations on\nbenchmark datasets, surgVisDom and C2D2, demonstrate that our method, with\nslightly higher complexity, achieves superior results compared to\nstate-of-the-art results. Our approach's computational overhead remains\nsignificantly lower than conventional non-graph-based methodologies for\nspatio-temporal data.",
+                    "authors": "Osama Ahmad, Omer Abdul Jalil, Usman Nazir, Murtaza Taj",
+                    "published": "2023-10-04",
+                    "updated": "2023-10-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.01928v1",
+                    "title": "Constructing Temporal Dynamic Knowledge Graphs from Interactive Text-based Games",
+                    "abstract": "In natural language processing, interactive text-based games serve as a test\nbed for interactive AI systems. Prior work has proposed to play text-based\ngames by acting based on discrete knowledge graphs constructed by the Discrete\nGraph Updater (DGU) to represent the game state from the natural language\ndescription. While DGU has shown promising results with high interpretability,\nit suffers from lower knowledge graph accuracy due to its lack of temporality\nand limited generalizability to complex environments with objects with the same\nlabel. In order to address DGU's weaknesses while preserving its high\ninterpretability, we propose the Temporal Discrete Graph Updater (TDGU), a\nnovel neural network model that represents dynamic knowledge graphs as a\nsequence of timestamped graph events and models them using a temporal point\nbased graph neural network. Through experiments on the dataset collected from a\ntext-based game TextWorld, we show that TDGU outperforms the baseline DGU. We\nfurther show the importance of temporal information for TDGU's performance\nthrough an ablation study and demonstrate that TDGU has the ability to\ngeneralize to more complex environments with objects with the same label. All\nthe relevant code can be found at\n\\url{https://github.com/yukw777/temporal-discrete-graph-updater}.",
+                    "authors": "Keunwoo Peter Yu",
+                    "published": "2023-11-03",
+                    "updated": "2023-11-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02563v1",
+                    "title": "Kairos: Efficient Temporal Graph Analytics on a Single Machine",
+                    "abstract": "Many important societal problems are naturally modeled as algorithms over\ntemporal graphs. To date, however, most graph processing systems remain\ninefficient as they rely on distributed processing even for graphs that fit\nwell within a commodity server's available storage. In this paper, we introduce\nKairos, a temporal graph analytics system that provides application developers\na framework for efficiently implementing and executing algorithms over temporal\ngraphs on a single machine. Specifically, Kairos relies on fork-join\nparallelism and a highly optimized parallel data structure as core primitives\nto maximize performance of graph processing tasks needed for temporal graph\nanalytics. Furthermore, we introduce the notion of selective indexing and show\nhow it can be used with an efficient index to speedup temporal queries. Our\nexperiments on a 24-core server show that our algorithms obtain good parallel\nspeedups, and are significantly faster than equivalent algorithms in existing\ntemporal graph processing systems: up to 60x against a shared-memory approach,\nand several orders of magnitude when compared with distributed processing of\ngraphs that fit within a single server.",
+                    "authors": "Joana M. F. da Trindade, Julian Shun, Samuel Madden, Nesime Tatbul",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB",
+                        "cs.DC",
+                        "cs.PF"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1509.08960v1",
+                    "title": "Storing and Analyzing Historical Graph Data at Scale",
+                    "abstract": "The work on large-scale graph analytics to date has largely focused on the\nstudy of static properties of graph snapshots. However, a static view of\ninteractions between entities is often an oversimplification of several complex\nphenomena like the spread of epidemics, information diffusion, formation of\nonline communities}, and so on. Being able to find temporal interaction\npatterns, visualize the evolution of graph properties, or even simply compare\nthem across time, adds significant value in reasoning over graphs. However,\nbecause of lack of underlying data management support, an analyst today has to\nmanually navigate the added temporal complexity of dealing with large evolving\ngraphs. In this paper, we present a system, called Historical Graph Store, that\nenables users to store large volumes of historical graph data and to express\nand run complex temporal graph analytical tasks against that data. It consists\nof two key components: a Temporal Graph Index (TGI), that compactly stores\nlarge volumes of historical graph evolution data in a partitioned and\ndistributed fashion; it provides support for retrieving snapshots of the graph\nas of any timepoint in the past or evolution histories of individual nodes or\nneighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for\nexpressing complex temporal analytical tasks and for executing them in an\nefficient and scalable manner. Our experiments demonstrate our system's\nefficient storage, retrieval and analytics across a wide variety of queries on\nlarge volumes of historical graph data.",
+                    "authors": "Udayan Khurana, Amol Deshpande",
+                    "published": "2015-09-29",
+                    "updated": "2015-09-29",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1207.7103v1",
+                    "title": "Temporal Reachability Graphs",
+                    "abstract": "While a natural fit for modeling and understanding mobile networks,\ntime-varying graphs remain poorly understood. Indeed, many of the usual\nconcepts of static graphs have no obvious counterpart in time-varying ones. In\nthis paper, we introduce the notion of temporal reachability graphs. A\n(tau,delta)-reachability graph} is a time-varying directed graph derived from\nan existing connectivity graph. An edge exists from one node to another in the\nreachability graph at time t if there exists a journey (i.e., a spatiotemporal\npath) in the connectivity graph from the first node to the second, leaving\nafter t, with a positive edge traversal time tau, and arriving within a maximum\ndelay delta. We make three contributions. First, we develop the theoretical\nframework around temporal reachability graphs. Second, we harness our\ntheoretical findings to propose an algorithm for their efficient computation.\nFinally, we demonstrate the analytic power of the temporal reachability graph\nconcept by applying it to synthetic and real-life datasets. On top of defining\nclear upper bounds on communication capabilities, reachability graphs highlight\nasymmetric communication opportunities and offloading potential.",
+                    "authors": "John Whitbeck, Marcelo Dias de Amorim, Vania Conan, Jean-Loup Guillaume",
+                    "published": "2012-07-30",
+                    "updated": "2012-07-30",
+                    "primary_cat": "cs.NI",
+                    "cats": [
+                        "cs.NI",
+                        "C.2.1; F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.01594v1",
+                    "title": "Parameterized temporal exploration problems",
+                    "abstract": "In this paper we study the fixed-parameter tractability of the problem of\ndeciding whether a given temporal graph admits a temporal walk that visits all\nvertices (temporal exploration) or, in some problem variants, a certain subset\nof the vertices. Formally, a temporal graph is a sequence <G_1,...,G_L> of\ngraphs with V(G_t) = V(G) and E(G_t) a subset of E(G) for all t in [L] and some\nunderlying graph G, and a temporal walk is a time-respecting sequence of\nedge-traversals. We consider both the strict variant, in which edges must be\ntraversed in strictly increasing timesteps, and the non-strict variant, in\nwhich an arbitrary number of edges can be traversed in each timestep. For both\nvariants, we give FPT algorithms for the problem of finding a temporal walk\nthat visits a given set X of vertices, parameterized by |X|, and for the\nproblem of finding a temporal walk that visits at least k distinct vertices in\nV(G), parameterized by k. We also show W[2]-hardness for a set version of the\ntemporal exploration problem for both variants. For the non-strict variant, we\ngive an FPT algorithm for the temporal exploration problem parameterized by the\nlifetime of the input graph, and we show that the temporal exploration problem\ncan be solved in polynomial time if the graph in each timestep has at most two\nconnected components.",
+                    "authors": "Thomas Erlebach, Jakob T. Spooner",
+                    "published": "2022-12-03",
+                    "updated": "2022-12-03",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "05C85",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1502.04579v3",
+                    "title": "The complexity of optimal design of temporally connected graphs",
+                    "abstract": "We study the design of small cost temporally connected graphs, under various\nconstraints. We mainly consider undirected graphs of $n$ vertices, where each\nedge has an associated set of discrete availability instances (labels). A\njourney from vertex $u$ to vertex $v$ is a path from $u$ to $v$ where\nsuccessive path edges have strictly increasing labels. A graph is temporally\nconnected iff there is a $(u,v)$-journey for any pair of vertices $u,v,~u\\not=\nv$. We first give a simple polynomial-time algorithm to check whether a given\ntemporal graph is temporally connected. We then consider the case in which a\ndesigner of temporal graphs can \\emph{freely choose} availability instances for\nall edges and aims for temporal connectivity with very small \\emph{cost}; the\ncost is the total number of availability instances used. We achieve this via a\nsimple polynomial-time procedure which derives designs of cost linear in $n$.\nWe also show that the above procedure is (almost) optimal when the underlying\ngraph is a tree, by proving a lower bound on the cost for any tree. However,\nthere are pragmatic cases where one is not free to design a temporally\nconnected graph anew, but is instead \\emph{given} a temporal graph design with\nthe claim that it is temporally connected, and wishes to make it more\ncost-efficient by removing labels without destroying temporal connectivity\n(redundant labels). Our main technical result is that computing the maximum\nnumber of redundant labels is APX-hard, i.e., there is no PTAS unless $P=NP$.\nOn the positive side, we show that in dense graphs with random edge\navailabilities, there is asymptotically almost surely a very large number of\nredundant labels. A temporal design may, however, be \\emph{minimal}, i.e., no\nredundant labels exist. We show the existence of minimal temporal designs with\nat least $n \\log{n}$ labels.",
+                    "authors": "Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, Paul G. Spirakis",
+                    "published": "2015-02-16",
+                    "updated": "2016-07-06",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.03363v3",
+                    "title": "Spatio-Temporal Graph Scattering Transform",
+                    "abstract": "Although spatio-temporal graph neural networks have achieved great empirical\nsuccess in handling multiple correlated time series, they may be impractical in\nsome real-world scenarios due to a lack of sufficient high-quality training\ndata. Furthermore, spatio-temporal graph neural networks lack theoretical\ninterpretation. To address these issues, we put forth a novel mathematically\ndesigned framework to analyze spatio-temporal data. Our proposed\nspatio-temporal graph scattering transform (ST-GST) extends traditional\nscattering transforms to the spatio-temporal domain. It performs iterative\napplications of spatio-temporal graph wavelets and nonlinear activation\nfunctions, which can be viewed as a forward pass of spatio-temporal graph\nconvolutional networks without training. Since all the filter coefficients in\nST-GST are mathematically designed, it is promising for the real-world\nscenarios with limited training data, and also allows for a theoretical\nanalysis, which shows that the proposed ST-GST is stable to small perturbations\nof input signals and structures. Finally, our experiments show that i) ST-GST\noutperforms spatio-temporal graph convolutional networks by an increase of 35%\nin accuracy for MSR Action3D dataset; ii) it is better and computationally more\nefficient to design the transform based on separable spatio-temporal graphs\nthan the joint ones; and iii) the nonlinearity in ST-GST is critical to\nempirical performance.",
+                    "authors": "Chao Pan, Siheng Chen, Antonio Ortega",
+                    "published": "2020-12-06",
+                    "updated": "2021-02-09",
+                    "primary_cat": "eess.SP",
+                    "cats": [
+                        "eess.SP",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13250v1",
+                    "title": "Keyword-Aware Relative Spatio-Temporal Graph Networks for Video Question Answering",
+                    "abstract": "The main challenge in video question answering (VideoQA) is to capture and\nunderstand the complex spatial and temporal relations between objects based on\ngiven questions. Existing graph-based methods for VideoQA usually ignore\nkeywords in questions and employ a simple graph to aggregate features without\nconsidering relative relations between objects, which may lead to inferior\nperformance. In this paper, we propose a Keyword-aware Relative Spatio-Temporal\n(KRST) graph network for VideoQA. First, to make question features aware of\nkeywords, we employ an attention mechanism to assign high weights to keywords\nduring question encoding. The keyword-aware question features are then used to\nguide video graph construction. Second, because relations are relative, we\nintegrate the relative relation modeling to better capture the spatio-temporal\ndynamics among object nodes. Moreover, we disentangle the spatio-temporal\nreasoning into an object-level spatial graph and a frame-level temporal graph,\nwhich reduces the impact of spatial and temporal relation reasoning on each\nother. Extensive experiments on the TGIF-QA, MSVD-QA and MSRVTT-QA datasets\ndemonstrate the superiority of our KRST over multiple state-of-the-art methods.",
+                    "authors": "Yi Cheng, Hehe Fan, Dongyun Lin, Ying Sun, Mohan Kankanhalli, Joo-Hwee Lim",
+                    "published": "2023-07-25",
+                    "updated": "2023-07-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19508v1",
+                    "title": "Temporal Graph ODEs for Irregularly-Sampled Time Series",
+                    "abstract": "Modern graph representation learning works mostly under the assumption of\ndealing with regularly sampled temporal graph snapshots, which is far from\nrealistic, e.g., social networks and physical systems are characterized by\ncontinuous dynamics and sporadic observations. To address this limitation, we\nintroduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework,\nwhich learns both the temporal and spatial dynamics from graph streams where\nthe intervals between observations are not regularly spaced. We empirically\nvalidate the proposed approach on several graph benchmarks, showing that TG-ODE\ncan achieve state-of-the-art performance in irregular graph stream tasks.",
+                    "authors": "Alessio Gravina, Daniele Zambon, Davide Bacciu, Cesare Alippi",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1504.07976v3",
+                    "title": "On Temporal Graph Exploration",
+                    "abstract": "A temporal graph is a graph in which the edge set can change from one time\nstep to the next. The temporal graph exploration problem TEXP is the problem of\ncomputing a foremost exploration schedule for a temporal graph, i.e., a\ntemporal walk that starts at a given start node, visits all nodes of the graph,\nand has the smallest arrival time. In the first part of the paper, we consider\nonly undirected temporal graphs that are connected at each time step. For such\ntemporal graphs with $n$ nodes, we show that it is \\NP-hard to approximate TEXP\nwith ratio $O(n^{1-\\varepsilon})$ for every $\\varepsilon>0$. We also provide an\nexplicit construction of temporal graphs that require $\\Theta(n^2)$ time steps\nto be explored. In the second part of the paper, we still consider temporal\ngraphs that are connected in each time step, but we assume that the underlying\ngraph (i.e. the graph that contains all edges that are present in the temporal\ngraph in at least one time step) belongs to a specific class of graphs. Among\nother results, we show that temporal graphs can be explored in\n$O(n^{1.5}k^{1.5}\\log n)$ time steps if the underlying graph has treewidth $k$,\nin $O(n^{1.8}\\log n)$ time steps if the underlying graph is planar, and in\n$O(n\\log^3 n)$ time steps if the underlying graph is a $2\\times n$ grid. In the\nthird part of the paper, we consider settings where the graphs in future time\nsteps are not known and the exploration schedule is constructed online. We\nreplace the connectedness assumption by a weaker assumption and show that\n$m$-edge temporal graphs with regularly present edges and with\nprobabilistically present edges can be explored online in $O(m)$ time steps and\n$O(m \\log n)$ time steps with high probability, respectively. We finally show\nthat the latter result can be used to obtain a distributed algorithm for the\ngossiping problem in random temporal graphs.",
+                    "authors": "Thomas Erlebach, Michael Hoffmann, Frank Kammer",
+                    "published": "2015-04-29",
+                    "updated": "2021-03-16",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "05C85, 68M14",
+                        "C.2.4; F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.07016v2",
+                    "title": "On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions",
+                    "abstract": "This work formalizes the associational task of predicting node attribute\nevolution in temporal graphs from the perspective of learning equivariant\nrepresentations. We show that node representations in temporal graphs can be\ncast into two distinct frameworks: (a) The most popular approach, which we\ndenote as time-and-graph, where equivariant graph (e.g., GNN) and sequence\n(e.g., RNN) representations are intertwined to represent the temporal evolution\nof node attributes in the graph; and (b) an approach that we denote as\ntime-then-graph, where the sequences describing the node and edge dynamics are\nrepresented first, then fed as node and edge attributes into a static\nequivariant graph representation that comes after. Interestingly, we show that\ntime-then-graph representations have an expressivity advantage over\ntime-and-graph representations when both use component GNNs that are not\nmost-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is\nnot necessarily to obtain state-of-the-art results, our experiments show that\ntime-then-graph methods are capable of achieving better performance and\nefficiency than state-of-the-art time-and-graph methods in some real-world\ntasks, thereby showcasing that the time-then-graph framework is a worthy\naddition to the graph ML toolbox.",
+                    "authors": "Jianfei Gao, Bruno Ribeiro",
+                    "published": "2021-03-12",
+                    "updated": "2023-03-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.08889v3",
+                    "title": "Node Embedding over Temporal Graphs",
+                    "abstract": "In this work, we present a method for node embedding in temporal graphs. We\npropose an algorithm that learns the evolution of a temporal graph's nodes and\nedges over time and incorporates this dynamics in a temporal node embedding\nframework for different graph prediction tasks. We present a joint loss\nfunction that creates a temporal embedding of a node by learning to combine its\nhistorical temporal embeddings, such that it optimizes per given task (e.g.,\nlink prediction). The algorithm is initialized using static node embeddings,\nwhich are then aligned over the representations of a node at different time\npoints, and eventually adapted for the given task in a joint optimization. We\nevaluate the effectiveness of our approach over a variety of temporal graphs\nfor the two fundamental tasks of temporal link prediction and multi-label node\nclassification, comparing to competitive baselines and algorithmic\nalternatives. Our algorithm shows performance improvements across many of the\ndatasets and baselines and is found particularly effective for graphs that are\nless cohesive, with a lower clustering coefficient.",
+                    "authors": "Uriel Singer, Ido Guy, Kira Radinsky",
+                    "published": "2019-03-21",
+                    "updated": "2021-05-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2205.14269v1",
+                    "title": "Temporal graph patterns by timed automata",
+                    "abstract": "Temporal graphs represent graph evolution over time, and have been receiving\nconsiderable research attention. Work on expressing temporal graph patterns or\ndiscovering temporal motifs typically assumes relatively simple temporal\nconstraints, such as journeys or, more generally, existential constraints,\npossibly with finite delays. In this paper we propose to use timed automata to\nexpress temporal constraints, leading to a general and powerful notion of\ntemporal basic graph pattern (BGP). The new difficulty is the evaluation of the\ntemporal constraint on a large set of matchings. An important benefit of timed\nautomata is that they support an iterative state assignment, which can be\nuseful for early detection of matches and pruning of non-matches. We introduce\nalgorithms to retrieve all instances of a temporal BGP match in a graph, and\npresent results of an extensive experimental evaluation, demonstrating\ninteresting performance trade-offs. We show that an on-demand algorithm that\nprocesses total matchings incrementally over time is preferable when dealing\nwith cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and\nwhen connectivity of partial matchings can be guaranteed, the best performance\nis achieved by maintaining partial matchings over time and allowing automaton\nevaluation to be fully incremental.",
+                    "authors": "Amir Pouya Aghasadeghi, Jan Van den Bussche, Julia Stoyanovich",
+                    "published": "2022-05-27",
+                    "updated": "2022-05-27",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05078v1",
+                    "title": "TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification",
+                    "abstract": "Multivariate time series classification (MTSC) is an important data mining\ntask, which can be effectively solved by popular deep learning technology.\nUnfortunately, the existing deep learning-based methods neglect the hidden\ndependencies in different dimensions and also rarely consider the unique\ndynamic features of time series, which lack sufficient feature extraction\ncapability to obtain satisfactory classification accuracy. To address this\nproblem, we propose a novel temporal dynamic graph neural network (TodyNet)\nthat can extract hidden spatio-temporal dependencies without undefined graph\nstructure. It enables information flow among isolated but implicit\ninterdependent variables and captures the associations between different time\nslots by dynamic graph mechanism, which further improves the classification\nperformance of the model. Meanwhile, the hierarchical representations of graphs\ncannot be learned due to the limitation of GNNs. Thus, we also design a\ntemporal graph pooling layer to obtain a global graph-level representation for\ngraph learning with learnable temporal parameters. The dynamic graph, graph\ninformation propagation, and temporal convolution are jointly learned in an\nend-to-end framework. The experiments on 26 UEA benchmark datasets illustrate\nthat the proposed TodyNet outperforms existing deep learning-based methods in\nthe MTSC tasks.",
+                    "authors": "Huaiyuan Liu, Xianzhang Liu, Donghua Yang, Zhiyu Liang, Hongzhi Wang, Yong Cui, Jun Gu",
+                    "published": "2023-04-11",
+                    "updated": "2023-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.10830v1",
+                    "title": "Automated Dilated Spatio-Temporal Synchronous Graph Modeling for Traffic Prediction",
+                    "abstract": "Accurate traffic prediction is a challenging task in intelligent\ntransportation systems because of the complex spatio-temporal dependencies in\ntransportation networks. Many existing works utilize sophisticated temporal\nmodeling approaches to incorporate with graph convolution networks (GCNs) for\ncapturing short-term and long-term spatio-temporal dependencies. However, these\nseparated modules with complicated designs could restrict effectiveness and\nefficiency of spatio-temporal representation learning. Furthermore, most\nprevious works adopt the fixed graph construction methods to characterize the\nglobal spatio-temporal relations, which limits the learning capability of the\nmodel for different time periods and even different data scenarios. To overcome\nthese limitations, we propose an automated dilated spatio-temporal synchronous\ngraph network, named Auto-DSTSGN for traffic prediction. Specifically, we\ndesign an automated dilated spatio-temporal synchronous graph (Auto-DSTSG)\nmodule to capture the short-term and long-term spatio-temporal correlations by\nstacking deeper layers with dilation factors in an increasing order. Further,\nwe propose a graph structure search approach to automatically construct the\nspatio-temporal synchronous graph that can adapt to different data scenarios.\nExtensive experiments on four real-world datasets demonstrate that our model\ncan achieve about 10% improvements compared with the state-of-art methods.\nSource codes are available at https://github.com/jinguangyin/Auto-DSTSGN.",
+                    "authors": "Guangyin Jin, Fuxian Li, Jinlei Zhang, Mudan Wang, Jincai Huang",
+                    "published": "2022-07-22",
+                    "updated": "2022-07-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.09995v1",
+                    "title": "Temporal Reasoning Graph for Activity Recognition",
+                    "abstract": "Despite great success has been achieved in activity analysis, it still has\nmany challenges. Most existing work in activity recognition pay more attention\nto design efficient architecture or video sampling strategy. However, due to\nthe property of fine-grained action and long term structure in video, activity\nrecognition is expected to reason temporal relation between video sequences. In\nthis paper, we propose an efficient temporal reasoning graph (TRG) to\nsimultaneously capture the appearance features and temporal relation between\nvideo sequences at multiple time scales. Specifically, we construct learnable\ntemporal relation graphs to explore temporal relation on the multi-scale range.\nAdditionally, to facilitate multi-scale temporal relation extraction, we design\na multi-head temporal adjacent matrix to represent multi-kinds of temporal\nrelations. Eventually, a multi-head temporal relation aggregator is proposed to\nextract the semantic meaning of those features convolving through the graphs.\nExtensive experiments are performed on widely-used large-scale datasets, such\nas Something-Something and Charades, and the results show that our model can\nachieve state-of-the-art performance. Further analysis shows that temporal\nrelation reasoning with our TRG can extract discriminative features for\nactivity recognition.",
+                    "authors": "Jingran Zhang, Fumin Shen, Xing Xu, Heng Tao Shen",
+                    "published": "2019-08-27",
+                    "updated": "2019-08-27",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2101.00820v8",
+                    "title": "Temporal Contrastive Graph Learning for Video Action Recognition and Retrieval",
+                    "abstract": "Attempt to fully discover the temporal diversity and chronological\ncharacteristics for self-supervised video representation learning, this work\ntakes advantage of the temporal dependencies within videos and further proposes\na novel self-supervised method named Temporal Contrastive Graph Learning\n(TCGL). In contrast to the existing methods that ignore modeling elaborate\ntemporal dependencies, our TCGL roots in a hybrid graph contrastive learning\nstrategy to jointly regard the inter-snippet and intra-snippet temporal\ndependencies as self-supervision signals for temporal representation learning.\nTo model multi-scale temporal dependencies, our TCGL integrates the prior\nknowledge about the frame and snippet orders into graph structures, i.e., the\nintra-/inter- snippet temporal contrastive graphs. By randomly removing edges\nand masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL\ncan generate different correlated graph views. Then, specific contrastive\nlearning modules are designed to maximize the agreement between nodes in\ndifferent views. To adaptively learn the global context representation and\nrecalibrate the channel-wise features, we introduce an adaptive video snippet\norder prediction module, which leverages the relational knowledge among video\nsnippets to predict the actual snippet orders. Experimental results demonstrate\nthe superiority of our TCGL over the state-of-the-art methods on large-scale\naction recognition and video retrieval benchmarks.",
+                    "authors": "Yang Liu, Keze Wang, Haoyuan Lan, Liang Lin",
+                    "published": "2021-01-04",
+                    "updated": "2021-03-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.MM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.13684v3",
+                    "title": "Spatio-Temporal Joint Graph Convolutional Networks for Traffic Forecasting",
+                    "abstract": "Recent studies have shifted their focus towards formulating traffic\nforecasting as a spatio-temporal graph modeling problem. Typically, they\nconstructed a static spatial graph at each time step and then connected each\nnode with itself between adjacent time steps to create a spatio-temporal graph.\nHowever, this approach failed to explicitly reflect the correlations between\ndifferent nodes at different time steps, thus limiting the learning capability\nof graph neural networks. Additionally, those models overlooked the dynamic\nspatio-temporal correlations among nodes by using the same adjacency matrix\nacross different time steps. To address these limitations, we propose a novel\napproach called Spatio-Temporal Joint Graph Convolutional Networks (STJGCN) for\naccurate traffic forecasting on road networks over multiple future time steps.\nSpecifically, our method encompasses the construction of both pre-defined and\nadaptive spatio-temporal joint graphs (STJGs) between any two time steps, which\nrepresent comprehensive and dynamic spatio-temporal correlations. We further\nintroduce dilated causal spatio-temporal joint graph convolution layers on the\nSTJG to capture spatio-temporal dependencies from distinct perspectives with\nmultiple ranges. To aggregate information from different ranges, we propose a\nmulti-range attention mechanism. Finally, we evaluate our approach on five\npublic traffic datasets and experimental results demonstrate that STJGCN is not\nonly computationally efficient but also outperforms 11 state-of-the-art\nbaseline methods.",
+                    "authors": "Chuanpan Zheng, Xiaoliang Fan, Shirui Pan, Haibing Jin, Zhaopeng Peng, Zonghan Wu, Cheng Wang, Philip S. Yu",
+                    "published": "2021-11-25",
+                    "updated": "2023-06-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19453v1",
+                    "title": "Structural Parameters for Dense Temporal Graphs",
+                    "abstract": "Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.",
+                    "authors": "Jessica Enright, Samuel D. Hand, Laura Larios-Jones, Kitty Meeks",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "math.CO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07491v3",
+                    "title": "Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment",
+                    "abstract": "Temporal graph learning aims to generate high-quality representations for\ngraph-based tasks with dynamic information, which has recently garnered\nincreasing attention. In contrast to static graphs, temporal graphs are\ntypically organized as node interaction sequences over continuous time rather\nthan an adjacency matrix. Most temporal graph learning methods model current\ninteractions by incorporating historical neighborhood. However, such methods\nonly consider first-order temporal information while disregarding crucial\nhigh-order structural information, resulting in suboptimal performance. To\naddress this issue, we propose a self-supervised method called S2T for temporal\ngraph learning, which extracts both temporal and structural information to\nlearn more informative node representations. Notably, the initial node\nrepresentations combine first-order temporal and high-order structural\ninformation differently to calculate two conditional intensities. An alignment\nloss is then introduced to optimize the node representations, narrowing the gap\nbetween the two intensities and making them more informative. Concretely, in\naddition to modeling temporal information using historical neighbor sequences,\nwe further consider structural knowledge at both local and global levels. At\nthe local level, we generate structural intensity by aggregating features from\nhigh-order neighbor sequences. At the global level, a global representation is\ngenerated based on all nodes to adjust the structural intensity according to\nthe active statuses on different nodes. Extensive experiments demonstrate that\nthe proposed model S2T achieves at most 10.13% performance improvement compared\nwith the state-of-the-art competitors on several datasets.",
+                    "authors": "Meng Liu, Ke Liang, Yawei Zhao, Wenxuan Tu, Sihang Zhou, Xinbiao Gan, Xinwang Liu, Kunlun He",
+                    "published": "2023-02-15",
+                    "updated": "2024-04-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.02875v1",
+                    "title": "Multi-Task Edge Prediction in Temporally-Dynamic Video Graphs",
+                    "abstract": "Graph neural networks have shown to learn effective node representations,\nenabling node-, link-, and graph-level inference. Conventional graph networks\nassume static relations between nodes, while relations between entities in a\nvideo often evolve over time, with nodes entering and exiting dynamically. In\nsuch temporally-dynamic graphs, a core problem is inferring the future state of\nspatio-temporal edges, which can constitute multiple types of relations. To\naddress this problem, we propose MTD-GNN, a graph network for predicting\ntemporally-dynamic edges for multiple types of relations. We propose a\nfactorized spatio-temporal graph attention layer to learn dynamic node\nrepresentations and present a multi-task edge prediction loss that models\nmultiple relations simultaneously. The proposed architecture operates on top of\nscene graphs that we obtain from videos through object detection and\nspatio-temporal linking. Experimental evaluations on ActionGenome and CLEVRER\nshow that modeling multiple relations in our temporally-dynamic graph network\ncan be mutually beneficial, outperforming existing static and spatio-temporal\ngraph neural networks, as well as state-of-the-art predicate classification\nmethods.",
+                    "authors": "Osman \u00dclger, Julian Wiederer, Mohsen Ghafoorian, Vasileios Belagiannis, Pascal Mettes",
+                    "published": "2022-12-06",
+                    "updated": "2022-12-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.08312v2",
+                    "title": "ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks",
+                    "abstract": "Networks are a fundamental and flexible way of representing various complex\nsystems. Many domains such as communication, citation, procurement, biology,\nsocial media, and transportation can be modeled as a set of entities and their\nrelationships. Temporal networks are a specialization of general networks where\nthe temporal evolution of the system is as important to understand as the\nstructure of the entities and relationships. We present the Independent\nTemporal Motif (ITeM) to characterize temporal graphs from different domains.\nThe ITeMs are edge-disjoint temporal motifs that can be used to model the\nstructure and the evolution of the graph. For a given temporal graph, we\nproduce a feature vector of ITeM frequencies and apply this distribution to the\ntask of measuring the similarity of temporal graphs. We show that ITeM has\nhigher accuracy than other motif frequency-based approaches. We define various\nmetrics based on ITeM that reveal salient properties of a temporal network. We\nalso present importance sampling as a method for efficiently estimating the\nITeM counts. We evaluate our approach on both synthetic and real temporal\nnetworks.",
+                    "authors": "Sumit Purohit, Lawrence B. Holder, George Chin",
+                    "published": "2020-02-19",
+                    "updated": "2020-08-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07699v2",
+                    "title": "Time-aware Graph Structure Learning via Sequence Prediction on Temporal Graphs",
+                    "abstract": "Temporal Graph Learning, which aims to model the time-evolving nature of\ngraphs, has gained increasing attention and achieved remarkable performance\nrecently. However, in reality, graph structures are often incomplete and noisy,\nwhich hinders temporal graph networks (TGNs) from learning informative\nrepresentations. Graph contrastive learning uses data augmentation to generate\nplausible variations of existing data and learn robust representations.\nHowever, rule-based augmentation approaches may be suboptimal as they lack\nlearnability and fail to leverage rich information from downstream tasks. To\naddress these issues, we propose a Time-aware Graph Structure Learning (TGSL)\napproach via sequence prediction on temporal graphs, which learns better graph\nstructures for downstream tasks through adding potential temporal edges. In\nparticular, it predicts time-aware context embedding based on previously\nobserved interactions and uses the Gumble-Top-K to select the closest candidate\nedges to this context embedding. Additionally, several candidate sampling\nstrategies are proposed to ensure both efficiency and diversity. Furthermore,\nwe jointly learn the graph structure and TGNs in an end-to-end manner and\nperform inference on the refined graph. Extensive experiments on temporal link\nprediction benchmarks demonstrate that TGSL yields significant gains for the\npopular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive\nlearning methods on temporal graphs. We release the code at\nhttps://github.com/ViktorAxelsen/TGSL.",
+                    "authors": "Haozhen Zhang, Xueting Han, Xi Xiao, Jing Bai",
+                    "published": "2023-06-13",
+                    "updated": "2023-08-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.04962v1",
+                    "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering",
+                    "abstract": "Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.",
+                    "authors": "Meng Liu, Ke Liang, Yue Liu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-06-08",
+                    "updated": "2023-06-08",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2402.11036v1",
+                    "title": "Occlusion Resilient 3D Human Pose Estimation",
+                    "abstract": "Occlusions remain one of the key challenges in 3D body pose estimation from\nsingle-camera video sequences. Temporal consistency has been extensively used\nto mitigate their impact but the existing algorithms in the literature do not\nexplicitly model them.\n  Here, we apply this by representing the deforming body as a spatio-temporal\ngraph. We then introduce a refinement network that performs graph convolutions\nover this graph to output 3D poses. To ensure robustness to occlusions, we\ntrain this network with a set of binary masks that we use to disable some of\nthe edges as in drop-out techniques.\n  In effect, we simulate the fact that some joints can be hidden for periods of\ntime and train the network to be immune to that. We demonstrate the\neffectiveness of this approach compared to state-of-the-art techniques that\ninfer poses from single-camera sequences.",
+                    "authors": "Soumava Kumar Roy, Ilia Badanin, Sina Honari, Pascal Fua",
+                    "published": "2024-02-16",
+                    "updated": "2024-02-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Temporal AND Graph",
+                    "gt": "With recent advances in the field of deep learning, regressing 2D and 3D poses directly from images has become an effective approach to human pose estimation. Some approaches are fully supervised [21, 26, 27, 34, 35, 39, 42, 46, 47, 52, 53]. Others rely on self-supervision to reduce the required amount of training data [2, 4, 17, 28, 38, 48] and make it possible to capture people in the wild [15]. However, occlusions remain one of the primary challenges, especially in crowded scenes where people may hide each other. Our proposed solution relies on enforcing temporal consistency while explicitly modeling occlusions. As discussed in the remainder of this section, these two aspects have been handled separately in the past but loosely together. In this paper, we take our inspiration from the MC-Droput like method of [9] to enforce temporal consistency while also handling occlusions in a time consistent manner. Occlusions. One way to mitigate their influence is to learn camera specific weight for every joint in a calibrated multi camera setup [16, 30, 44]. This can be effective but does not generalize well to single, potentially moving, cameras. A more generic approach is to exploit temporal consistency in videos [6, 12, 23, 38]. The algorithm of [23] learns inter-joint dependencies using an LSTM, whereas [12] uses an Recurrent Neural Network (RNN) to enforce temporal smoothness for the detected joints. Unfortunately, these methods do not model the fact that occlusions exhibit temporally consistent patterns. The approach of [6] seeks to enhance the generalization ability of a prediction network by generating augmented pairs of 3D joints and 2D key-points with arbitrary per-joint occlusion labels. However, this arbitrary generation of occlusion labels fails to capture the inherent temporal pattern of the occluded key-points over any given time interval. Our method is in the same spirit but seeks to capture this pattern by using structured occlusion masks of [9]. The works of [40, 43] also propose to tackle occlusion by imposing pose priors and kinematic pose constraints on the predicted poses. However, the proposed algorithms fail to impose such constraints in long sequences of images involving many different forms of complex occlusion patterns. As shown in the experiment section, this adversely impacts performance even when using training sets that contain substantial amounts of occlusions. Spatio-Temporal Consistency. Recently, Graph Convolution Neural Networks (GCNNs) [8, 20, 24] have become increasingly popular to exploit the skeletal structure of human joints [1, 7, 29, 49, 51, 54]. In [1], predicted 2D joints locations are assembled into a graph and a network learns to combine different local features corresponding to different body parts to produce a global embedding, which is eventually used to decode the final 3D pose in a target frame. Similarly, the algorithm of [51] splits and recombines partwise feature representations to learn inter-joint dependencies across different body parts. In [49] weight and affinity modulation methods are introduced to learn a disentangled representation of a spatial skeletal graph. In [1, 29, 54] structured weight matrices are used to model inter-joint relationships, thus reducing the overall computational complexity of the framework. However, none of these methods explicitly handle occlusions.",
+                    "pre_questions": [],
+                    "main_content": "Introduction While there are many compelling algorithms [2, 4, 17, 28, 38, 46, 48, 52, 53] to capture the pose of a single clearly visible person, modeling partially occluded people in crowded scenes remains an open problem. To address it, several approaches often make strong assumptions [16, 30, 40, 43, 44], which limit their generalization abilities. In this context, exploiting temporal consistency from videos is particularly appealing because it only requires a much weaker assumption of motion continuity. Hence, it has been extensively used to mitigate the impact of occlusions [1, 7, 12, 18, 23, 29, 51, 54] by imposing regularization constraints, but without explicitly accounting for the occlusions. This compromises their robustness to them. In this paper, we aim to address this limitation. Given a sequence of consecutive frames, we represent the deforming body as a spatio-temporal graph such as the one de*work done while at Computer Vision Lab, EPFL Figure 1. Graph masking. G is our spatio-temporal graph. The solid colors denote graph nodes corresponding to the same joint over time. The gray edges are spatial edges connecting joints seen at the same time while the colored edges are temporal and connect nodes corresponding to the same joint over time. For clarity, we only show spatial and temporal connections for 11 joints. Along the temporal domain, each joint is connected to its temporal neighbor (i.e. \u2206= 1). Moreover, we also show temporal connection with \u2206= 2 for two joints (head and left foot) as an example. M represent the set of binary masks that are used to deactivate some of these edges to create the masked graph \u00af G, which is then fed to the refinement network. Refer to Section \u00a7 3.3 for more details. picted by Fig. 1, in which spatial edges connect body nodes in one frame to form a skeleton and temporal edges connect the same node at different times. We then introduce a refinement network that performs graph convolutions over this graph to output 3D poses. To ensure robustness to occlusions, we train this network with a set of binary masks that we use to disable some of the edges as in drop-out techniques [9, 10]. In effect, we simulate the fact that some joints can be hidden for periods of time and train the network to be immune to that. arXiv:2402.11036v1  [cs.CV]  16 Feb 2024 Our contribution is therefore an approach to explicitly modeling occlusions to increase the robustness of a lifting network that produces reliable 3D poses. We demonstrate the effectiveness of our approach on the benchmark Human3.6M [13], MPI-INF-3DHP [32] in addition to SportCenter [44] datasets against several baselines and state-ofthe-art methods that use a sequence acquired by a single camera at inference time and can be trained using either singleor multi-view image data. We train an occlusion-robust network to estimate 3D human poses from image sequences acquired using a single camera. As shown in Fig. 2, we first detect 2D joints in individual images. They are mapped to 3D by a lifting network and become the nodes of a spatio-temporal graph that represents the body deforming over time. This graph is fed to a refinement network that produces a 3D pose for a target frame in the middle of the sequence. A key component of this approach is the set of structured binary masks depicted by Fig. 1. They are used to deactivate some edges in the graph before it is fed to the refinement network during training. This increases robustness to occlusions. 3.1. Notations Let L = {Il, pl 3D}NL l=1 be a monocular sequence of labeled NL RGB images Il \u2208Rh\u00d7w\u00d73, featuring a person. pl 3D denotes the ground-truth 3D pose of the person\u2019s body and l is the image index. pl 3D stands for a full set of NJ body joints {Xl j}NJ j=1, where Xl j \u2208R3 denotes the 3D coordinates of joint j in image l. We use L for supervised single-view learning. For unsupervised learning, let U = {Iu,v}NU,NV u=1,v=1 be a longer multiview sequence of NU images captured in NV views simultaneously but without associated body poses. This represents an important training scenario because setting up multiple cameras is a relative inexpensive way to provide supervision without having to annotate, which is far more laborious. In the remainder of this paper, we drop the l and u indices when there is no ambiguity. A human body deforming in a sub-sequence of length T can be represented by a graph G(V, E) whose vertices V = {vtj | t = 1, 2, \u00b7 \u00b7 \u00b7 T; j = 1, 2, \u00b7 \u00b7 \u00b7 NJ} are the body Figure 2. Our approach. 3D joint coordinates are extracted from individual images by the lifting net LNet\u03a6 and become the nodes of a spatio-temporal graph G. Some of its edges are masked to produce a reduced graph \u00af G. It is fed to a refinement network RNet\u0398 that returns the pose in the selected target frame tp. The masking operation is depicted by Fig. 1 (Refer to Section \u00a7 3.2 and 3.3 for more details). joints Xl j corresponding to T frames and whose edges E are both spatial and temporal. In Fig. 1, the spatial edges are shown in gray; they define the skeleton within each temporal frame. The temporal edges are shown in color and connect joints over time. In practice, we connect a joint in image l to all its temporal neighbors from frame l \u2212T 2 to l+ T 2 with a temporal stride \u2206= {1, 2, 3 \u00b7 \u00b7 \u00b7 \u2206max}, where \u2206max is the maximum temporal stride we consider in the window of size T. We denote by A = [aij] the adjacency matrix of the graph such that aij = 1 if nodes i and j are connected and 0 otherwise. N = T\u2217NJ represent the total number of joints (or noded) in the graph G. 3.2. Lifting Network (LNet\u03a6) We start from 2D joint detections obtained by an off-theshelf joint detector [44]. In each image I, the lifting network LNet\u03a6, with trainable weights \u03a6 maps these 2D detections to 3D points that we treat as estimates \u02dc p3D of the true body pose p3D. This is depicted on the left side of Fig. 2. Under the assumption that intrinsic camera parameters K are known, we use the standard approach of [14, 15, 36, 46] to map the predictions of LNet\u03a6 into coordinates expressed into the camera coordinate system. These are expressed in terms of droot, the distance of the root joint to the camera and drel j the distance difference for each joint with respect to that of the root. We write   \\lab e l {e q n : 2 d_ 3d _ l i f t _ d ep t h }   \\begin  {ali g n e d }   ( d^ { r oo t} +d ^ { r e l } _j)\\begin {pmatrix} x_j \\\\ y_j \\\\ 1 \\end {pmatrix} & = \\Mat {K} \\begin {pmatrix} X^C_j \\\\ Y^C_j \\\\ (d^{root}+d^{rel}_j) \\end {pmatrix} \\\\ & = \\Mat {K} \\left [ \\Mat {R} \\begin {pmatrix} X_j \\\\ Y_j \\\\ Z_j \\end {pmatrix} + \\Vec {t} \\right ]~~~~ , \\end {aligned}  (1) where XC j , Y C j denote the first two 3D coordinates of joint j in the camera coordinate system and xj, yj denote their projection on to the un-distorted image space respectively. (Xj, Yj, Zj) is the joint in the world coordinate and K \u2208R3\u00d73, R \u2208R3\u00d73, and t \u2208R3\u00d71 are the intrinsic matrix, rotation matrix, and translation vector of the camera respectively. As in previous work [31, 42, 46], we use the ground-truth value of droot. However an analytical approximation can be obtained if necessary [14]. The lifting network LNet\u03a6 is trained to predict these distances by learning a set of weights \u03a6. Within each continuous sequence of frames the resulting 3D points are then assembled into a spatio-temporal graph G. 3.3. Refinement Network (RNet\u0398) The spatio-temporal graph G built on the predictions of LNet is a raw assembly of lifted 2D poses and one can expect many of its 3D nodes to be inaccurate, especially when there are occlusions. The problem is compounded by the fact that LNet does not deliver an uncertainty estimate for its predictions. We therefore feed it to a refinement network RNet\u0398 whose role is to exploit temporal consistency constraints to output an accurate 3D pose for the central frame of the sequence it has been constructed from, as shown on the right side of Fig. 2. We will refer to this frame as the target frame. Our challenge is to make RNet robust to occlusions. 3.3.1 Robustness to Occlusions In practice, occlusions hide parts of the body. Hence, some of the 2D detections and the resulting 3D lifted points that LNet produces are bound to be incorrect. To make our RNet robust to this, we take our inspiration from MCDropout [10], which must be able to ignore some nodes in G and yet deliver the correct target pose. The original MC-Dropout idea involves dropping weights at random by introducing random binary masks that define which weights are used or ignored. Unfortunately, this does not reflect the true behavior of occlusions. Occluded body joints tend to be spatial neighbors and the occlusions exhibit temporal consistency. Hence the masks should be correlated both spatially and temporally. Therefore, as in [9], we define a fixed set of pre-computed parameterized binary masks M = [M i]NM i=1 = \u2126(NM, \u03b2, \u03b1), where \u2126is the parameterized mask generating function, NM is the total number of masks, M i = {0, 1}N j=1, \u03b2 denotes the number of 1\u2019s in each mask, and \u03b1 controls the amount of overlap between masks. The larger the overlap, the higher the chances that the same nodes will be dropped in subsequent frames, thus enforcing a degree of temporal consistency that depends on \u03b1. As shown in Fig. 1, during training, we randomly pick masks from the generated set in M and use them to disconnect some edges in G. This produces subgraphs \u00af G, which we feed to RNet. 3.3.2 Architecture and Losses We implement RNet\u0398 as a Graph Convolutional Neural Network (GCNN) [8, 20, 24]. In its successive layers, a feature vector is assigned to each node of the graph and averaged with its neighbors according to a set of learned weights in \u0398. The results are then pooled as in ordinary CNNs. Finally, the output is fed to a linear layer with output dimensionality of NJ that predicts the incremental rootrelative depth \u2206drel j for each joint of the target frame tp. These are added to the predictions of LNet to yield the final refined depth of all joints, which are transformed to \u02c6 ptp 3D using Eq. (1) for the target frame tp, as shown in Fig. 3. The spatio-temporal graph G should encode the spatial and temporal connections between the joints in the temporal window of size T. As the 3D joint positions are correlated, we therefore need to learn these correlations within T. Figure 3. Architecture of the refinement network. RNet\u0398 is a set of GCNNs that operates on the masked graph \u00af G. Each relationship-specific GCN is trained on a different set of connections between the joints, which are eventually fused and processed by the embedding-fusion network with parameters \u0398f. Thus, we connect the joints across time with different values of the temporal stride \u2206, which are intended to model relationships at different temporal scales. Let S be the set of all temporal connections generated using different values of \u2206s. Hence, we have |S| + 1 different edge types, |S| temporal types and one spatial type. Each type is processed by a separate relationship-specific GCNN that combines information about the joint using both spatial and temporal neighbors. Relation-Specific GCN. The initial value of node vtj is set to drel j , predicted by the lifting network as shown in Eq. (1) for the frame t \u2208[1, 2, ...T]. This yields the initial feature matrix H \u2208RN. For masking purposes, H is multiplied by one of the binary masks M i \u2208M to obtain the feature matrix \u00af H = H \u2299M i of the masked graph \u00af G. This is possible because \u00af G has the same structure as G, with some of its node features set to 0 according to the location of zeros in M i. As shown in Fig. 1, in the graph G (or \u00af G) we consider |S| + 1 different connections between the joints, which are individually processed by a relationship-specific GCN RNet\u0398r. Each of these RNet\u0398r takes as input the initial feature matrix \u00af H and outputs Zr \u2208R\u00af d for every node vtj. Thereafter, we pass {Zr}|S|+1 r=1 through a pooling operation \u03a0 to obtain the final feature matrix Z = \u03a0({Zr}) \u2208RN\u00d7\u00af d for the graph \u00af G. Z is further passed through an additional embedding-fusion neural network RNet\u0398f that returns \u2206ptp = \b \u2206drel j \tNJ j=1, which is further added to drel j predicted by the lifting network LNet\u03a6. The summed value yields the estimated 3D pose \u02c6 ptp 3D using Eq. (1) for the frame tp. Fig. 3 shows a diagrammatic representation of operations by the refinement network RNet\u0398. Training Losses. For supervised learning exploiting the labeled image set L, we take the loss for a sequence of length T to be   \\l ab e l {e q n :lo ss_ ref in e _net} L(\\Mat {\\Phi }, \\Mat {\\Theta }) = L_{\\textrm {MSE}} \\Big (\\hat {\\Mat {p}}^{t_p}_{3D}, \\Mat {p}^{t_p}_{3D} \\Big )~~,  (2) where LMSE is mean squared error loss, while \u02c6 ptp 3D and ptp 3D are the estimated and ground-truth poses in the target frame tp. To exploit the unlabeled image multi-view set U, we replace the missing ground-truth poses ptp 3D in Eq. (2) by 3D pseudo labels, which are generated by running the robust weighted triangulation scheme of [44] on the joints detected by the 2D pose estimator. 3.4. Implementation Details Lifting Network. LNet\u03a6 consists of a multi-layer perceptron network with 2 hidden layers with a hidden size of 2048. The first two layers are composed of a linear layer, each followed by ReLU activation and 10% dropout while the last layer is a linear layer with the output dimension set to NJ. Given an input image I, LNet\u03a6 takes as input the 2D predictions of a 2D pose estimator model \u02c6 p \u2208RNJ\u00d72 as the input. We implement the 2D pose estimator model of [44] to extract the initial 2D key-points, which are further normalized in the range of [\u22121, 1] to yield \u02c6 p. Refinement Network. The value of T, i.e. the number of frames in each window, is set 31. This results in 31 \u2217NJ nodes in the graph G, where NJ is the number of estimated joints. We choose \u2206= {1, 3, 5, 7} resulting in 4 types of temporal edges and 1 of spatial ones in G. In M, we have set NM and \u03b1 to 32 and 1.8 respectively. This results in \u03b2 = 292 in each M i \u2208M when NJ is set 17 for Human 3.6M [13] and MPI-INF-3DHP [32] datasets, and 223 when we use 13 joints for SportCenter dataset [44] in our experiments. Each relationship-specific network RNet\u0398r consists of 2 hidden linear layers with the hidden sizes set to 16 and 32 respectively, each followed by ReLU activation. The final layer is a linear layer with its output dimension set to 64, thus resulting in Zr \u2208RN\u00d764. We have assigned \u03a0 to max pooling operation to obtain the Z. The embedding-fusion neural network RNet\u0398f is composed of a single linear layer with the output dimension set to NJ. We always predict the 3D pose of the central frame ( i.e. tp = 15) present in the time window T. We use the Adam optimizer [19] for optimizing all the parameters of LNet\u03a6 and RNet\u0398. As a warm startup for the first 1K iterations, we train \u03a6 with a constant learning rate of 10-4 on the labeled set L by minimizing the following the loss function   \\l a bel  { e qn:l oss _ lift_net} L(\\Mat {\\Phi }) = L_{\\textrm {MSE}} \\Big (\\tilde {\\Mat {p}}_{3D}, \\Mat {p}_{3D} \\Big ) \\; ,  (3) where \u02dc p3D are the 3D predictions by LNet\u03a6. Thereafter we train both set of parameters \u03a6 and \u0398 by minimizing the loss of Eq. (2) with a constant learning rate of 5\u00d710-5 and 1 \u00d710-4 respectively. 4. Experiments We perform experiments in the semi-supervised learning setup to validate the performance of our proposed method. More specifically, training of the networks is done on the labeled set L and the unlabeled multi-view set U1. In both cases, the inference occurs on single-view images. 4.1. Datasets and Metrics We briefly describe the datasets and metrics we use to perform our experiments. Human 3.6M [13]. It is the most widely used indoor dataset for single and multi-view 3D pose estimation. It consists of 3.6 million images captured form 4 calibrated cameras. As in most published papers, we use subjects S1, S5, S6, S7, S8 for training and S9, S11 for testing. In the semi-supervised setup we follow two different training protocols: 1. L comprises every 10th frame sampled uniformly from the training set, while the remaining images are treated as being unlabeled [22] and form the set U. 2. As in [25, 37, 42], the supervised set L comprises images of subject S1, while images of the remaining training subjects constitute the multi-view dataset U. MPI-INF-3DHP [32]. It includes both indoor and outdoor images for single person 3D pose estimation. It features 8 subjects performing 8 different actions, which are recorded using 14 different cameras, thereby covering a wide range of 3D poses and viewing angles. It contains both indoor and complex outdoor scenes, covering a wide range of actions ranging from walking, sitting to challenging exercise poses with dynamic motions which undergo a considerable amount of occlusion. We follow the standard protocol and use the 5 chest-height cameras only. In the semi-supervised setup, we use the images of subject S1 to form L and the others are taken to belong to U. SportCenter [44]. The images were captured during a game of amateur basketball featuring a total of 13 different people, with 10 of them being players at any given time. The images are captured using 8 fixed and calibrated cameras, out of which 6 cameras are used for pose estimation while the remaining 2 are used for tracking the players. The players are occluded either by other players or by various objects, such as the nets metal frames. Substantial changes in illumination occur, thus making pose-estimation even more challenging. The dataset consists of 315,000 images out of which only 560 images are provided with 3,740 1We also provide results for the fully-supervised setup in the supplementary material. (a) Iskakov et al. [16] (b) Roy et al. [44] (c) Ours Figure 4. SportCenter. Qualitative results on the samples from the \u201cHard\u201d test set for (a) Iskakov et al. [16], (b) Roy et al. [44] and (c) Ours. 2D annotated poses and 700 3D annotated poses. We use two subjects for evaluation, while the remaining ones are used for training in the semi-supervised setup. The test set is partioned into \u201ceasy\u201d and \u201chard\u201d cases, the difference being that the hard cases feature far stronger occlusions. Fig. 4 depicts four of them. Metrics. At training time, we learn weights for the whole network of Fig. 2 that is designed to operate on sequences. The result is a fully trained lifting network LNet\u03a6 that can operate on single views and that we test in this section. Hence, we report the Mean Per-Joint Position Error (MPJPE), the normalized NMPJPE, and the procrustes aligned PMPJPE in milimeters between the LNet\u03a6 predictions and the ground truth 3D poses. 4.2. Quantitative Results Semi Supervised Human 3.6M. We report the results for Human 3.6M data in Table 1. Considering only 10% of the dataset as the labeled set L, our approach consistently outperforms the best baseline [44] in all three evaluation metric. We also outperform the other baselines when considering all the samples of subject S1 as the labeled set L (Only S1). This setup is more encouraging because some baseMPJPE NMPJPE PMPJPE 80 100 120 121.1 119.5 99 104.4 102.1 81.1 100.4 98.6 75.8 3D Pose Error in mms Iskakov et al. [16] Roy et al. [44] Ours Figure 5. Comparative study on the SportCenter dataset in the semi-supervised setup. Table 1. Quantitative results Human3.6M (Semi-supervised). Best results are shown in bold. 10% of All Data Method MPJPE \u2193 NMPJPE \u2193 PMPJPE \u2193 Kundu et.al. [22] 50.8 Roy et al. [44] 56.9 56.6 45.4 Ours 55.2 55.0 43.5 Only S1 Rhodin et al. [41] 131.7 122.6 98.2 Pavlako et al. [37] 110.7 97.6 74.5 Li et al. [28] 88.8 80.1 66.5 Rhodin et al. [42] 80.1 65.1 Kocabas et al. [21] 67.0 60.2 Pavllo et al. [38] 64.7 61.8 Iqbal et al. [15] 62.8 59.6 51.4 Kundu et al. [22] 52 Roy et al. [44] 60.8 60.4 48.4 Ours 58.2 57.3 46.7 lines [15, 22] rely on additional datasets and/or part based puppet models to instill prior human skeleton knowledge into the underlying networks and to improve their generalization ability. In contrast, we use no such additional knowledge, which is advantageously replaced by the occlusionresistant processing of our spatio-temporal graph. Another highlight is outperforming the approach in [44], which models neither temporal consistency nor occlusions, showing the impact of these components. MPI-INF-3DHP. In Table 2, we report similar results on the MPI-INF-3DHP dataset. As for H36M, we outperform the other competing methods by merely processing the masked graph G without adding any other prior knowledge. Table 2. Quantitative results MPI-INF-3DHP (Semi-supervised). Best results are shown in bold. Method MPJPE \u2193 NMPJPE \u2193 PMPJPE \u2193 Rhodin et al. [42] 121.8 Kocabas et al. [21] 119.9 Iqbal et al. [15] 113.8 102.2 Roy et al. [44] 102.2 99.6 93.6 Ours 100.1 99.3 91.2 Table 3. Quantitative results on the \u201cEasy\u201d and \u201cHard\u201d samples of the SportCenter dataset. We report the MPJPE in mms. The best results are bold. The baseline numbers are the published ones. Method Easy Hard All Iskakov et al. [16] 113.2 155.6 121.1 Roy et al. [44] 98.7 139.2 104.4 Ours 94.2 129.2 100.4 SportCenter. In Fig. 5 and Table 3, we compare our approach to the two methods [16, 44] for which there are published results. Again we outperform them in all three evaluation metrics, especially on the hard samples that feature considerable amounts of occlusion. This confirms the importance of our proposed approach to masking joints during training. Fig. 4 provides a qualitative comparison between our method and the baselines [16, 44] on \u201cHard\u201d samples from the test set. On these images, our method performs substantially better. 4.3. Ablation Study In this section, we use the Human 3.6M [13] dataset to study the impact of varying the temporal parameters in the semisupervised setup. We provide an additional ablation study about the mask generation parameters in the supplementary material. Unless otherwise specified, the hyper-parameters are set to their default values, as discussed in Section \u00a73.4. Choosing the value of tp. Table 5 shows what happens when we choose different values for tp, the index of the target frame within a sequence of length T = 31. The prediction accuracy drops significantly as we get closer to the end of the sequence, indicating that both passed and future poses contribute to prediction accuracy. It therefore makes sense to predict the pose at the center of the sequence, that is, tp = 15. Choosing the sequence length T. Fig. 6 illustrates what happens for different values of the sequence length T from 5 to 61. For smaller values of T, the human body does not undergo much deformation. As a result, the graph G does not contain much temporal information, which results in higher 5 11 15 21 25 31 35 41 45 51 55 61 T 58 59 60 61 62 63 64 65 66 MPJPE 64.7 63.1 61.5 59.7 58.9 58.2 58.2 58.3 58.4 58.5 58.7 59.3 Figure 6. A comparative study choosing different values of sequence length T. Figure 7. A comparative study of generating different number of structured masks using [9] prediction errors. As we increase T, we get the smallest error for T = 31. After that, the error increases again because the poses within the sequence become too diverse. Choosing different temporal strides \u2206in S. Table 4 shows the consequences of including different temporal strides in the set S. S = \u2205yields a graph G containing only spatial connections, which unsurprisingly yields higher errors by ignoring temporal consistency. Successive additions of temporal connections progressively boosts performance as the refinement network can then exploit diverse, yet complementary temporal relationships between the nodes in G. The best results are obtained for S = {1, 3, 5, 7}. Adding even more temporal edges does not yield any additional improvements as these extra temporal edges do not model any new inter-joint temporal dependencies. Table 4. A comparative study of choosing different values of S that defines different temporal relationships between joints in G. S \u2205 {1} {3} {5} {7} {1, 3} {1, 5} {1, 7} {1, 3, 7} {1, 3, 5, 7} {1, 3, 5, 7, 9, 11} MPJPE \u2193 62.1 61.0 60.7 60.5 60.4 59.9 59.3 59.1 58.6 58.2 58.3 Table 5. A comparative study of choosing the value of tp for the sequence length of T = 31 frames. tp 0 2 4 8 15 (Ours) 20 25 30 MPJPE 61.5 60.9 60.1 59.3 58.2 58.5 59.7 61.3 Table 6. Dropping nodes in G using structured masks (Ours) vs MC-Dropout [10]. \u03c4 denotes the dropout rate. MC-Dropout [10] \u03c4 0.0 0.1 0.2 0.3 0.4 0.5 Ours MPJPE \u2193 60.2 60.9 61.5 61.8 62.4 63.1 58.2 Table 7. Varying the parameter \u03b1 that controls the amount of overlap between masks. \u00af \u03c4 denotes the rate of nodes masked in G. It plays the same role as the dropout rate \u03c4 for MC-Dropout [10]. \u03b1 1.0 1.2 1.4 1.8 2.0 2.5 3.0 3.5 \u00af \u03c4 0 0.17 0.25 0.33 0.5 0.60 0.67 0.72 MPJPE \u2193 60.2 60.1 59.6 58.2 59 61.2 63.6 65.4 Here, we study the impact of different parameters, i.e. NM, \u03b2 and \u03b1, of the mask generation process \u2126in the overall performance of our proposed method (Refer to Section \u00a7 3.3.1 in the main text for more details) on the Human 3.6M dataset [13] in the semi-supervised setup. Structured Masks [9] vs MC-Dropout [10]. Recall that we use structured masks to drop nodes from the spatio-temporal graph G to produce \u00af G, which is then fed to the refinement network. Table 6 shows the impact of randomly dropping graph nodes, as in MC-Dropout [10], with a dropout rate of \u03c4. Hence, \u03c4 = 0.0 means that no nodes are dropped. We do better for all values of \u03c4. Mask Overlap (\u03b1 parameter) In Table 7, we report the impact of varying the \u03b1, the parameter that controls the amount of overlap between the generated masks M i \u2208M. It also decides the number of ones (i.e. \u03b2) in each of the masks M i . All the nodes are present in the graph \u00af G when \u03b1 is set to 1. As we increase the value of \u03b1, more nodes are structurally dropped from the graph G to obtain \u00af G, with the lowest error obtained when \u03b1 = 1.8. As we further increase \u03b1, more nodes are dropped from G. This results in not having sufficient number of nodes in \u00af G that are needed to preserve the spatial and temporal dependencies between the nodes, leading to higher error. Number of parameters (NM parameter) Fig. 7 shows the performance of our approach as a function of NM, the number of masks in M. For NM = 0, we do not Table 8. Quantitative results Human3.6M (Fully-supervised). Methods MPJPE \u2193 NMPJE \u2193 PMPJE \u2193 Rogez et al. [43] 87.7 71.6 Rhodin et al. [42] 66.8 Zhou et al. [53] 64.9 Martinez et al. [31] 62.9 52.1 Sun et al. [45] 59.6 Yang et al. [50] 58.6 Pavlakos et al. [36] 56.2 Habibie et al. [11] 65.7 Kocabas et al. [21] 51.8 51.6 45.0 Iqbal et al. [15] 50.2 49.9 36.9 Kundu et al. [22] 50 Roy et al. [44] 55.3 52.4 44.2 Ci et al. [7] 52.7 Pavllo et al. [38] 51.8 40.0 Liu et al. [29] 52.4 Iskakov et al. [16] (vol.) 49.9 Cai et al. [1] 50.6 Zeng et al. [51] 49.9 Zou et al. [54] 49.4 39.1 Xu et al. [49] 51.9 Ours 51.0 50.2 39.4 use any mask over the graph G, thereby indicating that none of the nodes are masked in G to obtain \u00af G. Initially the performance degrades as we increase the number of masks NM. However we see a boost in the performance from NM = 8 as the generated masks become more diverse with the best result obtained for NM = 32. This in turn aids our networks to efficiently model different forms of occlusions. The error plateaus after that as the masks are not diverse enough to capture any new occlusion pattern. 5. Quantitative Results Fully Supervised We now evaluate our approach on the Human 3.6M and MPI-INF-3DHP datasets in the fully supervised setup: We use all the 2D and 3D ground truth training annotations that are provided. We report the results for H36M and MPI in Table 8 and 9. To generate the numbers for [44], we used our own implementation. The others are the published ones. Here, the result are more mixed. Our approach does well overall but the methods of [1, 3, 15, 51, 54] outperform us on some of measures in one of the two datasets. We attribute this to the following differences: First, a pipeline such as that of [54] relies on a Cascaded Pyramid Network 2D point detector [5], which is reported to be more powerful that the one we use [44]. We therefore tried using it but this did not change the overall performance of our apTable 9. Quantitative results MPI-INF-3DHP (Fully-supervised). Best results are shown in bold.\u2020 indicates cross dataset evaluation without further fine-tuning. Method 3DPCK\u2191 MPJPE\u2193 Mehta et al. [32] 75.7 117.6 Mehta et al. [33] 76.6 124.7 Pavllo et al. [38] 86.0 84.0 Chen et al. [3] 87.9 78.8 Zeng et al. [51]\u2020 77.6 Ci et al. [7]\u2020 74.0 Xu et al. [49] \u2020 80.1 Zou et al. [54] 86.1 Ours 85.6 78.1 Table 10. A comparative study of the performance of our proposed method using the 2D detections of Roy et al. [44] vs 2D Mocap key-points on the Human 3.6M dataset. Method MPJPE \u2193 NMPJPE \u2193 PMPJPE \u2193 Roy et al. [44] 51.0 50.2 39.4 Mocap 42.5 43.0 33.8 proach. This suggests that we need to use a more complex deeper backbone network similar to the one used in [54] to take advantage of it. Second, the method of [15] leverages additional datasets in training of their estimation networks, while the approaches of [1, 51, 54] enforce spatial constraints on the weights learned by the GCNN based estimation networks. We do neither of these things, but they could be integrated into our own GCNNs. In short, even though our network operates under more challenging conditions, it still delivers comparable results, which confirms the power of our occlusion-handling scheme. Moreover, we do not enforce any additional weight modulation and sharing practices of [1, 51, 54], which are key for their good performance in the fully supervised setup. Furthermore, the methods of [1, 3, 51, 54] have not been demonstrated in the semi-supervised framework and it is not entirely clear what they would do in this training mode. 6. Limitations A limitation of our proposed approach is that it relies on a pre-trained joint 2D detector [44], whose effectiveness or lack thereof directly impacts our final results. To demonstrate this, we ran an experiment in which we replaced the 2D detections by their ground-truth values and report the results in Table 10. Unsurprisingly, the metrics are substantially improved. This points toward the fact that the 2D detector should be trained as well and made part of the trainable end-to-end pipeline. 7. Conclusion We have proposed an effective approach to enhancing the robustness to occlusions of a single-view 3D human pose estimation network. To this end, we perform graph convolutions over a spatio-temporal graph defined on the 3D joints predicted by a lifting network. During training, we use structured binary masks to disable some nodes together with the corresponding edges. This mimics the fact some joints can be hidden over a given period of time and trains our lifting network to be resilient to that. Our experiments show that this simple method delivers excellent results and enables us to outperform more complex state-of-the-art methods on semi-supervised scenarios. However, they also show that some of the priors that these methods exploit could be profitably incorporated into our framework for a further performance boost. We will focus on this in future work."
+                },
+                {
+                    "url": "http://arxiv.org/abs/2003.07581v1",
+                    "title": "Weakly-Supervised 3D Human Pose Learning via Multi-view Images in the Wild",
+                    "abstract": "One major challenge for monocular 3D human pose estimation in-the-wild is the\nacquisition of training data that contains unconstrained images annotated with\naccurate 3D poses. In this paper, we address this challenge by proposing a\nweakly-supervised approach that does not require 3D annotations and learns to\nestimate 3D poses from unlabeled multi-view data, which can be acquired easily\nin in-the-wild environments. We propose a novel end-to-end learning framework\nthat enables weakly-supervised training using multi-view consistency. Since\nmulti-view consistency is prone to degenerated solutions, we adopt a 2.5D pose\nrepresentation and propose a novel objective function that can only be\nminimized when the predictions of the trained model are consistent and\nplausible across all camera views. We evaluate our proposed approach on two\nlarge scale datasets (Human3.6M and MPII-INF-3DHP) where it achieves\nstate-of-the-art performance among semi-/weakly-supervised methods.",
+                    "authors": "Umar Iqbal, Pavlo Molchanov, Jan Kautz",
+                    "published": "2020-03-17",
+                    "updated": "2020-03-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.09554v3",
+                    "title": "TransFusion: Cross-view Fusion with Transformer for 3D Human Pose Estimation",
+                    "abstract": "Estimating the 2D human poses in each view is typically the first step in\ncalibrated multi-view 3D pose estimation. But the performance of 2D pose\ndetectors suffers from challenging situations such as occlusions and oblique\nviewing angles. To address these challenges, previous works derive\npoint-to-point correspondences between different views from epipolar geometry\nand utilize the correspondences to merge prediction heatmaps or feature\nrepresentations. Instead of post-prediction merge/calibration, here we\nintroduce a transformer framework for multi-view 3D pose estimation, aiming at\ndirectly improving individual 2D predictors by integrating information from\ndifferent views. Inspired by previous multi-modal transformers, we design a\nunified transformer architecture, named TransFusion, to fuse cues from both\ncurrent views and neighboring views. Moreover, we propose the concept of\nepipolar field to encode 3D positional information into the transformer model.\nThe 3D position encoding guided by the epipolar field provides an efficient way\nof encoding correspondences between pixels of different views. Experiments on\nHuman 3.6M and Ski-Pose show that our method is more efficient and has\nconsistent improvements compared to other fusion methods. Specifically, we\nachieve 25.8 mm MPJPE on Human 3.6M with only 5M parameters on 256 x 256\nresolution.",
+                    "authors": "Haoyu Ma, Liangjian Chen, Deying Kong, Zhe Wang, Xingwei Liu, Hao Tang, Xiangyi Yan, Yusheng Xie, Shih-Yao Lin, Xiaohui Xie",
+                    "published": "2021-10-18",
+                    "updated": "2021-12-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1704.02447v2",
+                    "title": "Towards 3D Human Pose Estimation in the Wild: a Weakly-supervised Approach",
+                    "abstract": "In this paper, we study the task of 3D human pose estimation in the wild.\nThis task is challenging due to lack of training data, as existing datasets are\neither in the wild images with 2D pose or in the lab images with 3D pose.\n  We propose a weakly-supervised transfer learning method that uses mixed 2D\nand 3D labels in a unified deep neutral network that presents two-stage\ncascaded structure. Our network augments a state-of-the-art 2D pose estimation\nsub-network with a 3D depth regression sub-network. Unlike previous two stage\napproaches that train the two sub-networks sequentially and separately, our\ntraining is end-to-end and fully exploits the correlation between the 2D pose\nand depth estimation sub-tasks. The deep features are better learnt through\nshared representations. In doing so, the 3D pose labels in controlled lab\nenvironments are transferred to in the wild images. In addition, we introduce a\n3D geometric constraint to regularize the 3D pose prediction, which is\neffective in the absence of ground truth depth labels. Our method achieves\ncompetitive results on both 2D and 3D benchmarks.",
+                    "authors": "Xingyi Zhou, Qixing Huang, Xiao Sun, Xiangyang Xue, Yichen Wei",
+                    "published": "2017-04-08",
+                    "updated": "2017-07-30",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08334v2",
+                    "title": "Masksembles for Uncertainty Estimation",
+                    "abstract": "Deep neural networks have amply demonstrated their prowess but estimating the\nreliability of their predictions remains challenging. Deep Ensembles are widely\nconsidered as being one of the best methods for generating uncertainty\nestimates but are very expensive to train and evaluate. MC-Dropout is another\npopular alternative, which is less expensive, but also less reliable. Our\ncentral intuition is that there is a continuous spectrum of ensemble-like\nmodels of which MC-Dropout and Deep Ensembles are extreme examples. The first\nuses an effectively infinite number of highly correlated models while the\nsecond relies on a finite number of independent models.\n  To combine the benefits of both, we introduce Masksembles. Instead of\nrandomly dropping parts of the network as in MC-dropout, Masksemble relies on a\nfixed number of binary masks, which are parameterized in a way that allows to\nchange correlations between individual models. Namely, by controlling the\noverlap between the masks and their density one can choose the optimal\nconfiguration for the task at hand. This leads to a simple and easy to\nimplement method with performance on par with Ensembles at a fraction of the\ncost. We experimentally validate Masksembles on two widely used datasets,\nCIFAR10 and ImageNet.",
+                    "authors": "Nikita Durasov, Timur Bagautdinov, Pierre Baque, Pascal Fua",
+                    "published": "2020-12-15",
+                    "updated": "2021-06-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.05317v1",
+                    "title": "Deep Kinematic Pose Regression",
+                    "abstract": "Learning articulated object pose is inherently difficult because the pose is\nhigh dimensional but has many structural constraints. Most existing work do not\nmodel such constraints and does not guarantee the geometric validity of their\npose estimation, therefore requiring a post-processing to recover the correct\ngeometry if desired, which is cumbersome and sub-optimal. In this work, we\npropose to directly embed a kinematic object model into the deep neutral\nnetwork learning for general articulated object pose estimation. The kinematic\nfunction is defined on the appropriately parameterized object motion variables.\nIt is differentiable and can be used in the gradient descent based optimization\nin network training. The prior knowledge on the object geometric model is fully\nexploited and the structure is guaranteed to be valid. We show convincing\nexperiment results on a toy example and the 3D human pose estimation problem.\nFor the latter we achieve state-of-the-art result on Human3.6M dataset.",
+                    "authors": "Xingyi Zhou, Xiao Sun, Wei Zhang, Shuang Liang, Yichen Wei",
+                    "published": "2016-09-17",
+                    "updated": "2016-09-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.00389v2",
+                    "title": "Adversarial PoseNet: A Structure-aware Convolutional Network for Human Pose Estimation",
+                    "abstract": "For human pose estimation in monocular images, joint occlusions and\noverlapping upon human bodies often result in deviated pose predictions. Under\nthese circumstances, biologically implausible pose predictions may be produced.\nIn contrast, human vision is able to predict poses by exploiting geometric\nconstraints of joint inter-connectivity. To address the problem by\nincorporating priors about the structure of human bodies, we propose a novel\nstructure-aware convolutional network to implicitly take such priors into\naccount during training of the deep network. Explicit learning of such\nconstraints is typically challenging. Instead, we design discriminators to\ndistinguish the real poses from the fake ones (such as biologically implausible\nones). If the pose generator (G) generates results that the discriminator fails\nto distinguish from real ones, the network successfully learns the priors.",
+                    "authors": "Yu Chen, Chunhua Shen, Xiu-Shen Wei, Lingqiao Liu, Jian Yang",
+                    "published": "2017-04-30",
+                    "updated": "2017-05-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.01601v4",
+                    "title": "Learning 3D Human Dynamics from Video",
+                    "abstract": "From an image of a person in action, we can easily guess the 3D motion of the\nperson in the immediate past and future. This is because we have a mental model\nof 3D human dynamics that we have acquired from observing visual sequences of\nhumans in motion. We present a framework that can similarly learn a\nrepresentation of 3D dynamics of humans from video via a simple but effective\ntemporal encoding of image features. At test time, from video, the learned\ntemporal representation give rise to smooth 3D mesh predictions. From a single\nimage, our model can recover the current 3D mesh as well as its 3D past and\nfuture motion. Our approach is designed so it can learn from videos with 2D\npose annotations in a semi-supervised manner. Though annotated data is always\nlimited, there are millions of videos uploaded daily on the Internet. In this\nwork, we harvest this Internet-scale source of unlabeled data by training our\nmodel on unlabeled video with pseudo-ground truth 2D pose obtained from an\noff-the-shelf 2D pose detector. Our experiments show that adding more videos\nwith pseudo-ground truth 2D pose monotonically improves 3D prediction\nperformance. We evaluate our model, Human Mesh and Motion Recovery (HMMR), on\nthe recent challenging dataset of 3D Poses in the Wild and obtain\nstate-of-the-art performance on the 3D prediction task without any fine-tuning.\nThe project website with video, code, and data can be found at\nhttps://akanazawa.github.io/human_dynamics/.",
+                    "authors": "Angjoo Kanazawa, Jason Y. Zhang, Panna Felsen, Jitendra Malik",
+                    "published": "2018-12-04",
+                    "updated": "2019-09-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.11166v3",
+                    "title": "Adversarial Inverse Graphics Networks: Learning 2D-to-3D Lifting and Image-to-Image Translation from Unpaired Supervision",
+                    "abstract": "Researchers have developed excellent feed-forward models that learn to map\nimages to desired outputs, such as to the images' latent factors, or to other\nimages, using supervised learning. Learning such mappings from unlabelled data,\nor improving upon supervised models by exploiting unlabelled data, remains\nelusive. We argue that there are two important parts to learning without\nannotations: (i) matching the predictions to the input observations, and (ii)\nmatching the predictions to known priors. We propose Adversarial Inverse\nGraphics networks (AIGNs): weakly supervised neural network models that combine\nfeedback from rendering their predictions, with distribution matching between\ntheir predictions and a collection of ground-truth factors. We apply AIGNs to\n3D human pose estimation and 3D structure and egomotion estimation, and\noutperform models supervised by only paired annotations. We further apply AIGNs\nto facial image transformation using super-resolution and inpainting renderers,\nwhile deliberately adding biases in the ground-truth datasets. Our model\nseamlessly incorporates such biases, rendering input faces towards young, old,\nfeminine, masculine or Tom Cruise-like equivalents (depending on the chosen\nbias), or adding lip and nose augmentations while inpainting concealed lips and\nnoses.",
+                    "authors": "Hsiao-Yu Fish Tung, Adam W. Harley, William Seto, Katerina Fragkiadaki",
+                    "published": "2017-05-31",
+                    "updated": "2017-09-02",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1705.07664v2",
+                    "title": "CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters",
+                    "abstract": "The rise of graph-structured data such as social networks, regulatory\nnetworks, citation graphs, and functional brain networks, in combination with\nresounding success of deep learning in various applications, has brought the\ninterest in generalizing deep learning models to non-Euclidean domains. In this\npaper, we introduce a new spectral domain convolutional architecture for deep\nlearning on graphs. The core ingredient of our model is a new class of\nparametric rational complex functions (Cayley polynomials) allowing to\nefficiently compute spectral filters on graphs that specialize on frequency\nbands of interest. Our model generates rich spectral filters that are localized\nin space, scales linearly with the size of the input data for\nsparsely-connected graphs, and can handle different constructions of Laplacian\noperators. Extensive experimental results show the superior performance of our\napproach, in comparison to other spectral domain convolutional architectures,\non spectral image classification, community detection, vertex classification\nand matrix completion tasks.",
+                    "authors": "Ron Levie, Federico Monti, Xavier Bresson, Michael M. Bronstein",
+                    "published": "2017-05-22",
+                    "updated": "2018-10-31",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1611.07828v2",
+                    "title": "Coarse-to-Fine Volumetric Prediction for Single-Image 3D Human Pose",
+                    "abstract": "This paper addresses the challenge of 3D human pose estimation from a single\ncolor image. Despite the general success of the end-to-end learning paradigm,\ntop performing approaches employ a two-step solution consisting of a\nConvolutional Network (ConvNet) for 2D joint localization and a subsequent\noptimization step to recover 3D pose. In this paper, we identify the\nrepresentation of 3D pose as a critical issue with current ConvNet approaches\nand make two important contributions towards validating the value of end-to-end\nlearning for this task. First, we propose a fine discretization of the 3D space\naround the subject and train a ConvNet to predict per voxel likelihoods for\neach joint. This creates a natural representation for 3D pose and greatly\nimproves performance over the direct regression of joint coordinates. Second,\nto further improve upon initial estimates, we employ a coarse-to-fine\nprediction scheme. This step addresses the large dimensionality increase and\nenables iterative refinement and repeated processing of the image features. The\nproposed approach outperforms all state-of-the-art methods on standard\nbenchmarks achieving a relative error reduction greater than 30% on average.\nAdditionally, we investigate using our volumetric representation in a related\narchitecture which is suboptimal compared to our end-to-end approach, but is of\npractical interest, since it enables training when no image with corresponding\n3D groundtruth is available, and allows us to present compelling results for\nin-the-wild images.",
+                    "authors": "Georgios Pavlakos, Xiaowei Zhou, Konstantinos G. Derpanis, Kostas Daniilidis",
+                    "published": "2016-11-23",
+                    "updated": "2017-07-26",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.02907v4",
+                    "title": "Semi-Supervised Classification with Graph Convolutional Networks",
+                    "abstract": "We present a scalable approach for semi-supervised learning on\ngraph-structured data that is based on an efficient variant of convolutional\nneural networks which operate directly on graphs. We motivate the choice of our\nconvolutional architecture via a localized first-order approximation of\nspectral graph convolutions. Our model scales linearly in the number of graph\nedges and learns hidden layer representations that encode both local graph\nstructure and features of nodes. In a number of experiments on citation\nnetworks and on a knowledge graph dataset we demonstrate that our approach\noutperforms related methods by a significant margin.",
+                    "authors": "Thomas N. Kipf, Max Welling",
+                    "published": "2016-09-09",
+                    "updated": "2017-02-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1803.04775v2",
+                    "title": "Learning Monocular 3D Human Pose Estimation from Multi-view Images",
+                    "abstract": "Accurate 3D human pose estimation from single images is possible with\nsophisticated deep-net architectures that have been trained on very large\ndatasets. However, this still leaves open the problem of capturing motions for\nwhich no such database exists. Manual annotation is tedious, slow, and\nerror-prone. In this paper, we propose to replace most of the annotations by\nthe use of multiple views, at training time only. Specifically, we train the\nsystem to predict the same pose in all views. Such a consistency constraint is\nnecessary but not sufficient to predict accurate poses. We therefore complement\nit with a supervised loss aiming to predict the correct pose in a small set of\nlabeled images, and with a regularization term that penalizes drift from\ninitial predictions. Furthermore, we propose a method to estimate camera pose\njointly with human pose, which lets us utilize multi-view footage where\ncalibration is difficult, e.g., for pan-tilt or moving handheld cameras. We\ndemonstrate the effectiveness of our approach on established benchmarks, as\nwell as on a new Ski dataset with rotating cameras and expert ski motion, for\nwhich annotations are truly hard to obtain.",
+                    "authors": "Helge Rhodin, J\u00f6rg Sp\u00f6rri, Isinsu Katircioglu, Victor Constantin, Fr\u00e9d\u00e9ric Meyer, Erich M\u00fcller, Mathieu Salzmann, Pascal Fua",
+                    "published": "2018-03-13",
+                    "updated": "2018-03-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.05293v3",
+                    "title": "Multiview-Consistent Semi-Supervised Learning for 3D Human Pose Estimation",
+                    "abstract": "The best performing methods for 3D human pose estimation from monocular\nimages require large amounts of in-the-wild 2D and controlled 3D pose annotated\ndatasets which are costly and require sophisticated systems to acquire. To\nreduce this annotation dependency, we propose Multiview-Consistent Semi\nSupervised Learning (MCSS) framework that utilizes similarity in pose\ninformation from unannotated, uncalibrated but synchronized multi-view videos\nof human motions as additional weak supervision signal to guide 3D human pose\nregression. Our framework applies hard-negative mining based on temporal\nrelations in multi-view videos to arrive at a multi-view consistent pose\nembedding. When jointly trained with limited 3D pose annotations, our approach\nimproves the baseline by 25% and state-of-the-art by 8.7%, whilst using\nsubstantially smaller networks. Lastly, but importantly, we demonstrate the\nadvantages of the learned embedding and establish view-invariant pose retrieval\nbenchmarks on two popular, publicly available multi-view human pose datasets,\nHuman 3.6M and MPI-INF-3DHP, to facilitate future research.",
+                    "authors": "Rahul Mitra, Nitesh B. Gundavarapu, Abhishek Sharma, Arjun Jain",
+                    "published": "2019-08-14",
+                    "updated": "2020-02-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1811.11742v2",
+                    "title": "3D human pose estimation in video with temporal convolutions and semi-supervised training",
+                    "abstract": "In this work, we demonstrate that 3D poses in video can be effectively\nestimated with a fully convolutional model based on dilated temporal\nconvolutions over 2D keypoints. We also introduce back-projection, a simple and\neffective semi-supervised training method that leverages unlabeled video data.\nWe start with predicted 2D keypoints for unlabeled video, then estimate 3D\nposes and finally back-project to the input 2D keypoints. In the supervised\nsetting, our fully-convolutional model outperforms the previous best result\nfrom the literature by 6 mm mean per-joint position error on Human3.6M,\ncorresponding to an error reduction of 11%, and the model also shows\nsignificant improvements on HumanEva-I. Moreover, experiments with\nback-projection show that it comfortably outperforms previous state-of-the-art\nresults in semi-supervised settings where labeled data is scarce. Code and\nmodels are available at https://github.com/facebookresearch/VideoPose3D",
+                    "authors": "Dario Pavllo, Christoph Feichtenhofer, David Grangier, Michael Auli",
+                    "published": "2018-11-28",
+                    "updated": "2019-03-29",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.04812v1",
+                    "title": "Unsupervised 3D Pose Estimation with Geometric Self-Supervision",
+                    "abstract": "We present an unsupervised learning approach to recover 3D human pose from 2D\nskeletal joints extracted from a single image. Our method does not require any\nmulti-view image data, 3D skeletons, correspondences between 2D-3D points, or\nuse previously learned 3D priors during training. A lifting network accepts 2D\nlandmarks as inputs and generates a corresponding 3D skeleton estimate. During\ntraining, the recovered 3D skeleton is reprojected on random camera viewpoints\nto generate new \"synthetic\" 2D poses. By lifting the synthetic 2D poses back to\n3D and re-projecting them in the original camera view, we can define\nself-consistency loss both in 3D and in 2D. The training can thus be self\nsupervised by exploiting the geometric self-consistency of the\nlift-reproject-lift process. We show that self-consistency alone is not\nsufficient to generate realistic skeletons, however adding a 2D pose\ndiscriminator enables the lifter to output valid 3D poses. Additionally, to\nlearn from 2D poses \"in the wild\", we train an unsupervised 2D domain adapter\nnetwork to allow for an expansion of 2D data. This improves results and\ndemonstrates the usefulness of 2D pose data for unsupervised 3D lifting.\nResults on Human3.6M dataset for 3D human pose estimation demonstrate that our\napproach improves upon the previous unsupervised methods by 30% and outperforms\nmany weakly supervised approaches that explicitly use 3D data.",
+                    "authors": "Ching-Hang Chen, Ambrish Tyagi, Amit Agrawal, Dylan Drover, Rohith MV, Stefan Stojanov, James M. Rehg",
+                    "published": "2019-04-09",
+                    "updated": "2019-04-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1606.09375v3",
+                    "title": "Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering",
+                    "abstract": "In this work, we are interested in generalizing convolutional neural networks\n(CNNs) from low-dimensional regular grids, where image, video and speech are\nrepresented, to high-dimensional irregular domains, such as social networks,\nbrain connectomes or words' embedding, represented by graphs. We present a\nformulation of CNNs in the context of spectral graph theory, which provides the\nnecessary mathematical background and efficient numerical schemes to design\nfast localized convolutional filters on graphs. Importantly, the proposed\ntechnique offers the same linear computational complexity and constant learning\ncomplexity as classical CNNs, while being universal to any graph structure.\nExperiments on MNIST and 20NEWS demonstrate the ability of this novel deep\nlearning system to learn local, stationary, and compositional features on\ngraphs.",
+                    "authors": "Micha\u00ebl Defferrard, Xavier Bresson, Pierre Vandergheynst",
+                    "published": "2016-06-30",
+                    "updated": "2017-02-05",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1508.06708v1",
+                    "title": "Maximum-Margin Structured Learning with Deep Networks for 3D Human Pose Estimation",
+                    "abstract": "This paper focuses on structured-output learning using deep neural networks\nfor 3D human pose estimation from monocular images. Our network takes an image\nand 3D pose as inputs and outputs a score value, which is high when the\nimage-pose pair matches and low otherwise. The network structure consists of a\nconvolutional neural network for image feature extraction, followed by two\nsub-networks for transforming the image features and pose into a joint\nembedding. The score function is then the dot-product between the image and\npose embeddings. The image-pose embedding and score function are jointly\ntrained using a maximum-margin cost function. Our proposed framework can be\ninterpreted as a special form of structured support vector machines where the\njoint feature space is discriminatively learned using deep neural networks. We\ntest our framework on the Human3.6m dataset and obtain state-of-the-art results\ncompared to other recent methods. Finally, we present visualizations of the\nimage-pose embedding space, demonstrating the network has learned a high-level\nembedding of body-orientation and pose-configuration.",
+                    "authors": "Sijin Li, Weichen Zhang, Antoni B. Chan",
+                    "published": "2015-08-27",
+                    "updated": "2015-08-27",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.08585v4",
+                    "title": "Exploiting temporal information for 3D pose estimation",
+                    "abstract": "In this work, we address the problem of 3D human pose estimation from a\nsequence of 2D human poses. Although the recent success of deep networks has\nled many state-of-the-art methods for 3D pose estimation to train deep networks\nend-to-end to predict from images directly, the top-performing approaches have\nshown the effectiveness of dividing the task of 3D pose estimation into two\nsteps: using a state-of-the-art 2D pose estimator to estimate the 2D pose from\nimages and then mapping them into 3D space. They also showed that a\nlow-dimensional representation like 2D locations of a set of joints can be\ndiscriminative enough to estimate 3D pose with high accuracy. However,\nestimation of 3D pose for individual frames leads to temporally incoherent\nestimates due to independent error in each frame causing jitter. Therefore, in\nthis work we utilize the temporal information across a sequence of 2D joint\nlocations to estimate a sequence of 3D poses. We designed a\nsequence-to-sequence network composed of layer-normalized LSTM units with\nshortcut connections connecting the input to the output on the decoder side and\nimposed temporal smoothness constraint during training. We found that the\nknowledge of temporal consistency improves the best reported result on\nHuman3.6M dataset by approximately $12.2\\%$ and helps our network to recover\ntemporally consistent 3D poses over a sequence of images even when the 2D pose\ndetector fails.",
+                    "authors": "Mir Rayat Imtiaz Hossain, James J. Little",
+                    "published": "2017-11-23",
+                    "updated": "2018-09-12",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2007.09389v1",
+                    "title": "SRNet: Improving Generalization in 3D Human Pose Estimation with a Split-and-Recombine Approach",
+                    "abstract": "Human poses that are rare or unseen in a training set are challenging for a\nnetwork to predict. Similar to the long-tailed distribution problem in visual\nrecognition, the small number of examples for such poses limits the ability of\nnetworks to model them. Interestingly, local pose distributions suffer less\nfrom the long-tail problem, i.e., local joint configurations within a rare pose\nmay appear within other poses in the training set, making them less rare. We\npropose to take advantage of this fact for better generalization to rare and\nunseen poses. To be specific, our method splits the body into local regions and\nprocesses them in separate network branches, utilizing the property that a\njoint position depends mainly on the joints within its local body region.\nGlobal coherence is maintained by recombining the global context from the rest\nof the body into each branch as a low-dimensional vector. With the reduced\ndimensionality of less relevant body areas, the training set distribution\nwithin network branches more closely reflects the statistics of local poses\ninstead of global body poses, without sacrificing information important for\njoint inference. The proposed split-and-recombine approach, called SRNet, can\nbe easily adapted to both single-image and temporal models, and it leads to\nappreciable improvements in the prediction of rare and unseen poses.",
+                    "authors": "Ailing Zeng, Xiao Sun, Fuyang Huang, Minhao Liu, Qiang Xu, Stephen Lin",
+                    "published": "2020-07-18",
+                    "updated": "2020-07-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1605.05180v1",
+                    "title": "Structured Prediction of 3D Human Pose with Deep Neural Networks",
+                    "abstract": "Most recent approaches to monocular 3D pose estimation rely on Deep Learning.\nThey either train a Convolutional Neural Network to directly regress from image\nto 3D pose, which ignores the dependencies between human joints, or model these\ndependencies via a max-margin structured learning framework, which involves a\nhigh computational cost at inference time.\n  In this paper, we introduce a Deep Learning regression architecture for\nstructured prediction of 3D human pose from monocular images that relies on an\novercomplete auto-encoder to learn a high-dimensional latent pose\nrepresentation and account for joint dependencies. We demonstrate that our\napproach outperforms state-of-the-art ones both in terms of structure\npreservation and prediction accuracy.",
+                    "authors": "Bugra Tekin, Isinsu Katircioglu, Mathieu Salzmann, Vincent Lepetit, Pascal Fua",
+                    "published": "2016-05-17",
+                    "updated": "2016-05-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1905.05754v1",
+                    "title": "Learnable Triangulation of Human Pose",
+                    "abstract": "We present two novel solutions for multi-view 3D human pose estimation based\non new learnable triangulation methods that combine 3D information from\nmultiple 2D views. The first (baseline) solution is a basic differentiable\nalgebraic triangulation with an addition of confidence weights estimated from\nthe input images. The second solution is based on a novel method of volumetric\naggregation from intermediate 2D backbone feature maps. The aggregated volume\nis then refined via 3D convolutions that produce final 3D joint heatmaps and\nallow modelling a human pose prior. Crucially, both approaches are end-to-end\ndifferentiable, which allows us to directly optimize the target metric. We\ndemonstrate transferability of the solutions across datasets and considerably\nimprove the multi-view state of the art on the Human3.6M dataset. Video\ndemonstration, annotations and additional materials will be posted on our\nproject page (https://saic-violet.github.io/learnable-triangulation).",
+                    "authors": "Karim Iskakov, Egor Burkov, Victor Lempitsky, Yury Malkov",
+                    "published": "2019-05-14",
+                    "updated": "2019-05-14",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.08229v4",
+                    "title": "Integral Human Pose Regression",
+                    "abstract": "State-of-the-art human pose estimation methods are based on heat map\nrepresentation. In spite of the good performance, the representation has a few\nissues in nature, such as not differentiable and quantization error. This work\nshows that a simple integral operation relates and unifies the heat map\nrepresentation and joint regression, thus avoiding the above issues. It is\ndifferentiable, efficient, and compatible with any heat map based methods. Its\neffectiveness is convincingly validated via comprehensive ablation experiments\nunder various settings, specifically on 3D pose estimation, for the first time.",
+                    "authors": "Xiao Sun, Bin Xiao, Fangyin Wei, Shuang Liang, Yichen Wei",
+                    "published": "2017-11-22",
+                    "updated": "2018-09-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.16385v1",
+                    "title": "Graph Stacked Hourglass Networks for 3D Human Pose Estimation",
+                    "abstract": "In this paper, we propose a novel graph convolutional network architecture,\nGraph Stacked Hourglass Networks, for 2D-to-3D human pose estimation tasks. The\nproposed architecture consists of repeated encoder-decoder, in which\ngraph-structured features are processed across three different scales of human\nskeletal representations. This multi-scale architecture enables the model to\nlearn both local and global feature representations, which are critical for 3D\nhuman pose estimation. We also introduce a multi-level feature learning\napproach using different-depth intermediate features and show the performance\nimprovements that result from exploiting multi-scale, multi-level feature\nrepresentations. Extensive experiments are conducted to validate our approach,\nand the results show that our model outperforms the state-of-the-art.",
+                    "authors": "Tianhan Xu, Wataru Takano",
+                    "published": "2021-03-30",
+                    "updated": "2021-03-30",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.02330v2",
+                    "title": "Self-Supervised Learning of 3D Human Pose using Multi-view Geometry",
+                    "abstract": "Training accurate 3D human pose estimators requires large amount of 3D\nground-truth data which is costly to collect. Various weakly or self supervised\npose estimation methods have been proposed due to lack of 3D data.\nNevertheless, these methods, in addition to 2D ground-truth poses, require\neither additional supervision in various forms (e.g. unpaired 3D ground truth\ndata, a small subset of labels) or the camera parameters in multiview settings.\nTo address these problems, we present EpipolarPose, a self-supervised learning\nmethod for 3D human pose estimation, which does not need any 3D ground-truth\ndata or camera extrinsics. During training, EpipolarPose estimates 2D poses\nfrom multi-view images, and then, utilizes epipolar geometry to obtain a 3D\npose and camera geometry which are subsequently used to train a 3D pose\nestimator. We demonstrate the effectiveness of our approach on standard\nbenchmark datasets i.e. Human3.6M and MPI-INF-3DHP where we set the new\nstate-of-the-art among weakly/self-supervised methods. Furthermore, we propose\na new performance measure Pose Structure Score (PSS) which is a scale\ninvariant, structure aware measure to evaluate the structural plausibility of a\npose with respect to its ground truth. Code and pretrained models are available\nat https://github.com/mkocabas/EpipolarPose",
+                    "authors": "Muhammed Kocabas, Salih Karagoz, Emre Akbas",
+                    "published": "2019-03-06",
+                    "updated": "2019-04-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.15865v3",
+                    "title": "On Triangulation as a Form of Self-Supervision for 3D Human Pose Estimation",
+                    "abstract": "Supervised approaches to 3D pose estimation from single images are remarkably\neffective when labeled data is abundant. However, as the acquisition of\nground-truth 3D labels is labor intensive and time consuming, recent attention\nhas shifted towards semi- and weakly-supervised learning. Generating an\neffective form of supervision with little annotations still poses major\nchallenge in crowded scenes. In this paper we propose to impose multi-view\ngeometrical constraints by means of a weighted differentiable triangulation and\nuse it as a form of self-supervision when no labels are available. We therefore\ntrain a 2D pose estimator in such a way that its predictions correspond to the\nre-projection of the triangulated 3D pose and train an auxiliary network on\nthem to produce the final 3D poses. We complement the triangulation with a\nweighting mechanism that alleviates the impact of noisy predictions caused by\nself-occlusion or occlusion from other subjects. We demonstrate the\neffectiveness of our semi-supervised approach on Human3.6M and MPI-INF-3DHP\ndatasets, as well as on a new multi-view multi-person dataset that features\nocclusion.",
+                    "authors": "Soumava Kumar Roy, Leonardo Citraro, Sina Honari, Pascal Fua",
+                    "published": "2022-03-29",
+                    "updated": "2022-06-28",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.02128v1",
+                    "title": "Interaction Order Prediction for Temporal Graphs",
+                    "abstract": "Link prediction in graphs is a task that has been widely investigated. It has\nbeen applied in various domains such as knowledge graph completion,\ncontent/item recommendation, social network recommendations and so on. The\ninitial focus of most research was on link prediction in static graphs.\nHowever, there has recently been abundant work on modeling temporal graphs, and\nconsequently one of the tasks that has been researched is link prediction in\ntemporal graphs. However, most of the existing work does not focus on the order\nof link formation, and only predicts the existence of links. In this study, we\naim to predict the order of node interactions.",
+                    "authors": "Nayana Bannur, Mashrin Srivastava, Harsha Vardhan",
+                    "published": "2023-02-04",
+                    "updated": "2023-02-04",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.12843v1",
+                    "title": "An embedding-based distance for temporal graphs",
+                    "abstract": "We define a distance between temporal graphs based on graph embeddings built\nusing time-respecting random walks. We study both the case of matched graphs,\nwhen there exists a known relation between the nodes, and the unmatched case,\nwhen such a relation is unavailable and the graphs may be of different sizes.\nWe illustrate the interest of our distance definition, using both real and\nsynthetic temporal network data, by showing its ability to discriminate between\ngraphs with different structural and temporal properties. Leveraging\nstate-of-the-art machine learning techniques, we propose an efficient\nimplementation of distance computation that is viable for large-scale temporal\ngraphs.",
+                    "authors": "Lorenzo Dall'Amico, Alain Barrat, Ciro Cattuto",
+                    "published": "2024-01-23",
+                    "updated": "2024-01-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.07016v2",
+                    "title": "On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions",
+                    "abstract": "This work formalizes the associational task of predicting node attribute\nevolution in temporal graphs from the perspective of learning equivariant\nrepresentations. We show that node representations in temporal graphs can be\ncast into two distinct frameworks: (a) The most popular approach, which we\ndenote as time-and-graph, where equivariant graph (e.g., GNN) and sequence\n(e.g., RNN) representations are intertwined to represent the temporal evolution\nof node attributes in the graph; and (b) an approach that we denote as\ntime-then-graph, where the sequences describing the node and edge dynamics are\nrepresented first, then fed as node and edge attributes into a static\nequivariant graph representation that comes after. Interestingly, we show that\ntime-then-graph representations have an expressivity advantage over\ntime-and-graph representations when both use component GNNs that are not\nmost-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is\nnot necessarily to obtain state-of-the-art results, our experiments show that\ntime-then-graph methods are capable of achieving better performance and\nefficiency than state-of-the-art time-and-graph methods in some real-world\ntasks, thereby showcasing that the time-then-graph framework is a worthy\naddition to the graph ML toolbox.",
+                    "authors": "Jianfei Gao, Bruno Ribeiro",
+                    "published": "2021-03-12",
+                    "updated": "2023-03-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08514v2",
+                    "title": "Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction",
+                    "abstract": "Understanding crowd motion dynamics is critical to real-world applications,\ne.g., surveillance systems and autonomous driving. This is challenging because\nit requires effectively modeling the socially aware crowd spatial interaction\nand complex temporal dependencies. We believe attention is the most important\nfactor for trajectory prediction. In this paper, we present STAR, a\nSpatio-Temporal grAph tRansformer framework, which tackles trajectory\nprediction by only attention mechanisms. STAR models intra-graph crowd\ninteraction by TGConv, a novel Transformer-based graph convolution mechanism.\nThe inter-graph temporal dependencies are modeled by separate temporal\nTransformers. STAR captures complex spatio-temporal interactions by\ninterleaving between spatial and temporal Transformers. To calibrate the\ntemporal prediction for the long-lasting effect of disappeared pedestrians, we\nintroduce a read-writable external memory module, consistently being updated by\nthe temporal Transformer. We show that with only attention mechanism, STAR\nachieves state-of-the-art performance on 5 commonly used real-world pedestrian\nprediction datasets.",
+                    "authors": "Cunjun Yu, Xiao Ma, Jiawei Ren, Haiyu Zhao, Shuai Yi",
+                    "published": "2020-05-18",
+                    "updated": "2020-07-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.RO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.11244v1",
+                    "title": "Using Compressed Suffix-Arrays for a Compact Representation of Temporal-Graphs",
+                    "abstract": "Temporal graphs represent binary relationships that change along time. They\ncan model the dynamism of, for example, social and communication networks.\nTemporal graphs are defined as sets of contacts that are edges tagged with the\ntemporal intervals when they are active. This work explores the use of the\nCompressed Suffix Array (CSA), a well-known compact and self-indexed data\nstructure in the area of text indexing, to represent large temporal graphs. The\nnew structure, called Temporal Graph CSA (TGCSA), is experimentally compared\nwith the most competitive compact data structures in the state-of-the-art,\nnamely, EDGELOG and CET. The experimental results show that TGCSA obtains a\ngood space-time trade-off. It uses a reasonable space and is efficient for\nsolving complex temporal queries. Furthermore, TGCSA has wider expressive\ncapabilities than EDGELOG and CET, because it is able to represent temporal\ngraphs where contacts on an edge can temporally overlap.",
+                    "authors": "Nieves R. Brisaboa, Diego Caro, Antonio Fari\u00f1a, M. Andrea Rodriguez",
+                    "published": "2018-12-28",
+                    "updated": "2018-12-28",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.07503v1",
+                    "title": "Temporal Aggregation and Propagation Graph Neural Networks for Dynamic Representation",
+                    "abstract": "Temporal graphs exhibit dynamic interactions between nodes over continuous\ntime, whose topologies evolve with time elapsing.\n  The whole temporal neighborhood of nodes reveals the varying preferences of\nnodes.\n  However, previous works usually generate dynamic representation with limited\nneighbors for simplicity, which results in both inferior performance and high\nlatency of online inference.\n  Therefore, in this paper, we propose a novel method of temporal graph\nconvolution with the whole neighborhood, namely Temporal Aggregation and\nPropagation Graph Neural Networks (TAP-GNN).\n  Specifically, we firstly analyze the computational complexity of the dynamic\nrepresentation problem by unfolding the temporal graph in a message-passing\nparadigm.\n  The expensive complexity motivates us to design the AP (aggregation and\npropagation) block, which significantly reduces the repeated computation of\nhistorical neighbors.\n  The final TAP-GNN supports online inference in the graph stream scenario,\nwhich incorporates the temporal information into node embeddings with a\ntemporal activation function and a projection layer besides several AP blocks.\n  Experimental results on various real-life temporal networks show that our\nproposed TAP-GNN outperforms existing temporal graph methods by a large margin\nin terms of both predictive performance and online inference latency.\n  Our code is available at \\url{https://github.com/doujiang-zheng/TAP-GNN}.",
+                    "authors": "Tongya Zheng, Xinchao Wang, Zunlei Feng, Jie Song, Yunzhi Hao, Mingli Song, Xingen Wang, Xinyu Wang, Chun Chen",
+                    "published": "2023-04-15",
+                    "updated": "2023-04-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.05018v2",
+                    "title": "Time-varying Graph Learning Under Structured Temporal Priors",
+                    "abstract": "This paper endeavors to learn time-varying graphs by using structured\ntemporal priors that assume underlying relations between arbitrary two graphs\nin the graph sequence. Different from many existing chain structure based\nmethods in which the priors like temporal homogeneity can only describe the\nvariations of two consecutive graphs, we propose a structure named\n\\emph{temporal graph} to characterize the underlying real temporal relations.\nUnder this framework, the chain structure is actually a special case of our\ntemporal graph. We further proposed Alternating Direction Method of Multipliers\n(ADMM), a distributed algorithm, to solve the induced optimization problem.\nNumerical experiments demonstrate the superiorities of our method.",
+                    "authors": "Xiang Zhang, Qiao Wang",
+                    "published": "2021-10-11",
+                    "updated": "2022-02-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.SP"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.08889v3",
+                    "title": "Node Embedding over Temporal Graphs",
+                    "abstract": "In this work, we present a method for node embedding in temporal graphs. We\npropose an algorithm that learns the evolution of a temporal graph's nodes and\nedges over time and incorporates this dynamics in a temporal node embedding\nframework for different graph prediction tasks. We present a joint loss\nfunction that creates a temporal embedding of a node by learning to combine its\nhistorical temporal embeddings, such that it optimizes per given task (e.g.,\nlink prediction). The algorithm is initialized using static node embeddings,\nwhich are then aligned over the representations of a node at different time\npoints, and eventually adapted for the given task in a joint optimization. We\nevaluate the effectiveness of our approach over a variety of temporal graphs\nfor the two fundamental tasks of temporal link prediction and multi-label node\nclassification, comparing to competitive baselines and algorithmic\nalternatives. Our algorithm shows performance improvements across many of the\ndatasets and baselines and is found particularly effective for graphs that are\nless cohesive, with a lower clustering coefficient.",
+                    "authors": "Uriel Singer, Ido Guy, Kira Radinsky",
+                    "published": "2019-03-21",
+                    "updated": "2021-05-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1706.09480v1",
+                    "title": "A Temporal Tree Decomposition for Generating Temporal Graphs",
+                    "abstract": "Discovering the underlying structures present in large real world graphs is a\nfundamental scientific problem. Recent work at the intersection of formal\nlanguage theory and graph theory has found that a Hyperedge Replacement Grammar\n(HRG) can be extracted from a tree decomposition of any graph. This HRG can be\nused to generate new graphs that share properties that are similar to the\noriginal graph. Because the extracted HRG is directly dependent on the shape\nand contents of the of tree decomposition, it is unlikely that informative\ngraph-processes are actually being captured with the extraction algorithm. To\naddress this problem, the current work presents a new extraction algorithm\ncalled temporal HRG (tHRG) that learns HRG production rules from a temporal\ntree decomposition of the graph. We observe problems with the assumptions that\nare made in a temporal HRG model. In experiments on large real world networks,\nwe show and provide reasoning as to why tHRG does not perform as well as HRG\nand other graph generators.",
+                    "authors": "Corey Pennycuff, Salvador Aguinaga, Tim Weninger",
+                    "published": "2017-06-28",
+                    "updated": "2017-06-28",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.14199v2",
+                    "title": "MTRGL:Effective Temporal Correlation Discerning through Multi-modal Temporal Relational Graph Learning",
+                    "abstract": "In this study, we explore the synergy of deep learning and financial market\napplications, focusing on pair trading. This market-neutral strategy is\nintegral to quantitative finance and is apt for advanced deep-learning\ntechniques. A pivotal challenge in pair trading is discerning temporal\ncorrelations among entities, necessitating the integration of diverse data\nmodalities. Addressing this, we introduce a novel framework, Multi-modal\nTemporal Relation Graph Learning (MTRGL). MTRGL combines time series data and\ndiscrete features into a temporal graph and employs a memory-based temporal\ngraph neural network. This approach reframes temporal correlation\nidentification as a temporal graph link prediction task, which has shown\nempirical success. Our experiments on real-world datasets confirm the superior\nperformance of MTRGL, emphasizing its promise in refining automated pair\ntrading strategies.",
+                    "authors": "Junwei Su, Shan Wu, Jinhui Li",
+                    "published": "2024-01-25",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "econ.GN",
+                        "q-fin.EC",
+                        "q-fin.TR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13250v1",
+                    "title": "Keyword-Aware Relative Spatio-Temporal Graph Networks for Video Question Answering",
+                    "abstract": "The main challenge in video question answering (VideoQA) is to capture and\nunderstand the complex spatial and temporal relations between objects based on\ngiven questions. Existing graph-based methods for VideoQA usually ignore\nkeywords in questions and employ a simple graph to aggregate features without\nconsidering relative relations between objects, which may lead to inferior\nperformance. In this paper, we propose a Keyword-aware Relative Spatio-Temporal\n(KRST) graph network for VideoQA. First, to make question features aware of\nkeywords, we employ an attention mechanism to assign high weights to keywords\nduring question encoding. The keyword-aware question features are then used to\nguide video graph construction. Second, because relations are relative, we\nintegrate the relative relation modeling to better capture the spatio-temporal\ndynamics among object nodes. Moreover, we disentangle the spatio-temporal\nreasoning into an object-level spatial graph and a frame-level temporal graph,\nwhich reduces the impact of spatial and temporal relation reasoning on each\nother. Extensive experiments on the TGIF-QA, MSVD-QA and MSRVTT-QA datasets\ndemonstrate the superiority of our KRST over multiple state-of-the-art methods.",
+                    "authors": "Yi Cheng, Hehe Fan, Dongyun Lin, Ying Sun, Mohan Kankanhalli, Joo-Hwee Lim",
+                    "published": "2023-07-25",
+                    "updated": "2023-07-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.08312v2",
+                    "title": "ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks",
+                    "abstract": "Networks are a fundamental and flexible way of representing various complex\nsystems. Many domains such as communication, citation, procurement, biology,\nsocial media, and transportation can be modeled as a set of entities and their\nrelationships. Temporal networks are a specialization of general networks where\nthe temporal evolution of the system is as important to understand as the\nstructure of the entities and relationships. We present the Independent\nTemporal Motif (ITeM) to characterize temporal graphs from different domains.\nThe ITeMs are edge-disjoint temporal motifs that can be used to model the\nstructure and the evolution of the graph. For a given temporal graph, we\nproduce a feature vector of ITeM frequencies and apply this distribution to the\ntask of measuring the similarity of temporal graphs. We show that ITeM has\nhigher accuracy than other motif frequency-based approaches. We define various\nmetrics based on ITeM that reveal salient properties of a temporal network. We\nalso present importance sampling as a method for efficiently estimating the\nITeM counts. We evaluate our approach on both synthetic and real temporal\nnetworks.",
+                    "authors": "Sumit Purohit, Lawrence B. Holder, George Chin",
+                    "published": "2020-02-19",
+                    "updated": "2020-08-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02212v1",
+                    "title": "Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by\nattaching the time scope. Existing temporal knowledge graph question answering\n(TKGQA) models solely approach simple questions, owing to the prior assumption\nthat each question only contains a single temporal fact with explicit/implicit\ntemporal constraints. Hence, they perform poorly on questions which own\nmultiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint\n\\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts\n\\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly\nreasoning multiple temporal facts for accurately answering \\emph{complex}\ntemporal questions. Specifically, JMFRN first retrieves question-related\ntemporal facts from TKG for each entity of the given complex question. For\njoint reasoning, we design two different attention (\\ie entity-aware and\ntime-aware) modules, which are suitable for universal settings, to aggregate\nentities and timestamps information of retrieved facts. Moreover, to filter\nincorrect type answers, we introduce an additional answer type discrimination\ntask. Extensive experiments demonstrate our proposed method significantly\noutperforms the state-of-art on the well-known complex temporal question\nbenchmark TimeQuestions.",
+                    "authors": "Rikui Huang, Wei Wei, Xiaoye Qu, Wenfeng Xie, Xianling Mao, Dangyang Chen",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.05653v1",
+                    "title": "Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition",
+                    "abstract": "Accurate spatial-temporal traffic flow forecasting is essential for helping\ntraffic managers to take control measures and drivers to choose the optimal\ntravel routes. Recently, graph convolutional networks (GCNs) have been widely\nused in traffic flow prediction owing to their powerful ability to capture\nspatial-temporal dependencies. The design of the spatial-temporal graph\nadjacency matrix is a key to the success of GCNs, and it is still an open\nquestion. This paper proposes reconstructing the binary adjacency matrix via\ntensor decomposition, and a traffic flow forecasting method is proposed. First,\nwe reformulate the spatial-temporal fusion graph adjacency matrix into a\nthree-way adjacency tensor. Then, we reconstructed the adjacency tensor via\nTucker decomposition, wherein more informative and global spatial-temporal\ndependencies are encoded. Finally, a Spatial-temporal Synchronous Graph\nConvolutional module for localized spatial-temporal correlations learning and a\nDilated Convolution module for global correlations learning are assembled to\naggregate and learn the comprehensive spatial-temporal dependencies of the road\nnetwork. Experimental results on four open-access datasets demonstrate that the\nproposed model outperforms state-of-the-art approaches in terms of the\nprediction performance and computational cost.",
+                    "authors": "Qin Li, Xuan Yang, Yong Wang, Yuankai Wu, Deqiang He",
+                    "published": "2022-12-12",
+                    "updated": "2022-12-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.01012v1",
+                    "title": "Graph-Level Embedding for Time-Evolving Graphs",
+                    "abstract": "Graph representation learning (also known as network embedding) has been\nextensively researched with varying levels of granularity, ranging from nodes\nto graphs. While most prior work in this area focuses on node-level\nrepresentation, limited research has been conducted on graph-level embedding,\nparticularly for dynamic or temporal networks. However, learning\nlow-dimensional graph-level representations for dynamic networks is critical\nfor various downstream graph retrieval tasks such as temporal graph similarity\nranking, temporal graph isomorphism, and anomaly detection. In this paper, we\npresent a novel method for temporal graph-level embedding that addresses this\ngap. Our approach involves constructing a multilayer graph and using a modified\nrandom walk with temporal backtracking to generate temporal contexts for the\ngraph's nodes. We then train a \"document-level\" language model on these\ncontexts to generate graph-level embeddings. We evaluate our proposed model on\nfive publicly available datasets for the task of temporal graph similarity\nranking, and our model outperforms baseline methods. Our experimental results\ndemonstrate the effectiveness of our method in generating graph-level\nembeddings for dynamic networks.",
+                    "authors": "Lili Wang, Chenghan Huang, Weicheng Ma, Xinyuan Cao, Soroush Vosoughi",
+                    "published": "2023-06-01",
+                    "updated": "2023-06-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1306.0493v1",
+                    "title": "Graph Metrics for Temporal Networks",
+                    "abstract": "Temporal networks, i.e., networks in which the interactions among a set of\nelementary units change over time, can be modelled in terms of time-varying\ngraphs, which are time-ordered sequences of graphs over a set of nodes. In such\ngraphs, the concepts of node adjacency and reachability crucially depend on the\nexact temporal ordering of the links. Consequently, all the concepts and\nmetrics proposed and used for the characterisation of static complex networks\nhave to be redefined or appropriately extended to time-varying graphs, in order\nto take into account the effects of time ordering on causality. In this chapter\nwe discuss how to represent temporal networks and we review the definitions of\nwalks, paths, connectedness and connected components valid for graphs in which\nthe links fluctuate over time. We then focus on temporal node-node distance,\nand we discuss how to characterise link persistence and the temporal\nsmall-world behaviour in this class of networks. Finally, we discuss the\nextension of classic centrality measures, including closeness, betweenness and\nspectral centrality, to the case of time-varying graphs, and we review the work\non temporal motifs analysis and the definition of modularity for temporal\ngraphs.",
+                    "authors": "Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, Vito Latora",
+                    "published": "2013-06-03",
+                    "updated": "2013-06-03",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.03363v3",
+                    "title": "Spatio-Temporal Graph Scattering Transform",
+                    "abstract": "Although spatio-temporal graph neural networks have achieved great empirical\nsuccess in handling multiple correlated time series, they may be impractical in\nsome real-world scenarios due to a lack of sufficient high-quality training\ndata. Furthermore, spatio-temporal graph neural networks lack theoretical\ninterpretation. To address these issues, we put forth a novel mathematically\ndesigned framework to analyze spatio-temporal data. Our proposed\nspatio-temporal graph scattering transform (ST-GST) extends traditional\nscattering transforms to the spatio-temporal domain. It performs iterative\napplications of spatio-temporal graph wavelets and nonlinear activation\nfunctions, which can be viewed as a forward pass of spatio-temporal graph\nconvolutional networks without training. Since all the filter coefficients in\nST-GST are mathematically designed, it is promising for the real-world\nscenarios with limited training data, and also allows for a theoretical\nanalysis, which shows that the proposed ST-GST is stable to small perturbations\nof input signals and structures. Finally, our experiments show that i) ST-GST\noutperforms spatio-temporal graph convolutional networks by an increase of 35%\nin accuracy for MSR Action3D dataset; ii) it is better and computationally more\nefficient to design the transform based on separable spatio-temporal graphs\nthan the joint ones; and iii) the nonlinearity in ST-GST is critical to\nempirical performance.",
+                    "authors": "Chao Pan, Siheng Chen, Antonio Ortega",
+                    "published": "2020-12-06",
+                    "updated": "2021-02-09",
+                    "primary_cat": "eess.SP",
+                    "cats": [
+                        "eess.SP",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1912.03904v1",
+                    "title": "Weighted temporal event graphs",
+                    "abstract": "The times of temporal-network events and their correlations contain\ninformation on the function of the network and they influence dynamical\nprocesses taking place on it. To extract information out of correlated event\ntimes, techniques such as the analysis of temporal motifs have been developed.\nWe discuss a recently-introduced, more general framework that maps\ntemporal-network structure into static graphs while retaining information on\ntime-respecting paths and the time differences between their consequent events.\nThis framework builds on weighted temporal event graphs: directed, acyclic\ngraphs (DAGs) that contain a superposition of all temporal paths. We introduce\nthe reader to the temporal event-graph mapping and associated computational\nmethods and illustrate its use by applying the framework to temporal-network\npercolation.",
+                    "authors": "Jari Saram\u00e4ki, Mikko Kivel\u00e4, M\u00e1rton Karsai",
+                    "published": "2019-12-09",
+                    "updated": "2019-12-09",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.00278v1",
+                    "title": "An Introduction to Temporal Graphs: An Algorithmic Perspective",
+                    "abstract": "A \\emph{temporal graph} is, informally speaking, a graph that changes with\ntime. When time is discrete and only the relationships between the\nparticipating entities may change and not the entities themselves, a temporal\ngraph may be viewed as a sequence $G_1,G_2\\ldots,G_l$ of static graphs over the\nsame (static) set of nodes $V$. Though static graphs have been extensively\nstudied, for their temporal generalization we are still far from having a\nconcrete set of structural and algorithmic principles. Recent research shows\nthat many graph properties and problems become radically different and usually\nsubstantially more difficult when an extra time dimension in added to them.\nMoreover, there is already a rich and rapidly growing set of modern systems and\napplications that can be naturally modeled and studied via temporal graphs.\nThis, further motivates the need for the development of a temporal extension of\ngraph theory. We survey here recent results on temporal graphs and temporal\ngraph problems that have appeared in the Computer Science community.",
+                    "authors": "Othon Michail",
+                    "published": "2015-03-01",
+                    "updated": "2015-03-01",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS",
+                        "05C85, 05C40, 05C38, 05C78, 05C80, 68R10, 68M14, 68M10, 68W25"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.07993v2",
+                    "title": "RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion",
+                    "abstract": "Temporal factors are tied to the growth of facts in realistic applications,\nsuch as the progress of diseases and the development of political situation,\ntherefore, research on Temporal Knowledge Graph (TKG) attracks much attention.\nIn TKG, relation patterns inherent with temporality are required to be studied\nfor representation learning and reasoning across temporal facts. However,\nexisting methods can hardly model temporal relation patterns, nor can capture\nthe intrinsic connections between relations when evolving over time, lacking of\ninterpretability. In this paper, we propose a novel temporal modeling method\nwhich represents temporal entities as Rotations in Quaternion Vector Space\n(RotateQVS) and relations as complex vectors in Hamilton's quaternion space. We\ndemonstrate our method can model key patterns of relations in TKG, such as\nsymmetry, asymmetry, inverse, and can further capture time-evolved relations by\ntheory. Empirically, we show that our method can boost the performance of link\nprediction tasks over four temporal knowledge graph benchmarks.",
+                    "authors": "Kai Chen, Ye Wang, Yitong Li, Aiping Li",
+                    "published": "2022-03-15",
+                    "updated": "2022-03-17",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04350v2",
+                    "title": "Time-Variant Graph Classification",
+                    "abstract": "Graphs are commonly used to represent objects, such as images and text, for\npattern classification. In a dynamic world, an object may continuously evolve\nover time, and so does the graph extracted from the underlying object. These\nchanges in graph structure with respect to the temporal order present a new\nrepresentation of the graph, in which an object corresponds to a set of\ntime-variant graphs. In this paper, we formulate a novel time-variant graph\nclassification task and propose a new graph feature, called a graph-shapelet\npattern, for learning and classifying time-variant graphs. Graph-shapelet\npatterns are compact and discriminative graph transformation subsequences. A\ngraph-shapelet pattern can be regarded as a graphical extension of a shapelet\n-- a class of discriminative features designed for vector-based temporal data\nclassification. To discover graph-shapelet patterns, we propose to convert a\ntime-variant graph sequence into time-series data and use the discovered\nshapelets to find graph transformation subsequences as graph-shapelet patterns.\nBy converting each graph-shapelet pattern into a unique tokenized graph\ntransformation sequence, we can measure the similarity between two\ngraph-shapelet patterns and therefore classify time-variant graphs. Experiments\non both synthetic and real-world data demonstrate the superior performance of\nthe proposed algorithms.",
+                    "authors": "Haishuai Wang",
+                    "published": "2016-09-14",
+                    "updated": "2017-06-12",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.11979v1",
+                    "title": "MTGA: Multi-view Temporal Granularity aligned Aggregation for Event-based Lip-reading",
+                    "abstract": "Lip-reading is to utilize the visual information of the speaker's lip\nmovements to recognize words and sentences. Existing event-based lip-reading\nsolutions integrate different frame rate branches to learn spatio-temporal\nfeatures of varying granularities. However, aggregating events into event\nframes inevitably leads to the loss of fine-grained temporal information within\nframes. To remedy this drawback, we propose a novel framework termed Multi-view\nTemporal Granularity aligned Aggregation (MTGA). Specifically, we first present\na novel event representation method, namely time-segmented voxel graph list,\nwhere the most significant local voxels are temporally connected into a graph\nlist. Then we design a spatio-temporal fusion module based on temporal\ngranularity alignment, where the global spatial features extracted from event\nframes, together with the local relative spatial and temporal features\ncontained in voxel graph list are effectively aligned and integrated. Finally,\nwe design a temporal aggregation module that incorporates positional encoding,\nwhich enables the capture of local absolute spatial and global temporal\ninformation. Experiments demonstrate that our method outperforms both the\nevent-based and video-based lip-reading counterparts. Our code will be publicly\navailable.",
+                    "authors": "Wenhao Zhang, Jun Wang, Yong Luo, Lei Yu, Wei Yu, Zheng He",
+                    "published": "2024-04-18",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1509.08960v1",
+                    "title": "Storing and Analyzing Historical Graph Data at Scale",
+                    "abstract": "The work on large-scale graph analytics to date has largely focused on the\nstudy of static properties of graph snapshots. However, a static view of\ninteractions between entities is often an oversimplification of several complex\nphenomena like the spread of epidemics, information diffusion, formation of\nonline communities}, and so on. Being able to find temporal interaction\npatterns, visualize the evolution of graph properties, or even simply compare\nthem across time, adds significant value in reasoning over graphs. However,\nbecause of lack of underlying data management support, an analyst today has to\nmanually navigate the added temporal complexity of dealing with large evolving\ngraphs. In this paper, we present a system, called Historical Graph Store, that\nenables users to store large volumes of historical graph data and to express\nand run complex temporal graph analytical tasks against that data. It consists\nof two key components: a Temporal Graph Index (TGI), that compactly stores\nlarge volumes of historical graph evolution data in a partitioned and\ndistributed fashion; it provides support for retrieving snapshots of the graph\nas of any timepoint in the past or evolution histories of individual nodes or\nneighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for\nexpressing complex temporal analytical tasks and for executing them in an\nefficient and scalable manner. Our experiments demonstrate our system's\nefficient storage, retrieval and analytics across a wide variety of queries on\nlarge volumes of historical graph data.",
+                    "authors": "Udayan Khurana, Amol Deshpande",
+                    "published": "2015-09-29",
+                    "updated": "2015-09-29",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.06260v1",
+                    "title": "In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs",
+                    "abstract": "A graph whose edges only appear at certain points in time is called a\ntemporal graph (among other names). These graphs are temporally connected if\nall ordered pairs of vertices are connected by a path that traverses edges in\nchronological order (a temporal path). Reachability in temporal graphs departs\nsignificantly from standard reachability; in particular, it is not transitive,\nwith structural and algorithmic consequences. For instance, temporally\nconnected graphs do not always admit spanning trees, i.e., subsets of edges\nthat form a tree and preserve temporal connectivity among the nodes.\n  In this paper, we revisit fundamental questions about the loss of\nuniversality of spanning trees. To start, we show that deciding if a spanning\ntree exists in a given temporal graph is NP-complete. What could be appropriate\nreplacement for the concept? Beyond having minimum size, spanning trees enjoy\nthe feature of enabling reachability along the same underlying paths in both\ndirections, a pretty uncommon feature in temporal graphs. We explore\nrelaxations in this direction and show that testing the existence of\nbidirectional spanning structures (bi-spanners) is tractable in general. On the\ndown side, finding \\emph{minimum} such structures is NP-hard even in simple\ntemporal graphs. Still, the fact that bidirectionality can be tested\nefficiently may find applications, e.g. for routing and security, and the\ncorresponding primitive that we introduce in the algorithm may be of\nindependent interest.",
+                    "authors": "Arnaud Casteigts, Timoth\u00e9e Corsini",
+                    "published": "2023-12-11",
+                    "updated": "2023-12-11",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DC",
+                        "68R10, 68W15",
+                        "G.2.2; C.2.4"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2205.14269v1",
+                    "title": "Temporal graph patterns by timed automata",
+                    "abstract": "Temporal graphs represent graph evolution over time, and have been receiving\nconsiderable research attention. Work on expressing temporal graph patterns or\ndiscovering temporal motifs typically assumes relatively simple temporal\nconstraints, such as journeys or, more generally, existential constraints,\npossibly with finite delays. In this paper we propose to use timed automata to\nexpress temporal constraints, leading to a general and powerful notion of\ntemporal basic graph pattern (BGP). The new difficulty is the evaluation of the\ntemporal constraint on a large set of matchings. An important benefit of timed\nautomata is that they support an iterative state assignment, which can be\nuseful for early detection of matches and pruning of non-matches. We introduce\nalgorithms to retrieve all instances of a temporal BGP match in a graph, and\npresent results of an extensive experimental evaluation, demonstrating\ninteresting performance trade-offs. We show that an on-demand algorithm that\nprocesses total matchings incrementally over time is preferable when dealing\nwith cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and\nwhen connectivity of partial matchings can be guaranteed, the best performance\nis achieved by maintaining partial matchings over time and allowing automaton\nevaluation to be fully incremental.",
+                    "authors": "Amir Pouya Aghasadeghi, Jan Van den Bussche, Julia Stoyanovich",
+                    "published": "2022-05-27",
+                    "updated": "2022-05-27",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.13517v1",
+                    "title": "Temporal Graph Signal Decomposition",
+                    "abstract": "Temporal graph signals are multivariate time series with individual\ncomponents associated with nodes of a fixed graph structure. Data of this kind\narises in many domains including activity of social network users, sensor\nnetwork readings over time, and time course gene expression within the\ninteraction network of a model organism. Traditional matrix decomposition\nmethods applied to such data fall short of exploiting structural regularities\nencoded in the underlying graph and also in the temporal patterns of the\nsignal. How can we take into account such structure to obtain a succinct and\ninterpretable representation of temporal graph signals?\n  We propose a general, dictionary-based framework for temporal graph signal\ndecomposition (TGSD). The key idea is to learn a low-rank, joint encoding of\nthe data via a combination of graph and time dictionaries. We propose a highly\nscalable decomposition algorithm for both complete and incomplete data, and\ndemonstrate its advantage for matrix decomposition, imputation of missing\nvalues, temporal interpolation, clustering, period estimation, and rank\nestimation in synthetic and real-world data ranging from traffic patterns to\nsocial media activity. Our framework achieves 28% reduction in RMSE compared to\nbaselines for temporal interpolation when as many as 75% of the observations\nare missing. It scales best among baselines taking under 20 seconds on 3.5\nmillion data points and produces the most parsimonious models. To the best of\nour knowledge, TGSD is the first framework to jointly model graph signals by\ntemporal and graph dictionaries.",
+                    "authors": "Maxwell McNeil, Lin Zhang, Petko Bogdanov",
+                    "published": "2021-06-25",
+                    "updated": "2021-06-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07699v2",
+                    "title": "Time-aware Graph Structure Learning via Sequence Prediction on Temporal Graphs",
+                    "abstract": "Temporal Graph Learning, which aims to model the time-evolving nature of\ngraphs, has gained increasing attention and achieved remarkable performance\nrecently. However, in reality, graph structures are often incomplete and noisy,\nwhich hinders temporal graph networks (TGNs) from learning informative\nrepresentations. Graph contrastive learning uses data augmentation to generate\nplausible variations of existing data and learn robust representations.\nHowever, rule-based augmentation approaches may be suboptimal as they lack\nlearnability and fail to leverage rich information from downstream tasks. To\naddress these issues, we propose a Time-aware Graph Structure Learning (TGSL)\napproach via sequence prediction on temporal graphs, which learns better graph\nstructures for downstream tasks through adding potential temporal edges. In\nparticular, it predicts time-aware context embedding based on previously\nobserved interactions and uses the Gumble-Top-K to select the closest candidate\nedges to this context embedding. Additionally, several candidate sampling\nstrategies are proposed to ensure both efficiency and diversity. Furthermore,\nwe jointly learn the graph structure and TGNs in an end-to-end manner and\nperform inference on the refined graph. Extensive experiments on temporal link\nprediction benchmarks demonstrate that TGSL yields significant gains for the\npopular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive\nlearning methods on temporal graphs. We release the code at\nhttps://github.com/ViktorAxelsen/TGSL.",
+                    "authors": "Haozhen Zhang, Xueting Han, Xi Xiao, Jing Bai",
+                    "published": "2023-06-13",
+                    "updated": "2023-08-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.11886v1",
+                    "title": "Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs",
+                    "abstract": "Temporal bipartite graphs are widely used to denote time-evolving\nrelationships between two disjoint sets of nodes, such as customer-product\ninteractions in E-commerce and user-group memberships in social networks.\nTemporal butterflies, $(2,2)$-bicliques that occur within a short period and in\na prescribed order, are essential in modeling the structural and sequential\npatterns of such graphs. Counting the number of temporal butterflies is thus a\nfundamental task in analyzing temporal bipartite graphs. However, existing\nalgorithms for butterfly counting on static bipartite graphs and motif counting\non temporal unipartite graphs are inefficient for this purpose. In this paper,\nwe present a general framework with three sampling strategies for temporal\nbutterfly counting. Since exact counting can be time-consuming on large graphs,\nour approach alternatively computes approximate estimates accurately and\nefficiently. We also provide analytical bounds on the number of samples each\nstrategy requires to obtain estimates with small relative errors and high\nprobability. We finally evaluate our framework on six real-world datasets and\ndemonstrate its superior accuracy and efficiency compared to several baselines.\nOverall, our proposed framework and sampling strategies provide efficient and\naccurate approaches to approximating temporal butterfly counts on large-scale\ntemporal bipartite graphs.",
+                    "authors": "Jiaxi Pu, Yanhao Wang, Yuchen Li, Xuan Zhou",
+                    "published": "2023-10-18",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.DB",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10738v3",
+                    "title": "Deep Temporal Graph Clustering",
+                    "abstract": "Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.",
+                    "authors": "Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-05-18",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.04782v1",
+                    "title": "A Survey on Temporal Knowledge Graph: Representation Learning and Applications",
+                    "abstract": "Knowledge graphs have garnered significant research attention and are widely\nused to enhance downstream applications. However, most current studies mainly\nfocus on static knowledge graphs, whose facts do not change with time, and\ndisregard their dynamic evolution over time. As a result, temporal knowledge\ngraphs have attracted more attention because a large amount of structured\nknowledge exists only within a specific period. Knowledge graph representation\nlearning aims to learn low-dimensional vector embeddings for entities and\nrelations in a knowledge graph. The representation learning of temporal\nknowledge graphs incorporates time information into the standard knowledge\ngraph framework and can model the dynamics of entities and relations over time.\nIn this paper, we conduct a comprehensive survey of temporal knowledge graph\nrepresentation learning and its applications. We begin with an introduction to\nthe definitions, datasets, and evaluation metrics for temporal knowledge graph\nrepresentation learning. Next, we propose a taxonomy based on the core\ntechnologies of temporal knowledge graph representation learning methods, and\nprovide an in-depth analysis of different methods in each category. Finally, we\npresent various downstream applications related to the temporal knowledge\ngraphs. In the end, we conclude the paper and have an outlook on the future\nresearch directions in this area.",
+                    "authors": "Li Cai, Xin Mao, Yuhao Zhou, Zhaoguang Long, Changxu Wu, Man Lan",
+                    "published": "2024-03-02",
+                    "updated": "2024-03-02",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.10364v3",
+                    "title": "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks",
+                    "abstract": "Recent years have seen a surge in research on dynamic graph representation\nlearning, which aims to model temporal graphs that are dynamic and evolving\nconstantly over time. However, current work typically models graph dynamics\nwith recurrent neural networks (RNNs), making them suffer seriously from\ncomputation and memory overheads on large temporal graphs. So far, scalability\nof dynamic graph representation learning on large temporal graphs remains one\nof the major challenges. In this paper, we present a scalable framework, namely\nSpikeNet, to efficiently capture the temporal and structural patterns of\ntemporal graphs. We explore a new direction in that we can capture the evolving\ndynamics of temporal graphs with spiking neural networks (SNNs) instead of\nRNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics\nas spike trains of neuron populations and enable spike-based propagation in an\nefficient way. Experiments on three large real-world temporal graph datasets\ndemonstrate that SpikeNet outperforms strong baselines on the temporal node\nclassification task with lower computational costs. Particularly, SpikeNet\ngeneralizes to a large temporal graph (2.7M nodes and 13.9M edges) with\nsignificantly fewer parameters and computation overheads.Our code is publicly\navailable at \\url{https://github.com/EdisonLeeeee/SpikeNet}.",
+                    "authors": "Jintang Li, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, Changhua Meng",
+                    "published": "2022-08-15",
+                    "updated": "2023-05-18",
+                    "primary_cat": "cs.NE",
+                    "cats": [
+                        "cs.NE",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.08311v1",
+                    "title": "De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs",
+                    "abstract": "We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware\ngraph neural network architecture for time-resolved data on dynamic graphs. Our\napproach accounts for temporal-topological patterns that unfold in the causal\ntopology of dynamic graphs, which is determined by causal walks, i.e.\ntemporally ordered sequences of links by which nodes can influence each other\nover time. Our architecture builds on multiple layers of higher-order De Bruijn\ngraphs, an iterative line graph construction where nodes in a De Bruijn graph\nof order k represent walks of length k-1, while edges represent walks of length\nk. We develop a graph neural network architecture that utilizes De Bruijn\ngraphs to implement a message passing scheme that follows a non-Markovian\ndynamics, which enables us to learn patterns in the causal topology of a\ndynamic graph. Addressing the issue that De Bruijn graphs with different orders\nk can be used to model the same data set, we further apply statistical model\nselection to determine the optimal graph topology to be used for message\npassing. An evaluation in synthetic and empirical data sets suggests that\nDBGNNs can leverage temporal patterns in dynamic graphs, which substantially\nimproves the performance in a supervised node classification task.",
+                    "authors": "Lisi Qarkaxhija, Vincenzo Perri, Ingo Scholtes",
+                    "published": "2022-09-17",
+                    "updated": "2022-09-17",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.10379v1",
+                    "title": "ChronoR: Rotation Based Temporal Knowledge Graph Embedding",
+                    "abstract": "Despite the importance and abundance of temporal knowledge graphs, most of\nthe current research has been focused on reasoning on static graphs. In this\npaper, we study the challenging problem of inference over temporal knowledge\ngraphs. In particular, the task of temporal link prediction. In general, this\nis a difficult task due to data non-stationarity, data heterogeneity, and its\ncomplex temporal dependencies. We propose Chronological Rotation embedding\n(ChronoR), a novel model for learning representations for entities, relations,\nand time. Learning dense representations is frequently used as an efficient and\nversatile method to perform reasoning on knowledge graphs. The proposed model\nlearns a k-dimensional rotation transformation parametrized by relation and\ntime, such that after each fact's head entity is transformed using the\nrotation, it falls near its corresponding tail entity. By using high\ndimensional rotation as its transformation operator, ChronoR captures rich\ninteraction between the temporal and multi-relational characteristics of a\nTemporal Knowledge Graph. Experimentally, we show that ChronoR is able to\noutperform many of the state-of-the-art methods on the benchmark datasets for\ntemporal knowledge graph link prediction.",
+                    "authors": "Ali Sadeghian, Mohammadreza Armandpour, Anthony Colas, Daisy Zhe Wang",
+                    "published": "2021-03-18",
+                    "updated": "2021-03-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.15862v1",
+                    "title": "Restless Temporal Path Parameterized Above Lower Bounds",
+                    "abstract": "Reachability questions are one of the most fundamental algorithmic primitives\nin temporal graphs -- graphs whose edge set changes over discrete time steps. A\ncore problem here is the NP-hard Short Restless Temporal Path: given a temporal\ngraph $\\mathcal G$, two distinct vertices $s$ and $z$, and two numbers $\\delta$\nand $k$, is there a $\\delta$-restless temporal $s$-$z$ path of length at most\n$k$? A temporal path is a path whose edges appear in chronological order and a\ntemporal path is $\\delta$-restless if two consecutive path edges appear at most\n$\\delta$ time steps apart from each other. Among others, this problem has\napplications in neuroscience and epidemiology. While Short Restless Temporal\nPath is known to be computationally hard, e.g., it is NP-hard for only three\ntime steps and W[1]-hard when parameterized by the feedback vertex number of\nthe underlying graph, it is fixed-parameter tractable when parameterized by the\npath length $k$. We improve on this by showing that Short Restless Temporal\nPath can be solved in (randomized) $4^{k-d}|\\mathcal G|^{O(1)}$ time, where $d$\nis the minimum length of a temporal $s$-$z$ path.",
+                    "authors": "Philipp Zschoche",
+                    "published": "2022-03-29",
+                    "updated": "2022-03-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1811.08366v1",
+                    "title": "Temporal Graph Offset Reconstruction: Towards Temporally Robust Graph Representation Learning",
+                    "abstract": "Graphs are a commonly used construct for representing relationships between\nelements in complex high dimensional datasets. Many real-world phenomenon are\ndynamic in nature, meaning that any graph used to represent them is inherently\ntemporal. However, many of the machine learning models designed to capture\nknowledge about the structure of these graphs ignore this rich temporal\ninformation when creating representations of the graph. This results in models\nwhich do not perform well when used to make predictions about the future state\nof the graph -- especially when the delta between time stamps is not small. In\nthis work, we explore a novel training procedure and an associated unsupervised\nmodel which creates graph representations optimised to predict the future state\nof the graph. We make use of graph convolutional neural networks to encode the\ngraph into a latent representation, which we then use to train our temporal\noffset reconstruction method, inspired by auto-encoders, to predict a later\ntime point -- multiple time steps into the future. Using our method, we\ndemonstrate superior performance for the task of future link prediction\ncompared with none-temporal state-of-the-art baselines. We show our approach to\nbe capable of outperforming non-temporal baselines by 38% on a real world\ndataset.",
+                    "authors": "Stephen Bonner, John Brennan, Ibad Kureshi, Georgios Theodoropoulos, Andrew Stephen McGough, Boguslaw Obara",
+                    "published": "2018-11-20",
+                    "updated": "2018-11-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.12931v1",
+                    "title": "Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal forecasting has attracted tremendous attention in a wide\nrange of applications, and traffic flow prediction is a canonical and typical\nexample. The complex and long-range spatial-temporal correlations of traffic\nflow bring it to a most intractable challenge. Existing works typically utilize\nshallow graph convolution networks (GNNs) and temporal extracting modules to\nmodel spatial and temporal dependencies respectively. However, the\nrepresentation ability of such models is limited due to: (1) shallow GNNs are\nincapable to capture long-range spatial correlations, (2) only spatial\nconnections are considered and a mass of semantic connections are ignored,\nwhich are of great importance for a comprehensive understanding of traffic\nnetworks. To this end, we propose Spatial-Temporal Graph Ordinary Differential\nEquation Networks (STGODE). Specifically, we capture spatial-temporal dynamics\nthrough a tensor-based ordinary differential equation (ODE), as a result,\ndeeper networks can be constructed and spatial-temporal features are utilized\nsynchronously. To understand the network more comprehensively, semantical\nadjacency matrix is considered in our model, and a well-design temporal\ndialated convolution structure is used to capture long term temporal\ndependencies. We evaluate our model on multiple real-world traffic datasets and\nsuperior performance is achieved over state-of-the-art baselines.",
+                    "authors": "Zheng Fang, Qingqing Long, Guojie Song, Kunqing Xie",
+                    "published": "2021-06-24",
+                    "updated": "2021-06-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08909v2",
+                    "title": "Maximum 0-1 Timed Matching on Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs where the topology and/or other properties of the\ngraph change with time. They have been used to model applications with temporal\ninformation in various domains. Problems on static graphs become more\nchallenging to solve in temporal graphs because of dynamically changing\ntopology, and many recent works have explored graph problems on temporal\ngraphs. In this paper, we define a type of matching called {\\em 0-1 timed\nmatching} for temporal graphs, and investigate the problem of finding a {\\em\nmaximum 0-1 timed matching} for different classes of temporal graphs. We first\nprove that the problem is NP-Complete for rooted temporal trees when each edge\nis associated with two or more time intervals. We then propose an $O(n \\log n)$\ntime algorithm for the problem on a rooted temporal tree with $n$ nodes when\neach edge is associated with exactly one time interval. The problem is then\nshown to be NP-Complete also for bipartite temporal graphs even when each edge\nis associated with a single time interval and degree of each node is bounded by\na constant $k \\geq 3$. We next investigate approximation algorithms for the\nproblem for temporal graphs where each edge is associated with more than one\ntime intervals. It is first shown that there is no\n$\\frac{1}{n^{1-\\epsilon}}$-factor approximation algorithm for the problem for\nany $\\epsilon > 0$ even on a rooted temporal tree with $n$ nodes unless NP =\nZPP. We then present a $\\frac{5}{2\\mathcal{N}^* + 3}$-factor approximation\nalgorithm for the problem for general temporal graphs where $\\mathcal{N^*}$ is\nthe average number of edges overlapping in time with each edge in the temporal\ngraph. The same algorithm is also a constant-factor approximation algorithm for\ndegree bounded temporal graphs.",
+                    "authors": "Subhrangsu Mandal, Arobinda Gupta",
+                    "published": "2020-12-16",
+                    "updated": "2022-02-01",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.14303v1",
+                    "title": "TREND: TempoRal Event and Node Dynamics for Graph Representation Learning",
+                    "abstract": "Temporal graph representation learning has drawn significant attention for\nthe prevalence of temporal graphs in the real world. However, most existing\nworks resort to taking discrete snapshots of the temporal graph, or are not\ninductive to deal with new nodes, or do not model the exciting effects which is\nthe ability of events to influence the occurrence of another event. In this\nwork, We propose TREND, a novel framework for temporal graph representation\nlearning, driven by TempoRal Event and Node Dynamics and built upon a Hawkes\nprocess-based graph neural network (GNN). TREND presents a few major\nadvantages: (1) it is inductive due to its GNN architecture; (2) it captures\nthe exciting effects between events by the adoption of the Hawkes process; (3)\nas our main novelty, it captures the individual and collective characteristics\nof events by integrating both event and node dynamics, driving a more precise\nmodeling of the temporal process. Extensive experiments on four real-world\ndatasets demonstrate the effectiveness of our proposed model.",
+                    "authors": "Zhihao Wen, Yuan Fang",
+                    "published": "2022-03-27",
+                    "updated": "2022-03-27",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.05496v2",
+                    "title": "Temporal Graph Kernels for Classifying Dissemination Processes",
+                    "abstract": "Many real-world graphs or networks are temporal, e.g., in a social network\npersons only interact at specific points in time. This information directs\ndissemination processes on the network, such as the spread of rumors, fake\nnews, or diseases. However, the current state-of-the-art methods for supervised\ngraph classification are designed mainly for static graphs and may not be able\nto capture temporal information. Hence, they are not powerful enough to\ndistinguish between graphs modeling different dissemination processes. To\naddress this, we introduce a framework to lift standard graph kernels to the\ntemporal domain. Specifically, we explore three different approaches and\ninvestigate the trade-offs between loss of temporal information and efficiency.\nMoreover, to handle large-scale graphs, we propose stochastic variants of our\nkernels with provable approximation guarantees. We evaluate our methods on a\nwide range of real-world social networks. Our methods beat static kernels by a\nlarge margin in terms of accuracy while still being scalable to large graphs\nand data sets. Hence, we confirm that taking temporal information into account\nis crucial for the successful classification of dissemination processes.",
+                    "authors": "Lutz Oettershagen, Nils M. Kriege, Christopher Morris, Petra Mutzel",
+                    "published": "2019-10-14",
+                    "updated": "2021-08-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08323v2",
+                    "title": "TG-GAN: Continuous-time Temporal Graph Generation with Deep Generative Models",
+                    "abstract": "The recent deep generative models for static graphs that are now being\nactively developed have achieved significant success in areas such as molecule\ndesign. However, many real-world problems involve temporal graphs whose\ntopology and attribute values evolve dynamically over time, including important\napplications such as protein folding, human mobility networks, and social\nnetwork growth. As yet, deep generative models for temporal graphs are not yet\nwell understood and existing techniques for static graphs are not adequate for\ntemporal graphs since they cannot 1) encode and decode continuously-varying\ngraph topology chronologically, 2) enforce validity via temporal constraints,\nor 3) ensure efficiency for information-lossless temporal resolution. To\naddress these challenges, we propose a new model, called ``Temporal Graph\nGenerative Adversarial Network'' (TG-GAN) for continuous-time temporal graph\ngeneration, by modeling the deep generative process for truncated temporal\nrandom walks and their compositions. Specifically, we first propose a novel\ntemporal graph generator that jointly model truncated edge sequences, time\nbudgets, and node attributes, with novel activation functions that enforce\ntemporal validity constraints under recurrent architecture. In addition, a new\ntemporal graph discriminator is proposed, which combines time and node encoding\noperations over a recurrent architecture to distinguish the generated sequences\nfrom the real ones sampled by a newly-developed truncated temporal random walk\nsampler. Extensive experiments on both synthetic and real-world datasets\ndemonstrate TG-GAN significantly outperforms the comparison methods in\nefficiency and effectiveness.",
+                    "authors": "Liming Zhang, Liang Zhao, Shan Qin, Dieter Pfoser",
+                    "published": "2020-05-17",
+                    "updated": "2020-06-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.04434v1",
+                    "title": "Frequency Analysis of Temporal Graph Signals",
+                    "abstract": "This letter extends the concept of graph-frequency to graph signals that\nevolve with time. Our goal is to generalize and, in fact, unify the familiar\nconcepts from time- and graph-frequency analysis. To this end, we study a joint\ntemporal and graph Fourier transform (JFT) and demonstrate its attractive\nproperties. We build on our results to create filters which act on the joint\n(temporal and graph) frequency domain, and show how these can be used to\nperform interference cancellation. The proposed algorithms are distributed,\nhave linear complexity, and can approximate any desired joint filtering\nobjective.",
+                    "authors": "Andreas Loukas, Damien Foucard",
+                    "published": "2016-02-14",
+                    "updated": "2016-02-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SY",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.04962v1",
+                    "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering",
+                    "abstract": "Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.",
+                    "authors": "Meng Liu, Ke Liang, Yue Liu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-06-08",
+                    "updated": "2023-06-08",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05078v1",
+                    "title": "TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification",
+                    "abstract": "Multivariate time series classification (MTSC) is an important data mining\ntask, which can be effectively solved by popular deep learning technology.\nUnfortunately, the existing deep learning-based methods neglect the hidden\ndependencies in different dimensions and also rarely consider the unique\ndynamic features of time series, which lack sufficient feature extraction\ncapability to obtain satisfactory classification accuracy. To address this\nproblem, we propose a novel temporal dynamic graph neural network (TodyNet)\nthat can extract hidden spatio-temporal dependencies without undefined graph\nstructure. It enables information flow among isolated but implicit\ninterdependent variables and captures the associations between different time\nslots by dynamic graph mechanism, which further improves the classification\nperformance of the model. Meanwhile, the hierarchical representations of graphs\ncannot be learned due to the limitation of GNNs. Thus, we also design a\ntemporal graph pooling layer to obtain a global graph-level representation for\ngraph learning with learnable temporal parameters. The dynamic graph, graph\ninformation propagation, and temporal convolution are jointly learned in an\nend-to-end framework. The experiments on 26 UEA benchmark datasets illustrate\nthat the proposed TodyNet outperforms existing deep learning-based methods in\nthe MTSC tasks.",
+                    "authors": "Huaiyuan Liu, Xianzhang Liu, Donghua Yang, Zhiyu Liang, Hongzhi Wang, Yong Cui, Jun Gu",
+                    "published": "2023-04-11",
+                    "updated": "2023-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.03897v1",
+                    "title": "Temporal Graph Representation Learning with Adaptive Augmentation Contrastive",
+                    "abstract": "Temporal graph representation learning aims to generate low-dimensional\ndynamic node embeddings to capture temporal information as well as structural\nand property information. Current representation learning methods for temporal\nnetworks often focus on capturing fine-grained information, which may lead to\nthe model capturing random noise instead of essential semantic information.\nWhile graph contrastive learning has shown promise in dealing with noise, it\nonly applies to static graphs or snapshots and may not be suitable for handling\ntime-dependent noise. To alleviate the above challenge, we propose a novel\nTemporal Graph representation learning with Adaptive augmentation Contrastive\n(TGAC) model. The adaptive augmentation on the temporal graph is made by\ncombining prior knowledge with temporal information, and the contrastive\nobjective function is constructed by defining the augmented inter-view contrast\nand intra-view contrast. To complement TGAC, we propose three adaptive\naugmentation strategies that modify topological features to reduce noise from\nthe network. Our extensive experiments on various real networks demonstrate\nthat the proposed model outperforms other temporal graph representation\nlearning methods.",
+                    "authors": "Hongjiang Chen, Pengfei Jiao, Huijun Tang, Huaming Wu",
+                    "published": "2023-11-07",
+                    "updated": "2023-11-07",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.13177v1",
+                    "title": "It is all Connected: A New Graph Formulation for Spatio-Temporal Forecasting",
+                    "abstract": "With an ever-increasing number of sensors in modern society, spatio-temporal\ntime series forecasting has become a de facto tool to make informed decisions\nabout the future. Most spatio-temporal forecasting models typically comprise\ndistinct components that learn spatial and temporal dependencies. A common\nmethodology employs some Graph Neural Network (GNN) to capture relations\nbetween spatial locations, while another network, such as a recurrent neural\nnetwork (RNN), learns temporal correlations. By representing every recorded\nsample as its own node in a graph, rather than all measurements for a\nparticular location as a single node, temporal and spatial information is\nencoded in a similar manner. In this setting, GNNs can now directly learn both\ntemporal and spatial dependencies, jointly, while also alleviating the need for\nadditional temporal networks. Furthermore, the framework does not require\naligned measurements along the temporal dimension, meaning that it also\nnaturally facilitates irregular time series, different sampling frequencies or\nmissing data, without the need for data imputation. To evaluate the proposed\nmethodology, we consider wind speed forecasting as a case study, where our\nproposed framework outperformed other spatio-temporal models using GNNs with\neither Transformer or LSTM networks as temporal update functions.",
+                    "authors": "Lars \u00d8degaard Bentsen, Narada Dilp Warakagoda, Roy Stenbro, Paal Engelstad",
+                    "published": "2023-03-23",
+                    "updated": "2023-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.08733v1",
+                    "title": "Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast",
+                    "abstract": "Self-supervised learning on graphs has recently drawn a lot of attention due\nto its independence from labels and its robustness in representation. Current\nstudies on this topic mainly use static information such as graph structures\nbut cannot well capture dynamic information such as timestamps of edges.\nRealistic graphs are often dynamic, which means the interaction between nodes\noccurs at a specific time. This paper proposes a self-supervised dynamic graph\nrepresentation learning framework (DySubC), which defines a temporal subgraph\ncontrastive learning task to simultaneously learn the structural and\nevolutional features of a dynamic graph. Specifically, a novel temporal\nsubgraph sampling strategy is firstly proposed, which takes each node of the\ndynamic graph as the central node and uses both neighborhood structures and\nedge timestamps to sample the corresponding temporal subgraph. The subgraph\nrepresentation function is then designed according to the influence of\nneighborhood nodes on the central node after encoding the nodes in each\nsubgraph. Finally, the structural and temporal contrastive loss are defined to\nmaximize the mutual information between node representation and temporal\nsubgraph representation. Experiments on five real-world datasets demonstrate\nthat (1) DySubC performs better than the related baselines including two graph\ncontrastive learning models and four dynamic graph representation learning\nmodels in the downstream link prediction task, and (2) the use of temporal\ninformation can not only sample more effective subgraphs, but also learn better\nrepresentation by temporal contrastive loss.",
+                    "authors": "Linpu Jiang, Ke-Jia Chen, Jingqiang Chen",
+                    "published": "2021-12-16",
+                    "updated": "2021-12-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.04696v1",
+                    "title": "Nash Equilibria in Reverse Temporal Voronoi Games",
+                    "abstract": "We study Voronoi games on temporal graphs as introduced by Boehmer et al.\n(IJCAI 2021) where two players each select a vertex in a temporal graph with\nthe goal of reaching the other vertices earlier than the other player. In this\nwork, we consider the reverse temporal Voronoi game, that is, a player wants to\nmaximize the number of vertices reaching her earlier than the other player.\nSince temporal distances in temporal graphs are not symmetric in general, this\nyields a different game. We investigate the difference between the two games\nwith respect to the existence of Nash equilibria in various temporal graph\nclasses including temporal trees, cycles, grids, cliques and split graphs. Our\nextensive results show that the two games indeed behave quite differently\ndepending on the considered temporal graph class.",
+                    "authors": "Simeon Pawlowski, Vincent Froese",
+                    "published": "2024-02-07",
+                    "updated": "2024-02-07",
+                    "primary_cat": "cs.GT",
+                    "cats": [
+                        "cs.GT"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19453v1",
+                    "title": "Structural Parameters for Dense Temporal Graphs",
+                    "abstract": "Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.",
+                    "authors": "Jessica Enright, Samuel D. Hand, Laura Larios-Jones, Kitty Meeks",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "math.CO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.13684v3",
+                    "title": "Spatio-Temporal Joint Graph Convolutional Networks for Traffic Forecasting",
+                    "abstract": "Recent studies have shifted their focus towards formulating traffic\nforecasting as a spatio-temporal graph modeling problem. Typically, they\nconstructed a static spatial graph at each time step and then connected each\nnode with itself between adjacent time steps to create a spatio-temporal graph.\nHowever, this approach failed to explicitly reflect the correlations between\ndifferent nodes at different time steps, thus limiting the learning capability\nof graph neural networks. Additionally, those models overlooked the dynamic\nspatio-temporal correlations among nodes by using the same adjacency matrix\nacross different time steps. To address these limitations, we propose a novel\napproach called Spatio-Temporal Joint Graph Convolutional Networks (STJGCN) for\naccurate traffic forecasting on road networks over multiple future time steps.\nSpecifically, our method encompasses the construction of both pre-defined and\nadaptive spatio-temporal joint graphs (STJGs) between any two time steps, which\nrepresent comprehensive and dynamic spatio-temporal correlations. We further\nintroduce dilated causal spatio-temporal joint graph convolution layers on the\nSTJG to capture spatio-temporal dependencies from distinct perspectives with\nmultiple ranges. To aggregate information from different ranges, we propose a\nmulti-range attention mechanism. Finally, we evaluate our approach on five\npublic traffic datasets and experimental results demonstrate that STJGCN is not\nonly computationally efficient but also outperforms 11 state-of-the-art\nbaseline methods.",
+                    "authors": "Chuanpan Zheng, Xiaoliang Fan, Shirui Pan, Haibing Jin, Zhaopeng Peng, Zonghan Wu, Cheng Wang, Philip S. Yu",
+                    "published": "2021-11-25",
+                    "updated": "2023-06-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.09610v2",
+                    "title": "Storing and Querying Large-Scale Spatio-Temporal Graphs with High-Throughput Edge Insertions",
+                    "abstract": "Real-world graphs often contain spatio-temporal information and evolve over\ntime. Compared with static graphs, spatio-temporal graphs have very different\ncharacteristics, presenting more significant challenges in data volume, data\nvelocity, and query processing. In this paper, we describe three representative\napplications to understand the features of spatio-temporal graphs. Based on the\ncommonalities of the applications, we define a formal spatio-temporal graph\nmodel, where a graph consists of location vertices, object vertices, and event\nedges. Then we discuss a set of design goals to meet the requirements of the\napplications: (i) supporting up to 10 billion object vertices, 10 million\nlocation vertices, and 100 trillion edges in the graph, (ii) supporting up to 1\ntrillion new edges that are streamed in daily, and (iii) minimizing\ncross-machine communication for query processing. We propose and evaluate PAST,\na framework for efficient PArtitioning and query processing of Spatio-Temporal\ngraphs. Experimental results show that PAST successfully achieves the above\ngoals. It improves query performance by orders of magnitude compared with\nstate-of-the-art solutions, including JanusGraph, Greenplum, Spark and\nST-Hadoop.",
+                    "authors": "Mengsu Ding, Muqiao Yang, Shimin Chen",
+                    "published": "2019-04-21",
+                    "updated": "2020-10-20",
+                    "primary_cat": "cs.DC",
+                    "cats": [
+                        "cs.DC",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2101.00820v8",
+                    "title": "Temporal Contrastive Graph Learning for Video Action Recognition and Retrieval",
+                    "abstract": "Attempt to fully discover the temporal diversity and chronological\ncharacteristics for self-supervised video representation learning, this work\ntakes advantage of the temporal dependencies within videos and further proposes\na novel self-supervised method named Temporal Contrastive Graph Learning\n(TCGL). In contrast to the existing methods that ignore modeling elaborate\ntemporal dependencies, our TCGL roots in a hybrid graph contrastive learning\nstrategy to jointly regard the inter-snippet and intra-snippet temporal\ndependencies as self-supervision signals for temporal representation learning.\nTo model multi-scale temporal dependencies, our TCGL integrates the prior\nknowledge about the frame and snippet orders into graph structures, i.e., the\nintra-/inter- snippet temporal contrastive graphs. By randomly removing edges\nand masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL\ncan generate different correlated graph views. Then, specific contrastive\nlearning modules are designed to maximize the agreement between nodes in\ndifferent views. To adaptively learn the global context representation and\nrecalibrate the channel-wise features, we introduce an adaptive video snippet\norder prediction module, which leverages the relational knowledge among video\nsnippets to predict the actual snippet orders. Experimental results demonstrate\nthe superiority of our TCGL over the state-of-the-art methods on large-scale\naction recognition and video retrieval benchmarks.",
+                    "authors": "Yang Liu, Keze Wang, Haoyuan Lan, Liang Lin",
+                    "published": "2021-01-04",
+                    "updated": "2021-03-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.MM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.09114v1",
+                    "title": "Relational Temporal Graph Reasoning for Dual-task Dialogue Language Understanding",
+                    "abstract": "Dual-task dialog language understanding aims to tackle two correlative dialog\nlanguage understanding tasks simultaneously via leveraging their inherent\ncorrelations. In this paper, we put forward a new framework, whose core is\nrelational temporal graph reasoning.We propose a speaker-aware temporal graph\n(SATG) and a dual-task relational temporal graph (DRTG) to facilitate\nrelational temporal modeling in dialog understanding and dual-task reasoning.\nBesides, different from previous works that only achieve implicit\nsemantics-level interactions, we propose to model the explicit dependencies via\nintegrating prediction-level interactions. To implement our framework, we first\npropose a novel model Dual-tAsk temporal Relational rEcurrent Reasoning network\n(DARER), which first generates the context-, speaker- and temporal-sensitive\nutterance representations through relational temporal modeling of SATG, then\nconducts recurrent dual-task relational temporal graph reasoning on DRTG, in\nwhich process the estimated label distributions act as key clues in\nprediction-level interactions. And the relational temporal modeling in DARER is\nachieved by relational convolutional networks (RGCNs). Then we further propose\nRelational Temporal Transformer (ReTeFormer), which achieves fine-grained\nrelational temporal modeling via Relation- and Structure-aware Disentangled\nMulti-head Attention. Accordingly, we propose DARER with ReTeFormer (DARER2),\nwhich adopts two variants of ReTeFormer to achieve the relational temporal\nmodeling of SATG and DTRG, respectively. The extensive experiments on different\nscenarios verify that our models outperform state-of-the-art models by a large\nmargin. Remarkably, on the dialog sentiment classification task in the Mastodon\ndataset, DARER and DARER2 gain relative improvements of about 28% and 34% over\nthe previous best model in terms of F1.",
+                    "authors": "Bowen Xing, Ivor W. Tsang",
+                    "published": "2023-06-15",
+                    "updated": "2023-06-15",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2008.08282v2",
+                    "title": "Multiscale Snapshots: Visual Analysis of Temporal Summaries in Dynamic Graphs",
+                    "abstract": "The overview-driven visual analysis of large-scale dynamic graphs poses a\nmajor challenge. We propose Multiscale Snapshots, a visual analytics approach\nto analyze temporal summaries of dynamic graphs at multiple temporal scales.\nFirst, we recursively generate temporal summaries to abstract overlapping\nsequences of graphs into compact snapshots. Second, we apply graph embeddings\nto the snapshots to learn low-dimensional representations of each sequence of\ngraphs to speed up specific analytical tasks (e.g., similarity search). Third,\nwe visualize the evolving data from a coarse to fine-granular snapshots to\nsemi-automatically analyze temporal states, trends, and outliers. The approach\nenables to discover similar temporal summaries (e.g., recurring states),\nreduces the temporal data to speed up automatic analysis, and to explore both\nstructural and temporal properties of a dynamic graph. We demonstrate the\nusefulness of our approach by a quantitative evaluation and the application to\na real-world dataset.",
+                    "authors": "Eren Cakmak, Udo Schlegel, Dominik J\u00e4ckle, Daniel Keim, Tobias Schreck",
+                    "published": "2020-08-19",
+                    "updated": "2020-09-15",
+                    "primary_cat": "cs.HC",
+                    "cats": [
+                        "cs.HC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.05064v1",
+                    "title": "Adaptive Graph Spatial-Temporal Transformer Network for Traffic Flow Forecasting",
+                    "abstract": "Traffic flow forecasting on graphs has real-world applications in many\nfields, such as transportation system and computer networks. Traffic\nforecasting can be highly challenging due to complex spatial-temporal\ncorrelations and non-linear traffic patterns. Existing works mostly model such\nspatial-temporal dependencies by considering spatial correlations and temporal\ncorrelations separately and fail to model the direct spatial-temporal\ncorrelations. Inspired by the recent success of transformers in the graph\ndomain, in this paper, we propose to directly model the cross-spatial-temporal\ncorrelations on the spatial-temporal graph using local multi-head\nself-attentions. To reduce the time complexity, we set the attention receptive\nfield to the spatially neighboring nodes, and we also introduce an adaptive\ngraph to capture the hidden spatial-temporal dependencies. Based on these\nattention mechanisms, we propose a novel Adaptive Graph Spatial-Temporal\nTransformer Network (ASTTN), which stacks multiple spatial-temporal attention\nlayers to apply self-attention on the input graph, followed by linear layers\nfor predictions. Experimental results on public traffic network datasets,\nMETR-LA PEMS-BAY, PeMSD4, and PeMSD7, demonstrate the superior performance of\nour model.",
+                    "authors": "Aosong Feng, Leandros Tassiulas",
+                    "published": "2022-07-09",
+                    "updated": "2022-07-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.01928v1",
+                    "title": "Constructing Temporal Dynamic Knowledge Graphs from Interactive Text-based Games",
+                    "abstract": "In natural language processing, interactive text-based games serve as a test\nbed for interactive AI systems. Prior work has proposed to play text-based\ngames by acting based on discrete knowledge graphs constructed by the Discrete\nGraph Updater (DGU) to represent the game state from the natural language\ndescription. While DGU has shown promising results with high interpretability,\nit suffers from lower knowledge graph accuracy due to its lack of temporality\nand limited generalizability to complex environments with objects with the same\nlabel. In order to address DGU's weaknesses while preserving its high\ninterpretability, we propose the Temporal Discrete Graph Updater (TDGU), a\nnovel neural network model that represents dynamic knowledge graphs as a\nsequence of timestamped graph events and models them using a temporal point\nbased graph neural network. Through experiments on the dataset collected from a\ntext-based game TextWorld, we show that TDGU outperforms the baseline DGU. We\nfurther show the importance of temporal information for TDGU's performance\nthrough an ablation study and demonstrate that TDGU has the ability to\ngeneralize to more complex environments with objects with the same label. All\nthe relevant code can be found at\n\\url{https://github.com/yukw777/temporal-discrete-graph-updater}.",
+                    "authors": "Keunwoo Peter Yu",
+                    "published": "2023-11-03",
+                    "updated": "2023-11-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1502.04579v3",
+                    "title": "The complexity of optimal design of temporally connected graphs",
+                    "abstract": "We study the design of small cost temporally connected graphs, under various\nconstraints. We mainly consider undirected graphs of $n$ vertices, where each\nedge has an associated set of discrete availability instances (labels). A\njourney from vertex $u$ to vertex $v$ is a path from $u$ to $v$ where\nsuccessive path edges have strictly increasing labels. A graph is temporally\nconnected iff there is a $(u,v)$-journey for any pair of vertices $u,v,~u\\not=\nv$. We first give a simple polynomial-time algorithm to check whether a given\ntemporal graph is temporally connected. We then consider the case in which a\ndesigner of temporal graphs can \\emph{freely choose} availability instances for\nall edges and aims for temporal connectivity with very small \\emph{cost}; the\ncost is the total number of availability instances used. We achieve this via a\nsimple polynomial-time procedure which derives designs of cost linear in $n$.\nWe also show that the above procedure is (almost) optimal when the underlying\ngraph is a tree, by proving a lower bound on the cost for any tree. However,\nthere are pragmatic cases where one is not free to design a temporally\nconnected graph anew, but is instead \\emph{given} a temporal graph design with\nthe claim that it is temporally connected, and wishes to make it more\ncost-efficient by removing labels without destroying temporal connectivity\n(redundant labels). Our main technical result is that computing the maximum\nnumber of redundant labels is APX-hard, i.e., there is no PTAS unless $P=NP$.\nOn the positive side, we show that in dense graphs with random edge\navailabilities, there is asymptotically almost surely a very large number of\nredundant labels. A temporal design may, however, be \\emph{minimal}, i.e., no\nredundant labels exist. We show the existence of minimal temporal designs with\nat least $n \\log{n}$ labels.",
+                    "authors": "Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, Paul G. Spirakis",
+                    "published": "2015-02-16",
+                    "updated": "2016-07-06",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.19292v1",
+                    "title": "Fusing Temporal Graphs into Transformers for Time-Sensitive Question Answering",
+                    "abstract": "Answering time-sensitive questions from long documents requires temporal\nreasoning over the times in questions and documents. An important open question\nis whether large language models can perform such reasoning solely using a\nprovided text document, or whether they can benefit from additional temporal\ninformation extracted using other systems. We address this research question by\napplying existing temporal information extraction systems to construct temporal\ngraphs of events, times, and temporal relations in questions and documents. We\nthen investigate different approaches for fusing these graphs into Transformer\nmodels. Experimental results show that our proposed approach for fusing\ntemporal graphs into input text substantially enhances the temporal reasoning\ncapabilities of Transformer models with or without fine-tuning. Additionally,\nour proposed method outperforms various graph convolution-based approaches and\nestablishes a new state-of-the-art performance on SituatedQA and three splits\nof TimeQA.",
+                    "authors": "Xin Su, Phillip Howard, Nagib Hakim, Steven Bethard",
+                    "published": "2023-10-30",
+                    "updated": "2023-10-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1310.7898v1",
+                    "title": "Moving in temporal graphs with very sparse random availability of edges",
+                    "abstract": "In this work we consider temporal graphs, i.e. graphs, each edge of which is\nassigned a set of discrete time-labels drawn from a set of integers. The labels\nof an edge indicate the discrete moments in time at which the edge is\navailable. We also consider temporal paths in a temporal graph, i.e. paths\nwhose edges are assigned a strictly increasing sequence of labels. Furthermore,\nwe assume the uniform case (UNI-CASE), in which every edge of a graph is\nassigned exactly one time label from a set of integers and the time labels\nassigned to the edges of the graph are chosen randomly and independently, with\nthe selection following the uniform distribution. We call uniform random\ntemporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the\nexpected number of temporal paths of a given length in the uniform random\ntemporal clique. We define the term temporal distance of two vertices, which is\nthe arrival time, i.e. the time-label of the last edge, of the temporal path\nthat connects those vertices, which has the smallest arrival time amongst all\ntemporal paths that connect those vertices. We then propose and study two\nstatistical properties of temporal graphs. One is the maximum expected temporal\ndistance which is, as the term indicates, the maximum of all expected temporal\ndistances in the graph. The other one is the temporal diameter which, loosely\nspeaking, is the expectation of the maximum temporal distance in the graph. We\nderive the maximum expected temporal distance of a uniform random temporal star\ngraph as well as an upper bound on both the maximum expected temporal distance\nand the temporal diameter of the normalized version of the uniform random\ntemporal clique, in which the largest time-label available equals the number of\nvertices. Finally, we provide an algorithm that solves an optimization problem\non a specific type of temporal (multi)graphs of two vertices.",
+                    "authors": "Paul G. Spirakis, Eleni Ch. Akrida",
+                    "published": "2013-10-29",
+                    "updated": "2013-10-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1207.7103v1",
+                    "title": "Temporal Reachability Graphs",
+                    "abstract": "While a natural fit for modeling and understanding mobile networks,\ntime-varying graphs remain poorly understood. Indeed, many of the usual\nconcepts of static graphs have no obvious counterpart in time-varying ones. In\nthis paper, we introduce the notion of temporal reachability graphs. A\n(tau,delta)-reachability graph} is a time-varying directed graph derived from\nan existing connectivity graph. An edge exists from one node to another in the\nreachability graph at time t if there exists a journey (i.e., a spatiotemporal\npath) in the connectivity graph from the first node to the second, leaving\nafter t, with a positive edge traversal time tau, and arriving within a maximum\ndelay delta. We make three contributions. First, we develop the theoretical\nframework around temporal reachability graphs. Second, we harness our\ntheoretical findings to propose an algorithm for their efficient computation.\nFinally, we demonstrate the analytic power of the temporal reachability graph\nconcept by applying it to synthetic and real-life datasets. On top of defining\nclear upper bounds on communication capabilities, reachability graphs highlight\nasymmetric communication opportunities and offloading potential.",
+                    "authors": "John Whitbeck, Marcelo Dias de Amorim, Vania Conan, Jean-Loup Guillaume",
+                    "published": "2012-07-30",
+                    "updated": "2012-07-30",
+                    "primary_cat": "cs.NI",
+                    "cats": [
+                        "cs.NI",
+                        "C.2.1; F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.05631v2",
+                    "title": "ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling",
+                    "abstract": "The spatio-temporal graph learning is becoming an increasingly important\nobject of graph study. Many application domains involve highly dynamic graphs\nwhere temporal information is crucial, e.g. traffic networks and financial\ntransaction graphs. Despite the constant progress made on learning structured\ndata, there is still a lack of effective means to extract dynamic complex\nfeatures from spatio-temporal structures. Particularly, conventional models\nsuch as convolutional networks or recurrent neural networks are incapable of\nrevealing the temporal patterns in short or long terms and exploring the\nspatial properties in local or global scope from spatio-temporal graphs\nsimultaneously. To tackle this problem, we design a novel multi-scale\narchitecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series\nmodeling. In this U-shaped network, a paired sampling operation is proposed in\nspacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in\nspatial from its deterministic partition while abstracts multi-resolution\ntemporal dependencies through dilated recurrent skip connections; based on\nprevious settings in the downsampling, the unpooling (ST-Unpool) restores the\noriginal structure of spatio-temporal graphs and resumes regular intervals\nwithin graph sequences. Experiments on spatio-temporal prediction tasks\ndemonstrate that our model effectively captures comprehensive features in\nmultiple scales and achieves substantial improvements over mainstream methods\non several real-world datasets.",
+                    "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+                    "published": "2019-03-13",
+                    "updated": "2021-06-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.01727v2",
+                    "title": "Skeleton-Based Action Segmentation with Multi-Stage Spatial-Temporal Graph Convolutional Neural Networks",
+                    "abstract": "The ability to identify and temporally segment fine-grained actions in motion\ncapture sequences is crucial for applications in human movement analysis.\nMotion capture is typically performed with optical or inertial measurement\nsystems, which encode human movement as a time series of human joint locations\nand orientations or their higher-order representations. State-of-the-art action\nsegmentation approaches use multiple stages of temporal convolutions. The main\nidea is to generate an initial prediction with several layers of temporal\nconvolutions and refine these predictions over multiple stages, also with\ntemporal convolutions. Although these approaches capture long-term temporal\npatterns, the initial predictions do not adequately consider the spatial\nhierarchy among the human joints. To address this limitation, we recently\nintroduced multi-stage spatial-temporal graph convolutional neural networks\n(MS-GCN). Our framework replaces the initial stage of temporal convolutions\nwith spatial graph convolutions and dilated temporal convolutions, which better\nexploit the spatial configuration of the joints and their long-term temporal\ndynamics. Our framework was compared to four strong baselines on five tasks.\nExperimental results demonstrate that our framework is a strong baseline for\nskeleton-based action segmentation.",
+                    "authors": "Benjamin Filtjens, Bart Vanrumste, Peter Slaets",
+                    "published": "2022-02-03",
+                    "updated": "2022-10-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.16078v2",
+                    "title": "Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs",
+                    "abstract": "We present the Evolving Graph Fourier Transform (EFT), the first invertible\nspectral transform that captures evolving representations on temporal graphs.\nWe motivate our work by the inadequacy of existing methods for capturing the\nevolving graph spectra, which are also computationally expensive due to the\ntemporal aspect along with the graph vertex domain. We view the problem as an\noptimization over the Laplacian of the continuous time dynamic graph.\nAdditionally, we propose pseudo-spectrum relaxations that decompose the\ntransformation process, making it highly computationally efficient. The EFT\nmethod adeptly captures the evolving graph's structural and positional\nproperties, making it effective for downstream tasks on evolving graphs. Hence,\nas a reference implementation, we develop a simple neural model induced with\nEFT for capturing evolving graph spectra. We empirically validate our\ntheoretical findings on a number of large-scale and standard temporal graph\nbenchmarks and demonstrate that our model achieves state-of-the-art\nperformance.",
+                    "authors": "Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Manish Singh, Toyotaro Suzumura",
+                    "published": "2024-02-25",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.09791v2",
+                    "title": "Temporal Betweenness Centrality on Shortest Paths",
+                    "abstract": "Betweenness centrality measure assesses the importance of nodes in a graph\nand has been used in a variety of contexts. Betweenness centrality has also\nbeen extended to temporal graphs. Temporal graphs have edges that bear labels\naccording to the time of the interactions between the nodes. Betweenness\ncentrality has been extended to the temporal graph settings, and the notion of\npaths has been extended to temporal paths. Recent results by Bu{\\ss} et al. and\nRymar et al. showed that the betweenness centrality of all nodes in a temporal\ngraph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of\ntime units, m the number of temporal edges and n the number of nodes. In this\npaper, we improve the running time analysis of these previous approaches to\ncompute the betweenness centrality of all nodes in a temporal graph. We give an\nalgorithm that runs in O(n m T + n^2 T ).",
+                    "authors": "Mehdi Naima, Matthieu Latapy, Cl\u00e9mence Magnien",
+                    "published": "2023-04-19",
+                    "updated": "2023-06-06",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.12973v1",
+                    "title": "Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is one of the most fundamental problems in transportation\nscience and artificial intelligence. The key challenge is to effectively model\ncomplex spatial-temporal dependencies and correlations in modern traffic data.\nExisting methods, however, cannot accurately model both long-term and\nshort-term temporal correlations simultaneously, limiting their expressive\npower on complex spatial-temporal patterns. In this paper, we propose a novel\nspatial-temporal neural network framework: Attention-based Spatial-Temporal\nGraph Convolutional Recurrent Network (ASTGCRN), which consists of a graph\nconvolutional recurrent module (GCRN) and a global attention module. In\nparticular, GCRN integrates gated recurrent units and adaptive graph\nconvolutional networks for dynamically learning graph structures and capturing\nspatial dependencies and local temporal relationships. To effectively extract\nglobal temporal dependencies, we design a temporal attention layer and\nimplement it as three independent modules based on multi-head self-attention,\ntransformer, and informer respectively. Extensive experiments on five real\ntraffic datasets have demonstrated the excellent predictive performance of all\nour three models with all their average MAE, RMSE and MAPE across the test\ndatasets lower than the baseline methods.",
+                    "authors": "Haiyang Liu, Chunjiang Zhu, Detian Zhang, Qing Li",
+                    "published": "2023-02-25",
+                    "updated": "2023-02-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.15894v1",
+                    "title": "A Gated MLP Architecture for Learning Topological Dependencies in Spatio-Temporal Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) and Transformer have been increasingly adopted\nto learn the complex vector representations of spatio-temporal graphs,\ncapturing intricate spatio-temporal dependencies crucial for applications such\nas traffic datasets. Although many existing methods utilize multi-head\nattention mechanisms and message-passing neural networks (MPNNs) to capture\nboth spatial and temporal relations, these approaches encode temporal and\nspatial relations independently, and reflect the graph's topological\ncharacteristics in a limited manner. In this work, we introduce the Cycle to\nMixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial\ninvariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP).\nThe Cy2Mixer is composed of three blocks based on MLPs: A message-passing block\nfor encapsulating spatial information, a cycle message-passing block for\nenriching topological information through cyclic subgraphs, and a temporal\nblock for capturing temporal properties. We bolster the effectiveness of\nCy2Mixer with mathematical evidence emphasizing that our cycle message-passing\nblock is capable of offering differentiated information to the deep learning\nmodel compared to the message-passing block. Furthermore, empirical evaluations\nsubstantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art\nperformances across various traffic benchmark datasets.",
+                    "authors": "Yun Young Choi, Minho Lee, Sun Woo Park, Seunghwan Lee, Joohwan Ko",
+                    "published": "2024-01-29",
+                    "updated": "2024-01-29",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.00963v5",
+                    "title": "The Complexity of Finding Small Separators in Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs with time-stamped edges. We study the problem of\nfinding a small vertex set (the separator) with respect to two designated\nterminal vertices such that the removal of the set eliminates all temporal\npaths connecting one terminal to the other. Herein, we consider two models of\ntemporal paths: paths that pass through arbitrarily many edges per time step\n(non-strict) and paths that pass through at most one edge per time step\n(strict). Regarding the number of time steps of a temporal graph, we show a\ncomplexity dichotomy (NP-hardness versus polynomial-time solvability) for both\nproblem variants. Moreover we prove both problem variants to be NP-complete\neven on temporal graphs whose underlying graph is planar. We further show that,\non temporal graphs with planar underlying graph, if additionally the number of\ntime steps is constant, then the problem variant for strict paths is solvable\nin quasi-linear time. Finally, we introduce and motivate the notion of a\ntemporal core (vertices whose incident edges change over time). We prove that\nthe non-strict variant is fixed-parameter tractable when parameterized by the\nsize of the temporal core, while the strict variant remains NP-complete, even\nfor constant-size temporal cores.",
+                    "authors": "Philipp Zschoche, Till Fluschnik, Hendrik Molter, Rolf Niedermeier",
+                    "published": "2017-11-02",
+                    "updated": "2018-07-25",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.02875v1",
+                    "title": "Multi-Task Edge Prediction in Temporally-Dynamic Video Graphs",
+                    "abstract": "Graph neural networks have shown to learn effective node representations,\nenabling node-, link-, and graph-level inference. Conventional graph networks\nassume static relations between nodes, while relations between entities in a\nvideo often evolve over time, with nodes entering and exiting dynamically. In\nsuch temporally-dynamic graphs, a core problem is inferring the future state of\nspatio-temporal edges, which can constitute multiple types of relations. To\naddress this problem, we propose MTD-GNN, a graph network for predicting\ntemporally-dynamic edges for multiple types of relations. We propose a\nfactorized spatio-temporal graph attention layer to learn dynamic node\nrepresentations and present a multi-task edge prediction loss that models\nmultiple relations simultaneously. The proposed architecture operates on top of\nscene graphs that we obtain from videos through object detection and\nspatio-temporal linking. Experimental evaluations on ActionGenome and CLEVRER\nshow that modeling multiple relations in our temporally-dynamic graph network\ncan be mutually beneficial, outperforming existing static and spatio-temporal\ngraph neural networks, as well as state-of-the-art predicate classification\nmethods.",
+                    "authors": "Osman \u00dclger, Julian Wiederer, Mohsen Ghafoorian, Vasileios Belagiannis, Pascal Mettes",
+                    "published": "2022-12-06",
+                    "updated": "2022-12-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13624v1",
+                    "title": "Towards Linear Spanners in All Temporal Cliques",
+                    "abstract": "Many real-world networks, like transportation networks and social networks,\nare dynamic in the sense that the edge set may change over time, but these\nchanges are known in advance. This behavior is captured by the temporal graphs\nmodel, which has recently become a trending topic in theoretical computer\nscience. A core open problem in the field is to prove the existence of\nlinear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of\ncomplete temporal graphs that ensure all-pairs reachability via temporal paths.\nSo far, the best known result is the existence of temporal spanners with\n$\\mathcal{O}(n\\log n)$ many edges. We present significant progress towards\nproving that linear-size temporal spanners exist in all temporal cliques.\n  We adapt techniques used in previous works and heavily expand and generalize\nthem to provide a simpler and more intuitive proof of the $\\mathcal{O}(n\\log\nn)$ bound. Moreover, we use our novel approach to show that a large class of\ntemporal cliques, called edge-pivot graphs, admit linear-size temporal\nspanners. To contrast this, we investigate other classes of temporal cliques\nthat do not belong to the class of edge-pivot graphs. We introduce two such\ngraph classes and we develop novel techniques for establishing the existence of\nlinear temporal spanners in these graph classes as well.",
+                    "authors": "Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, Armin Wells",
+                    "published": "2024-02-21",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.02852v1",
+                    "title": "Introduction to a Temporal Graph Benchmark",
+                    "abstract": "A temporal graph is a data structure, consisting of nodes and edges in which\nthe edges are associated with time labels. To analyze the temporal graph, the\nfirst step is to find a proper graph dataset/benchmark. While many temporal\ngraph datasets exist online, none could be found that used the interval labels\nin which each edge is associated with a starting and ending time. Therefore we\ncreate a temporal graph data based on Wikipedia reference graph for temporal\nanalysis. This report aims to provide more details of this graph benchmark to\nthose who are interested in using it.",
+                    "authors": "Wouter Ligtenberg, Yulong Pei",
+                    "published": "2017-02-20",
+                    "updated": "2017-02-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.09039v1",
+                    "title": "Spatial-temporal Memories Enhanced Graph Autoencoder for Anomaly Detection in Dynamic Graphs",
+                    "abstract": "Anomaly detection in dynamic graphs presents a significant challenge due to\nthe temporal evolution of graph structures and attributes. The conventional\napproaches that tackle this problem typically employ an unsupervised learning\nframework, capturing normality patterns with exclusive normal data during\ntraining and identifying deviations as anomalies during testing. However, these\nmethods face critical drawbacks: they either only depend on proxy tasks for\ngeneral representation without directly pinpointing normal patterns, or they\nneglect to differentiate between spatial and temporal normality patterns,\nleading to diminished efficacy in anomaly detection. To address these\nchallenges, we introduce a novel Spatial-Temporal memories-enhanced graph\nautoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs)\nand gated temporal convolution layers to extract spatial features and temporal\nfeatures, respectively. Then STRIPE incorporates separate spatial and temporal\nmemory networks, which capture and store prototypes of normal patterns, thereby\npreserving the uniqueness of spatial and temporal normality. After that,\nthrough a mutual attention mechanism, these stored patterns are then retrieved\nand integrated with encoded graph embeddings. Finally, the integrated features\nare fed into the decoder to reconstruct the graph streams which serve as the\nproxy task for anomaly detection. This comprehensive approach not only\nminimizes reconstruction errors but also refines the model by emphasizing the\ncompactness and distinctiveness of the embeddings in relation to the nearest\nmemory prototypes. Through extensive testing, STRIPE has demonstrated a\nsuperior capability to discern anomalies by effectively leveraging the distinct\nspatial and temporal dynamics of dynamic graphs, significantly outperforming\nexisting methodologies, with an average improvement of 15.39% on AUC values.",
+                    "authors": "Jie Liu, Xuequn Shang, Xiaolin Han, Wentao Zhang, Hongzhi Yin",
+                    "published": "2024-03-14",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.12587v1",
+                    "title": "TGLib: An Open-Source Library for Temporal Graph Analysis",
+                    "abstract": "We initiate an open-source library for the efficient analysis of temporal\ngraphs. We consider one of the standard models of dynamic networks in which\neach edge has a discrete timestamp and transition time. Recently there has been\na massive interest in analyzing such temporal graphs. Common computational data\nmining and analysis tasks include the computation of temporal distances,\ncentrality measures, and network statistics like topological overlap,\nburstiness, or temporal diameter. To fulfill the increasing demand for\nefficient and easy-to-use implementations of temporal graph algorithms, we\nintroduce the open-source library TGLib, which integrates efficient data\nstructures and algorithms for temporal graph analysis. TGLib is highly\nefficient and versatile, providing simple and convenient C++ and Python\ninterfaces, targeting computer scientists, practitioners, students, and the\n(temporal) network research community.",
+                    "authors": "Lutz Oettershagen, Petra Mutzel",
+                    "published": "2022-09-26",
+                    "updated": "2022-09-26",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07491v3",
+                    "title": "Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment",
+                    "abstract": "Temporal graph learning aims to generate high-quality representations for\ngraph-based tasks with dynamic information, which has recently garnered\nincreasing attention. In contrast to static graphs, temporal graphs are\ntypically organized as node interaction sequences over continuous time rather\nthan an adjacency matrix. Most temporal graph learning methods model current\ninteractions by incorporating historical neighborhood. However, such methods\nonly consider first-order temporal information while disregarding crucial\nhigh-order structural information, resulting in suboptimal performance. To\naddress this issue, we propose a self-supervised method called S2T for temporal\ngraph learning, which extracts both temporal and structural information to\nlearn more informative node representations. Notably, the initial node\nrepresentations combine first-order temporal and high-order structural\ninformation differently to calculate two conditional intensities. An alignment\nloss is then introduced to optimize the node representations, narrowing the gap\nbetween the two intensities and making them more informative. Concretely, in\naddition to modeling temporal information using historical neighbor sequences,\nwe further consider structural knowledge at both local and global levels. At\nthe local level, we generate structural intensity by aggregating features from\nhigh-order neighbor sequences. At the global level, a global representation is\ngenerated based on all nodes to adjust the structural intensity according to\nthe active statuses on different nodes. Extensive experiments demonstrate that\nthe proposed model S2T achieves at most 10.13% performance improvement compared\nwith the state-of-the-art competitors on several datasets.",
+                    "authors": "Meng Liu, Ke Liang, Yawei Zhao, Wenxuan Tu, Sihang Zhou, Xinbiao Gan, Xinwang Liu, Kunlun He",
+                    "published": "2023-02-15",
+                    "updated": "2024-04-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1401.1919v1",
+                    "title": "Temporal Graph Traversals: Definitions, Algorithms, and Applications",
+                    "abstract": "A temporal graph is a graph in which connections between vertices are active\nat specific times, and such temporal information leads to completely new\npatterns and knowledge that are not present in a non-temporal graph. In this\npaper, we study traversal problems in a temporal graph. Graph traversals, such\nas DFS and BFS, are basic operations for processing and studying a graph. While\nboth DFS and BFS are well-known simple concepts, it is non-trivial to adopt the\nsame notions from a non-temporal graph to a temporal graph. We analyze the\ndifficulties of defining temporal graph traversals and propose new definitions\nof DFS and BFS for a temporal graph. We investigate the properties of temporal\nDFS and BFS, and propose efficient algorithms with optimal complexity. In\nparticular, we also study important applications of temporal DFS and BFS. We\nverify the efficiency and importance of our graph traversal algorithms in real\nworld temporal graphs.",
+                    "authors": "Silu Huang, James Cheng, Huanhuan Wu",
+                    "published": "2014-01-09",
+                    "updated": "2014-01-09",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.12003v1",
+                    "title": "On Finding Separators in Temporal Split and Permutation Graphs",
+                    "abstract": "Removing all connections between two vertices s and z in a graph by removing\na minimum number of vertices is a fundamental problem in algorithmic graph\ntheory. This (s,z)-separation problem is well-known to be polynomial solvable\nand serves as an important primitive in many applications related to network\nconnectivity. We study the NP-hard temporal (s,z)-separation problem on\ntemporal graphs, which are graphs with fixed vertex sets but edge sets that\nchange over discrete time steps. We tackle this problem by restricting the\nlayers (i.e., graphs characterized by edges that are present at a certain point\nin time) to specific graph classes. We restrict the layers of the temporal\ngraphs to be either all split graphs or all permutation graphs (both being\nperfect graph classes) and provide both intractability and tractability\nresults. In particular, we show that in general the problem remains NP-hard\nboth on temporal split and temporal permutation graphs, but we also spot\npromising islands of fixed-parameter tractability particularly based on\nparameterizations that measure the amount of \"change over time\".",
+                    "authors": "Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken",
+                    "published": "2021-05-25",
+                    "updated": "2021-05-25",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2108.08719v5",
+                    "title": "Temporal Graph Functional Dependencies [Extended Version]",
+                    "abstract": "Data dependencies have been extended to graphs to characterize topological\nand value constraints. Existing data dependencies are defined to capture\ninconsistencies in static graphs. Nevertheless, inconsistencies may occur over\nevolving graphs and only for certain time periods. The need for capturing such\ninconsistencies in temporal graphs is evident in anomaly detection and\npredictive dynamic network analysis. This paper introduces a class of data\ndependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs\ngeneralize functional dependencies to temporal graphs as a sequence of graph\nsnapshots that are induced by time intervals, and enforce both topological\nconstraints and attribute value dependencies that must be satisfied by these\nsnapshots. (1) We establish the complexity results for the satisfiability and\nimplication problems of TGFDs. (2) We propose a sound and complete\naxiomatization system for TGFDs. (3) We also present efficient parallel\nalgorithms to detect inconsistencies in temporal graphs as violations of TGFDs.\nThe algorithm exploits data and temporal locality induced by time intervals,\nand uses incremental pattern matching and load balancing strategies to enable\nfeasible error detection in large temporal graphs. Using real datasets, we\nexperimentally verify that our algorithms achieve lower runtimes compared to\nexisting baselines, while improving the accuracy over error detection using\nexisting graph data constraints, e.g., GFDs and GTARs with 55% and 74% gain in\nF1-score, respectively.",
+                    "authors": "Morteza Alipourlangouri, Adam Mansfield, Fei Chiang, Yinghui Wu",
+                    "published": "2021-08-19",
+                    "updated": "2022-07-26",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2310.05517v1",
+                    "title": "WeatherGNN: Exploiting Complicated Relationships in Numerical Weather Prediction Bias Correction",
+                    "abstract": "Numerical weather prediction (NWP) may be inaccurate or biased due to\nincomplete atmospheric physical processes, insufficient spatial-temporal\nresolution, and inherent uncertainty of weather. Previous studies have\nattempted to correct biases by using handcrafted features and domain knowledge,\nor by applying general machine learning models naively. They do not fully\nexplore the complicated meteorologic interactions and spatial dependencies in\nthe atmosphere dynamically, which limits their applicability in NWP\nbias-correction. Specifically, weather factors interact with each other in\ncomplex ways, and these interactions can vary regionally. In addition, the\ninteractions between weather factors are further complicated by the spatial\ndependencies between regions, which are influenced by varied terrain and\natmospheric motions. To address these issues, we propose WeatherGNN, an NWP\nbias-correction method that utilizes Graph Neural Networks (GNN) to learn\nmeteorologic and geographic relationships in a unified framework. Our approach\nincludes a factor-wise GNN that captures meteorological interactions within\neach grid (a specific location) adaptively, and a fast hierarchical GNN that\ncaptures spatial dependencies between grids dynamically. Notably, the fast\nhierarchical GNN achieves linear complexity with respect to the number of\ngrids, enhancing model efficiency and scalability. Our experimental results on\ntwo real-world datasets demonstrate the superiority of WeatherGNN in comparison\nwith other SOTA methods, with an average improvement of 40.50\\% on RMSE\ncompared to the original NWP.",
+                    "authors": "Binqing Wu, Weiqi Chen, Wengwei Wang, Bingqing Peng, Liang Sun, Ling Chen",
+                    "published": "2023-10-09",
+                    "updated": "2023-10-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Temporal AND Graph",
+                    "gt": "Bias-correction for NWP. Bias-correction methods have evolved from classical statistical methods, e.g., correcting the variance and average (Zhang et al. 2019), to shallow machine learning methods, e.g., deep belief networks (Hu et al. 2021) and SVM (Yoshikane and Yoshimura 2022). At present, a majority of DL works have emerged and achieved advantageous correcting effects due to their strong representative abilities. They mainly rely on LSTM (Li et al. 2022; Yang et al. 2022), CNN (Han et al. 2021), or their hybrid models (Han et al. 2022) to correct certain common weather factors, e.g., wind speed and precipitation. Some advanced models have also been applied to NWP bias-correction tasks and have undergone impressive improvement. For example, a recent work (Ge et al. 2022) uses AFNO (Guibas et al. 2021a) to learn continuous status of the atmosphere from sparse and non-uniform weather observational data for gridfree bias-correction. However, these studies rarely consider meteorologic and geographic relationships within NWP comprehensively. Therefore, how to fully use such relationships to correct the bias within NWP is still an open problem. DL methods for spatial-temporal modeling. DL methods for spatial-temporal modeling have shown promising results in various applications, e.g., video action recognition (Cai, Yao, and Chen 2021), time series analysis (Chen, Gel, and Poor 2022; Liu et al. 2022), and earth system modeling (Gao et al. 2022). These methods can capture relationships between spatial and temporal dimensions and help to understand the underlying structure and dynamics of the spatialtemporal data. Some of them have been widely used due to their good generalization and model capacity, e.g., 3D convolutions (Guo et al. 2019; Luo and Yuille 2019), attention (Yan et al. 2019; Karim et al. 2022; Wei et al. 2022), Vison Transformers (ViT) (Dosovitskiy et al. 2020), and spatial-temporal graph neural networks (STGNNs) (Cai et al. 2019; VazquezEnriquez et al. 2021). In particular, STGNNs demonstrate superior performance when dealing with complex spatialtemporal data. They combine the strengths of GNNs with RNNs, CNNs, or attentions to capture dynamic changes in spatial dependencies over time (Yu, Yin, and Zhu 2018; Bai et al. 2020; Wu et al. 2020; Chen et al. 2020). However, STGNNs face the challenges of designing graph structures in particular scenarios and performing efficient message passing across the graph, especially on large-scale datasets. DL methods for medium-range global weather forecasting. Since 2022, DL weather models have made significant progress in medium-range global weather forecasting (Rasp et al. 2023). For example, FourCastNet (Pathak et al. 2022) generates global forecasts based on AFNO. Pangu (Bi et al. 2023), Fengwu (Chen et al. 2023a), Fuxi (Chen et al. 2023b), and ClimaX (Nguyen et al. 2023) extend hierarchical ViT architectures by plug-and-play modules, e.g., model-specific encoder-decoders and buffer mechanisms, to make longer global forecasts. GraphCast (Lam et al. 2022) follows a GNN architecture and designs a multi-scale unweighted mesh graph to make autoregressive global forecasts. However, due to computational constraints, these global models do not consider the complex relationships between weather factors and terrain as WeatherGNN does. Thus, they fail to capture the detailed local weather patterns characterized by the complex interactions between different weather factors and the corresponding terrain. This leads to a gap between global weather forecasting and local weather forecasting, which highlights the need for bias-correction models in local NWP.",
+                    "pre_questions": [],
+                    "main_content": "Introduction With decades of evolution, numerical weather prediction (NWP) has become the widely accepted and effective method for weather forecasting (Bauer, Thorpe, and Brunet 2015). NWP has developed from numerically solving mathematical equations derived from physical laws (Moran and Moran 2009) to generating by data-driven weather forecasting models (Bi et al. 2023; Chen et al. 2023b; Nguyen et al. 2023). Despite its advancements, NWP still faces challenges, e.g., incomplete atmospheric physical processes, insufficient spatialtemporal resolution, and inherent weather uncertainty (Gneiting and Raftery 2005; Yoshikane and Yoshimura 2022; Li *These authors contributed equally. \u2020Corresponding author. Copyright \u00a9 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Grid A Grid B Grid C Grid D A B C D (a) (b) Figure 1: (a) Pearson Correlation Matrices of Different Weather Factors. Warm colors indicate a strong correlation, while cool colors indicate a weak correlation. (b) Locations and Terrains of the Four Grids. Grids A, C and D are on the uphill, while B is in a valley. et al. 2022). These limitations can lead to inaccuracies or biases in the forecasted results. As there is a growing demand for accurate weather forecasting in various applications, e.g., wind power forecasting (Han et al. 2022; Li et al. 2022), it motivates to incorporate post-modeling bias-correction process to enhance the accuracy and reliability of NWP. Local NWP bias-correction, aims to reduce the difference between origin NWP and observations for a specific region. (Maraun 2016; Zhang et al. 2019; Yoshikane and Yoshimura 2022; Yang et al. 2022). Previous studies have attempted to address this task using different approaches, ranging from classical statistical methods (Zhang et al. 2019) to shallow machine learning methods (Hu et al. 2021; Yoshikane and Yoshimura 2022), and even deep learning (DL) methods (Han et al. 2022; Li et al. 2022). However, these approaches often rely on handcrafted features and extensive domain knowledge or naive application of general data-driven models, overlooking the intricate and dynamic meteorological interactions between weather factors on different terrains and the spatial dependencies between different regions. To address this issue, we argue that two significant aspects of relationships within local NWP are still underestimated for bias-correction. Firstly, different weather factors interact in complicated ways, while the interactions vary regionally. Although physics could interpret partially, much more highly comarXiv:2310.05517v1  [cs.LG]  9 Oct 2023 (a) (b) (c) Figure 2: (a) Grid Distribution and Terrain of the Ningbo Dataset. (b) and (c) DTW similarity of 100m wind speed at one oceanic grid and one land grid with other grids. plex and nonlinear dependencies among different weather factors still remain untractable from the data-driven perspective. For instance, air temperature, humidity, and rainfall are highly interdependent, as an increase in air temperature leads to a rise in atmospheric humidity, facilitating cloud formation and precipitation (Moran and Moran 2009). Similarly, air pressure, wind speed, and wind direction also display intricate interrelationships. In addition, some external factors, especially topography, exert a significant influence on meteorological conditions (Moran and Moran 2009). Mountains, plateaus, and canyons affect wind direction and speed, leading to unique climate phenomena, e.g., canyon wind and valley wind. Terrain also influences temperature distribution via its effect on solar radiation, with height, slope, and orientation playing critical roles. Fig. 1 illustrates how weather factors correlate in different grids, where each grid represents a specific region. Grids A and B exhibit different correlation patterns due to different terrains (A is located uphill, whereas B sits in a valley. ) Secondly, spatial dependencies among different regions/grids are complicated due to varied terrain and atmospheric motions. The weather conditions in one region can significantly impact other regions, leading to potential spatial dependencies. For example, the spatial distribution and intensity of rainfall can affect the rainfall in surrounding areas. In addition, as depicted in Fig. 2, the similarity of 100m wind speed between different grids is highly coincidental with the similarity of terrain, where wind speed patterns on land and ocean are contrasting. Therefore, investigating the spatial dependencies of different regions is crucial for effectively correcting NWP biases. To this end, we propose WeatherGNN, a GNN-based model that leverages meteorologic and geographic relationships efficiently for local NWP bias-correction. WeatherGNN mainly consists of a factor-wise GNN that employs factor and geographic embeddings to learn intra-grid meteorological interactions considering terrain heterogeneity, and a fast hierarchical GNN that adopts a pre-defined hierarchical structure and a dynamic adjustment to learn inter-grid spatial dependencies according to domain knowledge and weather dynamics. The main contributions are summarized as: \u2022 We propose WeatherGNN that considers meteorologic and geographic relationships via GNNs for local NWP bias-correction in a unified framework. To the best of our knowledge, none of the preceding works have incorporated GNNs and domain knowledge simultaneously for this task. \u2022 We introduce a factor-wise GNN to model terrain-specific meteorologic interactions adaptively and a fast hierarchical GNN to capture hierarchical spatial relationships dynamically. By leveraging domain knowledge, fast hierarchical message passing can achieve a linear complexity with respect to the number of grids, enhancing the efficiency and scalability of WeatherGNN. \u2022 Extensive experimental results on two real-world datasets demonstrate the superiority of WeatherGNN, with an average improvement of 40.50% on RMSE compared to the original NWP. We formalize the problem of local NWP bias-correction and describe how to model both intra-grid meteorologic interactions and inter-grid spatial dependencies using WeatherGNN. Problem Definition The goal of local NWP bias-correction is to reduce the difference between origin NWP and observations for a specific region. The NWP data are represented as a sequence [Xi]T i=1, and [Xi]T i=1 \u2208RN\u00d7Fe\u00d7T , where N denotes the number of grids in this region 1, Fe denotes the number of weather factors (e.g., temperature, humidity, and wind speed), and T is the length of sequence. Similarly, [Yi]T i=1 \u2208RN\u00d7Fe\u00d7T represents the corresponding weather observations. Moreover, each grid has associated geographic information denoted as Z \u2208RN\u00d7Fg, where Fg is the dimension of geographic features (e.g., longitude, latitude, and altitude). The local NWP bias-correction problem aims to learn a function f(\u00b7) that maps weather forecasts to observations incorporating the geographic features: {[Xi]i\u2208\u2126(t); Z} f(\u00b7) \u2212 \u2212 \u2192Yt, \u2126(t) = {t \u2212\u03c4, \u00b7 \u00b7 \u00b7 , t \u22121 {[Xi]i\u2208\u2126(t); Z} \u00b7 \u2212 \u2212 \u2192Yt, \u2126(t) = {t \u2212\u03c4, \u00b7 \u00b7 \u00b7 , t \u22121, t, t + 1, \u00b7 \u00b7 \u00b7 , t + \u03c4}, (1) where \u2126(t) denotes a temporal window around time step t with length T = 2\u03c4 + 1 , as we consider a period of time before and after t when correcting Xt. For simplicity, in the remainder of the paper, we denote [Xi]i\u2208\u2126(t) and Yt by X and Y , respectively. 1A region tends to appear as a rectangle containing H \u00d7 W grids, and here we flatten the shape with N = H \u00d7 W. \ud835\udc68 \"!\"#$% \ud835\udc7a \"# \ud835\udc7a Geographic data Hierarchical structure learning Self-Attention Factor-wise graph learning Fast hierarchical message passing Message passing NWP data \u2026 \ud835\udc68!\"#%& Output Fast hierarchical GNN Factor-wise GNN ta grid spatial relations message (a) The Framework of WeatherGNN (b) The Illustration of  Message Pa 3: An Overview of WeatherGNN. (a) The Framework of WeatherGNN (b) The Illustration of Message P Figure 3: An Overview of WeatherGNN. Model Overview As illustrated in Fig. 3, WeatherGNN follows a two-branch architecture. The NWP sequences associated with the geographic features are input into factor-wise GNN and fast hierarchical GNN to capture the intra-grid meteorologic interactions and inter-grid spatial dependencies, respectively, and then mapped to corrected results. Learning Meteorologic Interactions via Factor-Wise Graph Neural Networks As previously discussed, accurately capturing the meteorologic interactions in different terrains is crucial for effectively correcting NWP biases. However, manually defining the correlations between different factors for each grid is challenging due to the significant time cost involved, as well as issues with applicability. To address this problem, we propose a factorwise graph learning (FGL) module that allows for automatic exploration of the hidden interrelationships between weather factors for each grid, while also considering variations in the terrain. Factor-wise graph learning. The FGL module first randomly initializes a learnable factor embedding dictionary Ef \u2208RFe\u00d7d for all weather factors, where each row corresponds to the embedding vector for each factor, and d is the dimension of factor embedding. This embedding is jointly optimized through model training to learn the hidden dependencies among different factors. Then, we take the geographic information of each grid Z as input and encode it with an MLP to obtain the grid-specific geographic embedding matrix Eg = MLP(Z) \u2208RN\u00d7d of all grids, where N is the number of grids. Given the factor embedding and gridspecific geographic embedding, we can infer relationships between weather factors for each grid by first computing grid-specific factor embedding E and then multiplying E and E\u22a4: Ei = Ef + Eg,i, Aintra,i = Softmax(EiE\u22a4 i ), Aintra = {Aintra,i}N i=1, (2) {} where Ei \u2208RFe\u00d7d is the grid-specific factor embedding of grid i considering geographic information. Aintra,i \u2208RFe\u00d7Fe represents the adjacency matrix of intra-grid factor-wise graph of grid i. FGL module can efficiently discover meteorologic interactions for each grid and has interpretability. Factor-wise GNN. Finally, enhanced by FGL, factor-wise GNN can be formulated as: Hi = GNN(Xi, Aintra,i), (3) where Xi \u2208RFe\u00d7T is the NWP data of grid i, and Hi \u2208 RFe\u00d7d is the corresponding output hidden state considering meteorologic interactions. GNN(\u00b7) can be different variants of Graph Neural Networks, and we choose GCN (Kipf and Welling 2016) for simplicity. This factor-wise message passing is performed for each grid in parallel, obtaining the final output H = {Hi}N i=1 \u2208RN\u00d7Fe\u00d7d. Moreover, according to Lemma 1, the factor-wise GNN has an O(N) complexity. Learning Spatial Dependencies via Fast Hierarchical Graph Neural Networks Another crucial aspect of accurate bias-correction is incorporating the complicated spatial dependencies that exist between different grids. However, due to the intricate nature of terrains and varying weather conditions, achieving this is a nontrivial task. To address this challenge, we propose the fast hierarchical GNN (FHGNN) that can effectively capture the inter-grid spatial dependencies. FHGNN involves several steps. First, we compute the initial spatial proximity of grids based on meteorologic and geometric distance and then construct the hierarchical structure by iteratively clustering grids into multi-level clusters (i.e., super-grids), where grids from the same cluster in lower levels are more relevant and should interact with each other. Next, we adjust the spatial proximity with the attention matrix based on the current weather conditions. Finally, a fast hierarchical message passing (FHMP) module is introduced to model the inter-grid spatial dependencies, which conducts fine-grained interactions among grids at low level but coarse-grained interactions at high level. Furthermore, FHGNN is able to achieve a linear complexity w.r.t. the number of grids, while vanilla GNN has a square complexity. Constructing hierarchical structure based on domain knowledge. We construct the hierarchical structure of grids based on pre-defined heuristic rules considering meteorologic and geographic distance. We calculate meteorologic distance matrix W by computing dynamic time warping (DTW) (M\u00fcller 2007) distance between weather sequences of each grid and the 3D geographic distance matrix D based on the latitude, longitude, and altitude information of grids obtained from geographic features Z. Specifically, the two distance matrices are calculated as follows: W f ij = DTW(Xf i , Xf j ), W ij = 1 Fe \u03a3Fe f=1W f ij, (4) Dij = q \u03bblatd2 lat,ij + \u03bblond2 lon,ij + \u03bbaltd2 alt,ij, (5) where Xf i and Xf j are the time series of the f-th weather factor of grid i and j in the whole training data, respectively. W f ij is the (i, j)-th entry of W f, which is the DTW distance matrix of all gird-pairs w.r.t weather factor f. W represents the average of DTW distance matrix of all weather factors. dlat,ij, dlon,ij, dalt,ij, are the latitude, longitude, and altitude distance between grid i and j, respectively, with \u03bb(\u00b7) being the corresponding coefficients to adjust the importance of these distances for calculating the geographic distance. Then, Gaussian kernels are applied to compute the corresponding similarity matrices, i.e., Amet and Ageo, which are further combined to represent the inter-grid spatial proximity matrix. The process is formulated as: Amet = exp(\u2212W 2/\u03c32 met), Ageo = exp(\u2212D2/\u03c32 geo), Ainter = Amet + Ageo, (6) where \u03c3(\u00b7) are hyperparameters to control the scale of the corresponding Gaussian kernels, which ensures both matrices have a similar range of values. Afterward, we adopt a clustering algorithm, e.g., K-means, to cluster grids into multi-level super-grids based on Ainter to construct the hierarchical structure. The clustering procedure is performed for L iterations, and at the l-th iteration, we cluster the grids at level l into the next coarsened super-grids at level l +1. We denote the assignment matrix returned from the clustering algorithm at level l as Sl \u2208{0, 1}N l\u00d7N l+1, where each row contains one 1, and others are 0s representing the assignment of each grid at level l to a super-grid at level l + 1. N l is the number of grids at level l. Besides, we compute the spatial proximity matrix Al for each level. The construction procedure of the hierarchical structure can be formulated as: Sl \u2190K-means(Al), Al = (Sl\u22121)\u22a4Al\u22121Sl\u22121, A0 = Ainter, (7) where, Al \u2208RN l\u00d7N l (l = 1, 2, \u00b7 \u00b7 \u00b7 , L) is the spatial proximity matrix at level l, which takes Al\u22121 and generates a coarsened proximity matrix denoting the connectivity strength between super-grids at level l. Moreover, we generate mask matrix M l to make the spatial proximity matrices sparse, where the (i, j)-th entry M l ij = 1 if grids i and j belong to the same cluster, and M l ij = 0 otherwise, as grids belonging to the same cluster have stronger interrelationships that are preferred to reserve. Dynamic adjustment of spatial dependencies based on NWP data. Spatial dependencies are also dependent on the weather conditions. For example, in windy weather, a grid has a strong correlation with its upwind grids. Thus, we encode the input NWP data X and utilize the attention matrix to adaptively adjust the spatial proximity matrices. This dynamic adjustment is formulated as 2: H0 Q = XW Q, H0 K = XW K, Hl Q = (Sl\u22121)\u22a4Hl\u22121 Q , Hl K = (Sl\u22121)\u22a4Hl\u22121 K , (8) \u02dc A l = M l \u2299Softmax(Hl QHl K \u22a4/ \u221a d \u2299Al). (9) In Equation 8, H0 Q, H0 K \u2208RN\u00d7d are calculated by linear projections of input NWP data X \u2208RN\u00d7Fe\u00d7T with parameters W Q, W K \u2208RFe\u00d7T \u00d7d, respectively. These representations 2We introduce the aggregation and sparsification procedure in a matrix form for ease of understanding, while in our implementation, the cluster assignment, mask, and spatial proximity are represented by sparse matrix. are iteratively aggregated according to the cluster assignment matrix, generating representations Hl Q, Hl K \u2208RN l\u00d7d for super-grids at each level. In Equation 9, \u2299denotes elementwise product and the spatial proximity matrix is adjusted with the attention matrix. Moreover, the mask M l is used to make the spatial proximity matrix sparse, where only interactions of grids belonging to a same cluster are reserved. Fast hierarchical message passing. Hierarchical message passing (FHMP) module enables the model to capture the hierarchical inter-grid spatial dependencies. The main idea of FHMP is conducting fine-grained message passing among low-level grids but coarse-grained interactions at high level to simplify and distill the redundant spatial dependencies as well as accelerate the computation. Formally, FHMP module can be formulated as: Message : \u02c6 H l = HlW l, Hl = (Sl\u22121)\u22a4Hl\u22121, Aggregation : \u02dc H l vl = 1 |Nvl| X ul \u02dc A l ulvl \u02c6 H l ul, \u2200vl \u2208[0, 1, 2, \u00b7 \u00b7 \u00b7 N l \u22121], Nvl = {ul| \u02dc Al ulvl \u0338= 0}, Duplication : H\u2032 = \u02dc H 0 + L X l=1 l\u22121 Y i=0 Si \u02dc H l, Update : H\u2032\u2032 = H + H\u2032W , (10) where \u02c6 H l \u2208RN l\u00d7d are calculated by linear projections of Hl, representing the message of grids at level l, and H0 = H is the output of the factor-wise GNN (see Equation 3). For a specific grid vl at level l, its neighbors Nvl are identified by the spatial proximity matrix \u02dc A l. vl then aggregates its neighbors\u2019 messages according to the proximity strength in \u02dc A l. The duplication stage is the key design of FHMP module 3. It duplicates the messages from the supergrids at each level to their containing grids at level 0 based on assignment matrices [Si]L\u22121 i=0 , and the grids at level 0 belonging to the same super-grid share the same message from \u02c6 H l, as illustrated in Fig. 4. With appropriate hierarchical structure4, all grid-pairs at level 0 can interact. After collecting the messages from all levels, the hidden representations of grids at level 0 are updated based on integrated messages with a residual connection. According to Lemma 1, both dynamic adjustment and FHMP in FHGNN have a linear complexity w.r.t. the number of grids. The proof is in Appendix A. Lemma 1. The complexity of factor-wise GNN and fast hierarchical GNN is O(N), where N is the number of grids. Bias-Correction Output Given the output H\u2032\u2032 \u2208RN\u00d7d of FHGNN, we feed it into an MLP-based decoder to produce corrected weather factors for 3Since each row of Ql\u22121 i=0 Si only contains one 1 and others are 0s, the matrix multiplication of Ql\u22121 i=0 Si \u02dc H l is implemented with indexing operation. 4The conclusion holds if we establish \u230alogkN\u230b+1 levels, where k is the cluster size. target grid Level 0 Level 1 Level 2 grid spatial relationship cluster assignment message duplication target grid Level 0 grid spatial relationship cluster assignment message duplication target grid Level 0 Level 1 grid spatial relationship cluster assignment message duplication target grid Level 0 grid spatial relationship cluster assignment message duplication target grid Level 0 grid spatial relationship cluster assignment message duplication target grid Level 0 Level 1 grid spatial relationship cluster assignment message duplication Figure 4: An Overview of Fast Hierarchical Message Passing. each grid at the target time step at once. We adopt the L1 loss function to compare the difference between corrected results and ground truth, which can be formulated as: L( \u02c6 Y , Y ) = PFe f=1 wf\u2225\u02c6 Y f \u2212Y f\u22251, where \u02c6 Y = MLP \u0000H\u2032\u2032\u0001 , and \u02c6 Y f and Y f are the corrected results and the ground truth of the weather factor f, and wf is a hyperparameter representing the corresponding weights. Experiments Datasets We collect two real-world bias-correction datasets: Ningbo and Ningxia, covering two different terrain types in China. Each grid in both datasets has three types of data, i.e., geographic data, NWP data, and observational weather data. In addition, geographic data contain latitude, longitude, and DEM (commonly used in geographic information systems to represent terrain) information. Ningbo dataset depicts a coastline area with latitude range 28.85\u25e6N\u221230.56\u25e6N and longitude range 120.91\u25e6E\u2212122.29\u25e6E. There are 58\u00d747 grids with a grid size of 0.03 degree in latitude and longitude. Both NWP and observational weather data have hourly records including 10 weather factors from 1/Jan/2021 to 1/Apr/2021. Ningxia 5 dataset features mountainous and hilly terrain with latitude range 34.5\u25e6N\u221242\u25e6N and longitude range 106\u25e6E\u2212116\u25e6E. There are 31\u00d741 grids with grid size of 0.25 degree in latitude and longitude. Both NWP and observational weather data have hourly records including 8 weather factors from 1/Jan/2021 to 1/Jan/2022. In our experiments, we divide each dataset into training/validation/test subsets using a 7:1:2 ratio in chronological order. We define a temporal window of 7 time steps for NWP bias-correction, including the target time step, as well as the previous and next three steps. More dataset details are in Appendix B. Baselines and Experimental Settings We compare WeatherGNN6 with state-of-the-art models, including: BiLSTM-T (Yang et al. 2022): using BiLSTM considering multiple covariates for bias-correction; HybridCBA (Han et al. 2022): combining CNN, BiLSTM, and attention mechanism to deal with relationships between target 5We are working on making this dataset open-source. 6Our code is available at https://anonymous.4open.science/r/ WeatherGNN-D6DB. Table 1: Bias-correction performance comparison of each weather factor on the Ningbo and Ningxia datasets. Bold and Underline indicate the best and second best performance, respectively. \u2206denotes the relative improvement between WeatherGNN and best baselines/NWP. \u2217indicates the backbone models of global weather forecasting models. Factor Metric NWP BiLSTM-T HybridCBA ConvLSTM AFNO\u2217 Swin\u2217 STGCN HGCN\u2217 MegaCRN WeatherGNN \u2206Baseline \u2206NWP Ningbo 100ws MAE 2.26 1.98 1.53 1.37 0.84 0.91 0.94 0.89 0.87 0.81 3.57% 64.16% RMSE 2.74 2.70 2.34 2.03 1.17 1.26 1.31 1.25 1.21 1.15 1.71% 58.03% 10ws MAE 1.38 1.37 1.18 0.91 0.58 0.67 0.65 0.63 0.61 0.56 3.45% 54.35% RMSE 1.71 1.69 1.65 1.28 0.81 0.87 0.91 0.88 0.85 0.79 2.47% 49.12% h MAE 15.37 14.48 12.32 7.61 5.86 5.96 6.35 5.81 5.95 5.65 2.75% 63.24% RMSE 18.28 18.44 15.29 10.35 7.26 7.32 8.29 7.28 7.80 7.13 1.79% 61.00% 2t MAE 1.28 1.20 1.19 1.16 0.93 1.10 1.12 1.04 0.91 0.91 0.00% 28.91% RMSE 1.74 1.54 1.58 1.51 1.27 1.34 1.47 1.31 1.23 1.26 -2.44% 27.59% tp MAE 0.143 0.412 0.331 0.309 0.123 0.240 0.282 0.212 0.131 0.116 5.69% 18.88% RMSE 0.495 0.811 0.763 0.655 0.391 0.587 0.627 0.502 0.435 0.342 12.53% 30.91% Ningxia 100ws(U) MAE 2.93 2.69 2.33 2.22 2.00 2.12 2.33 2.08 1.95 1.79 8.21% 38.91% RMSE 3.83 3.41 2.99 2.87 2.58 2.81 3.01 2.69 2.54 2.41 6.59% 37.08% 100ws(V) MAE 3.39 2.79 2.67 2.51 2.25 2.30 2.51 2.29 2.27 2.14 4.89% 36.87% RMSE 4.52 3.59 3.43 3.24 2.93 3.11 3.22 3.03 2.94 2.69 8.19% 40.49% 10ws(U) MAE 1.79 1.65 1.44 1.40 1.22 1.22 1.52 1.33 1.23 1.18 3.28% 34.08% RMSE 2.38 2.16 1.87 1.84 1.60 1.64 1.97 1.73 1.60 1.53 4.38% 35.71% 10ws(V) MAE 2.03 1.73 1.55 1.50 1.32 1.41 1.56 1.38 1.35 1.22 7.58% 39.90% RMSE 2.74 2.24 2.02 1.96 1.75 2.08 2.01 1.85 1.80 1.61 8.00% 41.24% 2t MAE 2.81 2.71 2.72 2.44 2.27 2.27 2.54 2.20 2.28 2.23 -1.36% 20.64% RMSE 3.74 3.49 3.54 3.15 2.91 2.89 3.27 2.79 2.92 2.85 -2.15% 23.80% Table 2: Ablation study on the 100m wind speed of the Ningbo and Ningxia datasets. Factor Ningbo 100ws Ningxia 100ws(U) Metric MAE RMSE MAE RMSE Variant shared-F 0.84 1.19 1.87 2.49 no-F 0.92 1.27 1.95 2.57 geo-H 0.91 1.26 2.04 2.61 met-H 0.89 1.26 1.93 2.58 static-H 0.86 1.23 1.90 2.52 no-H 0.96 1.32 2.35 2.83 WeatherGNN 0.81 1.15 1.79 2.41 factor and other factors; ConvLSTM (Shi et al. 2015): extending LSTM with convolutional gates; AFNO (Guibas et al. 2021b): adopting Fourier neural operator to capture features adaptively. Since FourCastNet (Pathak et al. 2022) is purely on AFNO, we regard AFNO as the backbone model of FourCastNet; Swin (Liu et al. 2021): constructing a hierarchical transformer by a shifted windowing scheme. Since Pangu (Bi et al. 2023) is the variation of Swin with two additional strategies, i.e., a 3D transformer encoder to formulate data and a hierarchical aggregation algorithm to alleviate errors, we treat Swin as the backbone model of Pangu; HGCN (Guo et al. 2021): operating hierarchical GNNs to utilize hierarchical spatial dependencies. Since GraphCast (Lam et al. 2022) adopts static hierarchical graphs, we treat HGCN as the backbone model of GraphCast. STGCN (Yu, Yin, and Zhu 2018): deploying graph convolution and temporal convolution to capture spatial and temporal relationships; MegaCRN (Jiang et al. 2023): introducing adaptive graphs to learn underlying heterogeneous spatial dependencies. Notably, for our local NWP bias-correction task, we compare the performance of backbone models, i.e., AFNO, Swin, and HGCN, as that of global weather models. Baselines and WeatherGNN are implemented with Pytorch, executed on a server with one 32GB Tesla V100 GPU card, and well-tuned according to the performance on the validation set. The hyperparameter settings are summarized in Appendix C. We optimize all models using Adam optimizer Time per Iteration GPU Memory Usage Figure 5: Model Efficiency Comparison. with an initial learning rate of 0.003 and set the maximum number of epochs to 100. We halt training when the validation loss does not decrease for 15 consecutive epochs. Performance Comparison We use Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) to measure the performance of all models. As shown in Table 1, the results lead to the following findings: (1) NWP can be significantly corrected, and our proposed WeatherGNN has an average improvement of over 40% in correcting weather factors compared with the original NWP. (2) Although baselines, especially AFNO and MegaCRN, have shown competitive performance, WeatherGNN achieves the best performance in 17 out of 20 cases across two datasets, despite the slight inferiority in 2m temperature correction. One possible reason is that the 2m temperature factor varies slowly in time and space, and thus considering complicated meteorologic and geographic relationships for correcting this measure may not be necessary. (3) The bias-correction of WeatherGNN on wind speed is significant. Given the fact that the mechanism of wind formation is complex and wind speed changes over time and space rapidly, it is possible that the dynamic adjustment in fast hierarchical GNN helps WeatherGNN adapt to weather dynamics. Model Analysis Ablation study. To evaluate the effectiveness of factor-wise GNN and fast hierarchical GNN of WeatherGNN, we con2t h 10ws 100ws Ground Truth NWP AFNO MegaCRN WeatherGNN BiLSTM-T Figure 6: Visualization of Bias-Correction on Ningbo Dataset. Each row corresponds to a meteorologic factor and each column corresponds to an algorithm. duct ablation studies on correcting the 100m wind speed of two datasets. For factor-wise GNN, we design variants: (1) shared-F: only using the factor embedding to construct a shared factor graph for all grids, ignoring spatial heterogeneity; (2) no-F: replacing the factor graphs with a one-layer MLP to encode the weather information without considering the meteorological interactions explicitly. For fast hierarchical GNN, we design variants: (3) geo-H: constructing the hierarchy only using geographic distances; (4) met-H: constructing the hierarchy only using DTW similarity of weather factor time series; (5) static-H: removing the dynamic adjustment and only adopting the static hierarchy when performing fast hierarchical message passing; (6) no-H: only using the Ainter calculated by Eq. 6 to model spatial dependencies between grids without constructing the hierarchy. All designs in WeatherGNN are proven to be effective based on the results in Table 2. Besides, we have other findings: (1) Terrain is crucial for bias-correction, even when it is solely used as input (as shown in \"no-F\"). By comparing \"shared-F\" and \"no-F\", we observe that modeling the relationships between factors explicitly can further improve the correction outcomes. Notably, making such relationships adapt to the changing terrain can enhance the correction effect. This discovery validates the effectiveness of our factor-wise GNN. (2) Constructing a hierarchical structure with geographic and meteorologic distances significantly improves the biascorrection performance. The meteorologic distance is found to be more effective than geographic distance, possibly because the influence of geography on weather factors is partly reflected in the weather factor sequences and DTW similarity can help to discover underlying spatial dependencies. Besides, the meteorologic distance is helpful to unveil remote inter-grid dependencies. Furthermore, the hierarchical design integrating both factors achieves the best results. Model efficiency. We evaluate the efficiency of WeatherGNN and baselines by increasing the number of grids and measuring running time and GPU memory usage. Fig. 5 illustrates that WeatherGNN (linear complexity) performs faster and requires less GPU memory than baselines. More results are in Appendix D. The efficiency advantages of WeatherGNN indicate good scalability, showing strong potential for application in large regions (e.g., continental or global applications). Grid 2555 Grid 500 Grid 500 pres 2rh tp 2t 100wd 100ws 10wd 10ws 10vor 10div Grid 2555 pres 2rh tp 2t 100wd 100ws 10wd 10ws 10vor 10div Grid 500 pres 2rh tp 2t 100wd 100ws 10wd 10ws 10vor 10div Grid 2555 pres 2rh tp 2t 100wd 100ws 10wd 10ws 10vor 10div Weather factor Related weight 0.35 0.21 0.14 0.13 0.36 0.08 0.09 0.17 0.12 0.07 0.23 0.15 Top-3 related factors of 10ws Top-3 related factors of 100ws Selected grid Figure 7: The Illustration of Learned Factor-Wise Graphs of Two Grids on Two Different Types of Terrains. Case study. We conduct case studies of bias-correction effects of different models and the learned factor-wise graph of WeatherGNN. Also, studies of prior hierarchical structures based on meteorologic and geometric distance and dynamic adjustment of spatial dependencies are in Appendix E. The cases of extreme weather, i.e., blustery weather, are in Appendix F. Bias-correction effects: We conduct a case study to investigate the bias-correction effects. We visualize the observation data at 22:00 6/Apr/2021 with origin NWP as well as corrected outputs of AFNO, MegaCRN, and WeatherGNN on measures of 2m temperature(2t), humidity(h), 10m wind speed(10ws), and 100m wind speed(100ws). As shown in Fig. 6, NWP has a large deviation from the ground truth, while baselines and WeatherGNN can effectively reduce this discrepancy. In particular, due to the comprehensive consideration of the relationships among factors and among grids, WeatherGNN demonstrates stable and excellent biascorrection effects. Factor-wise graphs: Fig. 7 shows an example of the learned factor-wise graphs selected randomly. Grid 500 locates in the mountains and Grid 2555 is in the ocean. 10ws and 100ws at both grids are closely related to each other. However, 10ws of Grid 500 is more relevant to pressure, as the mountainous regions have diverse terrain and are prone to rapid changes in air pressure, resulting in great effects on wind speeds. On the other hand, 10ws of Grid 2555 is affected by 10div (10m horizontal divergence, a measure of the local spreading or divergence of wind field in a horizontal plane at the height of 10 meters). One of the possible reasons is that on the sea horizon, the expansion of air in the horizontal direction has a significant impact on wind speed. Conclusion and Future Work In this paper, we propose WeatherGNN, a GNN-based model that leverages meteorologic and geographic relationships efficiently for local NWP bias correction. Specifically, we introduce a factor-wise GNN and a fast hierarchical GNN to capture intra-grid and inter-grid dependencies in weather factors, achieving linear complexity with respect to the number of grids. Extensive experimental results demonstrate the superiority of WeatherGNN. In the future, we will investigate the use of WeatherGNN for other meteorological applications, e.g., weather forecasting and downsampling. We also plan to apply WeatherGNN to larger real-world regions to investigate its scalability and robustness across different climatic and geographical conditions."
+                },
+                {
+                    "url": "http://arxiv.org/abs/2010.11929v2",
+                    "title": "An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale",
+                    "abstract": "While the Transformer architecture has become the de-facto standard for\nnatural language processing tasks, its applications to computer vision remain\nlimited. In vision, attention is either applied in conjunction with\nconvolutional networks, or used to replace certain components of convolutional\nnetworks while keeping their overall structure in place. We show that this\nreliance on CNNs is not necessary and a pure transformer applied directly to\nsequences of image patches can perform very well on image classification tasks.\nWhen pre-trained on large amounts of data and transferred to multiple mid-sized\nor small image recognition benchmarks (ImageNet, CIFAR-100, VTAB, etc.), Vision\nTransformer (ViT) attains excellent results compared to state-of-the-art\nconvolutional networks while requiring substantially fewer computational\nresources to train.",
+                    "authors": "Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby",
+                    "published": "2020-10-22",
+                    "updated": "2021-06-03",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.12093v1",
+                    "title": "Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is of great importance to transportation management and\npublic safety, and very challenging due to the complicated spatial-temporal\ndependency and essential uncertainty brought about by the road network and\ntraffic conditions. Latest studies mainly focus on modeling the spatial\ndependency by utilizing graph convolutional networks (GCNs) throughout a fixed\nweighted graph. However, edges, i.e., the correlations between pair-wise nodes,\nare much more complicated and interact with each other. In this paper, we\npropose the Multi-Range Attentive Bicomponent GCN (MRA-BGCN), a novel deep\nlearning model for traffic forecasting. We first build the node-wise graph\naccording to the road network distance and the edge-wise graph according to\nvarious edge interaction patterns. Then, we implement the interactions of both\nnodes and edges using bicomponent graph convolution. The multi-range attention\nmechanism is introduced to aggregate information in different neighborhood\nranges and automatically learn the importance of different ranges. Extensive\nexperiments on two real-world road network traffic datasets, METR-LA and\nPEMS-BAY, show that our MRA-BGCN achieves the state-of-the-art results.",
+                    "authors": "Weiqi Chen, Ling Chen, Yu Xie, Wei Cao, Yusong Gao, Xiaojie Feng",
+                    "published": "2019-11-27",
+                    "updated": "2019-11-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.11214v1",
+                    "title": "FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators",
+                    "abstract": "FourCastNet, short for Fourier Forecasting Neural Network, is a global\ndata-driven weather forecasting model that provides accurate short to\nmedium-range global predictions at $0.25^{\\circ}$ resolution. FourCastNet\naccurately forecasts high-resolution, fast-timescale variables such as the\nsurface wind speed, precipitation, and atmospheric water vapor. It has\nimportant implications for planning wind energy resources, predicting extreme\nweather events such as tropical cyclones, extra-tropical cyclones, and\natmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF\nIntegrated Forecasting System (IFS), a state-of-the-art Numerical Weather\nPrediction (NWP) model, at short lead times for large-scale variables, while\noutperforming IFS for variables with complex fine-scale structure, including\nprecipitation. FourCastNet generates a week-long forecast in less than 2\nseconds, orders of magnitude faster than IFS. The speed of FourCastNet enables\nthe creation of rapid and inexpensive large-ensemble forecasts with thousands\nof ensemble-members for improving probabilistic forecasting. We discuss how\ndata-driven deep learning models such as FourCastNet are a valuable addition to\nthe meteorology toolkit to aid and augment NWP models.",
+                    "authors": "Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, Animashree Anandkumar",
+                    "published": "2022-02-22",
+                    "updated": "2022-02-22",
+                    "primary_cat": "physics.ao-ph",
+                    "cats": [
+                        "physics.ao-ph",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.09783v1",
+                    "title": "Spatial-Temporal Transformer for 3D Point Cloud Sequences",
+                    "abstract": "Effective learning of spatial-temporal information within a point cloud\nsequence is highly important for many down-stream tasks such as 4D semantic\nsegmentation and 3D action recognition. In this paper, we propose a novel\nframework named Point Spatial-Temporal Transformer (PST2) to learn\nspatial-temporal representations from dynamic 3D point cloud sequences. Our\nPST2 consists of two major modules: a Spatio-Temporal Self-Attention (STSA)\nmodule and a Resolution Embedding (RE) module. Our STSA module is introduced to\ncapture the spatial-temporal context information across adjacent frames, while\nthe RE module is proposed to aggregate features across neighbors to enhance the\nresolution of feature maps. We test the effectiveness our PST2 with two\ndifferent tasks on point cloud sequences, i.e., 4D semantic segmentation and 3D\naction recognition. Extensive experiments on three benchmarks show that our\nPST2 outperforms existing methods on all datasets. The effectiveness of our\nSTSA and RE modules have also been justified with ablation experiments.",
+                    "authors": "Yimin Wei, Hao Liu, Tingting Xie, Qiuhong Ke, Yulan Guo",
+                    "published": "2021-10-19",
+                    "updated": "2021-10-19",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2007.02842v2",
+                    "title": "Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting",
+                    "abstract": "Modeling complex spatial and temporal correlations in the correlated time\nseries data is indispensable for understanding the traffic dynamics and\npredicting the future status of an evolving traffic system. Recent works focus\non designing complicated graph neural network architectures to capture shared\npatterns with the help of pre-defined graphs. In this paper, we argue that\nlearning node-specific patterns is essential for traffic forecasting while the\npre-defined graph is avoidable. To this end, we propose two adaptive modules\nfor enhancing Graph Convolutional Network (GCN) with new capabilities: 1) a\nNode Adaptive Parameter Learning (NAPL) module to capture node-specific\npatterns; 2) a Data Adaptive Graph Generation (DAGG) module to infer the\ninter-dependencies among different traffic series automatically. We further\npropose an Adaptive Graph Convolutional Recurrent Network (AGCRN) to capture\nfine-grained spatial and temporal correlations in traffic series automatically\nbased on the two modules and recurrent networks. Our experiments on two\nreal-world traffic datasets show AGCRN outperforms state-of-the-art by a\nsignificant margin without pre-defined graphs about spatial connections.",
+                    "authors": "Lei Bai, Lina Yao, Can Li, Xianzhi Wang, Can Wang",
+                    "published": "2020-07-06",
+                    "updated": "2020-10-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.10197v2",
+                    "title": "A Dynamic Spatial-temporal Attention Network for Early Anticipation of Traffic Accidents",
+                    "abstract": "The rapid advancement of sensor technologies and artificial intelligence are\ncreating new opportunities for traffic safety enhancement. Dashboard cameras\n(dashcams) have been widely deployed on both human driving vehicles and\nautomated driving vehicles. A computational intelligence model that can\naccurately and promptly predict accidents from the dashcam video will enhance\nthe preparedness for accident prevention. The spatial-temporal interaction of\ntraffic agents is complex. Visual cues for predicting a future accident are\nembedded deeply in dashcam video data. Therefore, the early anticipation of\ntraffic accidents remains a challenge. Inspired by the attention behavior of\nhumans in visually perceiving accident risks, this paper proposes a Dynamic\nSpatial-Temporal Attention (DSTA) network for the early accident anticipation\nfrom dashcam videos. The DSTA-network learns to select discriminative temporal\nsegments of a video sequence with a Dynamic Temporal Attention (DTA) module. It\nalso learns to focus on the informative spatial regions of frames with a\nDynamic Spatial Attention (DSA) module. A Gated Recurrent Unit (GRU) is trained\njointly with the attention modules to predict the probability of a future\naccident. The evaluation of the DSTA-network on two benchmark datasets confirms\nthat it has exceeded the state-of-the-art performance. A thorough ablation\nstudy that assesses the DSTA-network at the component level reveals how the\nnetwork achieves such performance. Furthermore, this paper proposes a method to\nfuse the prediction scores from two complementary models and verifies its\neffectiveness in further boosting the performance of early accident\nanticipation.",
+                    "authors": "Muhammad Monjurul Karim, Yu Li, Ruwen Qin, Zhaozheng Yin",
+                    "published": "2021-06-18",
+                    "updated": "2021-12-21",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2308.15560v2",
+                    "title": "WeatherBench 2: A benchmark for the next generation of data-driven global weather models",
+                    "abstract": "WeatherBench 2 is an update to the global, medium-range (1-14 day) weather\nforecasting benchmark proposed by Rasp et al. (2020), designed with the aim to\naccelerate progress in data-driven weather modeling. WeatherBench 2 consists of\nan open-source evaluation framework, publicly available training, ground truth\nand baseline data as well as a continuously updated website with the latest\nmetrics and state-of-the-art models:\nhttps://sites.research.google/weatherbench. This paper describes the design\nprinciples of the evaluation framework and presents results for current\nstate-of-the-art physical and data-driven weather models. The metrics are based\non established practices for evaluating weather forecasts at leading\noperational weather centers. We define a set of headline scores to provide an\noverview of model performance. In addition, we also discuss caveats in the\ncurrent evaluation setup and challenges for the future of data-driven weather\nforecasting.",
+                    "authors": "Stephan Rasp, Stephan Hoyer, Alexander Merose, Ian Langmore, Peter Battaglia, Tyler Russel, Alvaro Sanchez-Gonzalez, Vivian Yang, Rob Carver, Shreya Agrawal, Matthew Chantry, Zied Ben Bouallegue, Peter Dueben, Carla Bromberg, Jared Sisk, Luke Barrington, Aaron Bell, Fei Sha",
+                    "published": "2023-08-29",
+                    "updated": "2024-01-26",
+                    "primary_cat": "physics.ao-ph",
+                    "cats": [
+                        "physics.ao-ph",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.12794v2",
+                    "title": "GraphCast: Learning skillful medium-range global weather forecasting",
+                    "abstract": "Global medium-range weather forecasting is critical to decision-making across\nmany social and economic domains. Traditional numerical weather prediction uses\nincreased compute resources to improve forecast accuracy, but cannot directly\nuse historical weather data to improve the underlying model. We introduce a\nmachine learning-based method called \"GraphCast\", which can be trained directly\nfrom reanalysis data. It predicts hundreds of weather variables, over 10 days\nat 0.25 degree resolution globally, in under one minute. We show that GraphCast\nsignificantly outperforms the most accurate operational deterministic systems\non 90% of 1380 verification targets, and its forecasts support better severe\nevent prediction, including tropical cyclones, atmospheric rivers, and extreme\ntemperatures. GraphCast is a key advance in accurate and efficient weather\nforecasting, and helps realize the promise of machine learning for modeling\ncomplex dynamical systems.",
+                    "authors": "Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Ferran Alet, Suman Ravuri, Timo Ewalds, Zach Eaton-Rosen, Weihua Hu, Alexander Merose, Stephan Hoyer, George Holland, Oriol Vinyals, Jacklynn Stott, Alexander Pritzel, Shakir Mohamed, Peter Battaglia",
+                    "published": "2022-12-24",
+                    "updated": "2023-08-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "physics.ao-ph"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.09305v3",
+                    "title": "SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction",
+                    "abstract": "One unique property of time series is that the temporal relations are largely\npreserved after downsampling into two sub-sequences. By taking advantage of\nthis property, we propose a novel neural network architecture that conducts\nsample convolution and interaction for temporal modeling and forecasting, named\nSCINet. Specifically, SCINet is a recursive downsample-convolve-interact\narchitecture. In each layer, we use multiple convolutional filters to extract\ndistinct yet valuable temporal features from the downsampled sub-sequences or\nfeatures. By combining these rich features aggregated from multiple\nresolutions, SCINet effectively models time series with complex temporal\ndynamics. Experimental results show that SCINet achieves significant\nforecasting accuracy improvements over both existing convolutional models and\nTransformer-based solutions across various real-world time series forecasting\ndatasets. Our codes and data are available at\nhttps://github.com/cure-lab/SCINet.",
+                    "authors": "Minhao Liu, Ailing Zeng, Muxi Chen, Zhijian Xu, Qiuxia Lai, Lingna Ma, Qiang Xu",
+                    "published": "2021-06-17",
+                    "updated": "2022-10-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1709.04875v4",
+                    "title": "Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting",
+                    "abstract": "Timely accurate traffic forecast is crucial for urban traffic control and\nguidance. Due to the high nonlinearity and complexity of traffic flow,\ntraditional methods cannot satisfy the requirements of mid-and-long term\nprediction tasks and often neglect spatial and temporal dependencies. In this\npaper, we propose a novel deep learning framework, Spatio-Temporal Graph\nConvolutional Networks (STGCN), to tackle the time series prediction problem in\ntraffic domain. Instead of applying regular convolutional and recurrent units,\nwe formulate the problem on graphs and build the model with complete\nconvolutional structures, which enable much faster training speed with fewer\nparameters. Experiments show that our model STGCN effectively captures\ncomprehensive spatio-temporal correlations through modeling multi-scale traffic\nnetworks and consistently outperforms state-of-the-art baselines on various\nreal-world traffic datasets.",
+                    "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+                    "published": "2017-09-14",
+                    "updated": "2018-07-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.11650v1",
+                    "title": "Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks",
+                    "abstract": "Modeling multivariate time series has long been a subject that has attracted\nresearchers from a diverse range of fields including economics, finance, and\ntraffic. A basic assumption behind multivariate time series forecasting is that\nits variables depend on one another but, upon looking closely, it is fair to\nsay that existing methods fail to fully exploit latent spatial dependencies\nbetween pairs of variables. In recent years, meanwhile, graph neural networks\n(GNNs) have shown high capability in handling relational dependencies. GNNs\nrequire well-defined graph structures for information propagation which means\nthey cannot be applied directly for multivariate time series where the\ndependencies are not known in advance. In this paper, we propose a general\ngraph neural network framework designed specifically for multivariate time\nseries data. Our approach automatically extracts the uni-directed relations\namong variables through a graph learning module, into which external knowledge\nlike variable attributes can be easily integrated. A novel mix-hop propagation\nlayer and a dilated inception layer are further proposed to capture the spatial\nand temporal dependencies within the time series. The graph learning, graph\nconvolution, and temporal convolution modules are jointly learned in an\nend-to-end framework. Experimental results show that our proposed model\noutperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets\nand achieves on-par performance with other approaches on two traffic datasets\nwhich provide extra structural information.",
+                    "authors": "Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, Xiaojun Chang, Chengqi Zhang",
+                    "published": "2020-05-24",
+                    "updated": "2020-05-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.02948v1",
+                    "title": "FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead",
+                    "abstract": "We present FengWu, an advanced data-driven global medium-range weather\nforecast system based on Artificial Intelligence (AI). Different from existing\ndata-driven weather forecast methods, FengWu solves the medium-range forecast\nproblem from a multi-modal and multi-task perspective. Specifically, a deep\nlearning architecture equipped with model-specific encoder-decoders and\ncross-modal fusion Transformer is elaborately designed, which is learned under\nthe supervision of an uncertainty loss to balance the optimization of different\npredictors in a region-adaptive manner. Besides this, a replay buffer mechanism\nis introduced to improve medium-range forecast performance. With 39-year data\ntraining based on the ERA5 reanalysis, FengWu is able to accurately reproduce\nthe atmospheric dynamics and predict the future land and atmosphere states at\n37 vertical levels on a 0.25{\\deg} latitude-longitude resolution. Hindcasts of\n6-hourly weather in 2018 based on ERA5 demonstrate that FengWu performs better\nthan GraphCast in predicting 80\\% of the 880 reported predictands, e.g.,\nreducing the root mean square error (RMSE) of 10-day lead global z500\nprediction from 733 to 651 $m^{2}/s^2$. In addition, the inference cost of each\niteration is merely 600ms on NVIDIA Tesla A100 hardware. The results suggest\nthat FengWu can significantly improve the forecast skill and extend the\nskillful global medium-range weather forecast out to 10.75 days lead (with ACC\nof z500 > 0.6) for the first time.",
+                    "authors": "Kang Chen, Tao Han, Junchao Gong, Lei Bai, Fenghua Ling, Jing-Jia Luo, Xi Chen, Leiming Ma, Tianning Zhang, Rui Su, Yuanzheng Ci, Bin Li, Xiaokang Yang, Wanli Ouyang",
+                    "published": "2023-04-06",
+                    "updated": "2023-04-06",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG",
+                        "physics.ao-ph"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.12873v3",
+                    "title": "FuXi: A cascade machine learning forecasting system for 15-day global weather forecast",
+                    "abstract": "Over the past few years, due to the rapid development of machine learning\n(ML) models for weather forecasting, state-of-the-art ML models have shown\nsuperior performance compared to the European Centre for Medium-Range Weather\nForecasts (ECMWF)'s high-resolution forecast (HRES) in 10-day forecasts at a\nspatial resolution of 0.25 degree. However, the challenge remains to perform\ncomparably to the ECMWF ensemble mean (EM) in 15-day forecasts. Previous\nstudies have demonstrated the importance of mitigating the accumulation of\nforecast errors for effective long-term forecasts. Despite numerous efforts to\nreduce accumulation errors, including autoregressive multi-time step loss,\nusing a single model is found to be insufficient to achieve optimal performance\nin both short and long lead times. Therefore, we present FuXi, a cascaded ML\nweather forecasting system that provides 15-day global forecasts with a\ntemporal resolution of 6 hours and a spatial resolution of 0.25 degree. FuXi is\ndeveloped using 39 years of the ECMWF ERA5 reanalysis dataset. The performance\nevaluation, based on latitude-weighted root mean square error (RMSE) and\nanomaly correlation coefficient (ACC), demonstrates that FuXi has comparable\nforecast performance to ECMWF EM in 15-day forecasts, making FuXi the first\nML-based weather forecasting system to accomplish this achievement.",
+                    "authors": "Lei Chen, Xiaohui Zhong, Feng Zhang, Yuan Cheng, Yinghui Xu, Yuan Qi, Hao Li",
+                    "published": "2023-06-22",
+                    "updated": "2023-10-20",
+                    "primary_cat": "physics.ao-ph",
+                    "cats": [
+                        "physics.ao-ph",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.05833v2",
+                    "title": "Earthformer: Exploring Space-Time Transformers for Earth System Forecasting",
+                    "abstract": "Conventionally, Earth system (e.g., weather and climate) forecasting relies\non numerical simulation with complex physical models and are hence both\nexpensive in computation and demanding on domain expertise. With the explosive\ngrowth of the spatiotemporal Earth observation data in the past decade,\ndata-driven models that apply Deep Learning (DL) are demonstrating impressive\npotential for various Earth system forecasting tasks. The Transformer as an\nemerging DL architecture, despite its broad success in other domains, has\nlimited adoption in this area. In this paper, we propose Earthformer, a\nspace-time Transformer for Earth system forecasting. Earthformer is based on a\ngeneric, flexible and efficient space-time attention block, named Cuboid\nAttention. The idea is to decompose the data into cuboids and apply\ncuboid-level self-attention in parallel. These cuboids are further connected\nwith a collection of global vectors. We conduct experiments on the MovingMNIST\ndataset and a newly proposed chaotic N-body MNIST dataset to verify the\neffectiveness of cuboid attention and figure out the best design of\nEarthformer. Experiments on two real-world benchmarks about precipitation\nnowcasting and El Nino/Southern Oscillation (ENSO) forecasting show Earthformer\nachieves state-of-the-art performance. Code is available:\nhttps://github.com/amazon-science/earth-forecasting-transformer .",
+                    "authors": "Zhihan Gao, Xingjian Shi, Hao Wang, Yi Zhu, Yuyang Wang, Mu Li, Dit-Yan Yeung",
+                    "published": "2022-07-12",
+                    "updated": "2023-03-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CV"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.13587v2",
+                    "title": "Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers",
+                    "abstract": "Vision transformers have delivered tremendous success in representation\nlearning. This is primarily due to effective token mixing through self\nattention. However, this scales quadratically with the number of pixels, which\nbecomes infeasible for high-resolution inputs. To cope with this challenge, we\npropose Adaptive Fourier Neural Operator (AFNO) as an efficient token mixer\nthat learns to mix in the Fourier domain. AFNO is based on a principled\nfoundation of operator learning which allows us to frame token mixing as a\ncontinuous global convolution without any dependence on the input resolution.\nThis principle was previously used to design FNO, which solves global\nconvolution efficiently in the Fourier domain and has shown promise in learning\nchallenging PDEs. To handle challenges in visual representation learning such\nas discontinuities in images and high resolution inputs, we propose principled\narchitectural modifications to FNO which results in memory and computational\nefficiency. This includes imposing a block-diagonal structure on the channel\nmixing weights, adaptively sharing weights across tokens, and sparsifying the\nfrequency modes via soft-thresholding and shrinkage. The resulting model is\nhighly parallel with a quasi-linear complexity and has linear memory in the\nsequence size. AFNO outperforms self-attention mechanisms for few-shot\nsegmentation in terms of both efficiency and accuracy. For Cityscapes\nsegmentation with the Segformer-B3 backbone, AFNO can handle a sequence size of\n65k and outperforms other efficient self-attention mechanisms.",
+                    "authors": "John Guibas, Morteza Mardani, Zongyi Li, Andrew Tao, Anima Anandkumar, Bryan Catanzaro",
+                    "published": "2021-11-24",
+                    "updated": "2022-03-27",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2301.10343v5",
+                    "title": "ClimaX: A foundation model for weather and climate",
+                    "abstract": "Most state-of-the-art approaches for weather and climate modeling are based\non physics-informed numerical models of the atmosphere. These approaches aim to\nmodel the non-linear dynamics and complex interactions between multiple\nvariables, which are challenging to approximate. Additionally, many such\nnumerical models are computationally intensive, especially when modeling the\natmospheric phenomenon at a fine-grained spatial and temporal resolution.\nRecent data-driven approaches based on machine learning instead aim to directly\nsolve a downstream forecasting or projection task by learning a data-driven\nfunctional mapping using deep neural networks. However, these networks are\ntrained using curated and homogeneous climate datasets for specific\nspatiotemporal tasks, and thus lack the generality of numerical models. We\ndevelop and demonstrate ClimaX, a flexible and generalizable deep learning\nmodel for weather and climate science that can be trained using heterogeneous\ndatasets spanning different variables, spatio-temporal coverage, and physical\ngroundings. ClimaX extends the Transformer architecture with novel encoding and\naggregation blocks that allow effective use of available compute while\nmaintaining general utility. ClimaX is pre-trained with a self-supervised\nlearning objective on climate datasets derived from CMIP6. The pre-trained\nClimaX can then be fine-tuned to address a breadth of climate and weather\ntasks, including those that involve atmospheric variables and spatio-temporal\nscales unseen during pretraining. Compared to existing data-driven baselines,\nwe show that this generality in ClimaX results in superior performance on\nbenchmarks for weather forecasting and climate projections, even when\npretrained at lower resolutions and compute budgets. The source code is\navailable at https://github.com/microsoft/ClimaX.",
+                    "authors": "Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K. Gupta, Aditya Grover",
+                    "published": "2023-01-24",
+                    "updated": "2023-12-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.09305v3",
+                    "title": "SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction",
+                    "abstract": "One unique property of time series is that the temporal relations are largely\npreserved after downsampling into two sub-sequences. By taking advantage of\nthis property, we propose a novel neural network architecture that conducts\nsample convolution and interaction for temporal modeling and forecasting, named\nSCINet. Specifically, SCINet is a recursive downsample-convolve-interact\narchitecture. In each layer, we use multiple convolutional filters to extract\ndistinct yet valuable temporal features from the downsampled sub-sequences or\nfeatures. By combining these rich features aggregated from multiple\nresolutions, SCINet effectively models time series with complex temporal\ndynamics. Experimental results show that SCINet achieves significant\nforecasting accuracy improvements over both existing convolutional models and\nTransformer-based solutions across various real-world time series forecasting\ndatasets. Our codes and data are available at\nhttps://github.com/cure-lab/SCINet.",
+                    "authors": "Minhao Liu, Ailing Zeng, Muxi Chen, Zhijian Xu, Qiuxia Lai, Lingna Ma, Qiang Xu",
+                    "published": "2021-06-17",
+                    "updated": "2022-10-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.12293v1",
+                    "title": "DL-Corrector-Remapper: A grid-free bias-correction deep learning methodology for data-driven high-resolution global weather forecasting",
+                    "abstract": "Data-driven models, such as FourCastNet (FCN), have shown exemplary\nperformance in high-resolution global weather forecasting. This performance,\nhowever, is based on supervision on mesh-gridded weather data without the\nutilization of raw climate observational data, the gold standard ground truth.\nIn this work we develop a methodology to correct, remap, and fine-tune gridded\nuniform forecasts of FCN so it can be directly compared against observational\nground truth, which is sparse and non-uniform in space and time. This is akin\nto bias correction and post-processing of numerical weather prediction (NWP), a\nroutine operation at meteorological and weather forecasting centers across the\nglobe. The Adaptive Fourier Neural Operator (AFNO) architecture is used as the\nbackbone to learn continuous representations of the atmosphere. The spatially\nand temporally non-uniform output is evaluated by the non-uniform discrete\ninverse Fourier transform (NUIDFT) given the output query locations. We call\nthis network the Deep-Learning-Corrector-Remapper (DLCR). The improvement in\nDLCR's performance against the gold standard ground truth over the baseline's\nperformance shows its potential to correct, remap, and fine-tune the\nmesh-gridded forecasts under the supervision of observations.",
+                    "authors": "Tao Ge, Jaideep Pathak, Akshay Subramaniam, Karthik Kashinath",
+                    "published": "2022-10-21",
+                    "updated": "2022-10-21",
+                    "primary_cat": "physics.ao-ph",
+                    "cats": [
+                        "physics.ao-ph",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1207.7103v1",
+                    "title": "Temporal Reachability Graphs",
+                    "abstract": "While a natural fit for modeling and understanding mobile networks,\ntime-varying graphs remain poorly understood. Indeed, many of the usual\nconcepts of static graphs have no obvious counterpart in time-varying ones. In\nthis paper, we introduce the notion of temporal reachability graphs. A\n(tau,delta)-reachability graph} is a time-varying directed graph derived from\nan existing connectivity graph. An edge exists from one node to another in the\nreachability graph at time t if there exists a journey (i.e., a spatiotemporal\npath) in the connectivity graph from the first node to the second, leaving\nafter t, with a positive edge traversal time tau, and arriving within a maximum\ndelay delta. We make three contributions. First, we develop the theoretical\nframework around temporal reachability graphs. Second, we harness our\ntheoretical findings to propose an algorithm for their efficient computation.\nFinally, we demonstrate the analytic power of the temporal reachability graph\nconcept by applying it to synthetic and real-life datasets. On top of defining\nclear upper bounds on communication capabilities, reachability graphs highlight\nasymmetric communication opportunities and offloading potential.",
+                    "authors": "John Whitbeck, Marcelo Dias de Amorim, Vania Conan, Jean-Loup Guillaume",
+                    "published": "2012-07-30",
+                    "updated": "2012-07-30",
+                    "primary_cat": "cs.NI",
+                    "cats": [
+                        "cs.NI",
+                        "C.2.1; F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1509.08960v1",
+                    "title": "Storing and Analyzing Historical Graph Data at Scale",
+                    "abstract": "The work on large-scale graph analytics to date has largely focused on the\nstudy of static properties of graph snapshots. However, a static view of\ninteractions between entities is often an oversimplification of several complex\nphenomena like the spread of epidemics, information diffusion, formation of\nonline communities}, and so on. Being able to find temporal interaction\npatterns, visualize the evolution of graph properties, or even simply compare\nthem across time, adds significant value in reasoning over graphs. However,\nbecause of lack of underlying data management support, an analyst today has to\nmanually navigate the added temporal complexity of dealing with large evolving\ngraphs. In this paper, we present a system, called Historical Graph Store, that\nenables users to store large volumes of historical graph data and to express\nand run complex temporal graph analytical tasks against that data. It consists\nof two key components: a Temporal Graph Index (TGI), that compactly stores\nlarge volumes of historical graph evolution data in a partitioned and\ndistributed fashion; it provides support for retrieving snapshots of the graph\nas of any timepoint in the past or evolution histories of individual nodes or\nneighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for\nexpressing complex temporal analytical tasks and for executing them in an\nefficient and scalable manner. Our experiments demonstrate our system's\nefficient storage, retrieval and analytics across a wide variety of queries on\nlarge volumes of historical graph data.",
+                    "authors": "Udayan Khurana, Amol Deshpande",
+                    "published": "2015-09-29",
+                    "updated": "2015-09-29",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04350v2",
+                    "title": "Time-Variant Graph Classification",
+                    "abstract": "Graphs are commonly used to represent objects, such as images and text, for\npattern classification. In a dynamic world, an object may continuously evolve\nover time, and so does the graph extracted from the underlying object. These\nchanges in graph structure with respect to the temporal order present a new\nrepresentation of the graph, in which an object corresponds to a set of\ntime-variant graphs. In this paper, we formulate a novel time-variant graph\nclassification task and propose a new graph feature, called a graph-shapelet\npattern, for learning and classifying time-variant graphs. Graph-shapelet\npatterns are compact and discriminative graph transformation subsequences. A\ngraph-shapelet pattern can be regarded as a graphical extension of a shapelet\n-- a class of discriminative features designed for vector-based temporal data\nclassification. To discover graph-shapelet patterns, we propose to convert a\ntime-variant graph sequence into time-series data and use the discovered\nshapelets to find graph transformation subsequences as graph-shapelet patterns.\nBy converting each graph-shapelet pattern into a unique tokenized graph\ntransformation sequence, we can measure the similarity between two\ngraph-shapelet patterns and therefore classify time-variant graphs. Experiments\non both synthetic and real-world data demonstrate the superior performance of\nthe proposed algorithms.",
+                    "authors": "Haishuai Wang",
+                    "published": "2016-09-14",
+                    "updated": "2017-06-12",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.09641v2",
+                    "title": "Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal data forecasting of traffic flow is a challenging task\nbecause of complicated spatial dependencies and dynamical trends of temporal\npattern between different roads. Existing frameworks typically utilize given\nspatial adjacency graph and sophisticated mechanisms for modeling spatial and\ntemporal correlations. However, limited representations of given spatial graph\nstructure with incomplete adjacent connections may restrict effective\nspatial-temporal dependencies learning of those models. To overcome those\nlimitations, our paper proposes Spatial-Temporal Fusion Graph Neural Networks\n(STFGNN) for traffic flow forecasting. SFTGNN could effectively learn hidden\nspatial-temporal dependencies by a novel fusion operation of various spatial\nand temporal graphs, which is generated by a data-driven method. Meanwhile, by\nintegrating this fusion graph module and a novel gated convolution module into\na unified layer, SFTGNN could handle long sequences. Experimental results on\nseveral public traffic datasets demonstrate that our method achieves\nstate-of-the-art performance consistently than other baselines.",
+                    "authors": "Mengzhang Li, Zhanxing Zhu",
+                    "published": "2020-12-15",
+                    "updated": "2021-03-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.08312v2",
+                    "title": "ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks",
+                    "abstract": "Networks are a fundamental and flexible way of representing various complex\nsystems. Many domains such as communication, citation, procurement, biology,\nsocial media, and transportation can be modeled as a set of entities and their\nrelationships. Temporal networks are a specialization of general networks where\nthe temporal evolution of the system is as important to understand as the\nstructure of the entities and relationships. We present the Independent\nTemporal Motif (ITeM) to characterize temporal graphs from different domains.\nThe ITeMs are edge-disjoint temporal motifs that can be used to model the\nstructure and the evolution of the graph. For a given temporal graph, we\nproduce a feature vector of ITeM frequencies and apply this distribution to the\ntask of measuring the similarity of temporal graphs. We show that ITeM has\nhigher accuracy than other motif frequency-based approaches. We define various\nmetrics based on ITeM that reveal salient properties of a temporal network. We\nalso present importance sampling as a method for efficiently estimating the\nITeM counts. We evaluate our approach on both synthetic and real temporal\nnetworks.",
+                    "authors": "Sumit Purohit, Lawrence B. Holder, George Chin",
+                    "published": "2020-02-19",
+                    "updated": "2020-08-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1811.08366v1",
+                    "title": "Temporal Graph Offset Reconstruction: Towards Temporally Robust Graph Representation Learning",
+                    "abstract": "Graphs are a commonly used construct for representing relationships between\nelements in complex high dimensional datasets. Many real-world phenomenon are\ndynamic in nature, meaning that any graph used to represent them is inherently\ntemporal. However, many of the machine learning models designed to capture\nknowledge about the structure of these graphs ignore this rich temporal\ninformation when creating representations of the graph. This results in models\nwhich do not perform well when used to make predictions about the future state\nof the graph -- especially when the delta between time stamps is not small. In\nthis work, we explore a novel training procedure and an associated unsupervised\nmodel which creates graph representations optimised to predict the future state\nof the graph. We make use of graph convolutional neural networks to encode the\ngraph into a latent representation, which we then use to train our temporal\noffset reconstruction method, inspired by auto-encoders, to predict a later\ntime point -- multiple time steps into the future. Using our method, we\ndemonstrate superior performance for the task of future link prediction\ncompared with none-temporal state-of-the-art baselines. We show our approach to\nbe capable of outperforming non-temporal baselines by 38% on a real world\ndataset.",
+                    "authors": "Stephen Bonner, John Brennan, Ibad Kureshi, Georgios Theodoropoulos, Andrew Stephen McGough, Boguslaw Obara",
+                    "published": "2018-11-20",
+                    "updated": "2018-11-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.01727v2",
+                    "title": "Skeleton-Based Action Segmentation with Multi-Stage Spatial-Temporal Graph Convolutional Neural Networks",
+                    "abstract": "The ability to identify and temporally segment fine-grained actions in motion\ncapture sequences is crucial for applications in human movement analysis.\nMotion capture is typically performed with optical or inertial measurement\nsystems, which encode human movement as a time series of human joint locations\nand orientations or their higher-order representations. State-of-the-art action\nsegmentation approaches use multiple stages of temporal convolutions. The main\nidea is to generate an initial prediction with several layers of temporal\nconvolutions and refine these predictions over multiple stages, also with\ntemporal convolutions. Although these approaches capture long-term temporal\npatterns, the initial predictions do not adequately consider the spatial\nhierarchy among the human joints. To address this limitation, we recently\nintroduced multi-stage spatial-temporal graph convolutional neural networks\n(MS-GCN). Our framework replaces the initial stage of temporal convolutions\nwith spatial graph convolutions and dilated temporal convolutions, which better\nexploit the spatial configuration of the joints and their long-term temporal\ndynamics. Our framework was compared to four strong baselines on five tasks.\nExperimental results demonstrate that our framework is a strong baseline for\nskeleton-based action segmentation.",
+                    "authors": "Benjamin Filtjens, Bart Vanrumste, Peter Slaets",
+                    "published": "2022-02-03",
+                    "updated": "2022-10-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.00963v5",
+                    "title": "The Complexity of Finding Small Separators in Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs with time-stamped edges. We study the problem of\nfinding a small vertex set (the separator) with respect to two designated\nterminal vertices such that the removal of the set eliminates all temporal\npaths connecting one terminal to the other. Herein, we consider two models of\ntemporal paths: paths that pass through arbitrarily many edges per time step\n(non-strict) and paths that pass through at most one edge per time step\n(strict). Regarding the number of time steps of a temporal graph, we show a\ncomplexity dichotomy (NP-hardness versus polynomial-time solvability) for both\nproblem variants. Moreover we prove both problem variants to be NP-complete\neven on temporal graphs whose underlying graph is planar. We further show that,\non temporal graphs with planar underlying graph, if additionally the number of\ntime steps is constant, then the problem variant for strict paths is solvable\nin quasi-linear time. Finally, we introduce and motivate the notion of a\ntemporal core (vertices whose incident edges change over time). We prove that\nthe non-strict variant is fixed-parameter tractable when parameterized by the\nsize of the temporal core, while the strict variant remains NP-complete, even\nfor constant-size temporal cores.",
+                    "authors": "Philipp Zschoche, Till Fluschnik, Hendrik Molter, Rolf Niedermeier",
+                    "published": "2017-11-02",
+                    "updated": "2018-07-25",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.10830v1",
+                    "title": "Automated Dilated Spatio-Temporal Synchronous Graph Modeling for Traffic Prediction",
+                    "abstract": "Accurate traffic prediction is a challenging task in intelligent\ntransportation systems because of the complex spatio-temporal dependencies in\ntransportation networks. Many existing works utilize sophisticated temporal\nmodeling approaches to incorporate with graph convolution networks (GCNs) for\ncapturing short-term and long-term spatio-temporal dependencies. However, these\nseparated modules with complicated designs could restrict effectiveness and\nefficiency of spatio-temporal representation learning. Furthermore, most\nprevious works adopt the fixed graph construction methods to characterize the\nglobal spatio-temporal relations, which limits the learning capability of the\nmodel for different time periods and even different data scenarios. To overcome\nthese limitations, we propose an automated dilated spatio-temporal synchronous\ngraph network, named Auto-DSTSGN for traffic prediction. Specifically, we\ndesign an automated dilated spatio-temporal synchronous graph (Auto-DSTSG)\nmodule to capture the short-term and long-term spatio-temporal correlations by\nstacking deeper layers with dilation factors in an increasing order. Further,\nwe propose a graph structure search approach to automatically construct the\nspatio-temporal synchronous graph that can adapt to different data scenarios.\nExtensive experiments on four real-world datasets demonstrate that our model\ncan achieve about 10% improvements compared with the state-of-art methods.\nSource codes are available at https://github.com/jinguangyin/Auto-DSTSGN.",
+                    "authors": "Guangyin Jin, Fuxian Li, Jinlei Zhang, Mudan Wang, Jincai Huang",
+                    "published": "2022-07-22",
+                    "updated": "2022-07-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.06260v1",
+                    "title": "In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs",
+                    "abstract": "A graph whose edges only appear at certain points in time is called a\ntemporal graph (among other names). These graphs are temporally connected if\nall ordered pairs of vertices are connected by a path that traverses edges in\nchronological order (a temporal path). Reachability in temporal graphs departs\nsignificantly from standard reachability; in particular, it is not transitive,\nwith structural and algorithmic consequences. For instance, temporally\nconnected graphs do not always admit spanning trees, i.e., subsets of edges\nthat form a tree and preserve temporal connectivity among the nodes.\n  In this paper, we revisit fundamental questions about the loss of\nuniversality of spanning trees. To start, we show that deciding if a spanning\ntree exists in a given temporal graph is NP-complete. What could be appropriate\nreplacement for the concept? Beyond having minimum size, spanning trees enjoy\nthe feature of enabling reachability along the same underlying paths in both\ndirections, a pretty uncommon feature in temporal graphs. We explore\nrelaxations in this direction and show that testing the existence of\nbidirectional spanning structures (bi-spanners) is tractable in general. On the\ndown side, finding \\emph{minimum} such structures is NP-hard even in simple\ntemporal graphs. Still, the fact that bidirectionality can be tested\nefficiently may find applications, e.g. for routing and security, and the\ncorresponding primitive that we introduce in the algorithm may be of\nindependent interest.",
+                    "authors": "Arnaud Casteigts, Timoth\u00e9e Corsini",
+                    "published": "2023-12-11",
+                    "updated": "2023-12-11",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DC",
+                        "68R10, 68W15",
+                        "G.2.2; C.2.4"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.03251v3",
+                    "title": "Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of traditional Knowledge Graph\n(KG) that incorporates the dimension of time. Reasoning on TKGs is a crucial\ntask that aims to predict future facts based on historical occurrences. The key\nchallenge lies in uncovering structural dependencies within historical\nsubgraphs and temporal patterns. Most existing approaches model TKGs relying on\nentity modeling, as nodes in the graph play a crucial role in knowledge\nrepresentation. However, the real-world scenario often involves an extensive\nnumber of entities, with new entities emerging over time. This makes it\nchallenging for entity-dependent methods to cope with extensive volumes of\nentities, and effectively handling newly emerging entities also becomes a\nsignificant challenge. Therefore, we propose Temporal Inductive Path Neural\nNetwork (TiPNN), which models historical information in an entity-independent\nperspective. Specifically, TiPNN adopts a unified graph, namely history\ntemporal graph, to comprehensively capture and encapsulate information from\nhistory. Subsequently, we utilize the defined query-aware temporal paths on a\nhistory temporal graph to model historical path information related to queries\nfor reasoning. Extensive experiments illustrate that the proposed model not\nonly attains significant performance enhancements but also handles inductive\nsettings, while additionally facilitating the provision of reasoning evidence\nthrough history temporal graphs.",
+                    "authors": "Hao Dong, Pengyang Wang, Meng Xiao, Zhiyuan Ning, Pengfei Wang, Yuanchun Zhou",
+                    "published": "2023-09-06",
+                    "updated": "2024-01-25",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.09039v1",
+                    "title": "Spatial-temporal Memories Enhanced Graph Autoencoder for Anomaly Detection in Dynamic Graphs",
+                    "abstract": "Anomaly detection in dynamic graphs presents a significant challenge due to\nthe temporal evolution of graph structures and attributes. The conventional\napproaches that tackle this problem typically employ an unsupervised learning\nframework, capturing normality patterns with exclusive normal data during\ntraining and identifying deviations as anomalies during testing. However, these\nmethods face critical drawbacks: they either only depend on proxy tasks for\ngeneral representation without directly pinpointing normal patterns, or they\nneglect to differentiate between spatial and temporal normality patterns,\nleading to diminished efficacy in anomaly detection. To address these\nchallenges, we introduce a novel Spatial-Temporal memories-enhanced graph\nautoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs)\nand gated temporal convolution layers to extract spatial features and temporal\nfeatures, respectively. Then STRIPE incorporates separate spatial and temporal\nmemory networks, which capture and store prototypes of normal patterns, thereby\npreserving the uniqueness of spatial and temporal normality. After that,\nthrough a mutual attention mechanism, these stored patterns are then retrieved\nand integrated with encoded graph embeddings. Finally, the integrated features\nare fed into the decoder to reconstruct the graph streams which serve as the\nproxy task for anomaly detection. This comprehensive approach not only\nminimizes reconstruction errors but also refines the model by emphasizing the\ncompactness and distinctiveness of the embeddings in relation to the nearest\nmemory prototypes. Through extensive testing, STRIPE has demonstrated a\nsuperior capability to discern anomalies by effectively leveraging the distinct\nspatial and temporal dynamics of dynamic graphs, significantly outperforming\nexisting methodologies, with an average improvement of 15.39% on AUC values.",
+                    "authors": "Jie Liu, Xuequn Shang, Xiaolin Han, Wentao Zhang, Hongzhi Yin",
+                    "published": "2024-03-14",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.09995v1",
+                    "title": "Temporal Reasoning Graph for Activity Recognition",
+                    "abstract": "Despite great success has been achieved in activity analysis, it still has\nmany challenges. Most existing work in activity recognition pay more attention\nto design efficient architecture or video sampling strategy. However, due to\nthe property of fine-grained action and long term structure in video, activity\nrecognition is expected to reason temporal relation between video sequences. In\nthis paper, we propose an efficient temporal reasoning graph (TRG) to\nsimultaneously capture the appearance features and temporal relation between\nvideo sequences at multiple time scales. Specifically, we construct learnable\ntemporal relation graphs to explore temporal relation on the multi-scale range.\nAdditionally, to facilitate multi-scale temporal relation extraction, we design\na multi-head temporal adjacent matrix to represent multi-kinds of temporal\nrelations. Eventually, a multi-head temporal relation aggregator is proposed to\nextract the semantic meaning of those features convolving through the graphs.\nExtensive experiments are performed on widely-used large-scale datasets, such\nas Something-Something and Charades, and the results show that our model can\nachieve state-of-the-art performance. Further analysis shows that temporal\nrelation reasoning with our TRG can extract discriminative features for\nactivity recognition.",
+                    "authors": "Jingran Zhang, Fumin Shen, Xing Xu, Heng Tao Shen",
+                    "published": "2019-08-27",
+                    "updated": "2019-08-27",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2204.09236v1",
+                    "title": "Scalable Motif Counting for Large-scale Temporal Graphs",
+                    "abstract": "One fundamental problem in temporal graph analysis is to count the\noccurrences of small connected subgraph patterns (i.e., motifs), which benefits\na broad range of real-world applications, such as anomaly detection, structure\nprediction, and network representation learning. However, existing works\nfocused on exacting temporal motif are not scalable to large-scale temporal\ngraph data, due to their heavy computational costs or inherent inadequacy of\nparallelism. In this work, we propose a scalable parallel framework for exactly\ncounting temporal motifs in large-scale temporal graphs. We first categorize\nthe temporal motifs based on their distinct properties, and then design\ncustomized algorithms that offer efficient strategies to exactly count the\nmotif instances of each category. Moreover, our compact data structures, namely\ntriple and quadruple counters, enable our algorithms to directly identify the\ntemporal motif instances of each category, according to edge information and\nthe relationship between edges, therefore significantly improving the counting\nefficiency. Based on the proposed counting algorithms, we design a hierarchical\nparallel framework that features both inter- and intra-node parallel\nstrategies, and fully leverages the multi-threading capacity of modern CPU to\nconcurrently count all temporal motifs. Extensive experiments on sixteen\nreal-world temporal graph datasets demonstrate the superiority and capability\nof our proposed framework for temporal motif counting, achieving up to 538*\nspeedup compared to the state-of-the-art methods. The source code of our method\nis available at: https://github.com/steven-ccq/FAST-temporal-motif.",
+                    "authors": "Zhongqiang Gao, Chuanqi Cheng, Yanwei Yu, Lei Cao, Chao Huang, Junyu Dong",
+                    "published": "2022-04-20",
+                    "updated": "2022-04-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10738v3",
+                    "title": "Deep Temporal Graph Clustering",
+                    "abstract": "Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.",
+                    "authors": "Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-05-18",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13624v1",
+                    "title": "Towards Linear Spanners in All Temporal Cliques",
+                    "abstract": "Many real-world networks, like transportation networks and social networks,\nare dynamic in the sense that the edge set may change over time, but these\nchanges are known in advance. This behavior is captured by the temporal graphs\nmodel, which has recently become a trending topic in theoretical computer\nscience. A core open problem in the field is to prove the existence of\nlinear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of\ncomplete temporal graphs that ensure all-pairs reachability via temporal paths.\nSo far, the best known result is the existence of temporal spanners with\n$\\mathcal{O}(n\\log n)$ many edges. We present significant progress towards\nproving that linear-size temporal spanners exist in all temporal cliques.\n  We adapt techniques used in previous works and heavily expand and generalize\nthem to provide a simpler and more intuitive proof of the $\\mathcal{O}(n\\log\nn)$ bound. Moreover, we use our novel approach to show that a large class of\ntemporal cliques, called edge-pivot graphs, admit linear-size temporal\nspanners. To contrast this, we investigate other classes of temporal cliques\nthat do not belong to the class of edge-pivot graphs. We introduce two such\ngraph classes and we develop novel techniques for establishing the existence of\nlinear temporal spanners in these graph classes as well.",
+                    "authors": "Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, Armin Wells",
+                    "published": "2024-02-21",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.04962v1",
+                    "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering",
+                    "abstract": "Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.",
+                    "authors": "Meng Liu, Ke Liang, Yue Liu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-06-08",
+                    "updated": "2023-06-08",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.03651v1",
+                    "title": "Temporal Graph Analysis with TGX",
+                    "abstract": "Real-world networks, with their evolving relations, are best captured as\ntemporal graphs. However, existing software libraries are largely designed for\nstatic graphs where the dynamic nature of temporal graphs is ignored. Bridging\nthis gap, we introduce TGX, a Python package specially designed for analysis of\ntemporal networks that encompasses an automated pipeline for data loading, data\nprocessing, and analysis of evolving graphs. TGX provides access to eleven\nbuilt-in datasets and eight external Temporal Graph Benchmark (TGB) datasets as\nwell as any novel datasets in the .csv format. Beyond data loading, TGX\nfacilitates data processing functionalities such as discretization of temporal\ngraphs and node subsampling to accelerate working with larger datasets. For\ncomprehensive investigation, TGX offers network analysis by providing a diverse\nset of measures, including average node degree and the evolving number of nodes\nand edges per timestamp. Additionally, the package consolidates meaningful\nvisualization plots indicating the evolution of temporal patterns, such as\nTemporal Edge Appearance (TEA) and Temporal Edge Trafficc (TET) plots. The TGX\npackage is a robust tool for examining the features of temporal graphs and can\nbe used in various areas like studying social networks, citation networks, and\ntracking user interactions. We plan to continuously support and update TGX\nbased on community feedback. TGX is publicly available on:\nhttps://github.com/ComplexData-MILA/TGX.",
+                    "authors": "Razieh Shirzadkhani, Shenyang Huang, Elahe Kooshafar, Reihaneh Rabbany, Farimah Poursafaei",
+                    "published": "2024-02-06",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.13517v1",
+                    "title": "Temporal Graph Signal Decomposition",
+                    "abstract": "Temporal graph signals are multivariate time series with individual\ncomponents associated with nodes of a fixed graph structure. Data of this kind\narises in many domains including activity of social network users, sensor\nnetwork readings over time, and time course gene expression within the\ninteraction network of a model organism. Traditional matrix decomposition\nmethods applied to such data fall short of exploiting structural regularities\nencoded in the underlying graph and also in the temporal patterns of the\nsignal. How can we take into account such structure to obtain a succinct and\ninterpretable representation of temporal graph signals?\n  We propose a general, dictionary-based framework for temporal graph signal\ndecomposition (TGSD). The key idea is to learn a low-rank, joint encoding of\nthe data via a combination of graph and time dictionaries. We propose a highly\nscalable decomposition algorithm for both complete and incomplete data, and\ndemonstrate its advantage for matrix decomposition, imputation of missing\nvalues, temporal interpolation, clustering, period estimation, and rank\nestimation in synthetic and real-world data ranging from traffic patterns to\nsocial media activity. Our framework achieves 28% reduction in RMSE compared to\nbaselines for temporal interpolation when as many as 75% of the observations\nare missing. It scales best among baselines taking under 20 seconds on 3.5\nmillion data points and produces the most parsimonious models. To the best of\nour knowledge, TGSD is the first framework to jointly model graph signals by\ntemporal and graph dictionaries.",
+                    "authors": "Maxwell McNeil, Lin Zhang, Petko Bogdanov",
+                    "published": "2021-06-25",
+                    "updated": "2021-06-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.01012v1",
+                    "title": "Graph-Level Embedding for Time-Evolving Graphs",
+                    "abstract": "Graph representation learning (also known as network embedding) has been\nextensively researched with varying levels of granularity, ranging from nodes\nto graphs. While most prior work in this area focuses on node-level\nrepresentation, limited research has been conducted on graph-level embedding,\nparticularly for dynamic or temporal networks. However, learning\nlow-dimensional graph-level representations for dynamic networks is critical\nfor various downstream graph retrieval tasks such as temporal graph similarity\nranking, temporal graph isomorphism, and anomaly detection. In this paper, we\npresent a novel method for temporal graph-level embedding that addresses this\ngap. Our approach involves constructing a multilayer graph and using a modified\nrandom walk with temporal backtracking to generate temporal contexts for the\ngraph's nodes. We then train a \"document-level\" language model on these\ncontexts to generate graph-level embeddings. We evaluate our proposed model on\nfive publicly available datasets for the task of temporal graph similarity\nranking, and our model outperforms baseline methods. Our experimental results\ndemonstrate the effectiveness of our method in generating graph-level\nembeddings for dynamic networks.",
+                    "authors": "Lili Wang, Chenghan Huang, Weicheng Ma, Xinyuan Cao, Soroush Vosoughi",
+                    "published": "2023-06-01",
+                    "updated": "2023-06-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.01594v1",
+                    "title": "Parameterized temporal exploration problems",
+                    "abstract": "In this paper we study the fixed-parameter tractability of the problem of\ndeciding whether a given temporal graph admits a temporal walk that visits all\nvertices (temporal exploration) or, in some problem variants, a certain subset\nof the vertices. Formally, a temporal graph is a sequence <G_1,...,G_L> of\ngraphs with V(G_t) = V(G) and E(G_t) a subset of E(G) for all t in [L] and some\nunderlying graph G, and a temporal walk is a time-respecting sequence of\nedge-traversals. We consider both the strict variant, in which edges must be\ntraversed in strictly increasing timesteps, and the non-strict variant, in\nwhich an arbitrary number of edges can be traversed in each timestep. For both\nvariants, we give FPT algorithms for the problem of finding a temporal walk\nthat visits a given set X of vertices, parameterized by |X|, and for the\nproblem of finding a temporal walk that visits at least k distinct vertices in\nV(G), parameterized by k. We also show W[2]-hardness for a set version of the\ntemporal exploration problem for both variants. For the non-strict variant, we\ngive an FPT algorithm for the temporal exploration problem parameterized by the\nlifetime of the input graph, and we show that the temporal exploration problem\ncan be solved in polynomial time if the graph in each timestep has at most two\nconnected components.",
+                    "authors": "Thomas Erlebach, Jakob T. Spooner",
+                    "published": "2022-12-03",
+                    "updated": "2022-12-03",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "05C85",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.15894v1",
+                    "title": "A Gated MLP Architecture for Learning Topological Dependencies in Spatio-Temporal Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) and Transformer have been increasingly adopted\nto learn the complex vector representations of spatio-temporal graphs,\ncapturing intricate spatio-temporal dependencies crucial for applications such\nas traffic datasets. Although many existing methods utilize multi-head\nattention mechanisms and message-passing neural networks (MPNNs) to capture\nboth spatial and temporal relations, these approaches encode temporal and\nspatial relations independently, and reflect the graph's topological\ncharacteristics in a limited manner. In this work, we introduce the Cycle to\nMixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial\ninvariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP).\nThe Cy2Mixer is composed of three blocks based on MLPs: A message-passing block\nfor encapsulating spatial information, a cycle message-passing block for\nenriching topological information through cyclic subgraphs, and a temporal\nblock for capturing temporal properties. We bolster the effectiveness of\nCy2Mixer with mathematical evidence emphasizing that our cycle message-passing\nblock is capable of offering differentiated information to the deep learning\nmodel compared to the message-passing block. Furthermore, empirical evaluations\nsubstantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art\nperformances across various traffic benchmark datasets.",
+                    "authors": "Yun Young Choi, Minho Lee, Sun Woo Park, Seunghwan Lee, Joohwan Ko",
+                    "published": "2024-01-29",
+                    "updated": "2024-01-29",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07491v3",
+                    "title": "Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment",
+                    "abstract": "Temporal graph learning aims to generate high-quality representations for\ngraph-based tasks with dynamic information, which has recently garnered\nincreasing attention. In contrast to static graphs, temporal graphs are\ntypically organized as node interaction sequences over continuous time rather\nthan an adjacency matrix. Most temporal graph learning methods model current\ninteractions by incorporating historical neighborhood. However, such methods\nonly consider first-order temporal information while disregarding crucial\nhigh-order structural information, resulting in suboptimal performance. To\naddress this issue, we propose a self-supervised method called S2T for temporal\ngraph learning, which extracts both temporal and structural information to\nlearn more informative node representations. Notably, the initial node\nrepresentations combine first-order temporal and high-order structural\ninformation differently to calculate two conditional intensities. An alignment\nloss is then introduced to optimize the node representations, narrowing the gap\nbetween the two intensities and making them more informative. Concretely, in\naddition to modeling temporal information using historical neighbor sequences,\nwe further consider structural knowledge at both local and global levels. At\nthe local level, we generate structural intensity by aggregating features from\nhigh-order neighbor sequences. At the global level, a global representation is\ngenerated based on all nodes to adjust the structural intensity according to\nthe active statuses on different nodes. Extensive experiments demonstrate that\nthe proposed model S2T achieves at most 10.13% performance improvement compared\nwith the state-of-the-art competitors on several datasets.",
+                    "authors": "Meng Liu, Ke Liang, Yawei Zhao, Wenxuan Tu, Sihang Zhou, Xinbiao Gan, Xinwang Liu, Kunlun He",
+                    "published": "2023-02-15",
+                    "updated": "2024-04-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.12003v1",
+                    "title": "On Finding Separators in Temporal Split and Permutation Graphs",
+                    "abstract": "Removing all connections between two vertices s and z in a graph by removing\na minimum number of vertices is a fundamental problem in algorithmic graph\ntheory. This (s,z)-separation problem is well-known to be polynomial solvable\nand serves as an important primitive in many applications related to network\nconnectivity. We study the NP-hard temporal (s,z)-separation problem on\ntemporal graphs, which are graphs with fixed vertex sets but edge sets that\nchange over discrete time steps. We tackle this problem by restricting the\nlayers (i.e., graphs characterized by edges that are present at a certain point\nin time) to specific graph classes. We restrict the layers of the temporal\ngraphs to be either all split graphs or all permutation graphs (both being\nperfect graph classes) and provide both intractability and tractability\nresults. In particular, we show that in general the problem remains NP-hard\nboth on temporal split and temporal permutation graphs, but we also spot\npromising islands of fixed-parameter tractability particularly based on\nparameterizations that measure the amount of \"change over time\".",
+                    "authors": "Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken",
+                    "published": "2021-05-25",
+                    "updated": "2021-05-25",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.10364v3",
+                    "title": "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks",
+                    "abstract": "Recent years have seen a surge in research on dynamic graph representation\nlearning, which aims to model temporal graphs that are dynamic and evolving\nconstantly over time. However, current work typically models graph dynamics\nwith recurrent neural networks (RNNs), making them suffer seriously from\ncomputation and memory overheads on large temporal graphs. So far, scalability\nof dynamic graph representation learning on large temporal graphs remains one\nof the major challenges. In this paper, we present a scalable framework, namely\nSpikeNet, to efficiently capture the temporal and structural patterns of\ntemporal graphs. We explore a new direction in that we can capture the evolving\ndynamics of temporal graphs with spiking neural networks (SNNs) instead of\nRNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics\nas spike trains of neuron populations and enable spike-based propagation in an\nefficient way. Experiments on three large real-world temporal graph datasets\ndemonstrate that SpikeNet outperforms strong baselines on the temporal node\nclassification task with lower computational costs. Particularly, SpikeNet\ngeneralizes to a large temporal graph (2.7M nodes and 13.9M edges) with\nsignificantly fewer parameters and computation overheads.Our code is publicly\navailable at \\url{https://github.com/EdisonLeeeee/SpikeNet}.",
+                    "authors": "Jintang Li, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, Changhua Meng",
+                    "published": "2022-08-15",
+                    "updated": "2023-05-18",
+                    "primary_cat": "cs.NE",
+                    "cats": [
+                        "cs.NE",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08514v2",
+                    "title": "Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction",
+                    "abstract": "Understanding crowd motion dynamics is critical to real-world applications,\ne.g., surveillance systems and autonomous driving. This is challenging because\nit requires effectively modeling the socially aware crowd spatial interaction\nand complex temporal dependencies. We believe attention is the most important\nfactor for trajectory prediction. In this paper, we present STAR, a\nSpatio-Temporal grAph tRansformer framework, which tackles trajectory\nprediction by only attention mechanisms. STAR models intra-graph crowd\ninteraction by TGConv, a novel Transformer-based graph convolution mechanism.\nThe inter-graph temporal dependencies are modeled by separate temporal\nTransformers. STAR captures complex spatio-temporal interactions by\ninterleaving between spatial and temporal Transformers. To calibrate the\ntemporal prediction for the long-lasting effect of disappeared pedestrians, we\nintroduce a read-writable external memory module, consistently being updated by\nthe temporal Transformer. We show that with only attention mechanism, STAR\nachieves state-of-the-art performance on 5 commonly used real-world pedestrian\nprediction datasets.",
+                    "authors": "Cunjun Yu, Xiao Ma, Jiawei Ren, Haiyu Zhao, Shuai Yi",
+                    "published": "2020-05-18",
+                    "updated": "2020-07-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.RO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1306.0493v1",
+                    "title": "Graph Metrics for Temporal Networks",
+                    "abstract": "Temporal networks, i.e., networks in which the interactions among a set of\nelementary units change over time, can be modelled in terms of time-varying\ngraphs, which are time-ordered sequences of graphs over a set of nodes. In such\ngraphs, the concepts of node adjacency and reachability crucially depend on the\nexact temporal ordering of the links. Consequently, all the concepts and\nmetrics proposed and used for the characterisation of static complex networks\nhave to be redefined or appropriately extended to time-varying graphs, in order\nto take into account the effects of time ordering on causality. In this chapter\nwe discuss how to represent temporal networks and we review the definitions of\nwalks, paths, connectedness and connected components valid for graphs in which\nthe links fluctuate over time. We then focus on temporal node-node distance,\nand we discuss how to characterise link persistence and the temporal\nsmall-world behaviour in this class of networks. Finally, we discuss the\nextension of classic centrality measures, including closeness, betweenness and\nspectral centrality, to the case of time-varying graphs, and we review the work\non temporal motifs analysis and the definition of modularity for temporal\ngraphs.",
+                    "authors": "Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, Vito Latora",
+                    "published": "2013-06-03",
+                    "updated": "2013-06-03",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.07016v2",
+                    "title": "On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions",
+                    "abstract": "This work formalizes the associational task of predicting node attribute\nevolution in temporal graphs from the perspective of learning equivariant\nrepresentations. We show that node representations in temporal graphs can be\ncast into two distinct frameworks: (a) The most popular approach, which we\ndenote as time-and-graph, where equivariant graph (e.g., GNN) and sequence\n(e.g., RNN) representations are intertwined to represent the temporal evolution\nof node attributes in the graph; and (b) an approach that we denote as\ntime-then-graph, where the sequences describing the node and edge dynamics are\nrepresented first, then fed as node and edge attributes into a static\nequivariant graph representation that comes after. Interestingly, we show that\ntime-then-graph representations have an expressivity advantage over\ntime-and-graph representations when both use component GNNs that are not\nmost-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is\nnot necessarily to obtain state-of-the-art results, our experiments show that\ntime-then-graph methods are capable of achieving better performance and\nefficiency than state-of-the-art time-and-graph methods in some real-world\ntasks, thereby showcasing that the time-then-graph framework is a worthy\naddition to the graph ML toolbox.",
+                    "authors": "Jianfei Gao, Bruno Ribeiro",
+                    "published": "2021-03-12",
+                    "updated": "2023-03-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.12843v1",
+                    "title": "An embedding-based distance for temporal graphs",
+                    "abstract": "We define a distance between temporal graphs based on graph embeddings built\nusing time-respecting random walks. We study both the case of matched graphs,\nwhen there exists a known relation between the nodes, and the unmatched case,\nwhen such a relation is unavailable and the graphs may be of different sizes.\nWe illustrate the interest of our distance definition, using both real and\nsynthetic temporal network data, by showing its ability to discriminate between\ngraphs with different structural and temporal properties. Leveraging\nstate-of-the-art machine learning techniques, we propose an efficient\nimplementation of distance computation that is viable for large-scale temporal\ngraphs.",
+                    "authors": "Lorenzo Dall'Amico, Alain Barrat, Ciro Cattuto",
+                    "published": "2024-01-23",
+                    "updated": "2024-01-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.05496v2",
+                    "title": "Temporal Graph Kernels for Classifying Dissemination Processes",
+                    "abstract": "Many real-world graphs or networks are temporal, e.g., in a social network\npersons only interact at specific points in time. This information directs\ndissemination processes on the network, such as the spread of rumors, fake\nnews, or diseases. However, the current state-of-the-art methods for supervised\ngraph classification are designed mainly for static graphs and may not be able\nto capture temporal information. Hence, they are not powerful enough to\ndistinguish between graphs modeling different dissemination processes. To\naddress this, we introduce a framework to lift standard graph kernels to the\ntemporal domain. Specifically, we explore three different approaches and\ninvestigate the trade-offs between loss of temporal information and efficiency.\nMoreover, to handle large-scale graphs, we propose stochastic variants of our\nkernels with provable approximation guarantees. We evaluate our methods on a\nwide range of real-world social networks. Our methods beat static kernels by a\nlarge margin in terms of accuracy while still being scalable to large graphs\nand data sets. Hence, we confirm that taking temporal information into account\nis crucial for the successful classification of dissemination processes.",
+                    "authors": "Lutz Oettershagen, Nils M. Kriege, Christopher Morris, Petra Mutzel",
+                    "published": "2019-10-14",
+                    "updated": "2021-08-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.11074v1",
+                    "title": "On The Temporal Domain of Differential Equation Inspired Graph Neural Networks",
+                    "abstract": "Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling\ncomplex relationships in graph-structured data. A recent innovation in this\nfield is the family of Differential Equation-Inspired Graph Neural Networks\n(DE-GNNs), which leverage principles from continuous dynamical systems to model\ninformation flow on graphs with built-in properties such as feature smoothing\nor preservation. However, existing DE-GNNs rely on first or second-order\ntemporal dependencies. In this paper, we propose a neural extension to those\npre-defined temporal dependencies. We show that our model, called TDE-GNN, can\ncapture a wide range of temporal dynamics that go beyond typical first or\nsecond-order methods, and provide use cases where existing temporal models are\nchallenged. We demonstrate the benefit of learning the temporal dependencies\nusing our method rather than using pre-defined temporal dynamics on several\ngraph benchmarks.",
+                    "authors": "Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane Sch\u00f6nlieb",
+                    "published": "2024-01-20",
+                    "updated": "2024-01-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.00278v1",
+                    "title": "An Introduction to Temporal Graphs: An Algorithmic Perspective",
+                    "abstract": "A \\emph{temporal graph} is, informally speaking, a graph that changes with\ntime. When time is discrete and only the relationships between the\nparticipating entities may change and not the entities themselves, a temporal\ngraph may be viewed as a sequence $G_1,G_2\\ldots,G_l$ of static graphs over the\nsame (static) set of nodes $V$. Though static graphs have been extensively\nstudied, for their temporal generalization we are still far from having a\nconcrete set of structural and algorithmic principles. Recent research shows\nthat many graph properties and problems become radically different and usually\nsubstantially more difficult when an extra time dimension in added to them.\nMoreover, there is already a rich and rapidly growing set of modern systems and\napplications that can be naturally modeled and studied via temporal graphs.\nThis, further motivates the need for the development of a temporal extension of\ngraph theory. We survey here recent results on temporal graphs and temporal\ngraph problems that have appeared in the Computer Science community.",
+                    "authors": "Othon Michail",
+                    "published": "2015-03-01",
+                    "updated": "2015-03-01",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS",
+                        "05C85, 05C40, 05C38, 05C78, 05C80, 68R10, 68M14, 68M10, 68W25"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.08889v3",
+                    "title": "Node Embedding over Temporal Graphs",
+                    "abstract": "In this work, we present a method for node embedding in temporal graphs. We\npropose an algorithm that learns the evolution of a temporal graph's nodes and\nedges over time and incorporates this dynamics in a temporal node embedding\nframework for different graph prediction tasks. We present a joint loss\nfunction that creates a temporal embedding of a node by learning to combine its\nhistorical temporal embeddings, such that it optimizes per given task (e.g.,\nlink prediction). The algorithm is initialized using static node embeddings,\nwhich are then aligned over the representations of a node at different time\npoints, and eventually adapted for the given task in a joint optimization. We\nevaluate the effectiveness of our approach over a variety of temporal graphs\nfor the two fundamental tasks of temporal link prediction and multi-label node\nclassification, comparing to competitive baselines and algorithmic\nalternatives. Our algorithm shows performance improvements across many of the\ndatasets and baselines and is found particularly effective for graphs that are\nless cohesive, with a lower clustering coefficient.",
+                    "authors": "Uriel Singer, Ido Guy, Kira Radinsky",
+                    "published": "2019-03-21",
+                    "updated": "2021-05-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.17110v2",
+                    "title": "LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?",
+                    "abstract": "In an era marked by the increasing adoption of Large Language Models (LLMs)\nfor various tasks, there is a growing focus on exploring LLMs' capabilities in\nhandling web data, particularly graph data. Dynamic graphs, which capture\ntemporal network evolution patterns, are ubiquitous in real-world web data.\nEvaluating LLMs' competence in understanding spatial-temporal information on\ndynamic graphs is essential for their adoption in web applications, which\nremains unexplored in the literature. In this paper, we bridge the gap via\nproposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic\ngraphs, to the best of our knowledge, for the first time. Specifically, we\npropose the LLM4DyG benchmark, which includes nine specially designed tasks\nconsidering the capability evaluation of LLMs from both temporal and spatial\ndimensions. Then, we conduct extensive experiments to analyze the impacts of\ndifferent data generators, data statistics, prompting techniques, and LLMs on\nthe model performance. Finally, we propose Disentangled Spatial-Temporal\nThoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal\nunderstanding abilities. Our main observations are: 1) LLMs have preliminary\nspatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph\ntasks show increasing difficulties for LLMs as the graph size and density\nincrease, while not sensitive to the time span and data generation mechanism,\n3) the proposed DST2 prompting method can help to improve LLMs'\nspatial-temporal understanding abilities on dynamic graphs for most tasks. The\ndata and codes will be open-sourced at publication time.",
+                    "authors": "Zeyang Zhang, Xin Wang, Ziwei Zhang, Haoyang Li, Yijian Qin, Wenwu Zhu",
+                    "published": "2023-10-26",
+                    "updated": "2024-03-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.05631v2",
+                    "title": "ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling",
+                    "abstract": "The spatio-temporal graph learning is becoming an increasingly important\nobject of graph study. Many application domains involve highly dynamic graphs\nwhere temporal information is crucial, e.g. traffic networks and financial\ntransaction graphs. Despite the constant progress made on learning structured\ndata, there is still a lack of effective means to extract dynamic complex\nfeatures from spatio-temporal structures. Particularly, conventional models\nsuch as convolutional networks or recurrent neural networks are incapable of\nrevealing the temporal patterns in short or long terms and exploring the\nspatial properties in local or global scope from spatio-temporal graphs\nsimultaneously. To tackle this problem, we design a novel multi-scale\narchitecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series\nmodeling. In this U-shaped network, a paired sampling operation is proposed in\nspacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in\nspatial from its deterministic partition while abstracts multi-resolution\ntemporal dependencies through dilated recurrent skip connections; based on\nprevious settings in the downsampling, the unpooling (ST-Unpool) restores the\noriginal structure of spatio-temporal graphs and resumes regular intervals\nwithin graph sequences. Experiments on spatio-temporal prediction tasks\ndemonstrate that our model effectively captures comprehensive features in\nmultiple scales and achieves substantial improvements over mainstream methods\non several real-world datasets.",
+                    "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+                    "published": "2019-03-13",
+                    "updated": "2021-06-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.02128v1",
+                    "title": "Interaction Order Prediction for Temporal Graphs",
+                    "abstract": "Link prediction in graphs is a task that has been widely investigated. It has\nbeen applied in various domains such as knowledge graph completion,\ncontent/item recommendation, social network recommendations and so on. The\ninitial focus of most research was on link prediction in static graphs.\nHowever, there has recently been abundant work on modeling temporal graphs, and\nconsequently one of the tasks that has been researched is link prediction in\ntemporal graphs. However, most of the existing work does not focus on the order\nof link formation, and only predicts the existence of links. In this study, we\naim to predict the order of node interactions.",
+                    "authors": "Nayana Bannur, Mashrin Srivastava, Harsha Vardhan",
+                    "published": "2023-02-04",
+                    "updated": "2023-02-04",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.12587v1",
+                    "title": "TGLib: An Open-Source Library for Temporal Graph Analysis",
+                    "abstract": "We initiate an open-source library for the efficient analysis of temporal\ngraphs. We consider one of the standard models of dynamic networks in which\neach edge has a discrete timestamp and transition time. Recently there has been\na massive interest in analyzing such temporal graphs. Common computational data\nmining and analysis tasks include the computation of temporal distances,\ncentrality measures, and network statistics like topological overlap,\nburstiness, or temporal diameter. To fulfill the increasing demand for\nefficient and easy-to-use implementations of temporal graph algorithms, we\nintroduce the open-source library TGLib, which integrates efficient data\nstructures and algorithms for temporal graph analysis. TGLib is highly\nefficient and versatile, providing simple and convenient C++ and Python\ninterfaces, targeting computer scientists, practitioners, students, and the\n(temporal) network research community.",
+                    "authors": "Lutz Oettershagen, Petra Mutzel",
+                    "published": "2022-09-26",
+                    "updated": "2022-09-26",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2101.00820v8",
+                    "title": "Temporal Contrastive Graph Learning for Video Action Recognition and Retrieval",
+                    "abstract": "Attempt to fully discover the temporal diversity and chronological\ncharacteristics for self-supervised video representation learning, this work\ntakes advantage of the temporal dependencies within videos and further proposes\na novel self-supervised method named Temporal Contrastive Graph Learning\n(TCGL). In contrast to the existing methods that ignore modeling elaborate\ntemporal dependencies, our TCGL roots in a hybrid graph contrastive learning\nstrategy to jointly regard the inter-snippet and intra-snippet temporal\ndependencies as self-supervision signals for temporal representation learning.\nTo model multi-scale temporal dependencies, our TCGL integrates the prior\nknowledge about the frame and snippet orders into graph structures, i.e., the\nintra-/inter- snippet temporal contrastive graphs. By randomly removing edges\nand masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL\ncan generate different correlated graph views. Then, specific contrastive\nlearning modules are designed to maximize the agreement between nodes in\ndifferent views. To adaptively learn the global context representation and\nrecalibrate the channel-wise features, we introduce an adaptive video snippet\norder prediction module, which leverages the relational knowledge among video\nsnippets to predict the actual snippet orders. Experimental results demonstrate\nthe superiority of our TCGL over the state-of-the-art methods on large-scale\naction recognition and video retrieval benchmarks.",
+                    "authors": "Yang Liu, Keze Wang, Haoyuan Lan, Liang Lin",
+                    "published": "2021-01-04",
+                    "updated": "2021-03-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.MM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.11190v1",
+                    "title": "Using Motif Transitions for Temporal Graph Generation",
+                    "abstract": "Graph generative models are highly important for sharing surrogate data and\nbenchmarking purposes. Real-world complex systems often exhibit dynamic nature,\nwhere the interactions among nodes change over time in the form of a temporal\nnetwork. Most temporal network generation models extend the static graph\ngeneration models by incorporating temporality in the generation process. More\nrecently, temporal motifs are used to generate temporal networks with better\nsuccess. However, existing models are often restricted to a small set of\npredefined motif patterns due to the high computational cost of counting\ntemporal motifs. In this work, we develop a practical temporal graph generator,\nMotif Transition Model (MTM), to generate synthetic temporal networks with\nrealistic global and local features. Our key idea is modeling the arrival of\nnew events as temporal motif transition processes. We first calculate the\ntransition properties from the input graph and then simulate the motif\ntransition processes based on the transition probabilities and transition\nrates. We demonstrate that our model consistently outperforms the baselines\nwith respect to preserving various global and local temporal graph statistics\nand runtime performance.",
+                    "authors": "Penghang Liu, A. Erdem Sar\u0131y\u00fcce",
+                    "published": "2023-06-19",
+                    "updated": "2023-06-19",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0807.2357v1",
+                    "title": "Temporal Graphs",
+                    "abstract": "We introduce the idea of temporal graphs, a representation that encodes\ntemporal data into graphs while fully retaining the temporal information of the\noriginal data. This representation lets us explore the dynamic temporal\nproperties of data by using existing graph algorithms (such as shortest-path),\nwith no need for data-driven simulations. We also present a number of metrics\nthat can be used to study and explore temporal graphs. Finally, we use temporal\ngraphs to analyse real-world data and present the results of our analysis.",
+                    "authors": "Vassilis Kostakos",
+                    "published": "2008-07-15",
+                    "updated": "2008-07-15",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.09610v2",
+                    "title": "Storing and Querying Large-Scale Spatio-Temporal Graphs with High-Throughput Edge Insertions",
+                    "abstract": "Real-world graphs often contain spatio-temporal information and evolve over\ntime. Compared with static graphs, spatio-temporal graphs have very different\ncharacteristics, presenting more significant challenges in data volume, data\nvelocity, and query processing. In this paper, we describe three representative\napplications to understand the features of spatio-temporal graphs. Based on the\ncommonalities of the applications, we define a formal spatio-temporal graph\nmodel, where a graph consists of location vertices, object vertices, and event\nedges. Then we discuss a set of design goals to meet the requirements of the\napplications: (i) supporting up to 10 billion object vertices, 10 million\nlocation vertices, and 100 trillion edges in the graph, (ii) supporting up to 1\ntrillion new edges that are streamed in daily, and (iii) minimizing\ncross-machine communication for query processing. We propose and evaluate PAST,\na framework for efficient PArtitioning and query processing of Spatio-Temporal\ngraphs. Experimental results show that PAST successfully achieves the above\ngoals. It improves query performance by orders of magnitude compared with\nstate-of-the-art solutions, including JanusGraph, Greenplum, Spark and\nST-Hadoop.",
+                    "authors": "Mengsu Ding, Muqiao Yang, Shimin Chen",
+                    "published": "2019-04-21",
+                    "updated": "2020-10-20",
+                    "primary_cat": "cs.DC",
+                    "cats": [
+                        "cs.DC",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1810.06240v4",
+                    "title": "Comparing Temporal Graphs Using Dynamic Time Warping",
+                    "abstract": "Within many real-world networks the links between pairs of nodes change over\ntime. Thus, there has been a recent boom in studying temporal graphs.\nRecognizing patterns in temporal graphs requires a proximity measure to compare\ndifferent temporal graphs. To this end, we propose to study dynamic time\nwarping on temporal graphs. We define the dynamic temporal graph warping\ndistance (dtgw) to determine the dissimilarity of two temporal graphs. Our\nnovel measure is flexible and can be applied in various application domains. We\nshow that computing the dtgw-distance is a challenging (in general) NP-hard\noptimization problem and identify some polynomial-time solvable special cases.\nMoreover, we develop a quadratic programming formulation and an efficient\nheuristic. In experiments on real-word data we show that the heuristic performs\nvery well and that our dtgw-distance performs favorably in de-anonymizing\nnetworks compared to other approaches.",
+                    "authors": "Vincent Froese, Brijnesh Jain, Rolf Niedermeier, Malte Renken",
+                    "published": "2018-10-15",
+                    "updated": "2020-07-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.11979v1",
+                    "title": "MTGA: Multi-view Temporal Granularity aligned Aggregation for Event-based Lip-reading",
+                    "abstract": "Lip-reading is to utilize the visual information of the speaker's lip\nmovements to recognize words and sentences. Existing event-based lip-reading\nsolutions integrate different frame rate branches to learn spatio-temporal\nfeatures of varying granularities. However, aggregating events into event\nframes inevitably leads to the loss of fine-grained temporal information within\nframes. To remedy this drawback, we propose a novel framework termed Multi-view\nTemporal Granularity aligned Aggregation (MTGA). Specifically, we first present\na novel event representation method, namely time-segmented voxel graph list,\nwhere the most significant local voxels are temporally connected into a graph\nlist. Then we design a spatio-temporal fusion module based on temporal\ngranularity alignment, where the global spatial features extracted from event\nframes, together with the local relative spatial and temporal features\ncontained in voxel graph list are effectively aligned and integrated. Finally,\nwe design a temporal aggregation module that incorporates positional encoding,\nwhich enables the capture of local absolute spatial and global temporal\ninformation. Experiments demonstrate that our method outperforms both the\nevent-based and video-based lip-reading counterparts. Our code will be publicly\navailable.",
+                    "authors": "Wenhao Zhang, Jun Wang, Yong Luo, Lei Yu, Wei Yu, Zheng He",
+                    "published": "2024-04-18",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1912.03904v1",
+                    "title": "Weighted temporal event graphs",
+                    "abstract": "The times of temporal-network events and their correlations contain\ninformation on the function of the network and they influence dynamical\nprocesses taking place on it. To extract information out of correlated event\ntimes, techniques such as the analysis of temporal motifs have been developed.\nWe discuss a recently-introduced, more general framework that maps\ntemporal-network structure into static graphs while retaining information on\ntime-respecting paths and the time differences between their consequent events.\nThis framework builds on weighted temporal event graphs: directed, acyclic\ngraphs (DAGs) that contain a superposition of all temporal paths. We introduce\nthe reader to the temporal event-graph mapping and associated computational\nmethods and illustrate its use by applying the framework to temporal-network\npercolation.",
+                    "authors": "Jari Saram\u00e4ki, Mikko Kivel\u00e4, M\u00e1rton Karsai",
+                    "published": "2019-12-09",
+                    "updated": "2019-12-09",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19508v1",
+                    "title": "Temporal Graph ODEs for Irregularly-Sampled Time Series",
+                    "abstract": "Modern graph representation learning works mostly under the assumption of\ndealing with regularly sampled temporal graph snapshots, which is far from\nrealistic, e.g., social networks and physical systems are characterized by\ncontinuous dynamics and sporadic observations. To address this limitation, we\nintroduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework,\nwhich learns both the temporal and spatial dynamics from graph streams where\nthe intervals between observations are not regularly spaced. We empirically\nvalidate the proposed approach on several graph benchmarks, showing that TG-ODE\ncan achieve state-of-the-art performance in irregular graph stream tasks.",
+                    "authors": "Alessio Gravina, Daniele Zambon, Davide Bacciu, Cesare Alippi",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2008.08282v2",
+                    "title": "Multiscale Snapshots: Visual Analysis of Temporal Summaries in Dynamic Graphs",
+                    "abstract": "The overview-driven visual analysis of large-scale dynamic graphs poses a\nmajor challenge. We propose Multiscale Snapshots, a visual analytics approach\nto analyze temporal summaries of dynamic graphs at multiple temporal scales.\nFirst, we recursively generate temporal summaries to abstract overlapping\nsequences of graphs into compact snapshots. Second, we apply graph embeddings\nto the snapshots to learn low-dimensional representations of each sequence of\ngraphs to speed up specific analytical tasks (e.g., similarity search). Third,\nwe visualize the evolving data from a coarse to fine-granular snapshots to\nsemi-automatically analyze temporal states, trends, and outliers. The approach\nenables to discover similar temporal summaries (e.g., recurring states),\nreduces the temporal data to speed up automatic analysis, and to explore both\nstructural and temporal properties of a dynamic graph. We demonstrate the\nusefulness of our approach by a quantitative evaluation and the application to\na real-world dataset.",
+                    "authors": "Eren Cakmak, Udo Schlegel, Dominik J\u00e4ckle, Daniel Keim, Tobias Schreck",
+                    "published": "2020-08-19",
+                    "updated": "2020-09-15",
+                    "primary_cat": "cs.HC",
+                    "cats": [
+                        "cs.HC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.04434v1",
+                    "title": "Frequency Analysis of Temporal Graph Signals",
+                    "abstract": "This letter extends the concept of graph-frequency to graph signals that\nevolve with time. Our goal is to generalize and, in fact, unify the familiar\nconcepts from time- and graph-frequency analysis. To this end, we study a joint\ntemporal and graph Fourier transform (JFT) and demonstrate its attractive\nproperties. We build on our results to create filters which act on the joint\n(temporal and graph) frequency domain, and show how these can be used to\nperform interference cancellation. The proposed algorithms are distributed,\nhave linear complexity, and can approximate any desired joint filtering\nobjective.",
+                    "authors": "Andreas Loukas, Damien Foucard",
+                    "published": "2016-02-14",
+                    "updated": "2016-02-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SY",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.04782v1",
+                    "title": "A Survey on Temporal Knowledge Graph: Representation Learning and Applications",
+                    "abstract": "Knowledge graphs have garnered significant research attention and are widely\nused to enhance downstream applications. However, most current studies mainly\nfocus on static knowledge graphs, whose facts do not change with time, and\ndisregard their dynamic evolution over time. As a result, temporal knowledge\ngraphs have attracted more attention because a large amount of structured\nknowledge exists only within a specific period. Knowledge graph representation\nlearning aims to learn low-dimensional vector embeddings for entities and\nrelations in a knowledge graph. The representation learning of temporal\nknowledge graphs incorporates time information into the standard knowledge\ngraph framework and can model the dynamics of entities and relations over time.\nIn this paper, we conduct a comprehensive survey of temporal knowledge graph\nrepresentation learning and its applications. We begin with an introduction to\nthe definitions, datasets, and evaluation metrics for temporal knowledge graph\nrepresentation learning. Next, we propose a taxonomy based on the core\ntechnologies of temporal knowledge graph representation learning methods, and\nprovide an in-depth analysis of different methods in each category. Finally, we\npresent various downstream applications related to the temporal knowledge\ngraphs. In the end, we conclude the paper and have an outlook on the future\nresearch directions in this area.",
+                    "authors": "Li Cai, Xin Mao, Yuhao Zhou, Zhaoguang Long, Changxu Wu, Man Lan",
+                    "published": "2024-03-02",
+                    "updated": "2024-03-02",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1706.09480v1",
+                    "title": "A Temporal Tree Decomposition for Generating Temporal Graphs",
+                    "abstract": "Discovering the underlying structures present in large real world graphs is a\nfundamental scientific problem. Recent work at the intersection of formal\nlanguage theory and graph theory has found that a Hyperedge Replacement Grammar\n(HRG) can be extracted from a tree decomposition of any graph. This HRG can be\nused to generate new graphs that share properties that are similar to the\noriginal graph. Because the extracted HRG is directly dependent on the shape\nand contents of the of tree decomposition, it is unlikely that informative\ngraph-processes are actually being captured with the extraction algorithm. To\naddress this problem, the current work presents a new extraction algorithm\ncalled temporal HRG (tHRG) that learns HRG production rules from a temporal\ntree decomposition of the graph. We observe problems with the assumptions that\nare made in a temporal HRG model. In experiments on large real world networks,\nwe show and provide reasoning as to why tHRG does not perform as well as HRG\nand other graph generators.",
+                    "authors": "Corey Pennycuff, Salvador Aguinaga, Tim Weninger",
+                    "published": "2017-06-28",
+                    "updated": "2017-06-28",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08804v1",
+                    "title": "Temporal Graph Modeling for Skeleton-based Action Recognition",
+                    "abstract": "Graph Convolutional Networks (GCNs), which model skeleton data as graphs,\nhave obtained remarkable performance for skeleton-based action recognition.\nParticularly, the temporal dynamic of skeleton sequence conveys significant\ninformation in the recognition task. For temporal dynamic modeling, GCN-based\nmethods only stack multi-layer 1D local convolutions to extract temporal\nrelations between adjacent time steps. With the repeat of a lot of local\nconvolutions, the key temporal information with non-adjacent temporal distance\nmay be ignored due to the information dilution. Therefore, these methods still\nremain unclear how to fully explore temporal dynamic of skeleton sequence. In\nthis paper, we propose a Temporal Enhanced Graph Convolutional Network (TE-GCN)\nto tackle this limitation. The proposed TE-GCN constructs temporal relation\ngraph to capture complex temporal dynamic. Specifically, the constructed\ntemporal relation graph explicitly builds connections between semantically\nrelated temporal features to model temporal relations between both adjacent and\nnon-adjacent time steps. Meanwhile, to further explore the sufficient temporal\ndynamic, multi-head mechanism is designed to investigate multi-kinds of\ntemporal relations. Extensive experiments are performed on two widely used\nlarge-scale datasets, NTU-60 RGB+D and NTU-120 RGB+D. And experimental results\nshow that the proposed model achieves the state-of-the-art performance by\nmaking contribution to temporal modeling for action recognition.",
+                    "authors": "Jianan Li, Xuemei Xie, Zhifu Zhao, Yuhan Cao, Qingzhe Pan, Guangming Shi",
+                    "published": "2020-12-16",
+                    "updated": "2020-12-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02212v1",
+                    "title": "Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by\nattaching the time scope. Existing temporal knowledge graph question answering\n(TKGQA) models solely approach simple questions, owing to the prior assumption\nthat each question only contains a single temporal fact with explicit/implicit\ntemporal constraints. Hence, they perform poorly on questions which own\nmultiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint\n\\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts\n\\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly\nreasoning multiple temporal facts for accurately answering \\emph{complex}\ntemporal questions. Specifically, JMFRN first retrieves question-related\ntemporal facts from TKG for each entity of the given complex question. For\njoint reasoning, we design two different attention (\\ie entity-aware and\ntime-aware) modules, which are suitable for universal settings, to aggregate\nentities and timestamps information of retrieved facts. Moreover, to filter\nincorrect type answers, we introduce an additional answer type discrimination\ntask. Extensive experiments demonstrate our proposed method significantly\noutperforms the state-of-art on the well-known complex temporal question\nbenchmark TimeQuestions.",
+                    "authors": "Rikui Huang, Wei Wei, Xiaoye Qu, Wenfeng Xie, Xianling Mao, Dangyang Chen",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.04816v1",
+                    "title": "MTGER: Multi-view Temporal Graph Enhanced Temporal Reasoning over Time-Involved Document",
+                    "abstract": "The facts and time in the document are intricately intertwined, making\ntemporal reasoning over documents challenging. Previous work models time\nimplicitly, making it difficult to handle such complex relationships. To\naddress this issue, we propose MTGER, a novel Multi-view Temporal Graph\nEnhanced Temporal Reasoning framework for temporal reasoning over time-involved\ndocuments. Concretely, MTGER explicitly models the temporal relationships among\nfacts by multi-view temporal graphs. On the one hand, the heterogeneous\ntemporal graphs explicitly model the temporal and discourse relationships among\nfacts; on the other hand, the multi-view mechanism captures both time-focused\nand fact-focused information, allowing the two views to complement each other\nthrough adaptive fusion. To further improve the implicit reasoning capability\nof the model, we design a self-supervised time-comparing objective. Extensive\nexperimental results demonstrate the effectiveness of our method on the TimeQA\nand SituatedQA datasets. Furthermore, MTGER gives more consistent answers under\nquestion perturbations.",
+                    "authors": "Zheng Chu, Zekun Wang, Jiafeng Liang, Ming Liu, Bing Qin",
+                    "published": "2023-11-08",
+                    "updated": "2023-11-08",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.12973v1",
+                    "title": "Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is one of the most fundamental problems in transportation\nscience and artificial intelligence. The key challenge is to effectively model\ncomplex spatial-temporal dependencies and correlations in modern traffic data.\nExisting methods, however, cannot accurately model both long-term and\nshort-term temporal correlations simultaneously, limiting their expressive\npower on complex spatial-temporal patterns. In this paper, we propose a novel\nspatial-temporal neural network framework: Attention-based Spatial-Temporal\nGraph Convolutional Recurrent Network (ASTGCRN), which consists of a graph\nconvolutional recurrent module (GCRN) and a global attention module. In\nparticular, GCRN integrates gated recurrent units and adaptive graph\nconvolutional networks for dynamically learning graph structures and capturing\nspatial dependencies and local temporal relationships. To effectively extract\nglobal temporal dependencies, we design a temporal attention layer and\nimplement it as three independent modules based on multi-head self-attention,\ntransformer, and informer respectively. Extensive experiments on five real\ntraffic datasets have demonstrated the excellent predictive performance of all\nour three models with all their average MAE, RMSE and MAPE across the test\ndatasets lower than the baseline methods.",
+                    "authors": "Haiyang Liu, Chunjiang Zhu, Detian Zhang, Qing Li",
+                    "published": "2023-02-25",
+                    "updated": "2023-02-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1401.1919v1",
+                    "title": "Temporal Graph Traversals: Definitions, Algorithms, and Applications",
+                    "abstract": "A temporal graph is a graph in which connections between vertices are active\nat specific times, and such temporal information leads to completely new\npatterns and knowledge that are not present in a non-temporal graph. In this\npaper, we study traversal problems in a temporal graph. Graph traversals, such\nas DFS and BFS, are basic operations for processing and studying a graph. While\nboth DFS and BFS are well-known simple concepts, it is non-trivial to adopt the\nsame notions from a non-temporal graph to a temporal graph. We analyze the\ndifficulties of defining temporal graph traversals and propose new definitions\nof DFS and BFS for a temporal graph. We investigate the properties of temporal\nDFS and BFS, and propose efficient algorithms with optimal complexity. In\nparticular, we also study important applications of temporal DFS and BFS. We\nverify the efficiency and importance of our graph traversal algorithms in real\nworld temporal graphs.",
+                    "authors": "Silu Huang, James Cheng, Huanhuan Wu",
+                    "published": "2014-01-09",
+                    "updated": "2014-01-09",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.09791v2",
+                    "title": "Temporal Betweenness Centrality on Shortest Paths",
+                    "abstract": "Betweenness centrality measure assesses the importance of nodes in a graph\nand has been used in a variety of contexts. Betweenness centrality has also\nbeen extended to temporal graphs. Temporal graphs have edges that bear labels\naccording to the time of the interactions between the nodes. Betweenness\ncentrality has been extended to the temporal graph settings, and the notion of\npaths has been extended to temporal paths. Recent results by Bu{\\ss} et al. and\nRymar et al. showed that the betweenness centrality of all nodes in a temporal\ngraph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of\ntime units, m the number of temporal edges and n the number of nodes. In this\npaper, we improve the running time analysis of these previous approaches to\ncompute the betweenness centrality of all nodes in a temporal graph. We give an\nalgorithm that runs in O(n m T + n^2 T ).",
+                    "authors": "Mehdi Naima, Matthieu Latapy, Cl\u00e9mence Magnien",
+                    "published": "2023-04-19",
+                    "updated": "2023-06-06",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.14303v1",
+                    "title": "TREND: TempoRal Event and Node Dynamics for Graph Representation Learning",
+                    "abstract": "Temporal graph representation learning has drawn significant attention for\nthe prevalence of temporal graphs in the real world. However, most existing\nworks resort to taking discrete snapshots of the temporal graph, or are not\ninductive to deal with new nodes, or do not model the exciting effects which is\nthe ability of events to influence the occurrence of another event. In this\nwork, We propose TREND, a novel framework for temporal graph representation\nlearning, driven by TempoRal Event and Node Dynamics and built upon a Hawkes\nprocess-based graph neural network (GNN). TREND presents a few major\nadvantages: (1) it is inductive due to its GNN architecture; (2) it captures\nthe exciting effects between events by the adoption of the Hawkes process; (3)\nas our main novelty, it captures the individual and collective characteristics\nof events by integrating both event and node dynamics, driving a more precise\nmodeling of the temporal process. Extensive experiments on four real-world\ndatasets demonstrate the effectiveness of our proposed model.",
+                    "authors": "Zhihao Wen, Yuan Fang",
+                    "published": "2022-03-27",
+                    "updated": "2022-03-27",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.19292v1",
+                    "title": "Fusing Temporal Graphs into Transformers for Time-Sensitive Question Answering",
+                    "abstract": "Answering time-sensitive questions from long documents requires temporal\nreasoning over the times in questions and documents. An important open question\nis whether large language models can perform such reasoning solely using a\nprovided text document, or whether they can benefit from additional temporal\ninformation extracted using other systems. We address this research question by\napplying existing temporal information extraction systems to construct temporal\ngraphs of events, times, and temporal relations in questions and documents. We\nthen investigate different approaches for fusing these graphs into Transformer\nmodels. Experimental results show that our proposed approach for fusing\ntemporal graphs into input text substantially enhances the temporal reasoning\ncapabilities of Transformer models with or without fine-tuning. Additionally,\nour proposed method outperforms various graph convolution-based approaches and\nestablishes a new state-of-the-art performance on SituatedQA and three splits\nof TimeQA.",
+                    "authors": "Xin Su, Phillip Howard, Nagib Hakim, Steven Bethard",
+                    "published": "2023-10-30",
+                    "updated": "2023-10-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.05653v1",
+                    "title": "Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition",
+                    "abstract": "Accurate spatial-temporal traffic flow forecasting is essential for helping\ntraffic managers to take control measures and drivers to choose the optimal\ntravel routes. Recently, graph convolutional networks (GCNs) have been widely\nused in traffic flow prediction owing to their powerful ability to capture\nspatial-temporal dependencies. The design of the spatial-temporal graph\nadjacency matrix is a key to the success of GCNs, and it is still an open\nquestion. This paper proposes reconstructing the binary adjacency matrix via\ntensor decomposition, and a traffic flow forecasting method is proposed. First,\nwe reformulate the spatial-temporal fusion graph adjacency matrix into a\nthree-way adjacency tensor. Then, we reconstructed the adjacency tensor via\nTucker decomposition, wherein more informative and global spatial-temporal\ndependencies are encoded. Finally, a Spatial-temporal Synchronous Graph\nConvolutional module for localized spatial-temporal correlations learning and a\nDilated Convolution module for global correlations learning are assembled to\naggregate and learn the comprehensive spatial-temporal dependencies of the road\nnetwork. Experimental results on four open-access datasets demonstrate that the\nproposed model outperforms state-of-the-art approaches in terms of the\nprediction performance and computational cost.",
+                    "authors": "Qin Li, Xuan Yang, Yong Wang, Yuankai Wu, Deqiang He",
+                    "published": "2022-12-12",
+                    "updated": "2022-12-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.15862v1",
+                    "title": "Restless Temporal Path Parameterized Above Lower Bounds",
+                    "abstract": "Reachability questions are one of the most fundamental algorithmic primitives\nin temporal graphs -- graphs whose edge set changes over discrete time steps. A\ncore problem here is the NP-hard Short Restless Temporal Path: given a temporal\ngraph $\\mathcal G$, two distinct vertices $s$ and $z$, and two numbers $\\delta$\nand $k$, is there a $\\delta$-restless temporal $s$-$z$ path of length at most\n$k$? A temporal path is a path whose edges appear in chronological order and a\ntemporal path is $\\delta$-restless if two consecutive path edges appear at most\n$\\delta$ time steps apart from each other. Among others, this problem has\napplications in neuroscience and epidemiology. While Short Restless Temporal\nPath is known to be computationally hard, e.g., it is NP-hard for only three\ntime steps and W[1]-hard when parameterized by the feedback vertex number of\nthe underlying graph, it is fixed-parameter tractable when parameterized by the\npath length $k$. We improve on this by showing that Short Restless Temporal\nPath can be solved in (randomized) $4^{k-d}|\\mathcal G|^{O(1)}$ time, where $d$\nis the minimum length of a temporal $s$-$z$ path.",
+                    "authors": "Philipp Zschoche",
+                    "published": "2022-03-29",
+                    "updated": "2022-03-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.11244v1",
+                    "title": "Using Compressed Suffix-Arrays for a Compact Representation of Temporal-Graphs",
+                    "abstract": "Temporal graphs represent binary relationships that change along time. They\ncan model the dynamism of, for example, social and communication networks.\nTemporal graphs are defined as sets of contacts that are edges tagged with the\ntemporal intervals when they are active. This work explores the use of the\nCompressed Suffix Array (CSA), a well-known compact and self-indexed data\nstructure in the area of text indexing, to represent large temporal graphs. The\nnew structure, called Temporal Graph CSA (TGCSA), is experimentally compared\nwith the most competitive compact data structures in the state-of-the-art,\nnamely, EDGELOG and CET. The experimental results show that TGCSA obtains a\ngood space-time trade-off. It uses a reasonable space and is efficient for\nsolving complex temporal queries. Furthermore, TGCSA has wider expressive\ncapabilities than EDGELOG and CET, because it is able to represent temporal\ngraphs where contacts on an edge can temporally overlap.",
+                    "authors": "Nieves R. Brisaboa, Diego Caro, Antonio Fari\u00f1a, M. Andrea Rodriguez",
+                    "published": "2018-12-28",
+                    "updated": "2018-12-28",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.11886v1",
+                    "title": "Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs",
+                    "abstract": "Temporal bipartite graphs are widely used to denote time-evolving\nrelationships between two disjoint sets of nodes, such as customer-product\ninteractions in E-commerce and user-group memberships in social networks.\nTemporal butterflies, $(2,2)$-bicliques that occur within a short period and in\na prescribed order, are essential in modeling the structural and sequential\npatterns of such graphs. Counting the number of temporal butterflies is thus a\nfundamental task in analyzing temporal bipartite graphs. However, existing\nalgorithms for butterfly counting on static bipartite graphs and motif counting\non temporal unipartite graphs are inefficient for this purpose. In this paper,\nwe present a general framework with three sampling strategies for temporal\nbutterfly counting. Since exact counting can be time-consuming on large graphs,\nour approach alternatively computes approximate estimates accurately and\nefficiently. We also provide analytical bounds on the number of samples each\nstrategy requires to obtain estimates with small relative errors and high\nprobability. We finally evaluate our framework on six real-world datasets and\ndemonstrate its superior accuracy and efficiency compared to several baselines.\nOverall, our proposed framework and sampling strategies provide efficient and\naccurate approaches to approximating temporal butterfly counts on large-scale\ntemporal bipartite graphs.",
+                    "authors": "Jiaxi Pu, Yanhao Wang, Yuchen Li, Xuan Zhou",
+                    "published": "2023-10-18",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.DB",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.02852v1",
+                    "title": "Introduction to a Temporal Graph Benchmark",
+                    "abstract": "A temporal graph is a data structure, consisting of nodes and edges in which\nthe edges are associated with time labels. To analyze the temporal graph, the\nfirst step is to find a proper graph dataset/benchmark. While many temporal\ngraph datasets exist online, none could be found that used the interval labels\nin which each edge is associated with a starting and ending time. Therefore we\ncreate a temporal graph data based on Wikipedia reference graph for temporal\nanalysis. This report aims to provide more details of this graph benchmark to\nthose who are interested in using it.",
+                    "authors": "Wouter Ligtenberg, Yulong Pei",
+                    "published": "2017-02-20",
+                    "updated": "2017-02-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.02606v1",
+                    "title": "Learning adjacency matrix for dynamic graph neural network",
+                    "abstract": "In recent work, [1] introduced the concept of using a Block Adjacency Matrix\n(BA) for the representation of spatio-temporal data. While their method\nsuccessfully concatenated adjacency matrices to encapsulate spatio-temporal\nrelationships in a single graph, it formed a disconnected graph. This\nlimitation hampered the ability of Graph Convolutional Networks (GCNs) to\nperform message passing across nodes belonging to different time steps, as no\ntemporal links were present. To overcome this challenge, we introduce an\nencoder block specifically designed to learn these missing temporal links. The\nencoder block processes the BA and predicts connections between previously\nunconnected subgraphs, resulting in a Spatio-Temporal Block Adjacency Matrix\n(STBAM). This enriched matrix is then fed into a Graph Neural Network (GNN) to\ncapture the complex spatio-temporal topology of the network. Our evaluations on\nbenchmark datasets, surgVisDom and C2D2, demonstrate that our method, with\nslightly higher complexity, achieves superior results compared to\nstate-of-the-art results. Our approach's computational overhead remains\nsignificantly lower than conventional non-graph-based methodologies for\nspatio-temporal data.",
+                    "authors": "Osama Ahmad, Omer Abdul Jalil, Usman Nazir, Murtaza Taj",
+                    "published": "2023-10-04",
+                    "updated": "2023-10-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1310.7898v1",
+                    "title": "Moving in temporal graphs with very sparse random availability of edges",
+                    "abstract": "In this work we consider temporal graphs, i.e. graphs, each edge of which is\nassigned a set of discrete time-labels drawn from a set of integers. The labels\nof an edge indicate the discrete moments in time at which the edge is\navailable. We also consider temporal paths in a temporal graph, i.e. paths\nwhose edges are assigned a strictly increasing sequence of labels. Furthermore,\nwe assume the uniform case (UNI-CASE), in which every edge of a graph is\nassigned exactly one time label from a set of integers and the time labels\nassigned to the edges of the graph are chosen randomly and independently, with\nthe selection following the uniform distribution. We call uniform random\ntemporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the\nexpected number of temporal paths of a given length in the uniform random\ntemporal clique. We define the term temporal distance of two vertices, which is\nthe arrival time, i.e. the time-label of the last edge, of the temporal path\nthat connects those vertices, which has the smallest arrival time amongst all\ntemporal paths that connect those vertices. We then propose and study two\nstatistical properties of temporal graphs. One is the maximum expected temporal\ndistance which is, as the term indicates, the maximum of all expected temporal\ndistances in the graph. The other one is the temporal diameter which, loosely\nspeaking, is the expectation of the maximum temporal distance in the graph. We\nderive the maximum expected temporal distance of a uniform random temporal star\ngraph as well as an upper bound on both the maximum expected temporal distance\nand the temporal diameter of the normalized version of the uniform random\ntemporal clique, in which the largest time-label available equals the number of\nvertices. Finally, we provide an algorithm that solves an optimization problem\non a specific type of temporal (multi)graphs of two vertices.",
+                    "authors": "Paul G. Spirakis, Eleni Ch. Akrida",
+                    "published": "2013-10-29",
+                    "updated": "2013-10-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1502.04579v3",
+                    "title": "The complexity of optimal design of temporally connected graphs",
+                    "abstract": "We study the design of small cost temporally connected graphs, under various\nconstraints. We mainly consider undirected graphs of $n$ vertices, where each\nedge has an associated set of discrete availability instances (labels). A\njourney from vertex $u$ to vertex $v$ is a path from $u$ to $v$ where\nsuccessive path edges have strictly increasing labels. A graph is temporally\nconnected iff there is a $(u,v)$-journey for any pair of vertices $u,v,~u\\not=\nv$. We first give a simple polynomial-time algorithm to check whether a given\ntemporal graph is temporally connected. We then consider the case in which a\ndesigner of temporal graphs can \\emph{freely choose} availability instances for\nall edges and aims for temporal connectivity with very small \\emph{cost}; the\ncost is the total number of availability instances used. We achieve this via a\nsimple polynomial-time procedure which derives designs of cost linear in $n$.\nWe also show that the above procedure is (almost) optimal when the underlying\ngraph is a tree, by proving a lower bound on the cost for any tree. However,\nthere are pragmatic cases where one is not free to design a temporally\nconnected graph anew, but is instead \\emph{given} a temporal graph design with\nthe claim that it is temporally connected, and wishes to make it more\ncost-efficient by removing labels without destroying temporal connectivity\n(redundant labels). Our main technical result is that computing the maximum\nnumber of redundant labels is APX-hard, i.e., there is no PTAS unless $P=NP$.\nOn the positive side, we show that in dense graphs with random edge\navailabilities, there is asymptotically almost surely a very large number of\nredundant labels. A temporal design may, however, be \\emph{minimal}, i.e., no\nredundant labels exist. We show the existence of minimal temporal designs with\nat least $n \\log{n}$ labels.",
+                    "authors": "Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, Paul G. Spirakis",
+                    "published": "2015-02-16",
+                    "updated": "2016-07-06",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19453v1",
+                    "title": "Structural Parameters for Dense Temporal Graphs",
+                    "abstract": "Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.",
+                    "authors": "Jessica Enright, Samuel D. Hand, Laura Larios-Jones, Kitty Meeks",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "math.CO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.05064v1",
+                    "title": "Adaptive Graph Spatial-Temporal Transformer Network for Traffic Flow Forecasting",
+                    "abstract": "Traffic flow forecasting on graphs has real-world applications in many\nfields, such as transportation system and computer networks. Traffic\nforecasting can be highly challenging due to complex spatial-temporal\ncorrelations and non-linear traffic patterns. Existing works mostly model such\nspatial-temporal dependencies by considering spatial correlations and temporal\ncorrelations separately and fail to model the direct spatial-temporal\ncorrelations. Inspired by the recent success of transformers in the graph\ndomain, in this paper, we propose to directly model the cross-spatial-temporal\ncorrelations on the spatial-temporal graph using local multi-head\nself-attentions. To reduce the time complexity, we set the attention receptive\nfield to the spatially neighboring nodes, and we also introduce an adaptive\ngraph to capture the hidden spatial-temporal dependencies. Based on these\nattention mechanisms, we propose a novel Adaptive Graph Spatial-Temporal\nTransformer Network (ASTTN), which stacks multiple spatial-temporal attention\nlayers to apply self-attention on the input graph, followed by linear layers\nfor predictions. Experimental results on public traffic network datasets,\nMETR-LA PEMS-BAY, PeMSD4, and PeMSD7, demonstrate the superior performance of\nour model.",
+                    "authors": "Aosong Feng, Leandros Tassiulas",
+                    "published": "2022-07-09",
+                    "updated": "2022-07-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02563v1",
+                    "title": "Kairos: Efficient Temporal Graph Analytics on a Single Machine",
+                    "abstract": "Many important societal problems are naturally modeled as algorithms over\ntemporal graphs. To date, however, most graph processing systems remain\ninefficient as they rely on distributed processing even for graphs that fit\nwell within a commodity server's available storage. In this paper, we introduce\nKairos, a temporal graph analytics system that provides application developers\na framework for efficiently implementing and executing algorithms over temporal\ngraphs on a single machine. Specifically, Kairos relies on fork-join\nparallelism and a highly optimized parallel data structure as core primitives\nto maximize performance of graph processing tasks needed for temporal graph\nanalytics. Furthermore, we introduce the notion of selective indexing and show\nhow it can be used with an efficient index to speedup temporal queries. Our\nexperiments on a 24-core server show that our algorithms obtain good parallel\nspeedups, and are significantly faster than equivalent algorithms in existing\ntemporal graph processing systems: up to 60x against a shared-memory approach,\nand several orders of magnitude when compared with distributed processing of\ngraphs that fit within a single server.",
+                    "authors": "Joana M. F. da Trindade, Julian Shun, Samuel Madden, Nesime Tatbul",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB",
+                        "cs.DC",
+                        "cs.PF"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.05018v2",
+                    "title": "Time-varying Graph Learning Under Structured Temporal Priors",
+                    "abstract": "This paper endeavors to learn time-varying graphs by using structured\ntemporal priors that assume underlying relations between arbitrary two graphs\nin the graph sequence. Different from many existing chain structure based\nmethods in which the priors like temporal homogeneity can only describe the\nvariations of two consecutive graphs, we propose a structure named\n\\emph{temporal graph} to characterize the underlying real temporal relations.\nUnder this framework, the chain structure is actually a special case of our\ntemporal graph. We further proposed Alternating Direction Method of Multipliers\n(ADMM), a distributed algorithm, to solve the induced optimization problem.\nNumerical experiments demonstrate the superiorities of our method.",
+                    "authors": "Xiang Zhang, Qiao Wang",
+                    "published": "2021-10-11",
+                    "updated": "2022-02-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.SP"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.00518v1",
+                    "title": "DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is essential to intelligent transportation systems, which\nis challenging due to the complicated spatial and temporal dependencies within\na road network. Existing works usually learn spatial and temporal dependencies\nseparately, ignoring the dependencies crossing spatial and temporal dimensions.\nIn this paper, we propose DSTCGCN, a dynamic spatial-temporal cross graph\nconvolution network to learn dynamic spatial and temporal dependencies jointly\nvia graphs for traffic forecasting. Specifically, we introduce a fast Fourier\ntransform (FFT) based attentive selector to choose relevant time steps for each\ntime step based on time-varying traffic data. Given the selected time steps, we\nintroduce a dynamic cross graph construction module, consisting of the spatial\ngraph construction, temporal connection graph construction, and fusion modules,\nto learn dynamic spatial-temporal cross dependencies without pre-defined\npriors. Extensive experiments on six real-world datasets demonstrate that\nDSTCGCN achieves the state-of-the-art performance.",
+                    "authors": "Binqing Wu, Ling Chen",
+                    "published": "2023-07-02",
+                    "updated": "2023-07-02",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.07503v1",
+                    "title": "Temporal Aggregation and Propagation Graph Neural Networks for Dynamic Representation",
+                    "abstract": "Temporal graphs exhibit dynamic interactions between nodes over continuous\ntime, whose topologies evolve with time elapsing.\n  The whole temporal neighborhood of nodes reveals the varying preferences of\nnodes.\n  However, previous works usually generate dynamic representation with limited\nneighbors for simplicity, which results in both inferior performance and high\nlatency of online inference.\n  Therefore, in this paper, we propose a novel method of temporal graph\nconvolution with the whole neighborhood, namely Temporal Aggregation and\nPropagation Graph Neural Networks (TAP-GNN).\n  Specifically, we firstly analyze the computational complexity of the dynamic\nrepresentation problem by unfolding the temporal graph in a message-passing\nparadigm.\n  The expensive complexity motivates us to design the AP (aggregation and\npropagation) block, which significantly reduces the repeated computation of\nhistorical neighbors.\n  The final TAP-GNN supports online inference in the graph stream scenario,\nwhich incorporates the temporal information into node embeddings with a\ntemporal activation function and a projection layer besides several AP blocks.\n  Experimental results on various real-life temporal networks show that our\nproposed TAP-GNN outperforms existing temporal graph methods by a large margin\nin terms of both predictive performance and online inference latency.\n  Our code is available at \\url{https://github.com/doujiang-zheng/TAP-GNN}.",
+                    "authors": "Tongya Zheng, Xinchao Wang, Zunlei Feng, Jie Song, Yunzhi Hao, Mingli Song, Xingen Wang, Xinyu Wang, Chun Chen",
+                    "published": "2023-04-15",
+                    "updated": "2023-04-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.04696v1",
+                    "title": "Nash Equilibria in Reverse Temporal Voronoi Games",
+                    "abstract": "We study Voronoi games on temporal graphs as introduced by Boehmer et al.\n(IJCAI 2021) where two players each select a vertex in a temporal graph with\nthe goal of reaching the other vertices earlier than the other player. In this\nwork, we consider the reverse temporal Voronoi game, that is, a player wants to\nmaximize the number of vertices reaching her earlier than the other player.\nSince temporal distances in temporal graphs are not symmetric in general, this\nyields a different game. We investigate the difference between the two games\nwith respect to the existence of Nash equilibria in various temporal graph\nclasses including temporal trees, cycles, grids, cliques and split graphs. Our\nextensive results show that the two games indeed behave quite differently\ndepending on the considered temporal graph class.",
+                    "authors": "Simeon Pawlowski, Vincent Froese",
+                    "published": "2024-02-07",
+                    "updated": "2024-02-07",
+                    "primary_cat": "cs.GT",
+                    "cats": [
+                        "cs.GT"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2205.14269v1",
+                    "title": "Temporal graph patterns by timed automata",
+                    "abstract": "Temporal graphs represent graph evolution over time, and have been receiving\nconsiderable research attention. Work on expressing temporal graph patterns or\ndiscovering temporal motifs typically assumes relatively simple temporal\nconstraints, such as journeys or, more generally, existential constraints,\npossibly with finite delays. In this paper we propose to use timed automata to\nexpress temporal constraints, leading to a general and powerful notion of\ntemporal basic graph pattern (BGP). The new difficulty is the evaluation of the\ntemporal constraint on a large set of matchings. An important benefit of timed\nautomata is that they support an iterative state assignment, which can be\nuseful for early detection of matches and pruning of non-matches. We introduce\nalgorithms to retrieve all instances of a temporal BGP match in a graph, and\npresent results of an extensive experimental evaluation, demonstrating\ninteresting performance trade-offs. We show that an on-demand algorithm that\nprocesses total matchings incrementally over time is preferable when dealing\nwith cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and\nwhen connectivity of partial matchings can be guaranteed, the best performance\nis achieved by maintaining partial matchings over time and allowing automaton\nevaluation to be fully incremental.",
+                    "authors": "Amir Pouya Aghasadeghi, Jan Van den Bussche, Julia Stoyanovich",
+                    "published": "2022-05-27",
+                    "updated": "2022-05-27",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.08733v1",
+                    "title": "Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast",
+                    "abstract": "Self-supervised learning on graphs has recently drawn a lot of attention due\nto its independence from labels and its robustness in representation. Current\nstudies on this topic mainly use static information such as graph structures\nbut cannot well capture dynamic information such as timestamps of edges.\nRealistic graphs are often dynamic, which means the interaction between nodes\noccurs at a specific time. This paper proposes a self-supervised dynamic graph\nrepresentation learning framework (DySubC), which defines a temporal subgraph\ncontrastive learning task to simultaneously learn the structural and\nevolutional features of a dynamic graph. Specifically, a novel temporal\nsubgraph sampling strategy is firstly proposed, which takes each node of the\ndynamic graph as the central node and uses both neighborhood structures and\nedge timestamps to sample the corresponding temporal subgraph. The subgraph\nrepresentation function is then designed according to the influence of\nneighborhood nodes on the central node after encoding the nodes in each\nsubgraph. Finally, the structural and temporal contrastive loss are defined to\nmaximize the mutual information between node representation and temporal\nsubgraph representation. Experiments on five real-world datasets demonstrate\nthat (1) DySubC performs better than the related baselines including two graph\ncontrastive learning models and four dynamic graph representation learning\nmodels in the downstream link prediction task, and (2) the use of temporal\ninformation can not only sample more effective subgraphs, but also learn better\nrepresentation by temporal contrastive loss.",
+                    "authors": "Linpu Jiang, Ke-Jia Chen, Jingqiang Chen",
+                    "published": "2021-12-16",
+                    "updated": "2021-12-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1504.07976v3",
+                    "title": "On Temporal Graph Exploration",
+                    "abstract": "A temporal graph is a graph in which the edge set can change from one time\nstep to the next. The temporal graph exploration problem TEXP is the problem of\ncomputing a foremost exploration schedule for a temporal graph, i.e., a\ntemporal walk that starts at a given start node, visits all nodes of the graph,\nand has the smallest arrival time. In the first part of the paper, we consider\nonly undirected temporal graphs that are connected at each time step. For such\ntemporal graphs with $n$ nodes, we show that it is \\NP-hard to approximate TEXP\nwith ratio $O(n^{1-\\varepsilon})$ for every $\\varepsilon>0$. We also provide an\nexplicit construction of temporal graphs that require $\\Theta(n^2)$ time steps\nto be explored. In the second part of the paper, we still consider temporal\ngraphs that are connected in each time step, but we assume that the underlying\ngraph (i.e. the graph that contains all edges that are present in the temporal\ngraph in at least one time step) belongs to a specific class of graphs. Among\nother results, we show that temporal graphs can be explored in\n$O(n^{1.5}k^{1.5}\\log n)$ time steps if the underlying graph has treewidth $k$,\nin $O(n^{1.8}\\log n)$ time steps if the underlying graph is planar, and in\n$O(n\\log^3 n)$ time steps if the underlying graph is a $2\\times n$ grid. In the\nthird part of the paper, we consider settings where the graphs in future time\nsteps are not known and the exploration schedule is constructed online. We\nreplace the connectedness assumption by a weaker assumption and show that\n$m$-edge temporal graphs with regularly present edges and with\nprobabilistically present edges can be explored online in $O(m)$ time steps and\n$O(m \\log n)$ time steps with high probability, respectively. We finally show\nthat the latter result can be used to obtain a distributed algorithm for the\ngossiping problem in random temporal graphs.",
+                    "authors": "Thomas Erlebach, Michael Hoffmann, Frank Kammer",
+                    "published": "2015-04-29",
+                    "updated": "2021-03-16",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "05C85, 68M14",
+                        "C.2.4; F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.03363v3",
+                    "title": "Spatio-Temporal Graph Scattering Transform",
+                    "abstract": "Although spatio-temporal graph neural networks have achieved great empirical\nsuccess in handling multiple correlated time series, they may be impractical in\nsome real-world scenarios due to a lack of sufficient high-quality training\ndata. Furthermore, spatio-temporal graph neural networks lack theoretical\ninterpretation. To address these issues, we put forth a novel mathematically\ndesigned framework to analyze spatio-temporal data. Our proposed\nspatio-temporal graph scattering transform (ST-GST) extends traditional\nscattering transforms to the spatio-temporal domain. It performs iterative\napplications of spatio-temporal graph wavelets and nonlinear activation\nfunctions, which can be viewed as a forward pass of spatio-temporal graph\nconvolutional networks without training. Since all the filter coefficients in\nST-GST are mathematically designed, it is promising for the real-world\nscenarios with limited training data, and also allows for a theoretical\nanalysis, which shows that the proposed ST-GST is stable to small perturbations\nof input signals and structures. Finally, our experiments show that i) ST-GST\noutperforms spatio-temporal graph convolutional networks by an increase of 35%\nin accuracy for MSR Action3D dataset; ii) it is better and computationally more\nefficient to design the transform based on separable spatio-temporal graphs\nthan the joint ones; and iii) the nonlinearity in ST-GST is critical to\nempirical performance.",
+                    "authors": "Chao Pan, Siheng Chen, Antonio Ortega",
+                    "published": "2020-12-06",
+                    "updated": "2021-02-09",
+                    "primary_cat": "eess.SP",
+                    "cats": [
+                        "eess.SP",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.02875v1",
+                    "title": "Multi-Task Edge Prediction in Temporally-Dynamic Video Graphs",
+                    "abstract": "Graph neural networks have shown to learn effective node representations,\nenabling node-, link-, and graph-level inference. Conventional graph networks\nassume static relations between nodes, while relations between entities in a\nvideo often evolve over time, with nodes entering and exiting dynamically. In\nsuch temporally-dynamic graphs, a core problem is inferring the future state of\nspatio-temporal edges, which can constitute multiple types of relations. To\naddress this problem, we propose MTD-GNN, a graph network for predicting\ntemporally-dynamic edges for multiple types of relations. We propose a\nfactorized spatio-temporal graph attention layer to learn dynamic node\nrepresentations and present a multi-task edge prediction loss that models\nmultiple relations simultaneously. The proposed architecture operates on top of\nscene graphs that we obtain from videos through object detection and\nspatio-temporal linking. Experimental evaluations on ActionGenome and CLEVRER\nshow that modeling multiple relations in our temporally-dynamic graph network\ncan be mutually beneficial, outperforming existing static and spatio-temporal\ngraph neural networks, as well as state-of-the-art predicate classification\nmethods.",
+                    "authors": "Osman \u00dclger, Julian Wiederer, Mohsen Ghafoorian, Vasileios Belagiannis, Pascal Mettes",
+                    "published": "2022-12-06",
+                    "updated": "2022-12-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.09677v1",
+                    "title": "A Simple Temporal Information Matching Mechanism for Entity Alignment Between Temporal Knowledge Graphs",
+                    "abstract": "Entity alignment (EA) aims to find entities in different knowledge graphs\n(KGs) that refer to the same object in the real world. Recent studies\nincorporate temporal information to augment the representations of KGs. The\nexisting methods for EA between temporal KGs (TKGs) utilize a time-aware\nattention mechanism to incorporate relational and temporal information into\nentity embeddings. The approaches outperform the previous methods by using\ntemporal information. However, we believe that it is not necessary to learn the\nembeddings of temporal information in KGs since most TKGs have uniform temporal\nrepresentations. Therefore, we propose a simple graph neural network (GNN)\nmodel combined with a temporal information matching mechanism, which achieves\nbetter performance with less time and fewer parameters. Furthermore, since\nalignment seeds are difficult to label in real-world applications, we also\npropose a method to generate unsupervised alignment seeds via the temporal\ninformation of TKG. Extensive experiments on public datasets indicate that our\nsupervised method significantly outperforms the previous methods and the\nunsupervised one has competitive performance.",
+                    "authors": "Li Cai, Xin Mao, Meirong Ma, Hao Yuan, Jianchao Zhu, Man Lan",
+                    "published": "2022-09-20",
+                    "updated": "2022-09-20",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1601.05909v2",
+                    "title": "Efficient Processing of Reachability and Time-Based Path Queries in a Temporal Graph",
+                    "abstract": "A temporal graph is a graph in which vertices communicate with each other at\nspecific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is\nmodeled by an edge from $A$ to $B$ with starting time \"11 a.m.\" and duration \"7\nmins\". Temporal graphs can be used to model many networks with time-related\nactivities, but efficient algorithms for analyzing temporal graphs are severely\ninadequate. We study fundamental problems such as answering reachability and\ntime-based path queries in a temporal graph, and propose an efficient indexing\ntechnique specifically designed for processing these queries in a temporal\ngraph. Our results show that our method is efficient and scalable in both index\nconstruction and query processing.",
+                    "authors": "Huanhuan Wu, Yuzhen Huang, James Cheng, Jinfeng Li, Yiping Ke",
+                    "published": "2016-01-22",
+                    "updated": "2016-01-25",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.06411v1",
+                    "title": "On the Size and the Approximability of Minimum Temporally Connected Subgraphs",
+                    "abstract": "We consider temporal graphs with discrete time labels and investigate the\nsize and the approximability of minimum temporally connected spanning\nsubgraphs. We present a family of minimally connected temporal graphs with $n$\nvertices and $\\Omega(n^2)$ edges, thus resolving an open question of (Kempe,\nKleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal\nconnectivity certificates. Next, we consider the problem of computing a minimum\nweight subset of temporal edges that preserve connectivity of a given temporal\ngraph either from a given vertex r (r-MTC problem) or among all vertex pairs\n(MTC problem). We show that the approximability of r-MTC is closely related to\nthe approximability of Directed Steiner Tree and that r-MTC can be solved in\npolynomial time if the underlying graph has bounded treewidth. We also show\nthat the best approximation ratio for MTC is at least $O(2^{\\log^{1-\\epsilon}\nn})$ and at most $O(\\min\\{n^{1+\\epsilon}, (\\Delta M)^{2/3+\\epsilon}\\})$, for\nany constant $\\epsilon > 0$, where $M$ is the number of temporal edges and\n$\\Delta$ is the maximum degree of the underlying graph. Furthermore, we prove\nthat the unweighted version of MTC is APX-hard and that MTC is efficiently\nsolvable in trees and $2$-approximable in cycles.",
+                    "authors": "Kyriakos Axiotis, Dimitris Fotakis",
+                    "published": "2016-02-20",
+                    "updated": "2016-02-20",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.13177v1",
+                    "title": "It is all Connected: A New Graph Formulation for Spatio-Temporal Forecasting",
+                    "abstract": "With an ever-increasing number of sensors in modern society, spatio-temporal\ntime series forecasting has become a de facto tool to make informed decisions\nabout the future. Most spatio-temporal forecasting models typically comprise\ndistinct components that learn spatial and temporal dependencies. A common\nmethodology employs some Graph Neural Network (GNN) to capture relations\nbetween spatial locations, while another network, such as a recurrent neural\nnetwork (RNN), learns temporal correlations. By representing every recorded\nsample as its own node in a graph, rather than all measurements for a\nparticular location as a single node, temporal and spatial information is\nencoded in a similar manner. In this setting, GNNs can now directly learn both\ntemporal and spatial dependencies, jointly, while also alleviating the need for\nadditional temporal networks. Furthermore, the framework does not require\naligned measurements along the temporal dimension, meaning that it also\nnaturally facilitates irregular time series, different sampling frequencies or\nmissing data, without the need for data imputation. To evaluate the proposed\nmethodology, we consider wind speed forecasting as a case study, where our\nproposed framework outperformed other spatio-temporal models using GNNs with\neither Transformer or LSTM networks as temporal update functions.",
+                    "authors": "Lars \u00d8degaard Bentsen, Narada Dilp Warakagoda, Roy Stenbro, Paal Engelstad",
+                    "published": "2023-03-23",
+                    "updated": "2023-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.01928v1",
+                    "title": "Constructing Temporal Dynamic Knowledge Graphs from Interactive Text-based Games",
+                    "abstract": "In natural language processing, interactive text-based games serve as a test\nbed for interactive AI systems. Prior work has proposed to play text-based\ngames by acting based on discrete knowledge graphs constructed by the Discrete\nGraph Updater (DGU) to represent the game state from the natural language\ndescription. While DGU has shown promising results with high interpretability,\nit suffers from lower knowledge graph accuracy due to its lack of temporality\nand limited generalizability to complex environments with objects with the same\nlabel. In order to address DGU's weaknesses while preserving its high\ninterpretability, we propose the Temporal Discrete Graph Updater (TDGU), a\nnovel neural network model that represents dynamic knowledge graphs as a\nsequence of timestamped graph events and models them using a temporal point\nbased graph neural network. Through experiments on the dataset collected from a\ntext-based game TextWorld, we show that TDGU outperforms the baseline DGU. We\nfurther show the importance of temporal information for TDGU's performance\nthrough an ablation study and demonstrate that TDGU has the ability to\ngeneralize to more complex environments with objects with the same label. All\nthe relevant code can be found at\n\\url{https://github.com/yukw777/temporal-discrete-graph-updater}.",
+                    "authors": "Keunwoo Peter Yu",
+                    "published": "2023-11-03",
+                    "updated": "2023-11-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2312.01217v1",
+                    "title": "Understanding Opinions Towards Climate Change on Social Media",
+                    "abstract": "Social media platforms such as Twitter (now known as X) have revolutionized\nhow the public engage with important societal and political topics. Recently,\nclimate change discussions on social media became a catalyst for political\npolarization and the spreading of misinformation. In this work, we aim to\nunderstand how real world events influence the opinions of individuals towards\nclimate change related topics on social media. To this end, we extracted and\nanalyzed a dataset of 13.6 millions tweets sent by 3.6 million users from 2006\nto 2019. Then, we construct a temporal graph from the user-user mentions\nnetwork and utilize the Louvain community detection algorithm to analyze the\nchanges in community structure around Conference of the Parties on Climate\nChange~(COP) events. Next, we also apply tools from the Natural Language\nProcessing literature to perform sentiment analysis and topic modeling on the\ntweets. Our work acts as a first step towards understanding the evolution of\npro-climate change communities around COP events. Answering these questions\nhelps us understand how to raise people's awareness towards climate change thus\nhopefully calling on more individuals to join the collaborative effort in\nslowing down climate change.",
+                    "authors": "Yashaswi Pupneja, Joseph Zou, Sacha L\u00e9vy, Shenyang Huang",
+                    "published": "2023-12-02",
+                    "updated": "2023-12-02",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Temporal AND Graph",
+                    "gt": "Climate Change on Social Media. Social media have created new arenas for public debates and revolutionized the discussion of prominent issues such as global climate change [20]. Various research on this topic have been conducted. [11] looked into user profile, tweet attitude, discussion Tackling Climate Change with Machine Learning: workshop at NeurIPS 2023. arXiv:2312.01217v1  [cs.SI]  2 Dec 2023 topics, and climate phenomenons. [2] built a random forest (RF) model to predict people\u2019s attitude towards climate change and environment protection based on psychological and demographic factors. Furthermore, [25] modeled the relationship between perceived climate change efficacy and news and user activities on social media by using multilevel regression. Temporal Graph Learning. Social networks can be modeled as a temporal graph where users are nodes and interactions are edges while the nodes and edges in the graph would naturally change over time [23, 29, 28]. The dynamic community detection task which aims to identify groups of individuals who are closely connected to each other on the temporal graph [21, 7, 4, 22]. Qin et al. [21] and Boudebza et al. [4] both proposed novel methods to detect stable communities, groups of nodes forming a coherent community throughout a period of time. In this work, we first apply the well-know Louvain community detection algorithm [3] to identify the growth or contraction of user communities of climate change topics on twitter. Misinformation detection. Misinformation related to climate change is a significant problem that has been widely researched. Several studies have examined the relationship between social media usage, belief in conspiracy theories, and misinformation, highlighting the gravity of the issue [12]. The adverse impact of such misinformation has been well-documented, underscoring the importance of inoculating people against misinformation related to climate change [18]. Research on debunking strategies has produced mixed results, highlighting the continued influence of misinformation and the need for effective measures [17, 5]. The identification of psychological factors that drive misinformation and hinder debunking [9] indicates the complexity of the issue and the need for targeted interventions to tackle it. Political polarization detection. Political polarization [8] is one of the crucial socio-political issues in twenty-first century. It intensifies political debates and may even threaten civil society. [8] demonstrated that political polarization happens naturally when the observable indicators of policy outcomes are not monotonic. Hence due to its commonness and harmfulness, it is important to monitor political polarization and its impact especially in public discussions about climate. [16] demonstrated that public opinion toward climate politics is closely consistent with people\u2019s positions on parties and the US general public has become quite politically polarized in recent years. Further studies [6, 19] showed similar alignment between polarized public opinions toward climate politics and partisan sorting. Considering the effect of events, [13] highlighted a large increase in polarization in 2021 during the 26th United Nations Conference of the Parties on Climate Change (COP26) and attributed it to growing right-wing activity. Moreover, [26] investigated hostile communication between polarized competing groups.",
+                    "pre_questions": [],
+                    "main_content": "Introduction Climate change is a widely debated topic, and a significant number of individuals still denies the effect of climate change. Hence, we seek to understand how real-world events would influence opinions regarding climate change on social media platforms. According to a survey by the Pew Research Center, 15% of adults in the US do not believe that the Earth is warming, and 36% believe that it is due to natural causes rather than human activity. The spread of misinformation and propaganda campaigns on social media has contributed to skepticism around climate change [14]. To address these challenges, we aim to analyze the growth or contraction of communities of climate change supporters and non-supporters on social media platforms. This analysis will provide insights into how real-world events such as the Conference of the Parties (COP) events shape public opinion on climate change. By analyzing the patterns of social media interactions and the spread of climate change discourse on social media platforms, effective communication strategies can be developed to promote climate change awareness and counter misinformation campaigns. The stakeholders of this study include policymakers, environmental organizations, and the general public. In this section, we first discuss how we constructed the twitter dataset which we used for this project in Section 3.1. Then we extract the user-user mentions temporal network from the full dataset to examine the user interactions on twitter 3.2. 3.1 Collecting Twitter Dataset To understand how people engage with climate change related topics on social media, we first collect dataset of tweets from Twitter, a popular social network for discussing trending topics. In particular, we focus our collection process on climate change related tweets, posts made by users on Twitter. We leveraged a recently released Kaggle dataset [11, 10] containing climate change related tweets and their attributes for our study. However, the dataset lacks the raw tweet text and other information. Therefore, we use the tweet ID from the dataset to recollect the tweets using the Twitter API for Academic Research. Our dataset contains 13.6 millions tweets sent by 3.6 million users from 2006 to 2019. Each tweet contains various information such as the sender, any mentions of other users, timestamp, any hashtags and the raw text of the tweet. We have also collected dates for relevant Conference of the Parties (COP) Events in the duration of the dataset (as seen in Appendix C). 3.2 Constructing Temporal Graph From the collected meta-data of tweets, we construct the user-user mentions network to be a weekly temporal graph. This network naturally shows how users interact with each other over time. However, 2 the edges might not necessarily indicate that two users shares the same opinion. For example, it is possible for a climate change supporter to mention another user who doesn\u2019t believe in climate change. In this work, we discretize the mentions network to be a weekly temporal graph. More specifically, we represent the temporal graph G as a series of graph snapshots, G = {Gt}T t=1 where Gt = {Vt, At} is the graph snapshot at time t and Vt, At represent the set of nodes and the adjacency matrix of Gt respectively. While processing the tweet dataset, we find that there exist a large number of users which only send climate related tweets sparsely. Therefore, the constructed temporal graph is disconnected and sparse thus forming isolated components rather communities of users. To increase the density of the network while focusing on users that are more active on climate change topics, we remove all users that have less than 100 edges (across all steps) from the network (both outgoing and incoming edges). In this way, we only preserve a dense core set of users. 4 Methodology climatechange 47.8% climateaction 38.8% environment 5.8% energy 5.4% globalwarming 1.5% creativity 0.7% (a) Distribution of top Hashtags in tweets. (b) Distribution of positive, negative and neutral tweets. Figure 1: Analysis of a). hashtags and b). sentiment in extracted tweets. Hashtags Analysis. The top [YP: 8] most used hashtags from tweets are shown in Figure 1a. Some interesting hashtags include creativity, spirituality, economy, education and \"its time to change\". In particular, the hashtags themselves might already contain views or opinion towards climate change topics such as \"its time to change\". Sentiment Analysis. Sentiment analysis is a technique used to determine the emotional tone behind a piece of text. We analyze the overall sentiment of tweets to understand the emotions associated with different topics related to climate change such as climate policy, environmental disasters or scientific research. Sentiment analysis also helps identify patterns in the emotional tone of different groups, such as climate change supporters or deniers. Here, we used the TextBlob library to detect the sentiments of the tweets which determined whether the texts were positive, negative or neutral. The results are summarized in the pie chart in Figure 1b. The majority of tweets are neutral while there remains 19.0% of tweets that have a negative sentiment. This shows that most users share a neutral sentiment towards climate change and it calls for more actions to engage the public in more positive involvement in climate change actions. We also acknowledge that negative sentiments such as fear and discontent are also considered as negative but can show awareness towards climate events. Temporal Graph Analysis Figure 2 shows the evolution of the number of edges and graph density over time. We also marked COP events by grey vertical lines. COP events are often accompanied by local peaks in the number of edges. This is likely because more discussion on climate change related topics happen around COP events annually. For graph density, we observe large peaks around COP 13, 14 and 17. The 3 11/22/2007 05/07/2009 01/18/2010 10/01/2010 06/15/2011 05/01/2012 03/31/2013 02/08/2014 11/26/2014 08/14/2015 06/06/2016 04/11/2017 01/15/2018 11/26/2018 08/13/2019 Time (weeks) 0 50000 100000 150000 200000 250000 300000 350000 Number of edges COP13 COP14 COP15 COP16 COP17 COP18 COP19 COP20 COP21 COP22 COP23 COP24 COP25 (a) number of edges 11/22/2007 05/07/2009 01/18/2010 10/01/2010 06/15/2011 05/01/2012 03/31/2013 02/08/2014 11/26/2014 08/14/2015 06/06/2016 04/11/2017 01/15/2018 11/26/2018 08/13/2019 Time (weeks) 0.0 0.2 0.4 0.6 0.8 1.0 Density COP13 COP14 COP15 COP16 COP17 COP18 COP19 COP20 COP21 COP22 COP23 COP24 COP25 (b) density of graph snapshots Figure 2: The evolution of a). the number of edges and b). graph density in the temporal user-user mentions network constructed from tweets. 08/09/2012 09/16/2012 11/11/2012 12/13/2012 02/11/2013 Time (weeks) 0 100 200 300 400 500 600 Number of communities COP18 Number of communities over time (weekly) (a) COP 18 07/31/2013 09/01/2013 10/07/2013 12/01/2013 01/23/2014 Time (weeks) 0 100 200 300 400 500 600 Number of communities COP19 Number of communities over time (weekly) (b) COP 19 Figure 3: The number of communities detected around a). COP 18 and b). COP 19 peaks around COP 13 and 14 can be a result of noise in data collection in early years of twitter. The peaks around COP 17 signals increased discussion between active twitter users around this time. This coincides with the fact that COP 17 has one of the most significant achievements as all countries agree to the reduction of emissions, including the US and emerging countries such as Brazil, China, India and South Africa [1]. Details on the time of COP events are in Appendix C. Community Detection on Temporal Graph. In this work, we aim to examine changes to the community structure of the user-user mentions network around the time of COP events. To this end, we utilize the fast and scalable Louvain algorithm [3] to detect communities on individual snapshots of the temporal graph. The Louvain algorithm optimizes the modularity Q of the graph, defined as follows in a directed graph, Q = 1 2m X ij [Aij \u2212kikj 2m ]\u03b4(ci, cj) (1) where A is the weighed adjacency matrix of the graph, ki and kj are the sum of the weights of edges of nodes i, j respectively, m is the sum of all of the edge weights in the graph, ci and cj are the communities of nodes i, j and lastly, \u03b4 is the kronecker delta function. The complexity of the Louvain algorithm is O(n \u00b7 log n) where n is the number of nodes. More details can be found in Appendix B. Overall, The number of communities seem to increase over time with local peaks periodically. We also examine the community structure of graph snapshots surround COP events (10 weeks before and 10 weeks after) with the Louvain algorithm. Figure 3 shows the change in number of communities around COP 18 and COP 19. For COP 18 and 19, there is a decrease in the number of communities. This shows that larger communities are formed likely due to increased user discussions. However, for COP 20 and COP 21, there is an increase of communities. Therefore, it is difficult to clearly draw conclusions based on the number of communities around COP events. This is also expected as the Louvain algorithm is computed based the graph structure alone and doesn\u2019t utilize the tweet text and other edge features. More community detection results are reported in Appendix D. 4 Figure 4: Significant topics extracted from the corpus. Topic Modeling. Topic models are a class of unsupervised machine learning that allows us to extract topics from a large corpus of text data. They are powerful techniques that are commonly used for identifying patterns and themes in large text datasets. A typical topic model works by identifying groups of words that tend to co-occur in the same documents or tweets. These groups of words are known as \"topics\" and can provide insights into the underlying themes and issues that are present in the data. In our analysis of opinions on Twitter, we used topic modeling to identify the main topics of conversation related to climate change. By using the mini-batch non-negative matrix factorization (NMF) algorithm [15], we were able to efficiently extract topics from a large-scale dataset and gain insights into the key themes and issues that are salient to the public. We first tokenized the tweets data and then trained the mini-batch NMF model on the preprocessed corpus by setting the number of topics as 10. We utilized the scikit-learn toolkit to run mini-batch NMF model. The training algorithm was run for iterations until convergence, i.e., a set of stable topics was obtained. After the matrix factorization had been done, we looked at the topic-word score matrix W and described each topic by the words with the highest relevance score. Figure 4 shows three obtained representative topics with their top 20 words about politics, CO2 emission, and weather. The politics topic is related to politicians (e.g., Trump), organizations (e.g., EPA) and actions to address and mitigate climate change. The CO2 emission topic includes global warming, Arctic ice melting, and sea level rising as consequences of CO2 emission. The weather topic shows people\u2019s concern about extreme and abnormal weather caused by global warming. 5 Pathway to Impact This project aims to provide valuable insights into opinions about climate change on Twitter, potentially impacting many stakeholders. For policy makers, our approach provides an understanding of public opinion and sentiment as guidance to decision-making. For Researchers in social sciences, our project contributes to the study of the patterns and dynamics of climate change-related online communication. For journalists, our study provides insights about when and how to report on climate change topics. For the public, this project can inform them about potential negative sentiment and opinions towards climate change events on social media thus help more individuals raise awareness of climate change topics. Future work can extend our work and apply more recent techniques such as Large Language Models [24] and Graph Neural Networks [27]. 6 Acknowledgement We thank Prof. David Rolnick and TA Michelle Lin for their support and guidance throughout the duration of this project. We also thank prof. Reihaneh Rabbany and prof. Guillaume Rabusseau for their discussions and support in this project. This research was supported by the Canadian Institute for Advanced Research (CIFAR AI chair program), Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship-Doctoral (PGS D) Award and Fonds de recherche du Qu\u00e9bec \u2013 Nature et Technologies (FRQNT) Doctoral Award. 5"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.07239v1",
+                    "title": "ROLAND: Graph Learning Framework for Dynamic Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) have been successfully applied to many\nreal-world static graphs. However, the success of static graphs has not fully\ntranslated to dynamic graphs due to the limitations in model design, evaluation\nsettings, and training strategies. Concretely, existing dynamic GNNs do not\nincorporate state-of-the-art designs from static GNNs, which limits their\nperformance. Current evaluation settings for dynamic GNNs do not fully reflect\nthe evolving nature of dynamic graphs. Finally, commonly used training methods\nfor dynamic GNNs are not scalable. Here we propose ROLAND, an effective graph\nrepresentation learning framework for real-world dynamic graphs. At its core,\nthe ROLAND framework can help researchers easily repurpose any static GNN to\ndynamic graphs. Our insight is to view the node embeddings at different GNN\nlayers as hierarchical node states and then recurrently update them over time.\nWe then introduce a live-update evaluation setting for dynamic graphs that\nmimics real-world use cases, where GNNs are making predictions and being\nupdated on a rolling basis. Finally, we propose a scalable and efficient\ntraining approach for dynamic GNNs via incremental training and meta-learning.\nWe conduct experiments over eight different dynamic graph datasets on future\nlink prediction tasks. Models built using the ROLAND framework achieve on\naverage 62.7% relative mean reciprocal rank (MRR) improvement over\nstate-of-the-art baselines under the standard evaluation settings on three\ndatasets. We find state-of-the-art baselines experience out-of-memory errors\nfor larger datasets, while ROLAND can easily scale to dynamic graphs with 56\nmillion edges. After re-implementing these baselines using the ROLAND training\nstrategy, ROLAND models still achieve on average 15.5% relative MRR improvement\nover the baselines.",
+                    "authors": "Jiaxuan You, Tianyu Du, Jure Leskovec",
+                    "published": "2022-08-15",
+                    "updated": "2022-08-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2007.02706v1",
+                    "title": "Polarization of Climate Politics Results from Partisan Sorting: Evidence from Finnish Twittersphere",
+                    "abstract": "Prior research shows that public opinion on climate politics sorts along\npartisan lines. However, they leave open the question of whether climate\npolitics and other politically salient issues exhibit tendencies for issue\nalignment, which the political polarization literature identifies as among the\nmost deleterious aspects of polarization. Using a network approach and social\nmedia data from the Twitter platform, we study polarization of public opinion\ntoward climate politics and ten other politically salient topics during the\n2019 Finnish elections as the emergence of opposing groups in a public forum.\nWe find that while climate politics is not particularly polarized compared to\nthe other topics, it is subject to partisan sorting and issue alignment within\nthe universalist-communitarian dimension of European politics that arose\nfollowing the growth of right-wing populism. Notably, climate politics is\nconsistently aligned with the immigration issue, and temporal trends indicate\nthat this phenomenon will likely persist.",
+                    "authors": "Ted Hsuan Yun Chen, Ali Salloum, Antti Gronow, Tuomas Yl\u00e4-Anttila, Mikko Kivel\u00e4",
+                    "published": "2020-07-06",
+                    "updated": "2020-07-06",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.12137v5",
+                    "title": "Growing polarisation around climate change on social media",
+                    "abstract": "Climate change and political polarisation are two of the 21st century's\ncritical socio-political issues. Here, we investigate their intersection by\nstudying the discussion around the UN Conference of The Parties on Climate\nChange (COP) using Twitter data from 2014 to 2021. First, we reveal a large\nincrease in ideological polarisation during COP26, following low polarisation\nbetween COP20 and COP25. Second, we show that this increase is driven by\ngrowing right-wing activity, a 4-fold increase since COP21 relative to\npro-climate groups. Finally, we identify a broad range of ''climate\ncontrarian'' views during COP26, emphasising the theme of ''political\nhypocrisy'' as a topic of cross-ideological appeal; contrarian views and\naccusations of hypocrisy have become key themes in the Twitter climate\ndiscussion since 2019. With future climate action reliant on negotiations at\nCOP27 and beyond, our results highlight the importance of monitoring\npolarisation, and its impacts, in the public climate discourse.",
+                    "authors": "Max Falkenberg, Alessandro Galeazzi, Maddalena Torricelli, Niccolo Di Marco, Francesca Larosa, Madalina Sas, Amin Mekacher, Warren Pearce, Fabiana Zollo, Walter Quattrociocchi, Andrea Baronchelli",
+                    "published": "2021-12-22",
+                    "updated": "2022-11-14",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.14883v2",
+                    "title": "TGL: A General Framework for Temporal GNN Training on Billion-Scale Graphs",
+                    "abstract": "Many real world graphs contain time domain information. Temporal Graph Neural\nNetworks capture temporal information as well as structural and contextual\ninformation in the generated dynamic node embeddings. Researchers have shown\nthat these embeddings achieve state-of-the-art performance in many different\ntasks. In this work, we propose TGL, a unified framework for large-scale\noffline Temporal Graph Neural Network training where users can compose various\nTemporal Graph Neural Networks with simple configuration files. TGL comprises\nfive main components, a temporal sampler, a mailbox, a node memory module, a\nmemory updater, and a message passing engine. We design a Temporal-CSR data\nstructure and a parallel sampler to efficiently sample temporal neighbors to\nformtraining mini-batches. We propose a novel random chunk scheduling technique\nthat mitigates the problem of obsolete node memory when training with a large\nbatch size. To address the limitations of current TGNNs only being evaluated on\nsmall-scale datasets, we introduce two large-scale real-world datasets with 0.2\nand 1.3 billion temporal edges. We evaluate the performance of TGL on four\nsmall-scale datasets with a single GPU and the two large datasets with multiple\nGPUs for both link prediction and node classification tasks. We compare TGL\nwith the open-sourced code of five methods and show that TGL achieves similar\nor better accuracy with an average of 13x speedup. Our temporal parallel\nsampler achieves an average of 173x speedup on a multi-core CPU compared with\nthe baselines. On a 4-GPU machine, TGL can train one epoch of more than one\nbillion temporal edges within 1-10 hours. To the best of our knowledge, this is\nthe first work that proposes a general framework for large-scale Temporal Graph\nNeural Networks training on multiple GPUs.",
+                    "authors": "Hongkuan Zhou, Da Zheng, Israt Nisa, Vasileios Ioannidis, Xiang Song, George Karypis",
+                    "published": "2022-03-28",
+                    "updated": "2022-06-30",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.10453v1",
+                    "title": "Detecting Stable Communities in Link Streams at Multiple Temporal Scales",
+                    "abstract": "Link streams model interactions over time in a wide range of fields. Under\nthis model, the challenge is to mine efficiently both temporal and topological\nstructures. Community detection and change point detection are one of the most\npowerful tools to analyze such evolving interactions. In this paper, we build\non both to detect stable community structures by identifying change points\nwithin meaningful communities. Unlike existing dynamic community detection\nalgorithms, the proposed method is able to discover stable communities\nefficiently at multiple temporal scales. We test the effectiveness of our\nmethod on synthetic networks, and on high-resolution time-varying networks of\ncontacts drawn from real social networks.",
+                    "authors": "Souaad Boudebza, Remy Cazabet, Omar Nouali, Faical Azouaou",
+                    "published": "2019-07-24",
+                    "updated": "2019-07-24",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2006.10637v3",
+                    "title": "Temporal Graph Networks for Deep Learning on Dynamic Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) have recently become increasingly popular due to\ntheir ability to learn complex systems of relations or interactions arising in\na broad spectrum of problems ranging from biology and particle physics to\nsocial networks and recommendation systems. Despite the plethora of different\nmodels for deep learning on graphs, few approaches have been proposed thus far\nfor dealing with graphs that present some sort of dynamic nature (e.g. evolving\nfeatures or connectivity over time). In this paper, we present Temporal Graph\nNetworks (TGNs), a generic, efficient framework for deep learning on dynamic\ngraphs represented as sequences of timed events. Thanks to a novel combination\nof memory modules and graph-based operators, TGNs are able to significantly\noutperform previous approaches being at the same time more computationally\nefficient. We furthermore show that several previous models for learning on\ndynamic graphs can be cast as specific instances of our framework. We perform a\ndetailed ablation study of different components of our framework and devise the\nbest configuration that achieves state-of-the-art performance on several\ntransductive and inductive prediction tasks for dynamic graphs.",
+                    "authors": "Emanuele Rossi, Ben Chamberlain, Fabrizio Frasca, Davide Eynard, Federico Monti, Michael Bronstein",
+                    "published": "2020-06-18",
+                    "updated": "2020-10-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2008.13051v1",
+                    "title": "Affective Polarization in Online Climate Change Discourse on Twitter",
+                    "abstract": "Online social media has become an important platform to organize around\ndifferent socio-cultural and political topics. An extensive scholarship has\ndiscussed how people are divided into echo-chamber-like groups. However, there\nis a lack of work related to quantifying hostile communication or\n\\textit{affective polarization} between two competing groups. This paper\nproposes a systematic, network-based methodology for examining affective\npolarization in online conversations. Further, we apply our framework to 100\nweeks of Twitter discourse about climate change. We find that deniers of\nclimate change (Disbelievers) are more hostile towards people who believe\n(Believers) in the anthropogenic cause of climate change than vice versa.\nMoreover, Disbelievers use more words and hashtags related to natural disasters\nduring more hostile weeks as compared to Believers. These findings bear\nimplications for studying affective polarization in online discourse,\nespecially concerning the subject of climate change. Lastly, we discuss our\nfindings in the context of increasingly important climate change communication\nresearch.",
+                    "authors": "Aman Tyagi, Joshua Uyheng, Kathleen M. Carley",
+                    "published": "2020-08-29",
+                    "updated": "2020-08-29",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1707.03186v3",
+                    "title": "Community Discovery in Dynamic Networks: a Survey",
+                    "abstract": "Networks built to model real world phenomena are characeterised by some\nproperties that have attracted the attention of the scientific community: (i)\nthey are organised according to community structure and (ii) their structure\nevolves with time. Many researchers have worked on methods that can efficiently\nunveil substructures in complex networks, giving birth to the field of\ncommunity discovery. A novel and challenging problem started capturing\nresearcher interest recently: the identification of evolving communities. To\nmodel the evolution of a system, dynamic networks can be used: nodes and edges\nare mutable and their presence, or absence, deeply impacts the community\nstructure that composes them. The aim of this survey is to present the\ndistinctive features and challenges of dynamic community discovery, and propose\na classification of published approaches. As a \"user manual\", this work\norganizes state of art methodologies into a taxonomy, based on their rationale,\nand their specific instanciation. Given a desired definition of network\ndynamics, community characteristics and analytical needs, this survey will\nsupport researchers to identify the set of approaches that best fit their\nneeds. The proposed classification could also help researchers to choose in\nwhich direction should future research be oriented.",
+                    "authors": "Giulio Rossetti, R\u00e9my Cazabet",
+                    "published": "2017-07-11",
+                    "updated": "2019-09-03",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph",
+                        "A.1; E.1; G.2.2; I.5.3"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.10129v2",
+                    "title": "Network Communities of Dynamical Influence",
+                    "abstract": "Fuelled by a desire for greater connectivity, networked systems now pervade\nour society at an unprecedented level that will affect it in ways we do not yet\nunderstand. In contrast, nature has already developed efficient networks that\ncan instigate rapid response and consensus, when key elements are stimulated.\nWe present a technique for identifying these key elements by investigating the\nrelationships between a system's most dominant eigenvectors. This approach\nreveals the most effective vertices for leading a network to rapid consensus\nwhen stimulated, as well as the communities that form under their dynamical\ninfluence. In applying this technique, the effectiveness of starling flocks was\nfound to be due, in part, to the low outdegree of every bird, where increasing\nthe number of outgoing connections can produce a less responsive flock. A\nlarger outdegree also affects the location of the birds with the most\ninfluence, where these influentially connected birds become more centrally\nlocated and in a poorer position to observe a predator and, hence, instigate an\nevasion manoeuvre. Finally, the technique was found to be effective in large\nvoxel-wise brain connectomes where subjects can be identified from their\ninfluential communities.",
+                    "authors": "Ruaridh Clark, Giuliano Punzo, Malcolm Macdonald",
+                    "published": "2019-08-27",
+                    "updated": "2019-10-05",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "nlin.AO",
+                        "physics.soc-ph"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0803.0476v2",
+                    "title": "Fast unfolding of communities in large networks",
+                    "abstract": "We propose a simple method to extract the community structure of large\nnetworks. Our method is a heuristic method that is based on modularity\noptimization. It is shown to outperform all other known community detection\nmethod in terms of computation time. Moreover, the quality of the communities\ndetected is very good, as measured by the so-called modularity. This is shown\nfirst by identifying language communities in a Belgian mobile phone network of\n2.6 million customers and by analyzing a web graph of 118 million nodes and\nmore than one billion links. The accuracy of our algorithm is also verified on\nad-hoc modular networks. .",
+                    "authors": "Vincent D. Blondel, Jean-Loup Guillaume, Renaud Lambiotte, Etienne Lefebvre",
+                    "published": "2008-03-04",
+                    "updated": "2008-07-25",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cond-mat.stat-mech",
+                        "cs.CY",
+                        "cs.DS"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.06411v1",
+                    "title": "On the Size and the Approximability of Minimum Temporally Connected Subgraphs",
+                    "abstract": "We consider temporal graphs with discrete time labels and investigate the\nsize and the approximability of minimum temporally connected spanning\nsubgraphs. We present a family of minimally connected temporal graphs with $n$\nvertices and $\\Omega(n^2)$ edges, thus resolving an open question of (Kempe,\nKleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal\nconnectivity certificates. Next, we consider the problem of computing a minimum\nweight subset of temporal edges that preserve connectivity of a given temporal\ngraph either from a given vertex r (r-MTC problem) or among all vertex pairs\n(MTC problem). We show that the approximability of r-MTC is closely related to\nthe approximability of Directed Steiner Tree and that r-MTC can be solved in\npolynomial time if the underlying graph has bounded treewidth. We also show\nthat the best approximation ratio for MTC is at least $O(2^{\\log^{1-\\epsilon}\nn})$ and at most $O(\\min\\{n^{1+\\epsilon}, (\\Delta M)^{2/3+\\epsilon}\\})$, for\nany constant $\\epsilon > 0$, where $M$ is the number of temporal edges and\n$\\Delta$ is the maximum degree of the underlying graph. Furthermore, we prove\nthat the unweighted version of MTC is APX-hard and that MTC is efficiently\nsolvable in trees and $2$-approximable in cycles.",
+                    "authors": "Kyriakos Axiotis, Dimitris Fotakis",
+                    "published": "2016-02-20",
+                    "updated": "2016-02-20",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.01928v1",
+                    "title": "Constructing Temporal Dynamic Knowledge Graphs from Interactive Text-based Games",
+                    "abstract": "In natural language processing, interactive text-based games serve as a test\nbed for interactive AI systems. Prior work has proposed to play text-based\ngames by acting based on discrete knowledge graphs constructed by the Discrete\nGraph Updater (DGU) to represent the game state from the natural language\ndescription. While DGU has shown promising results with high interpretability,\nit suffers from lower knowledge graph accuracy due to its lack of temporality\nand limited generalizability to complex environments with objects with the same\nlabel. In order to address DGU's weaknesses while preserving its high\ninterpretability, we propose the Temporal Discrete Graph Updater (TDGU), a\nnovel neural network model that represents dynamic knowledge graphs as a\nsequence of timestamped graph events and models them using a temporal point\nbased graph neural network. Through experiments on the dataset collected from a\ntext-based game TextWorld, we show that TDGU outperforms the baseline DGU. We\nfurther show the importance of temporal information for TDGU's performance\nthrough an ablation study and demonstrate that TDGU has the ability to\ngeneralize to more complex environments with objects with the same label. All\nthe relevant code can be found at\n\\url{https://github.com/yukw777/temporal-discrete-graph-updater}.",
+                    "authors": "Keunwoo Peter Yu",
+                    "published": "2023-11-03",
+                    "updated": "2023-11-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13250v1",
+                    "title": "Keyword-Aware Relative Spatio-Temporal Graph Networks for Video Question Answering",
+                    "abstract": "The main challenge in video question answering (VideoQA) is to capture and\nunderstand the complex spatial and temporal relations between objects based on\ngiven questions. Existing graph-based methods for VideoQA usually ignore\nkeywords in questions and employ a simple graph to aggregate features without\nconsidering relative relations between objects, which may lead to inferior\nperformance. In this paper, we propose a Keyword-aware Relative Spatio-Temporal\n(KRST) graph network for VideoQA. First, to make question features aware of\nkeywords, we employ an attention mechanism to assign high weights to keywords\nduring question encoding. The keyword-aware question features are then used to\nguide video graph construction. Second, because relations are relative, we\nintegrate the relative relation modeling to better capture the spatio-temporal\ndynamics among object nodes. Moreover, we disentangle the spatio-temporal\nreasoning into an object-level spatial graph and a frame-level temporal graph,\nwhich reduces the impact of spatial and temporal relation reasoning on each\nother. Extensive experiments on the TGIF-QA, MSVD-QA and MSRVTT-QA datasets\ndemonstrate the superiority of our KRST over multiple state-of-the-art methods.",
+                    "authors": "Yi Cheng, Hehe Fan, Dongyun Lin, Ying Sun, Mohan Kankanhalli, Joo-Hwee Lim",
+                    "published": "2023-07-25",
+                    "updated": "2023-07-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.01727v2",
+                    "title": "Skeleton-Based Action Segmentation with Multi-Stage Spatial-Temporal Graph Convolutional Neural Networks",
+                    "abstract": "The ability to identify and temporally segment fine-grained actions in motion\ncapture sequences is crucial for applications in human movement analysis.\nMotion capture is typically performed with optical or inertial measurement\nsystems, which encode human movement as a time series of human joint locations\nand orientations or their higher-order representations. State-of-the-art action\nsegmentation approaches use multiple stages of temporal convolutions. The main\nidea is to generate an initial prediction with several layers of temporal\nconvolutions and refine these predictions over multiple stages, also with\ntemporal convolutions. Although these approaches capture long-term temporal\npatterns, the initial predictions do not adequately consider the spatial\nhierarchy among the human joints. To address this limitation, we recently\nintroduced multi-stage spatial-temporal graph convolutional neural networks\n(MS-GCN). Our framework replaces the initial stage of temporal convolutions\nwith spatial graph convolutions and dilated temporal convolutions, which better\nexploit the spatial configuration of the joints and their long-term temporal\ndynamics. Our framework was compared to four strong baselines on five tasks.\nExperimental results demonstrate that our framework is a strong baseline for\nskeleton-based action segmentation.",
+                    "authors": "Benjamin Filtjens, Bart Vanrumste, Peter Slaets",
+                    "published": "2022-02-03",
+                    "updated": "2022-10-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.16078v2",
+                    "title": "Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs",
+                    "abstract": "We present the Evolving Graph Fourier Transform (EFT), the first invertible\nspectral transform that captures evolving representations on temporal graphs.\nWe motivate our work by the inadequacy of existing methods for capturing the\nevolving graph spectra, which are also computationally expensive due to the\ntemporal aspect along with the graph vertex domain. We view the problem as an\noptimization over the Laplacian of the continuous time dynamic graph.\nAdditionally, we propose pseudo-spectrum relaxations that decompose the\ntransformation process, making it highly computationally efficient. The EFT\nmethod adeptly captures the evolving graph's structural and positional\nproperties, making it effective for downstream tasks on evolving graphs. Hence,\nas a reference implementation, we develop a simple neural model induced with\nEFT for capturing evolving graph spectra. We empirically validate our\ntheoretical findings on a number of large-scale and standard temporal graph\nbenchmarks and demonstrate that our model achieves state-of-the-art\nperformance.",
+                    "authors": "Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Manish Singh, Toyotaro Suzumura",
+                    "published": "2024-02-25",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.13517v1",
+                    "title": "Temporal Graph Signal Decomposition",
+                    "abstract": "Temporal graph signals are multivariate time series with individual\ncomponents associated with nodes of a fixed graph structure. Data of this kind\narises in many domains including activity of social network users, sensor\nnetwork readings over time, and time course gene expression within the\ninteraction network of a model organism. Traditional matrix decomposition\nmethods applied to such data fall short of exploiting structural regularities\nencoded in the underlying graph and also in the temporal patterns of the\nsignal. How can we take into account such structure to obtain a succinct and\ninterpretable representation of temporal graph signals?\n  We propose a general, dictionary-based framework for temporal graph signal\ndecomposition (TGSD). The key idea is to learn a low-rank, joint encoding of\nthe data via a combination of graph and time dictionaries. We propose a highly\nscalable decomposition algorithm for both complete and incomplete data, and\ndemonstrate its advantage for matrix decomposition, imputation of missing\nvalues, temporal interpolation, clustering, period estimation, and rank\nestimation in synthetic and real-world data ranging from traffic patterns to\nsocial media activity. Our framework achieves 28% reduction in RMSE compared to\nbaselines for temporal interpolation when as many as 75% of the observations\nare missing. It scales best among baselines taking under 20 seconds on 3.5\nmillion data points and produces the most parsimonious models. To the best of\nour knowledge, TGSD is the first framework to jointly model graph signals by\ntemporal and graph dictionaries.",
+                    "authors": "Maxwell McNeil, Lin Zhang, Petko Bogdanov",
+                    "published": "2021-06-25",
+                    "updated": "2021-06-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05078v1",
+                    "title": "TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification",
+                    "abstract": "Multivariate time series classification (MTSC) is an important data mining\ntask, which can be effectively solved by popular deep learning technology.\nUnfortunately, the existing deep learning-based methods neglect the hidden\ndependencies in different dimensions and also rarely consider the unique\ndynamic features of time series, which lack sufficient feature extraction\ncapability to obtain satisfactory classification accuracy. To address this\nproblem, we propose a novel temporal dynamic graph neural network (TodyNet)\nthat can extract hidden spatio-temporal dependencies without undefined graph\nstructure. It enables information flow among isolated but implicit\ninterdependent variables and captures the associations between different time\nslots by dynamic graph mechanism, which further improves the classification\nperformance of the model. Meanwhile, the hierarchical representations of graphs\ncannot be learned due to the limitation of GNNs. Thus, we also design a\ntemporal graph pooling layer to obtain a global graph-level representation for\ngraph learning with learnable temporal parameters. The dynamic graph, graph\ninformation propagation, and temporal convolution are jointly learned in an\nend-to-end framework. The experiments on 26 UEA benchmark datasets illustrate\nthat the proposed TodyNet outperforms existing deep learning-based methods in\nthe MTSC tasks.",
+                    "authors": "Huaiyuan Liu, Xianzhang Liu, Donghua Yang, Zhiyu Liang, Hongzhi Wang, Yong Cui, Jun Gu",
+                    "published": "2023-04-11",
+                    "updated": "2023-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.14303v1",
+                    "title": "TREND: TempoRal Event and Node Dynamics for Graph Representation Learning",
+                    "abstract": "Temporal graph representation learning has drawn significant attention for\nthe prevalence of temporal graphs in the real world. However, most existing\nworks resort to taking discrete snapshots of the temporal graph, or are not\ninductive to deal with new nodes, or do not model the exciting effects which is\nthe ability of events to influence the occurrence of another event. In this\nwork, We propose TREND, a novel framework for temporal graph representation\nlearning, driven by TempoRal Event and Node Dynamics and built upon a Hawkes\nprocess-based graph neural network (GNN). TREND presents a few major\nadvantages: (1) it is inductive due to its GNN architecture; (2) it captures\nthe exciting effects between events by the adoption of the Hawkes process; (3)\nas our main novelty, it captures the individual and collective characteristics\nof events by integrating both event and node dynamics, driving a more precise\nmodeling of the temporal process. Extensive experiments on four real-world\ndatasets demonstrate the effectiveness of our proposed model.",
+                    "authors": "Zhihao Wen, Yuan Fang",
+                    "published": "2022-03-27",
+                    "updated": "2022-03-27",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.11886v1",
+                    "title": "Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs",
+                    "abstract": "Temporal bipartite graphs are widely used to denote time-evolving\nrelationships between two disjoint sets of nodes, such as customer-product\ninteractions in E-commerce and user-group memberships in social networks.\nTemporal butterflies, $(2,2)$-bicliques that occur within a short period and in\na prescribed order, are essential in modeling the structural and sequential\npatterns of such graphs. Counting the number of temporal butterflies is thus a\nfundamental task in analyzing temporal bipartite graphs. However, existing\nalgorithms for butterfly counting on static bipartite graphs and motif counting\non temporal unipartite graphs are inefficient for this purpose. In this paper,\nwe present a general framework with three sampling strategies for temporal\nbutterfly counting. Since exact counting can be time-consuming on large graphs,\nour approach alternatively computes approximate estimates accurately and\nefficiently. We also provide analytical bounds on the number of samples each\nstrategy requires to obtain estimates with small relative errors and high\nprobability. We finally evaluate our framework on six real-world datasets and\ndemonstrate its superior accuracy and efficiency compared to several baselines.\nOverall, our proposed framework and sampling strategies provide efficient and\naccurate approaches to approximating temporal butterfly counts on large-scale\ntemporal bipartite graphs.",
+                    "authors": "Jiaxi Pu, Yanhao Wang, Yuchen Li, Xuan Zhou",
+                    "published": "2023-10-18",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.DB",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08909v2",
+                    "title": "Maximum 0-1 Timed Matching on Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs where the topology and/or other properties of the\ngraph change with time. They have been used to model applications with temporal\ninformation in various domains. Problems on static graphs become more\nchallenging to solve in temporal graphs because of dynamically changing\ntopology, and many recent works have explored graph problems on temporal\ngraphs. In this paper, we define a type of matching called {\\em 0-1 timed\nmatching} for temporal graphs, and investigate the problem of finding a {\\em\nmaximum 0-1 timed matching} for different classes of temporal graphs. We first\nprove that the problem is NP-Complete for rooted temporal trees when each edge\nis associated with two or more time intervals. We then propose an $O(n \\log n)$\ntime algorithm for the problem on a rooted temporal tree with $n$ nodes when\neach edge is associated with exactly one time interval. The problem is then\nshown to be NP-Complete also for bipartite temporal graphs even when each edge\nis associated with a single time interval and degree of each node is bounded by\na constant $k \\geq 3$. We next investigate approximation algorithms for the\nproblem for temporal graphs where each edge is associated with more than one\ntime intervals. It is first shown that there is no\n$\\frac{1}{n^{1-\\epsilon}}$-factor approximation algorithm for the problem for\nany $\\epsilon > 0$ even on a rooted temporal tree with $n$ nodes unless NP =\nZPP. We then present a $\\frac{5}{2\\mathcal{N}^* + 3}$-factor approximation\nalgorithm for the problem for general temporal graphs where $\\mathcal{N^*}$ is\nthe average number of edges overlapping in time with each edge in the temporal\ngraph. The same algorithm is also a constant-factor approximation algorithm for\ndegree bounded temporal graphs.",
+                    "authors": "Subhrangsu Mandal, Arobinda Gupta",
+                    "published": "2020-12-16",
+                    "updated": "2022-02-01",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.03251v3",
+                    "title": "Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of traditional Knowledge Graph\n(KG) that incorporates the dimension of time. Reasoning on TKGs is a crucial\ntask that aims to predict future facts based on historical occurrences. The key\nchallenge lies in uncovering structural dependencies within historical\nsubgraphs and temporal patterns. Most existing approaches model TKGs relying on\nentity modeling, as nodes in the graph play a crucial role in knowledge\nrepresentation. However, the real-world scenario often involves an extensive\nnumber of entities, with new entities emerging over time. This makes it\nchallenging for entity-dependent methods to cope with extensive volumes of\nentities, and effectively handling newly emerging entities also becomes a\nsignificant challenge. Therefore, we propose Temporal Inductive Path Neural\nNetwork (TiPNN), which models historical information in an entity-independent\nperspective. Specifically, TiPNN adopts a unified graph, namely history\ntemporal graph, to comprehensively capture and encapsulate information from\nhistory. Subsequently, we utilize the defined query-aware temporal paths on a\nhistory temporal graph to model historical path information related to queries\nfor reasoning. Extensive experiments illustrate that the proposed model not\nonly attains significant performance enhancements but also handles inductive\nsettings, while additionally facilitating the provision of reasoning evidence\nthrough history temporal graphs.",
+                    "authors": "Hao Dong, Pengyang Wang, Meng Xiao, Zhiyuan Ning, Pengfei Wang, Yuanchun Zhou",
+                    "published": "2023-09-06",
+                    "updated": "2024-01-25",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.05653v1",
+                    "title": "Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition",
+                    "abstract": "Accurate spatial-temporal traffic flow forecasting is essential for helping\ntraffic managers to take control measures and drivers to choose the optimal\ntravel routes. Recently, graph convolutional networks (GCNs) have been widely\nused in traffic flow prediction owing to their powerful ability to capture\nspatial-temporal dependencies. The design of the spatial-temporal graph\nadjacency matrix is a key to the success of GCNs, and it is still an open\nquestion. This paper proposes reconstructing the binary adjacency matrix via\ntensor decomposition, and a traffic flow forecasting method is proposed. First,\nwe reformulate the spatial-temporal fusion graph adjacency matrix into a\nthree-way adjacency tensor. Then, we reconstructed the adjacency tensor via\nTucker decomposition, wherein more informative and global spatial-temporal\ndependencies are encoded. Finally, a Spatial-temporal Synchronous Graph\nConvolutional module for localized spatial-temporal correlations learning and a\nDilated Convolution module for global correlations learning are assembled to\naggregate and learn the comprehensive spatial-temporal dependencies of the road\nnetwork. Experimental results on four open-access datasets demonstrate that the\nproposed model outperforms state-of-the-art approaches in terms of the\nprediction performance and computational cost.",
+                    "authors": "Qin Li, Xuan Yang, Yong Wang, Yuankai Wu, Deqiang He",
+                    "published": "2022-12-12",
+                    "updated": "2022-12-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1509.08960v1",
+                    "title": "Storing and Analyzing Historical Graph Data at Scale",
+                    "abstract": "The work on large-scale graph analytics to date has largely focused on the\nstudy of static properties of graph snapshots. However, a static view of\ninteractions between entities is often an oversimplification of several complex\nphenomena like the spread of epidemics, information diffusion, formation of\nonline communities}, and so on. Being able to find temporal interaction\npatterns, visualize the evolution of graph properties, or even simply compare\nthem across time, adds significant value in reasoning over graphs. However,\nbecause of lack of underlying data management support, an analyst today has to\nmanually navigate the added temporal complexity of dealing with large evolving\ngraphs. In this paper, we present a system, called Historical Graph Store, that\nenables users to store large volumes of historical graph data and to express\nand run complex temporal graph analytical tasks against that data. It consists\nof two key components: a Temporal Graph Index (TGI), that compactly stores\nlarge volumes of historical graph evolution data in a partitioned and\ndistributed fashion; it provides support for retrieving snapshots of the graph\nas of any timepoint in the past or evolution histories of individual nodes or\nneighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for\nexpressing complex temporal analytical tasks and for executing them in an\nefficient and scalable manner. Our experiments demonstrate our system's\nefficient storage, retrieval and analytics across a wide variety of queries on\nlarge volumes of historical graph data.",
+                    "authors": "Udayan Khurana, Amol Deshpande",
+                    "published": "2015-09-29",
+                    "updated": "2015-09-29",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1912.03904v1",
+                    "title": "Weighted temporal event graphs",
+                    "abstract": "The times of temporal-network events and their correlations contain\ninformation on the function of the network and they influence dynamical\nprocesses taking place on it. To extract information out of correlated event\ntimes, techniques such as the analysis of temporal motifs have been developed.\nWe discuss a recently-introduced, more general framework that maps\ntemporal-network structure into static graphs while retaining information on\ntime-respecting paths and the time differences between their consequent events.\nThis framework builds on weighted temporal event graphs: directed, acyclic\ngraphs (DAGs) that contain a superposition of all temporal paths. We introduce\nthe reader to the temporal event-graph mapping and associated computational\nmethods and illustrate its use by applying the framework to temporal-network\npercolation.",
+                    "authors": "Jari Saram\u00e4ki, Mikko Kivel\u00e4, M\u00e1rton Karsai",
+                    "published": "2019-12-09",
+                    "updated": "2019-12-09",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.08311v1",
+                    "title": "De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs",
+                    "abstract": "We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware\ngraph neural network architecture for time-resolved data on dynamic graphs. Our\napproach accounts for temporal-topological patterns that unfold in the causal\ntopology of dynamic graphs, which is determined by causal walks, i.e.\ntemporally ordered sequences of links by which nodes can influence each other\nover time. Our architecture builds on multiple layers of higher-order De Bruijn\ngraphs, an iterative line graph construction where nodes in a De Bruijn graph\nof order k represent walks of length k-1, while edges represent walks of length\nk. We develop a graph neural network architecture that utilizes De Bruijn\ngraphs to implement a message passing scheme that follows a non-Markovian\ndynamics, which enables us to learn patterns in the causal topology of a\ndynamic graph. Addressing the issue that De Bruijn graphs with different orders\nk can be used to model the same data set, we further apply statistical model\nselection to determine the optimal graph topology to be used for message\npassing. An evaluation in synthetic and empirical data sets suggests that\nDBGNNs can leverage temporal patterns in dynamic graphs, which substantially\nimproves the performance in a supervised node classification task.",
+                    "authors": "Lisi Qarkaxhija, Vincenzo Perri, Ingo Scholtes",
+                    "published": "2022-09-17",
+                    "updated": "2022-09-17",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08804v1",
+                    "title": "Temporal Graph Modeling for Skeleton-based Action Recognition",
+                    "abstract": "Graph Convolutional Networks (GCNs), which model skeleton data as graphs,\nhave obtained remarkable performance for skeleton-based action recognition.\nParticularly, the temporal dynamic of skeleton sequence conveys significant\ninformation in the recognition task. For temporal dynamic modeling, GCN-based\nmethods only stack multi-layer 1D local convolutions to extract temporal\nrelations between adjacent time steps. With the repeat of a lot of local\nconvolutions, the key temporal information with non-adjacent temporal distance\nmay be ignored due to the information dilution. Therefore, these methods still\nremain unclear how to fully explore temporal dynamic of skeleton sequence. In\nthis paper, we propose a Temporal Enhanced Graph Convolutional Network (TE-GCN)\nto tackle this limitation. The proposed TE-GCN constructs temporal relation\ngraph to capture complex temporal dynamic. Specifically, the constructed\ntemporal relation graph explicitly builds connections between semantically\nrelated temporal features to model temporal relations between both adjacent and\nnon-adjacent time steps. Meanwhile, to further explore the sufficient temporal\ndynamic, multi-head mechanism is designed to investigate multi-kinds of\ntemporal relations. Extensive experiments are performed on two widely used\nlarge-scale datasets, NTU-60 RGB+D and NTU-120 RGB+D. And experimental results\nshow that the proposed model achieves the state-of-the-art performance by\nmaking contribution to temporal modeling for action recognition.",
+                    "authors": "Jianan Li, Xuemei Xie, Zhifu Zhao, Yuhan Cao, Qingzhe Pan, Guangming Shi",
+                    "published": "2020-12-16",
+                    "updated": "2020-12-16",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.GR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.01012v1",
+                    "title": "Graph-Level Embedding for Time-Evolving Graphs",
+                    "abstract": "Graph representation learning (also known as network embedding) has been\nextensively researched with varying levels of granularity, ranging from nodes\nto graphs. While most prior work in this area focuses on node-level\nrepresentation, limited research has been conducted on graph-level embedding,\nparticularly for dynamic or temporal networks. However, learning\nlow-dimensional graph-level representations for dynamic networks is critical\nfor various downstream graph retrieval tasks such as temporal graph similarity\nranking, temporal graph isomorphism, and anomaly detection. In this paper, we\npresent a novel method for temporal graph-level embedding that addresses this\ngap. Our approach involves constructing a multilayer graph and using a modified\nrandom walk with temporal backtracking to generate temporal contexts for the\ngraph's nodes. We then train a \"document-level\" language model on these\ncontexts to generate graph-level embeddings. We evaluate our proposed model on\nfive publicly available datasets for the task of temporal graph similarity\nranking, and our model outperforms baseline methods. Our experimental results\ndemonstrate the effectiveness of our method in generating graph-level\nembeddings for dynamic networks.",
+                    "authors": "Lili Wang, Chenghan Huang, Weicheng Ma, Xinyuan Cao, Soroush Vosoughi",
+                    "published": "2023-06-01",
+                    "updated": "2023-06-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19508v1",
+                    "title": "Temporal Graph ODEs for Irregularly-Sampled Time Series",
+                    "abstract": "Modern graph representation learning works mostly under the assumption of\ndealing with regularly sampled temporal graph snapshots, which is far from\nrealistic, e.g., social networks and physical systems are characterized by\ncontinuous dynamics and sporadic observations. To address this limitation, we\nintroduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework,\nwhich learns both the temporal and spatial dynamics from graph streams where\nthe intervals between observations are not regularly spaced. We empirically\nvalidate the proposed approach on several graph benchmarks, showing that TG-ODE\ncan achieve state-of-the-art performance in irregular graph stream tasks.",
+                    "authors": "Alessio Gravina, Daniele Zambon, Davide Bacciu, Cesare Alippi",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.05018v2",
+                    "title": "Time-varying Graph Learning Under Structured Temporal Priors",
+                    "abstract": "This paper endeavors to learn time-varying graphs by using structured\ntemporal priors that assume underlying relations between arbitrary two graphs\nin the graph sequence. Different from many existing chain structure based\nmethods in which the priors like temporal homogeneity can only describe the\nvariations of two consecutive graphs, we propose a structure named\n\\emph{temporal graph} to characterize the underlying real temporal relations.\nUnder this framework, the chain structure is actually a special case of our\ntemporal graph. We further proposed Alternating Direction Method of Multipliers\n(ADMM), a distributed algorithm, to solve the induced optimization problem.\nNumerical experiments demonstrate the superiorities of our method.",
+                    "authors": "Xiang Zhang, Qiao Wang",
+                    "published": "2021-10-11",
+                    "updated": "2022-02-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.SP"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1810.06240v4",
+                    "title": "Comparing Temporal Graphs Using Dynamic Time Warping",
+                    "abstract": "Within many real-world networks the links between pairs of nodes change over\ntime. Thus, there has been a recent boom in studying temporal graphs.\nRecognizing patterns in temporal graphs requires a proximity measure to compare\ndifferent temporal graphs. To this end, we propose to study dynamic time\nwarping on temporal graphs. We define the dynamic temporal graph warping\ndistance (dtgw) to determine the dissimilarity of two temporal graphs. Our\nnovel measure is flexible and can be applied in various application domains. We\nshow that computing the dtgw-distance is a challenging (in general) NP-hard\noptimization problem and identify some polynomial-time solvable special cases.\nMoreover, we develop a quadratic programming formulation and an efficient\nheuristic. In experiments on real-word data we show that the heuristic performs\nvery well and that our dtgw-distance performs favorably in de-anonymizing\nnetworks compared to other approaches.",
+                    "authors": "Vincent Froese, Brijnesh Jain, Rolf Niedermeier, Malte Renken",
+                    "published": "2018-10-15",
+                    "updated": "2020-07-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1502.04579v3",
+                    "title": "The complexity of optimal design of temporally connected graphs",
+                    "abstract": "We study the design of small cost temporally connected graphs, under various\nconstraints. We mainly consider undirected graphs of $n$ vertices, where each\nedge has an associated set of discrete availability instances (labels). A\njourney from vertex $u$ to vertex $v$ is a path from $u$ to $v$ where\nsuccessive path edges have strictly increasing labels. A graph is temporally\nconnected iff there is a $(u,v)$-journey for any pair of vertices $u,v,~u\\not=\nv$. We first give a simple polynomial-time algorithm to check whether a given\ntemporal graph is temporally connected. We then consider the case in which a\ndesigner of temporal graphs can \\emph{freely choose} availability instances for\nall edges and aims for temporal connectivity with very small \\emph{cost}; the\ncost is the total number of availability instances used. We achieve this via a\nsimple polynomial-time procedure which derives designs of cost linear in $n$.\nWe also show that the above procedure is (almost) optimal when the underlying\ngraph is a tree, by proving a lower bound on the cost for any tree. However,\nthere are pragmatic cases where one is not free to design a temporally\nconnected graph anew, but is instead \\emph{given} a temporal graph design with\nthe claim that it is temporally connected, and wishes to make it more\ncost-efficient by removing labels without destroying temporal connectivity\n(redundant labels). Our main technical result is that computing the maximum\nnumber of redundant labels is APX-hard, i.e., there is no PTAS unless $P=NP$.\nOn the positive side, we show that in dense graphs with random edge\navailabilities, there is asymptotically almost surely a very large number of\nredundant labels. A temporal design may, however, be \\emph{minimal}, i.e., no\nredundant labels exist. We show the existence of minimal temporal designs with\nat least $n \\log{n}$ labels.",
+                    "authors": "Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, Paul G. Spirakis",
+                    "published": "2015-02-16",
+                    "updated": "2016-07-06",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2108.08719v5",
+                    "title": "Temporal Graph Functional Dependencies [Extended Version]",
+                    "abstract": "Data dependencies have been extended to graphs to characterize topological\nand value constraints. Existing data dependencies are defined to capture\ninconsistencies in static graphs. Nevertheless, inconsistencies may occur over\nevolving graphs and only for certain time periods. The need for capturing such\ninconsistencies in temporal graphs is evident in anomaly detection and\npredictive dynamic network analysis. This paper introduces a class of data\ndependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs\ngeneralize functional dependencies to temporal graphs as a sequence of graph\nsnapshots that are induced by time intervals, and enforce both topological\nconstraints and attribute value dependencies that must be satisfied by these\nsnapshots. (1) We establish the complexity results for the satisfiability and\nimplication problems of TGFDs. (2) We propose a sound and complete\naxiomatization system for TGFDs. (3) We also present efficient parallel\nalgorithms to detect inconsistencies in temporal graphs as violations of TGFDs.\nThe algorithm exploits data and temporal locality induced by time intervals,\nand uses incremental pattern matching and load balancing strategies to enable\nfeasible error detection in large temporal graphs. Using real datasets, we\nexperimentally verify that our algorithms achieve lower runtimes compared to\nexisting baselines, while improving the accuracy over error detection using\nexisting graph data constraints, e.g., GFDs and GTARs with 55% and 74% gain in\nF1-score, respectively.",
+                    "authors": "Morteza Alipourlangouri, Adam Mansfield, Fei Chiang, Yinghui Wu",
+                    "published": "2021-08-19",
+                    "updated": "2022-07-26",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0807.2357v1",
+                    "title": "Temporal Graphs",
+                    "abstract": "We introduce the idea of temporal graphs, a representation that encodes\ntemporal data into graphs while fully retaining the temporal information of the\noriginal data. This representation lets us explore the dynamic temporal\nproperties of data by using existing graph algorithms (such as shortest-path),\nwith no need for data-driven simulations. We also present a number of metrics\nthat can be used to study and explore temporal graphs. Finally, we use temporal\ngraphs to analyse real-world data and present the results of our analysis.",
+                    "authors": "Vassilis Kostakos",
+                    "published": "2008-07-15",
+                    "updated": "2008-07-15",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.09791v2",
+                    "title": "Temporal Betweenness Centrality on Shortest Paths",
+                    "abstract": "Betweenness centrality measure assesses the importance of nodes in a graph\nand has been used in a variety of contexts. Betweenness centrality has also\nbeen extended to temporal graphs. Temporal graphs have edges that bear labels\naccording to the time of the interactions between the nodes. Betweenness\ncentrality has been extended to the temporal graph settings, and the notion of\npaths has been extended to temporal paths. Recent results by Bu{\\ss} et al. and\nRymar et al. showed that the betweenness centrality of all nodes in a temporal\ngraph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of\ntime units, m the number of temporal edges and n the number of nodes. In this\npaper, we improve the running time analysis of these previous approaches to\ncompute the betweenness centrality of all nodes in a temporal graph. We give an\nalgorithm that runs in O(n m T + n^2 T ).",
+                    "authors": "Mehdi Naima, Matthieu Latapy, Cl\u00e9mence Magnien",
+                    "published": "2023-04-19",
+                    "updated": "2023-06-06",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.03897v1",
+                    "title": "Temporal Graph Representation Learning with Adaptive Augmentation Contrastive",
+                    "abstract": "Temporal graph representation learning aims to generate low-dimensional\ndynamic node embeddings to capture temporal information as well as structural\nand property information. Current representation learning methods for temporal\nnetworks often focus on capturing fine-grained information, which may lead to\nthe model capturing random noise instead of essential semantic information.\nWhile graph contrastive learning has shown promise in dealing with noise, it\nonly applies to static graphs or snapshots and may not be suitable for handling\ntime-dependent noise. To alleviate the above challenge, we propose a novel\nTemporal Graph representation learning with Adaptive augmentation Contrastive\n(TGAC) model. The adaptive augmentation on the temporal graph is made by\ncombining prior knowledge with temporal information, and the contrastive\nobjective function is constructed by defining the augmented inter-view contrast\nand intra-view contrast. To complement TGAC, we propose three adaptive\naugmentation strategies that modify topological features to reduce noise from\nthe network. Our extensive experiments on various real networks demonstrate\nthat the proposed model outperforms other temporal graph representation\nlearning methods.",
+                    "authors": "Hongjiang Chen, Pengfei Jiao, Huijun Tang, Huaming Wu",
+                    "published": "2023-11-07",
+                    "updated": "2023-11-07",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08323v2",
+                    "title": "TG-GAN: Continuous-time Temporal Graph Generation with Deep Generative Models",
+                    "abstract": "The recent deep generative models for static graphs that are now being\nactively developed have achieved significant success in areas such as molecule\ndesign. However, many real-world problems involve temporal graphs whose\ntopology and attribute values evolve dynamically over time, including important\napplications such as protein folding, human mobility networks, and social\nnetwork growth. As yet, deep generative models for temporal graphs are not yet\nwell understood and existing techniques for static graphs are not adequate for\ntemporal graphs since they cannot 1) encode and decode continuously-varying\ngraph topology chronologically, 2) enforce validity via temporal constraints,\nor 3) ensure efficiency for information-lossless temporal resolution. To\naddress these challenges, we propose a new model, called ``Temporal Graph\nGenerative Adversarial Network'' (TG-GAN) for continuous-time temporal graph\ngeneration, by modeling the deep generative process for truncated temporal\nrandom walks and their compositions. Specifically, we first propose a novel\ntemporal graph generator that jointly model truncated edge sequences, time\nbudgets, and node attributes, with novel activation functions that enforce\ntemporal validity constraints under recurrent architecture. In addition, a new\ntemporal graph discriminator is proposed, which combines time and node encoding\noperations over a recurrent architecture to distinguish the generated sequences\nfrom the real ones sampled by a newly-developed truncated temporal random walk\nsampler. Extensive experiments on both synthetic and real-world datasets\ndemonstrate TG-GAN significantly outperforms the comparison methods in\nefficiency and effectiveness.",
+                    "authors": "Liming Zhang, Liang Zhao, Shan Qin, Dieter Pfoser",
+                    "published": "2020-05-17",
+                    "updated": "2020-06-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19453v1",
+                    "title": "Structural Parameters for Dense Temporal Graphs",
+                    "abstract": "Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.",
+                    "authors": "Jessica Enright, Samuel D. Hand, Laura Larios-Jones, Kitty Meeks",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "math.CO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.04434v1",
+                    "title": "Frequency Analysis of Temporal Graph Signals",
+                    "abstract": "This letter extends the concept of graph-frequency to graph signals that\nevolve with time. Our goal is to generalize and, in fact, unify the familiar\nconcepts from time- and graph-frequency analysis. To this end, we study a joint\ntemporal and graph Fourier transform (JFT) and demonstrate its attractive\nproperties. We build on our results to create filters which act on the joint\n(temporal and graph) frequency domain, and show how these can be used to\nperform interference cancellation. The proposed algorithms are distributed,\nhave linear complexity, and can approximate any desired joint filtering\nobjective.",
+                    "authors": "Andreas Loukas, Damien Foucard",
+                    "published": "2016-02-14",
+                    "updated": "2016-02-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SY",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02563v1",
+                    "title": "Kairos: Efficient Temporal Graph Analytics on a Single Machine",
+                    "abstract": "Many important societal problems are naturally modeled as algorithms over\ntemporal graphs. To date, however, most graph processing systems remain\ninefficient as they rely on distributed processing even for graphs that fit\nwell within a commodity server's available storage. In this paper, we introduce\nKairos, a temporal graph analytics system that provides application developers\na framework for efficiently implementing and executing algorithms over temporal\ngraphs on a single machine. Specifically, Kairos relies on fork-join\nparallelism and a highly optimized parallel data structure as core primitives\nto maximize performance of graph processing tasks needed for temporal graph\nanalytics. Furthermore, we introduce the notion of selective indexing and show\nhow it can be used with an efficient index to speedup temporal queries. Our\nexperiments on a 24-core server show that our algorithms obtain good parallel\nspeedups, and are significantly faster than equivalent algorithms in existing\ntemporal graph processing systems: up to 60x against a shared-memory approach,\nand several orders of magnitude when compared with distributed processing of\ngraphs that fit within a single server.",
+                    "authors": "Joana M. F. da Trindade, Julian Shun, Samuel Madden, Nesime Tatbul",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB",
+                        "cs.DC",
+                        "cs.PF"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.02852v1",
+                    "title": "Introduction to a Temporal Graph Benchmark",
+                    "abstract": "A temporal graph is a data structure, consisting of nodes and edges in which\nthe edges are associated with time labels. To analyze the temporal graph, the\nfirst step is to find a proper graph dataset/benchmark. While many temporal\ngraph datasets exist online, none could be found that used the interval labels\nin which each edge is associated with a starting and ending time. Therefore we\ncreate a temporal graph data based on Wikipedia reference graph for temporal\nanalysis. This report aims to provide more details of this graph benchmark to\nthose who are interested in using it.",
+                    "authors": "Wouter Ligtenberg, Yulong Pei",
+                    "published": "2017-02-20",
+                    "updated": "2017-02-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2204.09236v1",
+                    "title": "Scalable Motif Counting for Large-scale Temporal Graphs",
+                    "abstract": "One fundamental problem in temporal graph analysis is to count the\noccurrences of small connected subgraph patterns (i.e., motifs), which benefits\na broad range of real-world applications, such as anomaly detection, structure\nprediction, and network representation learning. However, existing works\nfocused on exacting temporal motif are not scalable to large-scale temporal\ngraph data, due to their heavy computational costs or inherent inadequacy of\nparallelism. In this work, we propose a scalable parallel framework for exactly\ncounting temporal motifs in large-scale temporal graphs. We first categorize\nthe temporal motifs based on their distinct properties, and then design\ncustomized algorithms that offer efficient strategies to exactly count the\nmotif instances of each category. Moreover, our compact data structures, namely\ntriple and quadruple counters, enable our algorithms to directly identify the\ntemporal motif instances of each category, according to edge information and\nthe relationship between edges, therefore significantly improving the counting\nefficiency. Based on the proposed counting algorithms, we design a hierarchical\nparallel framework that features both inter- and intra-node parallel\nstrategies, and fully leverages the multi-threading capacity of modern CPU to\nconcurrently count all temporal motifs. Extensive experiments on sixteen\nreal-world temporal graph datasets demonstrate the superiority and capability\nof our proposed framework for temporal motif counting, achieving up to 538*\nspeedup compared to the state-of-the-art methods. The source code of our method\nis available at: https://github.com/steven-ccq/FAST-temporal-motif.",
+                    "authors": "Zhongqiang Gao, Chuanqi Cheng, Yanwei Yu, Lei Cao, Chao Huang, Junyu Dong",
+                    "published": "2022-04-20",
+                    "updated": "2022-04-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.10379v1",
+                    "title": "ChronoR: Rotation Based Temporal Knowledge Graph Embedding",
+                    "abstract": "Despite the importance and abundance of temporal knowledge graphs, most of\nthe current research has been focused on reasoning on static graphs. In this\npaper, we study the challenging problem of inference over temporal knowledge\ngraphs. In particular, the task of temporal link prediction. In general, this\nis a difficult task due to data non-stationarity, data heterogeneity, and its\ncomplex temporal dependencies. We propose Chronological Rotation embedding\n(ChronoR), a novel model for learning representations for entities, relations,\nand time. Learning dense representations is frequently used as an efficient and\nversatile method to perform reasoning on knowledge graphs. The proposed model\nlearns a k-dimensional rotation transformation parametrized by relation and\ntime, such that after each fact's head entity is transformed using the\nrotation, it falls near its corresponding tail entity. By using high\ndimensional rotation as its transformation operator, ChronoR captures rich\ninteraction between the temporal and multi-relational characteristics of a\nTemporal Knowledge Graph. Experimentally, we show that ChronoR is able to\noutperform many of the state-of-the-art methods on the benchmark datasets for\ntemporal knowledge graph link prediction.",
+                    "authors": "Ali Sadeghian, Mohammadreza Armandpour, Anthony Colas, Daisy Zhe Wang",
+                    "published": "2021-03-18",
+                    "updated": "2021-03-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.09641v2",
+                    "title": "Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal data forecasting of traffic flow is a challenging task\nbecause of complicated spatial dependencies and dynamical trends of temporal\npattern between different roads. Existing frameworks typically utilize given\nspatial adjacency graph and sophisticated mechanisms for modeling spatial and\ntemporal correlations. However, limited representations of given spatial graph\nstructure with incomplete adjacent connections may restrict effective\nspatial-temporal dependencies learning of those models. To overcome those\nlimitations, our paper proposes Spatial-Temporal Fusion Graph Neural Networks\n(STFGNN) for traffic flow forecasting. SFTGNN could effectively learn hidden\nspatial-temporal dependencies by a novel fusion operation of various spatial\nand temporal graphs, which is generated by a data-driven method. Meanwhile, by\nintegrating this fusion graph module and a novel gated convolution module into\na unified layer, SFTGNN could handle long sequences. Experimental results on\nseveral public traffic datasets demonstrate that our method achieves\nstate-of-the-art performance consistently than other baselines.",
+                    "authors": "Mengzhang Li, Zhanxing Zhu",
+                    "published": "2020-12-15",
+                    "updated": "2021-03-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02212v1",
+                    "title": "Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by\nattaching the time scope. Existing temporal knowledge graph question answering\n(TKGQA) models solely approach simple questions, owing to the prior assumption\nthat each question only contains a single temporal fact with explicit/implicit\ntemporal constraints. Hence, they perform poorly on questions which own\nmultiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint\n\\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts\n\\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly\nreasoning multiple temporal facts for accurately answering \\emph{complex}\ntemporal questions. Specifically, JMFRN first retrieves question-related\ntemporal facts from TKG for each entity of the given complex question. For\njoint reasoning, we design two different attention (\\ie entity-aware and\ntime-aware) modules, which are suitable for universal settings, to aggregate\nentities and timestamps information of retrieved facts. Moreover, to filter\nincorrect type answers, we introduce an additional answer type discrimination\ntask. Extensive experiments demonstrate our proposed method significantly\noutperforms the state-of-art on the well-known complex temporal question\nbenchmark TimeQuestions.",
+                    "authors": "Rikui Huang, Wei Wei, Xiaoye Qu, Wenfeng Xie, Xianling Mao, Dangyang Chen",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1601.05909v2",
+                    "title": "Efficient Processing of Reachability and Time-Based Path Queries in a Temporal Graph",
+                    "abstract": "A temporal graph is a graph in which vertices communicate with each other at\nspecific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is\nmodeled by an edge from $A$ to $B$ with starting time \"11 a.m.\" and duration \"7\nmins\". Temporal graphs can be used to model many networks with time-related\nactivities, but efficient algorithms for analyzing temporal graphs are severely\ninadequate. We study fundamental problems such as answering reachability and\ntime-based path queries in a temporal graph, and propose an efficient indexing\ntechnique specifically designed for processing these queries in a temporal\ngraph. Our results show that our method is efficient and scalable in both index\nconstruction and query processing.",
+                    "authors": "Huanhuan Wu, Yuzhen Huang, James Cheng, Jinfeng Li, Yiping Ke",
+                    "published": "2016-01-22",
+                    "updated": "2016-01-25",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1706.09480v1",
+                    "title": "A Temporal Tree Decomposition for Generating Temporal Graphs",
+                    "abstract": "Discovering the underlying structures present in large real world graphs is a\nfundamental scientific problem. Recent work at the intersection of formal\nlanguage theory and graph theory has found that a Hyperedge Replacement Grammar\n(HRG) can be extracted from a tree decomposition of any graph. This HRG can be\nused to generate new graphs that share properties that are similar to the\noriginal graph. Because the extracted HRG is directly dependent on the shape\nand contents of the of tree decomposition, it is unlikely that informative\ngraph-processes are actually being captured with the extraction algorithm. To\naddress this problem, the current work presents a new extraction algorithm\ncalled temporal HRG (tHRG) that learns HRG production rules from a temporal\ntree decomposition of the graph. We observe problems with the assumptions that\nare made in a temporal HRG model. In experiments on large real world networks,\nwe show and provide reasoning as to why tHRG does not perform as well as HRG\nand other graph generators.",
+                    "authors": "Corey Pennycuff, Salvador Aguinaga, Tim Weninger",
+                    "published": "2017-06-28",
+                    "updated": "2017-06-28",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.08312v2",
+                    "title": "ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks",
+                    "abstract": "Networks are a fundamental and flexible way of representing various complex\nsystems. Many domains such as communication, citation, procurement, biology,\nsocial media, and transportation can be modeled as a set of entities and their\nrelationships. Temporal networks are a specialization of general networks where\nthe temporal evolution of the system is as important to understand as the\nstructure of the entities and relationships. We present the Independent\nTemporal Motif (ITeM) to characterize temporal graphs from different domains.\nThe ITeMs are edge-disjoint temporal motifs that can be used to model the\nstructure and the evolution of the graph. For a given temporal graph, we\nproduce a feature vector of ITeM frequencies and apply this distribution to the\ntask of measuring the similarity of temporal graphs. We show that ITeM has\nhigher accuracy than other motif frequency-based approaches. We define various\nmetrics based on ITeM that reveal salient properties of a temporal network. We\nalso present importance sampling as a method for efficiently estimating the\nITeM counts. We evaluate our approach on both synthetic and real temporal\nnetworks.",
+                    "authors": "Sumit Purohit, Lawrence B. Holder, George Chin",
+                    "published": "2020-02-19",
+                    "updated": "2020-08-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1401.1919v1",
+                    "title": "Temporal Graph Traversals: Definitions, Algorithms, and Applications",
+                    "abstract": "A temporal graph is a graph in which connections between vertices are active\nat specific times, and such temporal information leads to completely new\npatterns and knowledge that are not present in a non-temporal graph. In this\npaper, we study traversal problems in a temporal graph. Graph traversals, such\nas DFS and BFS, are basic operations for processing and studying a graph. While\nboth DFS and BFS are well-known simple concepts, it is non-trivial to adopt the\nsame notions from a non-temporal graph to a temporal graph. We analyze the\ndifficulties of defining temporal graph traversals and propose new definitions\nof DFS and BFS for a temporal graph. We investigate the properties of temporal\nDFS and BFS, and propose efficient algorithms with optimal complexity. In\nparticular, we also study important applications of temporal DFS and BFS. We\nverify the efficiency and importance of our graph traversal algorithms in real\nworld temporal graphs.",
+                    "authors": "Silu Huang, James Cheng, Huanhuan Wu",
+                    "published": "2014-01-09",
+                    "updated": "2014-01-09",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1207.7103v1",
+                    "title": "Temporal Reachability Graphs",
+                    "abstract": "While a natural fit for modeling and understanding mobile networks,\ntime-varying graphs remain poorly understood. Indeed, many of the usual\nconcepts of static graphs have no obvious counterpart in time-varying ones. In\nthis paper, we introduce the notion of temporal reachability graphs. A\n(tau,delta)-reachability graph} is a time-varying directed graph derived from\nan existing connectivity graph. An edge exists from one node to another in the\nreachability graph at time t if there exists a journey (i.e., a spatiotemporal\npath) in the connectivity graph from the first node to the second, leaving\nafter t, with a positive edge traversal time tau, and arriving within a maximum\ndelay delta. We make three contributions. First, we develop the theoretical\nframework around temporal reachability graphs. Second, we harness our\ntheoretical findings to propose an algorithm for their efficient computation.\nFinally, we demonstrate the analytic power of the temporal reachability graph\nconcept by applying it to synthetic and real-life datasets. On top of defining\nclear upper bounds on communication capabilities, reachability graphs highlight\nasymmetric communication opportunities and offloading potential.",
+                    "authors": "John Whitbeck, Marcelo Dias de Amorim, Vania Conan, Jean-Loup Guillaume",
+                    "published": "2012-07-30",
+                    "updated": "2012-07-30",
+                    "primary_cat": "cs.NI",
+                    "cats": [
+                        "cs.NI",
+                        "C.2.1; F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.17110v2",
+                    "title": "LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?",
+                    "abstract": "In an era marked by the increasing adoption of Large Language Models (LLMs)\nfor various tasks, there is a growing focus on exploring LLMs' capabilities in\nhandling web data, particularly graph data. Dynamic graphs, which capture\ntemporal network evolution patterns, are ubiquitous in real-world web data.\nEvaluating LLMs' competence in understanding spatial-temporal information on\ndynamic graphs is essential for their adoption in web applications, which\nremains unexplored in the literature. In this paper, we bridge the gap via\nproposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic\ngraphs, to the best of our knowledge, for the first time. Specifically, we\npropose the LLM4DyG benchmark, which includes nine specially designed tasks\nconsidering the capability evaluation of LLMs from both temporal and spatial\ndimensions. Then, we conduct extensive experiments to analyze the impacts of\ndifferent data generators, data statistics, prompting techniques, and LLMs on\nthe model performance. Finally, we propose Disentangled Spatial-Temporal\nThoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal\nunderstanding abilities. Our main observations are: 1) LLMs have preliminary\nspatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph\ntasks show increasing difficulties for LLMs as the graph size and density\nincrease, while not sensitive to the time span and data generation mechanism,\n3) the proposed DST2 prompting method can help to improve LLMs'\nspatial-temporal understanding abilities on dynamic graphs for most tasks. The\ndata and codes will be open-sourced at publication time.",
+                    "authors": "Zeyang Zhang, Xin Wang, Ziwei Zhang, Haoyang Li, Yijian Qin, Wenwu Zhu",
+                    "published": "2023-10-26",
+                    "updated": "2024-03-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2111.13684v3",
+                    "title": "Spatio-Temporal Joint Graph Convolutional Networks for Traffic Forecasting",
+                    "abstract": "Recent studies have shifted their focus towards formulating traffic\nforecasting as a spatio-temporal graph modeling problem. Typically, they\nconstructed a static spatial graph at each time step and then connected each\nnode with itself between adjacent time steps to create a spatio-temporal graph.\nHowever, this approach failed to explicitly reflect the correlations between\ndifferent nodes at different time steps, thus limiting the learning capability\nof graph neural networks. Additionally, those models overlooked the dynamic\nspatio-temporal correlations among nodes by using the same adjacency matrix\nacross different time steps. To address these limitations, we propose a novel\napproach called Spatio-Temporal Joint Graph Convolutional Networks (STJGCN) for\naccurate traffic forecasting on road networks over multiple future time steps.\nSpecifically, our method encompasses the construction of both pre-defined and\nadaptive spatio-temporal joint graphs (STJGs) between any two time steps, which\nrepresent comprehensive and dynamic spatio-temporal correlations. We further\nintroduce dilated causal spatio-temporal joint graph convolution layers on the\nSTJG to capture spatio-temporal dependencies from distinct perspectives with\nmultiple ranges. To aggregate information from different ranges, we propose a\nmulti-range attention mechanism. Finally, we evaluate our approach on five\npublic traffic datasets and experimental results demonstrate that STJGCN is not\nonly computationally efficient but also outperforms 11 state-of-the-art\nbaseline methods.",
+                    "authors": "Chuanpan Zheng, Xiaoliang Fan, Shirui Pan, Haibing Jin, Zhaopeng Peng, Zonghan Wu, Cheng Wang, Philip S. Yu",
+                    "published": "2021-11-25",
+                    "updated": "2023-06-13",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.12973v1",
+                    "title": "Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is one of the most fundamental problems in transportation\nscience and artificial intelligence. The key challenge is to effectively model\ncomplex spatial-temporal dependencies and correlations in modern traffic data.\nExisting methods, however, cannot accurately model both long-term and\nshort-term temporal correlations simultaneously, limiting their expressive\npower on complex spatial-temporal patterns. In this paper, we propose a novel\nspatial-temporal neural network framework: Attention-based Spatial-Temporal\nGraph Convolutional Recurrent Network (ASTGCRN), which consists of a graph\nconvolutional recurrent module (GCRN) and a global attention module. In\nparticular, GCRN integrates gated recurrent units and adaptive graph\nconvolutional networks for dynamically learning graph structures and capturing\nspatial dependencies and local temporal relationships. To effectively extract\nglobal temporal dependencies, we design a temporal attention layer and\nimplement it as three independent modules based on multi-head self-attention,\ntransformer, and informer respectively. Extensive experiments on five real\ntraffic datasets have demonstrated the excellent predictive performance of all\nour three models with all their average MAE, RMSE and MAPE across the test\ndatasets lower than the baseline methods.",
+                    "authors": "Haiyang Liu, Chunjiang Zhu, Detian Zhang, Qing Li",
+                    "published": "2023-02-25",
+                    "updated": "2023-02-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.13183v1",
+                    "title": "Resolving Sets in Temporal Graphs",
+                    "abstract": "A $\\textit{resolving set}$ $R$ in a graph $G$ is a set of vertices such that\nevery vertex of $G$ is uniquely identified by its distances to the vertices of\n$R$. Introduced in the 1970s, this concept has been since then extensively\nstudied from both combinatorial and algorithmic point of view. We propose a\ngeneralization of the concept of resolving sets to temporal graphs, i.e.,\ngraphs with edge sets that change over discrete time-steps. In this setting,\nthe $\\textit{temporal distance}$ from $u$ to $v$ is the earliest possible\ntime-step at which a journey with strictly increasing time-steps on edges\nleaving $u$ reaches $v$, i.e., the first time-step at which $v$ could receive a\nmessage broadcast from $u$. A $\\textit{temporal resolving set}$ of a temporal\ngraph $\\mathcal{G}$ is a subset $R$ of its vertices such that every vertex of\n$\\mathcal{G}$ is uniquely identified by its temporal distances from vertices of\n$R$.\n  We study the problem of finding a minimum-size temporal resolving set, and\nshow that it is NP-complete even on very restricted graph classes and with\nstrong constraints on the time-steps: temporal complete graphs where every edge\nappears in either time-step 1 or 2, temporal trees where every edge appears in\nat most two consecutive time-steps, and even temporal subdivided stars where\nevery edge appears in at most two (not necessarily consecutive) time-steps. On\nthe other hand, we give polynomial-time algorithms for temporal paths and\ntemporal stars where every edge appears in exactly one time-step, and give a\ncombinatorial analysis and algorithms for several temporal graph classes where\nthe edges appear in periodic time-steps.",
+                    "authors": "Jan Bok, Antoine Dailly, Tuomo Lehtil\u00e4",
+                    "published": "2024-03-19",
+                    "updated": "2024-03-19",
+                    "primary_cat": "math.CO",
+                    "cats": [
+                        "math.CO",
+                        "cs.DM",
+                        "cs.DS",
+                        "05C69, 68Rxx"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1609.04350v2",
+                    "title": "Time-Variant Graph Classification",
+                    "abstract": "Graphs are commonly used to represent objects, such as images and text, for\npattern classification. In a dynamic world, an object may continuously evolve\nover time, and so does the graph extracted from the underlying object. These\nchanges in graph structure with respect to the temporal order present a new\nrepresentation of the graph, in which an object corresponds to a set of\ntime-variant graphs. In this paper, we formulate a novel time-variant graph\nclassification task and propose a new graph feature, called a graph-shapelet\npattern, for learning and classifying time-variant graphs. Graph-shapelet\npatterns are compact and discriminative graph transformation subsequences. A\ngraph-shapelet pattern can be regarded as a graphical extension of a shapelet\n-- a class of discriminative features designed for vector-based temporal data\nclassification. To discover graph-shapelet patterns, we propose to convert a\ntime-variant graph sequence into time-series data and use the discovered\nshapelets to find graph transformation subsequences as graph-shapelet patterns.\nBy converting each graph-shapelet pattern into a unique tokenized graph\ntransformation sequence, we can measure the similarity between two\ngraph-shapelet patterns and therefore classify time-variant graphs. Experiments\non both synthetic and real-world data demonstrate the superior performance of\nthe proposed algorithms.",
+                    "authors": "Haishuai Wang",
+                    "published": "2016-09-14",
+                    "updated": "2017-06-12",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07699v2",
+                    "title": "Time-aware Graph Structure Learning via Sequence Prediction on Temporal Graphs",
+                    "abstract": "Temporal Graph Learning, which aims to model the time-evolving nature of\ngraphs, has gained increasing attention and achieved remarkable performance\nrecently. However, in reality, graph structures are often incomplete and noisy,\nwhich hinders temporal graph networks (TGNs) from learning informative\nrepresentations. Graph contrastive learning uses data augmentation to generate\nplausible variations of existing data and learn robust representations.\nHowever, rule-based augmentation approaches may be suboptimal as they lack\nlearnability and fail to leverage rich information from downstream tasks. To\naddress these issues, we propose a Time-aware Graph Structure Learning (TGSL)\napproach via sequence prediction on temporal graphs, which learns better graph\nstructures for downstream tasks through adding potential temporal edges. In\nparticular, it predicts time-aware context embedding based on previously\nobserved interactions and uses the Gumble-Top-K to select the closest candidate\nedges to this context embedding. Additionally, several candidate sampling\nstrategies are proposed to ensure both efficiency and diversity. Furthermore,\nwe jointly learn the graph structure and TGNs in an end-to-end manner and\nperform inference on the refined graph. Extensive experiments on temporal link\nprediction benchmarks demonstrate that TGSL yields significant gains for the\npopular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive\nlearning methods on temporal graphs. We release the code at\nhttps://github.com/ViktorAxelsen/TGSL.",
+                    "authors": "Haozhen Zhang, Xueting Han, Xi Xiao, Jing Bai",
+                    "published": "2023-06-13",
+                    "updated": "2023-08-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.07016v2",
+                    "title": "On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions",
+                    "abstract": "This work formalizes the associational task of predicting node attribute\nevolution in temporal graphs from the perspective of learning equivariant\nrepresentations. We show that node representations in temporal graphs can be\ncast into two distinct frameworks: (a) The most popular approach, which we\ndenote as time-and-graph, where equivariant graph (e.g., GNN) and sequence\n(e.g., RNN) representations are intertwined to represent the temporal evolution\nof node attributes in the graph; and (b) an approach that we denote as\ntime-then-graph, where the sequences describing the node and edge dynamics are\nrepresented first, then fed as node and edge attributes into a static\nequivariant graph representation that comes after. Interestingly, we show that\ntime-then-graph representations have an expressivity advantage over\ntime-and-graph representations when both use component GNNs that are not\nmost-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is\nnot necessarily to obtain state-of-the-art results, our experiments show that\ntime-then-graph methods are capable of achieving better performance and\nefficiency than state-of-the-art time-and-graph methods in some real-world\ntasks, thereby showcasing that the time-then-graph framework is a worthy\naddition to the graph ML toolbox.",
+                    "authors": "Jianfei Gao, Bruno Ribeiro",
+                    "published": "2021-03-12",
+                    "updated": "2023-03-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.10364v3",
+                    "title": "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks",
+                    "abstract": "Recent years have seen a surge in research on dynamic graph representation\nlearning, which aims to model temporal graphs that are dynamic and evolving\nconstantly over time. However, current work typically models graph dynamics\nwith recurrent neural networks (RNNs), making them suffer seriously from\ncomputation and memory overheads on large temporal graphs. So far, scalability\nof dynamic graph representation learning on large temporal graphs remains one\nof the major challenges. In this paper, we present a scalable framework, namely\nSpikeNet, to efficiently capture the temporal and structural patterns of\ntemporal graphs. We explore a new direction in that we can capture the evolving\ndynamics of temporal graphs with spiking neural networks (SNNs) instead of\nRNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics\nas spike trains of neuron populations and enable spike-based propagation in an\nefficient way. Experiments on three large real-world temporal graph datasets\ndemonstrate that SpikeNet outperforms strong baselines on the temporal node\nclassification task with lower computational costs. Particularly, SpikeNet\ngeneralizes to a large temporal graph (2.7M nodes and 13.9M edges) with\nsignificantly fewer parameters and computation overheads.Our code is publicly\navailable at \\url{https://github.com/EdisonLeeeee/SpikeNet}.",
+                    "authors": "Jintang Li, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, Changhua Meng",
+                    "published": "2022-08-15",
+                    "updated": "2023-05-18",
+                    "primary_cat": "cs.NE",
+                    "cats": [
+                        "cs.NE",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.09610v2",
+                    "title": "Storing and Querying Large-Scale Spatio-Temporal Graphs with High-Throughput Edge Insertions",
+                    "abstract": "Real-world graphs often contain spatio-temporal information and evolve over\ntime. Compared with static graphs, spatio-temporal graphs have very different\ncharacteristics, presenting more significant challenges in data volume, data\nvelocity, and query processing. In this paper, we describe three representative\napplications to understand the features of spatio-temporal graphs. Based on the\ncommonalities of the applications, we define a formal spatio-temporal graph\nmodel, where a graph consists of location vertices, object vertices, and event\nedges. Then we discuss a set of design goals to meet the requirements of the\napplications: (i) supporting up to 10 billion object vertices, 10 million\nlocation vertices, and 100 trillion edges in the graph, (ii) supporting up to 1\ntrillion new edges that are streamed in daily, and (iii) minimizing\ncross-machine communication for query processing. We propose and evaluate PAST,\na framework for efficient PArtitioning and query processing of Spatio-Temporal\ngraphs. Experimental results show that PAST successfully achieves the above\ngoals. It improves query performance by orders of magnitude compared with\nstate-of-the-art solutions, including JanusGraph, Greenplum, Spark and\nST-Hadoop.",
+                    "authors": "Mengsu Ding, Muqiao Yang, Shimin Chen",
+                    "published": "2019-04-21",
+                    "updated": "2020-10-20",
+                    "primary_cat": "cs.DC",
+                    "cats": [
+                        "cs.DC",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1310.7898v1",
+                    "title": "Moving in temporal graphs with very sparse random availability of edges",
+                    "abstract": "In this work we consider temporal graphs, i.e. graphs, each edge of which is\nassigned a set of discrete time-labels drawn from a set of integers. The labels\nof an edge indicate the discrete moments in time at which the edge is\navailable. We also consider temporal paths in a temporal graph, i.e. paths\nwhose edges are assigned a strictly increasing sequence of labels. Furthermore,\nwe assume the uniform case (UNI-CASE), in which every edge of a graph is\nassigned exactly one time label from a set of integers and the time labels\nassigned to the edges of the graph are chosen randomly and independently, with\nthe selection following the uniform distribution. We call uniform random\ntemporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the\nexpected number of temporal paths of a given length in the uniform random\ntemporal clique. We define the term temporal distance of two vertices, which is\nthe arrival time, i.e. the time-label of the last edge, of the temporal path\nthat connects those vertices, which has the smallest arrival time amongst all\ntemporal paths that connect those vertices. We then propose and study two\nstatistical properties of temporal graphs. One is the maximum expected temporal\ndistance which is, as the term indicates, the maximum of all expected temporal\ndistances in the graph. The other one is the temporal diameter which, loosely\nspeaking, is the expectation of the maximum temporal distance in the graph. We\nderive the maximum expected temporal distance of a uniform random temporal star\ngraph as well as an upper bound on both the maximum expected temporal distance\nand the temporal diameter of the normalized version of the uniform random\ntemporal clique, in which the largest time-label available equals the number of\nvertices. Finally, we provide an algorithm that solves an optimization problem\non a specific type of temporal (multi)graphs of two vertices.",
+                    "authors": "Paul G. Spirakis, Eleni Ch. Akrida",
+                    "published": "2013-10-29",
+                    "updated": "2013-10-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.02875v1",
+                    "title": "Multi-Task Edge Prediction in Temporally-Dynamic Video Graphs",
+                    "abstract": "Graph neural networks have shown to learn effective node representations,\nenabling node-, link-, and graph-level inference. Conventional graph networks\nassume static relations between nodes, while relations between entities in a\nvideo often evolve over time, with nodes entering and exiting dynamically. In\nsuch temporally-dynamic graphs, a core problem is inferring the future state of\nspatio-temporal edges, which can constitute multiple types of relations. To\naddress this problem, we propose MTD-GNN, a graph network for predicting\ntemporally-dynamic edges for multiple types of relations. We propose a\nfactorized spatio-temporal graph attention layer to learn dynamic node\nrepresentations and present a multi-task edge prediction loss that models\nmultiple relations simultaneously. The proposed architecture operates on top of\nscene graphs that we obtain from videos through object detection and\nspatio-temporal linking. Experimental evaluations on ActionGenome and CLEVRER\nshow that modeling multiple relations in our temporally-dynamic graph network\ncan be mutually beneficial, outperforming existing static and spatio-temporal\ngraph neural networks, as well as state-of-the-art predicate classification\nmethods.",
+                    "authors": "Osman \u00dclger, Julian Wiederer, Mohsen Ghafoorian, Vasileios Belagiannis, Pascal Mettes",
+                    "published": "2022-12-06",
+                    "updated": "2022-12-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.05496v2",
+                    "title": "Temporal Graph Kernels for Classifying Dissemination Processes",
+                    "abstract": "Many real-world graphs or networks are temporal, e.g., in a social network\npersons only interact at specific points in time. This information directs\ndissemination processes on the network, such as the spread of rumors, fake\nnews, or diseases. However, the current state-of-the-art methods for supervised\ngraph classification are designed mainly for static graphs and may not be able\nto capture temporal information. Hence, they are not powerful enough to\ndistinguish between graphs modeling different dissemination processes. To\naddress this, we introduce a framework to lift standard graph kernels to the\ntemporal domain. Specifically, we explore three different approaches and\ninvestigate the trade-offs between loss of temporal information and efficiency.\nMoreover, to handle large-scale graphs, we propose stochastic variants of our\nkernels with provable approximation guarantees. We evaluate our methods on a\nwide range of real-world social networks. Our methods beat static kernels by a\nlarge margin in terms of accuracy while still being scalable to large graphs\nand data sets. Hence, we confirm that taking temporal information into account\nis crucial for the successful classification of dissemination processes.",
+                    "authors": "Lutz Oettershagen, Nils M. Kriege, Christopher Morris, Petra Mutzel",
+                    "published": "2019-10-14",
+                    "updated": "2021-08-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.01594v1",
+                    "title": "Parameterized temporal exploration problems",
+                    "abstract": "In this paper we study the fixed-parameter tractability of the problem of\ndeciding whether a given temporal graph admits a temporal walk that visits all\nvertices (temporal exploration) or, in some problem variants, a certain subset\nof the vertices. Formally, a temporal graph is a sequence <G_1,...,G_L> of\ngraphs with V(G_t) = V(G) and E(G_t) a subset of E(G) for all t in [L] and some\nunderlying graph G, and a temporal walk is a time-respecting sequence of\nedge-traversals. We consider both the strict variant, in which edges must be\ntraversed in strictly increasing timesteps, and the non-strict variant, in\nwhich an arbitrary number of edges can be traversed in each timestep. For both\nvariants, we give FPT algorithms for the problem of finding a temporal walk\nthat visits a given set X of vertices, parameterized by |X|, and for the\nproblem of finding a temporal walk that visits at least k distinct vertices in\nV(G), parameterized by k. We also show W[2]-hardness for a set version of the\ntemporal exploration problem for both variants. For the non-strict variant, we\ngive an FPT algorithm for the temporal exploration problem parameterized by the\nlifetime of the input graph, and we show that the temporal exploration problem\ncan be solved in polynomial time if the graph in each timestep has at most two\nconnected components.",
+                    "authors": "Thomas Erlebach, Jakob T. Spooner",
+                    "published": "2022-12-03",
+                    "updated": "2022-12-03",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "05C85",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2101.00820v8",
+                    "title": "Temporal Contrastive Graph Learning for Video Action Recognition and Retrieval",
+                    "abstract": "Attempt to fully discover the temporal diversity and chronological\ncharacteristics for self-supervised video representation learning, this work\ntakes advantage of the temporal dependencies within videos and further proposes\na novel self-supervised method named Temporal Contrastive Graph Learning\n(TCGL). In contrast to the existing methods that ignore modeling elaborate\ntemporal dependencies, our TCGL roots in a hybrid graph contrastive learning\nstrategy to jointly regard the inter-snippet and intra-snippet temporal\ndependencies as self-supervision signals for temporal representation learning.\nTo model multi-scale temporal dependencies, our TCGL integrates the prior\nknowledge about the frame and snippet orders into graph structures, i.e., the\nintra-/inter- snippet temporal contrastive graphs. By randomly removing edges\nand masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL\ncan generate different correlated graph views. Then, specific contrastive\nlearning modules are designed to maximize the agreement between nodes in\ndifferent views. To adaptively learn the global context representation and\nrecalibrate the channel-wise features, we introduce an adaptive video snippet\norder prediction module, which leverages the relational knowledge among video\nsnippets to predict the actual snippet orders. Experimental results demonstrate\nthe superiority of our TCGL over the state-of-the-art methods on large-scale\naction recognition and video retrieval benchmarks.",
+                    "authors": "Yang Liu, Keze Wang, Haoyuan Lan, Liang Lin",
+                    "published": "2021-01-04",
+                    "updated": "2021-03-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.MM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.11190v1",
+                    "title": "Using Motif Transitions for Temporal Graph Generation",
+                    "abstract": "Graph generative models are highly important for sharing surrogate data and\nbenchmarking purposes. Real-world complex systems often exhibit dynamic nature,\nwhere the interactions among nodes change over time in the form of a temporal\nnetwork. Most temporal network generation models extend the static graph\ngeneration models by incorporating temporality in the generation process. More\nrecently, temporal motifs are used to generate temporal networks with better\nsuccess. However, existing models are often restricted to a small set of\npredefined motif patterns due to the high computational cost of counting\ntemporal motifs. In this work, we develop a practical temporal graph generator,\nMotif Transition Model (MTM), to generate synthetic temporal networks with\nrealistic global and local features. Our key idea is modeling the arrival of\nnew events as temporal motif transition processes. We first calculate the\ntransition properties from the input graph and then simulate the motif\ntransition processes based on the transition probabilities and transition\nrates. We demonstrate that our model consistently outperforms the baselines\nwith respect to preserving various global and local temporal graph statistics\nand runtime performance.",
+                    "authors": "Penghang Liu, A. Erdem Sar\u0131y\u00fcce",
+                    "published": "2023-06-19",
+                    "updated": "2023-06-19",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.08733v1",
+                    "title": "Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast",
+                    "abstract": "Self-supervised learning on graphs has recently drawn a lot of attention due\nto its independence from labels and its robustness in representation. Current\nstudies on this topic mainly use static information such as graph structures\nbut cannot well capture dynamic information such as timestamps of edges.\nRealistic graphs are often dynamic, which means the interaction between nodes\noccurs at a specific time. This paper proposes a self-supervised dynamic graph\nrepresentation learning framework (DySubC), which defines a temporal subgraph\ncontrastive learning task to simultaneously learn the structural and\nevolutional features of a dynamic graph. Specifically, a novel temporal\nsubgraph sampling strategy is firstly proposed, which takes each node of the\ndynamic graph as the central node and uses both neighborhood structures and\nedge timestamps to sample the corresponding temporal subgraph. The subgraph\nrepresentation function is then designed according to the influence of\nneighborhood nodes on the central node after encoding the nodes in each\nsubgraph. Finally, the structural and temporal contrastive loss are defined to\nmaximize the mutual information between node representation and temporal\nsubgraph representation. Experiments on five real-world datasets demonstrate\nthat (1) DySubC performs better than the related baselines including two graph\ncontrastive learning models and four dynamic graph representation learning\nmodels in the downstream link prediction task, and (2) the use of temporal\ninformation can not only sample more effective subgraphs, but also learn better\nrepresentation by temporal contrastive loss.",
+                    "authors": "Linpu Jiang, Ke-Jia Chen, Jingqiang Chen",
+                    "published": "2021-12-16",
+                    "updated": "2021-12-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.09677v1",
+                    "title": "A Simple Temporal Information Matching Mechanism for Entity Alignment Between Temporal Knowledge Graphs",
+                    "abstract": "Entity alignment (EA) aims to find entities in different knowledge graphs\n(KGs) that refer to the same object in the real world. Recent studies\nincorporate temporal information to augment the representations of KGs. The\nexisting methods for EA between temporal KGs (TKGs) utilize a time-aware\nattention mechanism to incorporate relational and temporal information into\nentity embeddings. The approaches outperform the previous methods by using\ntemporal information. However, we believe that it is not necessary to learn the\nembeddings of temporal information in KGs since most TKGs have uniform temporal\nrepresentations. Therefore, we propose a simple graph neural network (GNN)\nmodel combined with a temporal information matching mechanism, which achieves\nbetter performance with less time and fewer parameters. Furthermore, since\nalignment seeds are difficult to label in real-world applications, we also\npropose a method to generate unsupervised alignment seeds via the temporal\ninformation of TKG. Extensive experiments on public datasets indicate that our\nsupervised method significantly outperforms the previous methods and the\nunsupervised one has competitive performance.",
+                    "authors": "Li Cai, Xin Mao, Meirong Ma, Hao Yuan, Jianchao Zhu, Man Lan",
+                    "published": "2022-09-20",
+                    "updated": "2022-09-20",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.09114v1",
+                    "title": "Relational Temporal Graph Reasoning for Dual-task Dialogue Language Understanding",
+                    "abstract": "Dual-task dialog language understanding aims to tackle two correlative dialog\nlanguage understanding tasks simultaneously via leveraging their inherent\ncorrelations. In this paper, we put forward a new framework, whose core is\nrelational temporal graph reasoning.We propose a speaker-aware temporal graph\n(SATG) and a dual-task relational temporal graph (DRTG) to facilitate\nrelational temporal modeling in dialog understanding and dual-task reasoning.\nBesides, different from previous works that only achieve implicit\nsemantics-level interactions, we propose to model the explicit dependencies via\nintegrating prediction-level interactions. To implement our framework, we first\npropose a novel model Dual-tAsk temporal Relational rEcurrent Reasoning network\n(DARER), which first generates the context-, speaker- and temporal-sensitive\nutterance representations through relational temporal modeling of SATG, then\nconducts recurrent dual-task relational temporal graph reasoning on DRTG, in\nwhich process the estimated label distributions act as key clues in\nprediction-level interactions. And the relational temporal modeling in DARER is\nachieved by relational convolutional networks (RGCNs). Then we further propose\nRelational Temporal Transformer (ReTeFormer), which achieves fine-grained\nrelational temporal modeling via Relation- and Structure-aware Disentangled\nMulti-head Attention. Accordingly, we propose DARER with ReTeFormer (DARER2),\nwhich adopts two variants of ReTeFormer to achieve the relational temporal\nmodeling of SATG and DTRG, respectively. The extensive experiments on different\nscenarios verify that our models outperform state-of-the-art models by a large\nmargin. Remarkably, on the dialog sentiment classification task in the Mastodon\ndataset, DARER and DARER2 gain relative improvements of about 28% and 34% over\nthe previous best model in terms of F1.",
+                    "authors": "Bowen Xing, Ivor W. Tsang",
+                    "published": "2023-06-15",
+                    "updated": "2023-06-15",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.08889v3",
+                    "title": "Node Embedding over Temporal Graphs",
+                    "abstract": "In this work, we present a method for node embedding in temporal graphs. We\npropose an algorithm that learns the evolution of a temporal graph's nodes and\nedges over time and incorporates this dynamics in a temporal node embedding\nframework for different graph prediction tasks. We present a joint loss\nfunction that creates a temporal embedding of a node by learning to combine its\nhistorical temporal embeddings, such that it optimizes per given task (e.g.,\nlink prediction). The algorithm is initialized using static node embeddings,\nwhich are then aligned over the representations of a node at different time\npoints, and eventually adapted for the given task in a joint optimization. We\nevaluate the effectiveness of our approach over a variety of temporal graphs\nfor the two fundamental tasks of temporal link prediction and multi-label node\nclassification, comparing to competitive baselines and algorithmic\nalternatives. Our algorithm shows performance improvements across many of the\ndatasets and baselines and is found particularly effective for graphs that are\nless cohesive, with a lower clustering coefficient.",
+                    "authors": "Uriel Singer, Ido Guy, Kira Radinsky",
+                    "published": "2019-03-21",
+                    "updated": "2021-05-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.04816v1",
+                    "title": "MTGER: Multi-view Temporal Graph Enhanced Temporal Reasoning over Time-Involved Document",
+                    "abstract": "The facts and time in the document are intricately intertwined, making\ntemporal reasoning over documents challenging. Previous work models time\nimplicitly, making it difficult to handle such complex relationships. To\naddress this issue, we propose MTGER, a novel Multi-view Temporal Graph\nEnhanced Temporal Reasoning framework for temporal reasoning over time-involved\ndocuments. Concretely, MTGER explicitly models the temporal relationships among\nfacts by multi-view temporal graphs. On the one hand, the heterogeneous\ntemporal graphs explicitly model the temporal and discourse relationships among\nfacts; on the other hand, the multi-view mechanism captures both time-focused\nand fact-focused information, allowing the two views to complement each other\nthrough adaptive fusion. To further improve the implicit reasoning capability\nof the model, we design a self-supervised time-comparing objective. Extensive\nexperimental results demonstrate the effectiveness of our method on the TimeQA\nand SituatedQA datasets. Furthermore, MTGER gives more consistent answers under\nquestion perturbations.",
+                    "authors": "Zheng Chu, Zekun Wang, Jiafeng Liang, Ming Liu, Bing Qin",
+                    "published": "2023-11-08",
+                    "updated": "2023-11-08",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.03363v3",
+                    "title": "Spatio-Temporal Graph Scattering Transform",
+                    "abstract": "Although spatio-temporal graph neural networks have achieved great empirical\nsuccess in handling multiple correlated time series, they may be impractical in\nsome real-world scenarios due to a lack of sufficient high-quality training\ndata. Furthermore, spatio-temporal graph neural networks lack theoretical\ninterpretation. To address these issues, we put forth a novel mathematically\ndesigned framework to analyze spatio-temporal data. Our proposed\nspatio-temporal graph scattering transform (ST-GST) extends traditional\nscattering transforms to the spatio-temporal domain. It performs iterative\napplications of spatio-temporal graph wavelets and nonlinear activation\nfunctions, which can be viewed as a forward pass of spatio-temporal graph\nconvolutional networks without training. Since all the filter coefficients in\nST-GST are mathematically designed, it is promising for the real-world\nscenarios with limited training data, and also allows for a theoretical\nanalysis, which shows that the proposed ST-GST is stable to small perturbations\nof input signals and structures. Finally, our experiments show that i) ST-GST\noutperforms spatio-temporal graph convolutional networks by an increase of 35%\nin accuracy for MSR Action3D dataset; ii) it is better and computationally more\nefficient to design the transform based on separable spatio-temporal graphs\nthan the joint ones; and iii) the nonlinearity in ST-GST is critical to\nempirical performance.",
+                    "authors": "Chao Pan, Siheng Chen, Antonio Ortega",
+                    "published": "2020-12-06",
+                    "updated": "2021-02-09",
+                    "primary_cat": "eess.SP",
+                    "cats": [
+                        "eess.SP",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.04962v1",
+                    "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering",
+                    "abstract": "Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.",
+                    "authors": "Meng Liu, Ke Liang, Yue Liu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-06-08",
+                    "updated": "2023-06-08",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10738v3",
+                    "title": "Deep Temporal Graph Clustering",
+                    "abstract": "Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.",
+                    "authors": "Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-05-18",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.10830v1",
+                    "title": "Automated Dilated Spatio-Temporal Synchronous Graph Modeling for Traffic Prediction",
+                    "abstract": "Accurate traffic prediction is a challenging task in intelligent\ntransportation systems because of the complex spatio-temporal dependencies in\ntransportation networks. Many existing works utilize sophisticated temporal\nmodeling approaches to incorporate with graph convolution networks (GCNs) for\ncapturing short-term and long-term spatio-temporal dependencies. However, these\nseparated modules with complicated designs could restrict effectiveness and\nefficiency of spatio-temporal representation learning. Furthermore, most\nprevious works adopt the fixed graph construction methods to characterize the\nglobal spatio-temporal relations, which limits the learning capability of the\nmodel for different time periods and even different data scenarios. To overcome\nthese limitations, we propose an automated dilated spatio-temporal synchronous\ngraph network, named Auto-DSTSGN for traffic prediction. Specifically, we\ndesign an automated dilated spatio-temporal synchronous graph (Auto-DSTSG)\nmodule to capture the short-term and long-term spatio-temporal correlations by\nstacking deeper layers with dilation factors in an increasing order. Further,\nwe propose a graph structure search approach to automatically construct the\nspatio-temporal synchronous graph that can adapt to different data scenarios.\nExtensive experiments on four real-world datasets demonstrate that our model\ncan achieve about 10% improvements compared with the state-of-art methods.\nSource codes are available at https://github.com/jinguangyin/Auto-DSTSGN.",
+                    "authors": "Guangyin Jin, Fuxian Li, Jinlei Zhang, Mudan Wang, Jincai Huang",
+                    "published": "2022-07-22",
+                    "updated": "2022-07-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.02606v1",
+                    "title": "Learning adjacency matrix for dynamic graph neural network",
+                    "abstract": "In recent work, [1] introduced the concept of using a Block Adjacency Matrix\n(BA) for the representation of spatio-temporal data. While their method\nsuccessfully concatenated adjacency matrices to encapsulate spatio-temporal\nrelationships in a single graph, it formed a disconnected graph. This\nlimitation hampered the ability of Graph Convolutional Networks (GCNs) to\nperform message passing across nodes belonging to different time steps, as no\ntemporal links were present. To overcome this challenge, we introduce an\nencoder block specifically designed to learn these missing temporal links. The\nencoder block processes the BA and predicts connections between previously\nunconnected subgraphs, resulting in a Spatio-Temporal Block Adjacency Matrix\n(STBAM). This enriched matrix is then fed into a Graph Neural Network (GNN) to\ncapture the complex spatio-temporal topology of the network. Our evaluations on\nbenchmark datasets, surgVisDom and C2D2, demonstrate that our method, with\nslightly higher complexity, achieves superior results compared to\nstate-of-the-art results. Our approach's computational overhead remains\nsignificantly lower than conventional non-graph-based methodologies for\nspatio-temporal data.",
+                    "authors": "Osama Ahmad, Omer Abdul Jalil, Usman Nazir, Murtaza Taj",
+                    "published": "2023-10-04",
+                    "updated": "2023-10-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.11244v1",
+                    "title": "Using Compressed Suffix-Arrays for a Compact Representation of Temporal-Graphs",
+                    "abstract": "Temporal graphs represent binary relationships that change along time. They\ncan model the dynamism of, for example, social and communication networks.\nTemporal graphs are defined as sets of contacts that are edges tagged with the\ntemporal intervals when they are active. This work explores the use of the\nCompressed Suffix Array (CSA), a well-known compact and self-indexed data\nstructure in the area of text indexing, to represent large temporal graphs. The\nnew structure, called Temporal Graph CSA (TGCSA), is experimentally compared\nwith the most competitive compact data structures in the state-of-the-art,\nnamely, EDGELOG and CET. The experimental results show that TGCSA obtains a\ngood space-time trade-off. It uses a reasonable space and is efficient for\nsolving complex temporal queries. Furthermore, TGCSA has wider expressive\ncapabilities than EDGELOG and CET, because it is able to represent temporal\ngraphs where contacts on an edge can temporally overlap.",
+                    "authors": "Nieves R. Brisaboa, Diego Caro, Antonio Fari\u00f1a, M. Andrea Rodriguez",
+                    "published": "2018-12-28",
+                    "updated": "2018-12-28",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.03651v1",
+                    "title": "Temporal Graph Analysis with TGX",
+                    "abstract": "Real-world networks, with their evolving relations, are best captured as\ntemporal graphs. However, existing software libraries are largely designed for\nstatic graphs where the dynamic nature of temporal graphs is ignored. Bridging\nthis gap, we introduce TGX, a Python package specially designed for analysis of\ntemporal networks that encompasses an automated pipeline for data loading, data\nprocessing, and analysis of evolving graphs. TGX provides access to eleven\nbuilt-in datasets and eight external Temporal Graph Benchmark (TGB) datasets as\nwell as any novel datasets in the .csv format. Beyond data loading, TGX\nfacilitates data processing functionalities such as discretization of temporal\ngraphs and node subsampling to accelerate working with larger datasets. For\ncomprehensive investigation, TGX offers network analysis by providing a diverse\nset of measures, including average node degree and the evolving number of nodes\nand edges per timestamp. Additionally, the package consolidates meaningful\nvisualization plots indicating the evolution of temporal patterns, such as\nTemporal Edge Appearance (TEA) and Temporal Edge Trafficc (TET) plots. The TGX\npackage is a robust tool for examining the features of temporal graphs and can\nbe used in various areas like studying social networks, citation networks, and\ntracking user interactions. We plan to continuously support and update TGX\nbased on community feedback. TGX is publicly available on:\nhttps://github.com/ComplexData-MILA/TGX.",
+                    "authors": "Razieh Shirzadkhani, Shenyang Huang, Elahe Kooshafar, Reihaneh Rabbany, Farimah Poursafaei",
+                    "published": "2024-02-06",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.04696v1",
+                    "title": "Nash Equilibria in Reverse Temporal Voronoi Games",
+                    "abstract": "We study Voronoi games on temporal graphs as introduced by Boehmer et al.\n(IJCAI 2021) where two players each select a vertex in a temporal graph with\nthe goal of reaching the other vertices earlier than the other player. In this\nwork, we consider the reverse temporal Voronoi game, that is, a player wants to\nmaximize the number of vertices reaching her earlier than the other player.\nSince temporal distances in temporal graphs are not symmetric in general, this\nyields a different game. We investigate the difference between the two games\nwith respect to the existence of Nash equilibria in various temporal graph\nclasses including temporal trees, cycles, grids, cliques and split graphs. Our\nextensive results show that the two games indeed behave quite differently\ndepending on the considered temporal graph class.",
+                    "authors": "Simeon Pawlowski, Vincent Froese",
+                    "published": "2024-02-07",
+                    "updated": "2024-02-07",
+                    "primary_cat": "cs.GT",
+                    "cats": [
+                        "cs.GT"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07491v3",
+                    "title": "Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment",
+                    "abstract": "Temporal graph learning aims to generate high-quality representations for\ngraph-based tasks with dynamic information, which has recently garnered\nincreasing attention. In contrast to static graphs, temporal graphs are\ntypically organized as node interaction sequences over continuous time rather\nthan an adjacency matrix. Most temporal graph learning methods model current\ninteractions by incorporating historical neighborhood. However, such methods\nonly consider first-order temporal information while disregarding crucial\nhigh-order structural information, resulting in suboptimal performance. To\naddress this issue, we propose a self-supervised method called S2T for temporal\ngraph learning, which extracts both temporal and structural information to\nlearn more informative node representations. Notably, the initial node\nrepresentations combine first-order temporal and high-order structural\ninformation differently to calculate two conditional intensities. An alignment\nloss is then introduced to optimize the node representations, narrowing the gap\nbetween the two intensities and making them more informative. Concretely, in\naddition to modeling temporal information using historical neighbor sequences,\nwe further consider structural knowledge at both local and global levels. At\nthe local level, we generate structural intensity by aggregating features from\nhigh-order neighbor sequences. At the global level, a global representation is\ngenerated based on all nodes to adjust the structural intensity according to\nthe active statuses on different nodes. Extensive experiments demonstrate that\nthe proposed model S2T achieves at most 10.13% performance improvement compared\nwith the state-of-the-art competitors on several datasets.",
+                    "authors": "Meng Liu, Ke Liang, Yawei Zhao, Wenxuan Tu, Sihang Zhou, Xinbiao Gan, Xinwang Liu, Kunlun He",
+                    "published": "2023-02-15",
+                    "updated": "2024-04-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.11979v1",
+                    "title": "MTGA: Multi-view Temporal Granularity aligned Aggregation for Event-based Lip-reading",
+                    "abstract": "Lip-reading is to utilize the visual information of the speaker's lip\nmovements to recognize words and sentences. Existing event-based lip-reading\nsolutions integrate different frame rate branches to learn spatio-temporal\nfeatures of varying granularities. However, aggregating events into event\nframes inevitably leads to the loss of fine-grained temporal information within\nframes. To remedy this drawback, we propose a novel framework termed Multi-view\nTemporal Granularity aligned Aggregation (MTGA). Specifically, we first present\na novel event representation method, namely time-segmented voxel graph list,\nwhere the most significant local voxels are temporally connected into a graph\nlist. Then we design a spatio-temporal fusion module based on temporal\ngranularity alignment, where the global spatial features extracted from event\nframes, together with the local relative spatial and temporal features\ncontained in voxel graph list are effectively aligned and integrated. Finally,\nwe design a temporal aggregation module that incorporates positional encoding,\nwhich enables the capture of local absolute spatial and global temporal\ninformation. Experiments demonstrate that our method outperforms both the\nevent-based and video-based lip-reading counterparts. Our code will be publicly\navailable.",
+                    "authors": "Wenhao Zhang, Jun Wang, Yong Luo, Lei Yu, Wei Yu, Zheng He",
+                    "published": "2024-04-18",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.13177v1",
+                    "title": "It is all Connected: A New Graph Formulation for Spatio-Temporal Forecasting",
+                    "abstract": "With an ever-increasing number of sensors in modern society, spatio-temporal\ntime series forecasting has become a de facto tool to make informed decisions\nabout the future. Most spatio-temporal forecasting models typically comprise\ndistinct components that learn spatial and temporal dependencies. A common\nmethodology employs some Graph Neural Network (GNN) to capture relations\nbetween spatial locations, while another network, such as a recurrent neural\nnetwork (RNN), learns temporal correlations. By representing every recorded\nsample as its own node in a graph, rather than all measurements for a\nparticular location as a single node, temporal and spatial information is\nencoded in a similar manner. In this setting, GNNs can now directly learn both\ntemporal and spatial dependencies, jointly, while also alleviating the need for\nadditional temporal networks. Furthermore, the framework does not require\naligned measurements along the temporal dimension, meaning that it also\nnaturally facilitates irregular time series, different sampling frequencies or\nmissing data, without the need for data imputation. To evaluate the proposed\nmethodology, we consider wind speed forecasting as a case study, where our\nproposed framework outperformed other spatio-temporal models using GNNs with\neither Transformer or LSTM networks as temporal update functions.",
+                    "authors": "Lars \u00d8degaard Bentsen, Narada Dilp Warakagoda, Roy Stenbro, Paal Engelstad",
+                    "published": "2023-03-23",
+                    "updated": "2023-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.05631v2",
+                    "title": "ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling",
+                    "abstract": "The spatio-temporal graph learning is becoming an increasingly important\nobject of graph study. Many application domains involve highly dynamic graphs\nwhere temporal information is crucial, e.g. traffic networks and financial\ntransaction graphs. Despite the constant progress made on learning structured\ndata, there is still a lack of effective means to extract dynamic complex\nfeatures from spatio-temporal structures. Particularly, conventional models\nsuch as convolutional networks or recurrent neural networks are incapable of\nrevealing the temporal patterns in short or long terms and exploring the\nspatial properties in local or global scope from spatio-temporal graphs\nsimultaneously. To tackle this problem, we design a novel multi-scale\narchitecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series\nmodeling. In this U-shaped network, a paired sampling operation is proposed in\nspacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in\nspatial from its deterministic partition while abstracts multi-resolution\ntemporal dependencies through dilated recurrent skip connections; based on\nprevious settings in the downsampling, the unpooling (ST-Unpool) restores the\noriginal structure of spatio-temporal graphs and resumes regular intervals\nwithin graph sequences. Experiments on spatio-temporal prediction tasks\ndemonstrate that our model effectively captures comprehensive features in\nmultiple scales and achieves substantial improvements over mainstream methods\non several real-world datasets.",
+                    "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+                    "published": "2019-03-13",
+                    "updated": "2021-06-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.02128v1",
+                    "title": "Interaction Order Prediction for Temporal Graphs",
+                    "abstract": "Link prediction in graphs is a task that has been widely investigated. It has\nbeen applied in various domains such as knowledge graph completion,\ncontent/item recommendation, social network recommendations and so on. The\ninitial focus of most research was on link prediction in static graphs.\nHowever, there has recently been abundant work on modeling temporal graphs, and\nconsequently one of the tasks that has been researched is link prediction in\ntemporal graphs. However, most of the existing work does not focus on the order\nof link formation, and only predicts the existence of links. In this study, we\naim to predict the order of node interactions.",
+                    "authors": "Nayana Bannur, Mashrin Srivastava, Harsha Vardhan",
+                    "published": "2023-02-04",
+                    "updated": "2023-02-04",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2008.08282v2",
+                    "title": "Multiscale Snapshots: Visual Analysis of Temporal Summaries in Dynamic Graphs",
+                    "abstract": "The overview-driven visual analysis of large-scale dynamic graphs poses a\nmajor challenge. We propose Multiscale Snapshots, a visual analytics approach\nto analyze temporal summaries of dynamic graphs at multiple temporal scales.\nFirst, we recursively generate temporal summaries to abstract overlapping\nsequences of graphs into compact snapshots. Second, we apply graph embeddings\nto the snapshots to learn low-dimensional representations of each sequence of\ngraphs to speed up specific analytical tasks (e.g., similarity search). Third,\nwe visualize the evolving data from a coarse to fine-granular snapshots to\nsemi-automatically analyze temporal states, trends, and outliers. The approach\nenables to discover similar temporal summaries (e.g., recurring states),\nreduces the temporal data to speed up automatic analysis, and to explore both\nstructural and temporal properties of a dynamic graph. We demonstrate the\nusefulness of our approach by a quantitative evaluation and the application to\na real-world dataset.",
+                    "authors": "Eren Cakmak, Udo Schlegel, Dominik J\u00e4ckle, Daniel Keim, Tobias Schreck",
+                    "published": "2020-08-19",
+                    "updated": "2020-09-15",
+                    "primary_cat": "cs.HC",
+                    "cats": [
+                        "cs.HC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.06260v1",
+                    "title": "In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs",
+                    "abstract": "A graph whose edges only appear at certain points in time is called a\ntemporal graph (among other names). These graphs are temporally connected if\nall ordered pairs of vertices are connected by a path that traverses edges in\nchronological order (a temporal path). Reachability in temporal graphs departs\nsignificantly from standard reachability; in particular, it is not transitive,\nwith structural and algorithmic consequences. For instance, temporally\nconnected graphs do not always admit spanning trees, i.e., subsets of edges\nthat form a tree and preserve temporal connectivity among the nodes.\n  In this paper, we revisit fundamental questions about the loss of\nuniversality of spanning trees. To start, we show that deciding if a spanning\ntree exists in a given temporal graph is NP-complete. What could be appropriate\nreplacement for the concept? Beyond having minimum size, spanning trees enjoy\nthe feature of enabling reachability along the same underlying paths in both\ndirections, a pretty uncommon feature in temporal graphs. We explore\nrelaxations in this direction and show that testing the existence of\nbidirectional spanning structures (bi-spanners) is tractable in general. On the\ndown side, finding \\emph{minimum} such structures is NP-hard even in simple\ntemporal graphs. Still, the fact that bidirectionality can be tested\nefficiently may find applications, e.g. for routing and security, and the\ncorresponding primitive that we introduce in the algorithm may be of\nindependent interest.",
+                    "authors": "Arnaud Casteigts, Timoth\u00e9e Corsini",
+                    "published": "2023-12-11",
+                    "updated": "2023-12-11",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DC",
+                        "68R10, 68W15",
+                        "G.2.2; C.2.4"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13624v1",
+                    "title": "Towards Linear Spanners in All Temporal Cliques",
+                    "abstract": "Many real-world networks, like transportation networks and social networks,\nare dynamic in the sense that the edge set may change over time, but these\nchanges are known in advance. This behavior is captured by the temporal graphs\nmodel, which has recently become a trending topic in theoretical computer\nscience. A core open problem in the field is to prove the existence of\nlinear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of\ncomplete temporal graphs that ensure all-pairs reachability via temporal paths.\nSo far, the best known result is the existence of temporal spanners with\n$\\mathcal{O}(n\\log n)$ many edges. We present significant progress towards\nproving that linear-size temporal spanners exist in all temporal cliques.\n  We adapt techniques used in previous works and heavily expand and generalize\nthem to provide a simpler and more intuitive proof of the $\\mathcal{O}(n\\log\nn)$ bound. Moreover, we use our novel approach to show that a large class of\ntemporal cliques, called edge-pivot graphs, admit linear-size temporal\nspanners. To contrast this, we investigate other classes of temporal cliques\nthat do not belong to the class of edge-pivot graphs. We introduce two such\ngraph classes and we develop novel techniques for establishing the existence of\nlinear temporal spanners in these graph classes as well.",
+                    "authors": "Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, Armin Wells",
+                    "published": "2024-02-21",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.19292v1",
+                    "title": "Fusing Temporal Graphs into Transformers for Time-Sensitive Question Answering",
+                    "abstract": "Answering time-sensitive questions from long documents requires temporal\nreasoning over the times in questions and documents. An important open question\nis whether large language models can perform such reasoning solely using a\nprovided text document, or whether they can benefit from additional temporal\ninformation extracted using other systems. We address this research question by\napplying existing temporal information extraction systems to construct temporal\ngraphs of events, times, and temporal relations in questions and documents. We\nthen investigate different approaches for fusing these graphs into Transformer\nmodels. Experimental results show that our proposed approach for fusing\ntemporal graphs into input text substantially enhances the temporal reasoning\ncapabilities of Transformer models with or without fine-tuning. Additionally,\nour proposed method outperforms various graph convolution-based approaches and\nestablishes a new state-of-the-art performance on SituatedQA and three splits\nof TimeQA.",
+                    "authors": "Xin Su, Phillip Howard, Nagib Hakim, Steven Bethard",
+                    "published": "2023-10-30",
+                    "updated": "2023-10-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1306.0493v1",
+                    "title": "Graph Metrics for Temporal Networks",
+                    "abstract": "Temporal networks, i.e., networks in which the interactions among a set of\nelementary units change over time, can be modelled in terms of time-varying\ngraphs, which are time-ordered sequences of graphs over a set of nodes. In such\ngraphs, the concepts of node adjacency and reachability crucially depend on the\nexact temporal ordering of the links. Consequently, all the concepts and\nmetrics proposed and used for the characterisation of static complex networks\nhave to be redefined or appropriately extended to time-varying graphs, in order\nto take into account the effects of time ordering on causality. In this chapter\nwe discuss how to represent temporal networks and we review the definitions of\nwalks, paths, connectedness and connected components valid for graphs in which\nthe links fluctuate over time. We then focus on temporal node-node distance,\nand we discuss how to characterise link persistence and the temporal\nsmall-world behaviour in this class of networks. Finally, we discuss the\nextension of classic centrality measures, including closeness, betweenness and\nspectral centrality, to the case of time-varying graphs, and we review the work\non temporal motifs analysis and the definition of modularity for temporal\ngraphs.",
+                    "authors": "Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, Vito Latora",
+                    "published": "2013-06-03",
+                    "updated": "2013-06-03",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.12843v1",
+                    "title": "An embedding-based distance for temporal graphs",
+                    "abstract": "We define a distance between temporal graphs based on graph embeddings built\nusing time-respecting random walks. We study both the case of matched graphs,\nwhen there exists a known relation between the nodes, and the unmatched case,\nwhen such a relation is unavailable and the graphs may be of different sizes.\nWe illustrate the interest of our distance definition, using both real and\nsynthetic temporal network data, by showing its ability to discriminate between\ngraphs with different structural and temporal properties. Leveraging\nstate-of-the-art machine learning techniques, we propose an efficient\nimplementation of distance computation that is viable for large-scale temporal\ngraphs.",
+                    "authors": "Lorenzo Dall'Amico, Alain Barrat, Ciro Cattuto",
+                    "published": "2024-01-23",
+                    "updated": "2024-01-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.12003v1",
+                    "title": "On Finding Separators in Temporal Split and Permutation Graphs",
+                    "abstract": "Removing all connections between two vertices s and z in a graph by removing\na minimum number of vertices is a fundamental problem in algorithmic graph\ntheory. This (s,z)-separation problem is well-known to be polynomial solvable\nand serves as an important primitive in many applications related to network\nconnectivity. We study the NP-hard temporal (s,z)-separation problem on\ntemporal graphs, which are graphs with fixed vertex sets but edge sets that\nchange over discrete time steps. We tackle this problem by restricting the\nlayers (i.e., graphs characterized by edges that are present at a certain point\nin time) to specific graph classes. We restrict the layers of the temporal\ngraphs to be either all split graphs or all permutation graphs (both being\nperfect graph classes) and provide both intractability and tractability\nresults. In particular, we show that in general the problem remains NP-hard\nboth on temporal split and temporal permutation graphs, but we also spot\npromising islands of fixed-parameter tractability particularly based on\nparameterizations that measure the amount of \"change over time\".",
+                    "authors": "Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken",
+                    "published": "2021-05-25",
+                    "updated": "2021-05-25",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1805.06836v2",
+                    "title": "Deleting edges to restrict the size of an epidemic in temporal networks",
+                    "abstract": "Spreading processes on graphs are a natural model for a wide variety of\nreal-world phenomena, including information spread over social networks and\nbiological diseases spreading over contact networks. Often, the networks over\nwhich these processes spread are dynamic in nature, and can be modeled with\ntemporal graphs. Here, we study the problem of deleting edges from a given\ntemporal graph in order to reduce the number of vertices (temporally) reachable\nfrom a given starting point. This could be used to control the spread of a\ndisease, rumour, etc. in a temporal graph. In particular, our aim is to find a\ntemporal subgraph in which a process starting at any single vertex can be\ntransferred to only a limited number of other vertices using a\ntemporally-feasible path. We introduce a natural edge-deletion problem for\ntemporal graphs and provide positive and negative results on its computational\ncomplexity and approximability.",
+                    "authors": "Jessica Enright, Kitty Meeks, George B. Mertzios, Viktor Zamaraev",
+                    "published": "2018-05-17",
+                    "updated": "2021-02-11",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.09039v1",
+                    "title": "Spatial-temporal Memories Enhanced Graph Autoencoder for Anomaly Detection in Dynamic Graphs",
+                    "abstract": "Anomaly detection in dynamic graphs presents a significant challenge due to\nthe temporal evolution of graph structures and attributes. The conventional\napproaches that tackle this problem typically employ an unsupervised learning\nframework, capturing normality patterns with exclusive normal data during\ntraining and identifying deviations as anomalies during testing. However, these\nmethods face critical drawbacks: they either only depend on proxy tasks for\ngeneral representation without directly pinpointing normal patterns, or they\nneglect to differentiate between spatial and temporal normality patterns,\nleading to diminished efficacy in anomaly detection. To address these\nchallenges, we introduce a novel Spatial-Temporal memories-enhanced graph\nautoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs)\nand gated temporal convolution layers to extract spatial features and temporal\nfeatures, respectively. Then STRIPE incorporates separate spatial and temporal\nmemory networks, which capture and store prototypes of normal patterns, thereby\npreserving the uniqueness of spatial and temporal normality. After that,\nthrough a mutual attention mechanism, these stored patterns are then retrieved\nand integrated with encoded graph embeddings. Finally, the integrated features\nare fed into the decoder to reconstruct the graph streams which serve as the\nproxy task for anomaly detection. This comprehensive approach not only\nminimizes reconstruction errors but also refines the model by emphasizing the\ncompactness and distinctiveness of the embeddings in relation to the nearest\nmemory prototypes. Through extensive testing, STRIPE has demonstrated a\nsuperior capability to discern anomalies by effectively leveraging the distinct\nspatial and temporal dynamics of dynamic graphs, significantly outperforming\nexisting methodologies, with an average improvement of 15.39% on AUC values.",
+                    "authors": "Jie Liu, Xuequn Shang, Xiaolin Han, Wentao Zhang, Hongzhi Yin",
+                    "published": "2024-03-14",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.07117v1",
+                    "title": "On inefficiently connecting temporal networks",
+                    "abstract": "A temporal graph can be represented by a graph with an edge labelling, such\nthat an edge is present in the network if and only if the edge is assigned the\ncorresponding time label. A journey is a labelled path in a temporal graph such\nthat labels on successive edges of the path are increasing, and if all vertices\nadmit journeys to all other vertices, the temporal graph is temporally\nconnected. A temporal spanner is a sublabelling of the temporal graph such that\ntemporal connectivity is maintained. The study of temporal spanners has raised\ninterest since the early 2000's. Essentially two types of studies have been\nconducted: the positive side where families of temporal graphs are shown to\n(deterministically or stochastically) admit sparse temporal spanners, and the\nnegative side where constructions of temporal graphs with no sparse spanners\nare of importance. Often such studies considered temporal graphs with happy or\nsimple labellings, which associate exactly one label per edge. In this paper,\nwe focus on the negative side and consider proper labellings, where multiple\nlabels per edge are allowed. More precisely, we aim to construct dense\ntemporally connected graphs such that all labels are necessary for temporal\nconnectivity. Our contributions are multiple: we present the first labellings\nmaximizing a local density measure; exact or asymptotically tight results for\nbasic graph families, which are then extended to larger graph families; an\nextension of an efficient temporal graph labelling generator; and overall\ndenser labellings than previous work even when restricted to happy labellings.",
+                    "authors": "Esteban Christiann, Eric Sanlaville, Jason Schoeters",
+                    "published": "2023-12-12",
+                    "updated": "2023-12-12",
+                    "primary_cat": "cs.CC",
+                    "cats": [
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.12587v1",
+                    "title": "TGLib: An Open-Source Library for Temporal Graph Analysis",
+                    "abstract": "We initiate an open-source library for the efficient analysis of temporal\ngraphs. We consider one of the standard models of dynamic networks in which\neach edge has a discrete timestamp and transition time. Recently there has been\na massive interest in analyzing such temporal graphs. Common computational data\nmining and analysis tasks include the computation of temporal distances,\ncentrality measures, and network statistics like topological overlap,\nburstiness, or temporal diameter. To fulfill the increasing demand for\nefficient and easy-to-use implementations of temporal graph algorithms, we\nintroduce the open-source library TGLib, which integrates efficient data\nstructures and algorithms for temporal graph analysis. TGLib is highly\nefficient and versatile, providing simple and convenient C++ and Python\ninterfaces, targeting computer scientists, practitioners, students, and the\n(temporal) network research community.",
+                    "authors": "Lutz Oettershagen, Petra Mutzel",
+                    "published": "2022-09-26",
+                    "updated": "2022-09-26",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.11074v1",
+                    "title": "On The Temporal Domain of Differential Equation Inspired Graph Neural Networks",
+                    "abstract": "Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling\ncomplex relationships in graph-structured data. A recent innovation in this\nfield is the family of Differential Equation-Inspired Graph Neural Networks\n(DE-GNNs), which leverage principles from continuous dynamical systems to model\ninformation flow on graphs with built-in properties such as feature smoothing\nor preservation. However, existing DE-GNNs rely on first or second-order\ntemporal dependencies. In this paper, we propose a neural extension to those\npre-defined temporal dependencies. We show that our model, called TDE-GNN, can\ncapture a wide range of temporal dynamics that go beyond typical first or\nsecond-order methods, and provide use cases where existing temporal models are\nchallenged. We demonstrate the benefit of learning the temporal dependencies\nusing our method rather than using pre-defined temporal dynamics on several\ngraph benchmarks.",
+                    "authors": "Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane Sch\u00f6nlieb",
+                    "published": "2024-01-20",
+                    "updated": "2024-01-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.12931v1",
+                    "title": "Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal forecasting has attracted tremendous attention in a wide\nrange of applications, and traffic flow prediction is a canonical and typical\nexample. The complex and long-range spatial-temporal correlations of traffic\nflow bring it to a most intractable challenge. Existing works typically utilize\nshallow graph convolution networks (GNNs) and temporal extracting modules to\nmodel spatial and temporal dependencies respectively. However, the\nrepresentation ability of such models is limited due to: (1) shallow GNNs are\nincapable to capture long-range spatial correlations, (2) only spatial\nconnections are considered and a mass of semantic connections are ignored,\nwhich are of great importance for a comprehensive understanding of traffic\nnetworks. To this end, we propose Spatial-Temporal Graph Ordinary Differential\nEquation Networks (STGODE). Specifically, we capture spatial-temporal dynamics\nthrough a tensor-based ordinary differential equation (ODE), as a result,\ndeeper networks can be constructed and spatial-temporal features are utilized\nsynchronously. To understand the network more comprehensively, semantical\nadjacency matrix is considered in our model, and a well-design temporal\ndialated convolution structure is used to capture long term temporal\ndependencies. We evaluate our model on multiple real-world traffic datasets and\nsuperior performance is achieved over state-of-the-art baselines.",
+                    "authors": "Zheng Fang, Qingqing Long, Guojie Song, Kunqing Xie",
+                    "published": "2021-06-24",
+                    "updated": "2021-06-24",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.15862v1",
+                    "title": "Restless Temporal Path Parameterized Above Lower Bounds",
+                    "abstract": "Reachability questions are one of the most fundamental algorithmic primitives\nin temporal graphs -- graphs whose edge set changes over discrete time steps. A\ncore problem here is the NP-hard Short Restless Temporal Path: given a temporal\ngraph $\\mathcal G$, two distinct vertices $s$ and $z$, and two numbers $\\delta$\nand $k$, is there a $\\delta$-restless temporal $s$-$z$ path of length at most\n$k$? A temporal path is a path whose edges appear in chronological order and a\ntemporal path is $\\delta$-restless if two consecutive path edges appear at most\n$\\delta$ time steps apart from each other. Among others, this problem has\napplications in neuroscience and epidemiology. While Short Restless Temporal\nPath is known to be computationally hard, e.g., it is NP-hard for only three\ntime steps and W[1]-hard when parameterized by the feedback vertex number of\nthe underlying graph, it is fixed-parameter tractable when parameterized by the\npath length $k$. We improve on this by showing that Short Restless Temporal\nPath can be solved in (randomized) $4^{k-d}|\\mathcal G|^{O(1)}$ time, where $d$\nis the minimum length of a temporal $s$-$z$ path.",
+                    "authors": "Philipp Zschoche",
+                    "published": "2022-03-29",
+                    "updated": "2022-03-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1811.08366v1",
+                    "title": "Temporal Graph Offset Reconstruction: Towards Temporally Robust Graph Representation Learning",
+                    "abstract": "Graphs are a commonly used construct for representing relationships between\nelements in complex high dimensional datasets. Many real-world phenomenon are\ndynamic in nature, meaning that any graph used to represent them is inherently\ntemporal. However, many of the machine learning models designed to capture\nknowledge about the structure of these graphs ignore this rich temporal\ninformation when creating representations of the graph. This results in models\nwhich do not perform well when used to make predictions about the future state\nof the graph -- especially when the delta between time stamps is not small. In\nthis work, we explore a novel training procedure and an associated unsupervised\nmodel which creates graph representations optimised to predict the future state\nof the graph. We make use of graph convolutional neural networks to encode the\ngraph into a latent representation, which we then use to train our temporal\noffset reconstruction method, inspired by auto-encoders, to predict a later\ntime point -- multiple time steps into the future. Using our method, we\ndemonstrate superior performance for the task of future link prediction\ncompared with none-temporal state-of-the-art baselines. We show our approach to\nbe capable of outperforming non-temporal baselines by 38% on a real world\ndataset.",
+                    "authors": "Stephen Bonner, John Brennan, Ibad Kureshi, Georgios Theodoropoulos, Andrew Stephen McGough, Boguslaw Obara",
+                    "published": "2018-11-20",
+                    "updated": "2018-11-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.14199v2",
+                    "title": "MTRGL:Effective Temporal Correlation Discerning through Multi-modal Temporal Relational Graph Learning",
+                    "abstract": "In this study, we explore the synergy of deep learning and financial market\napplications, focusing on pair trading. This market-neutral strategy is\nintegral to quantitative finance and is apt for advanced deep-learning\ntechniques. A pivotal challenge in pair trading is discerning temporal\ncorrelations among entities, necessitating the integration of diverse data\nmodalities. Addressing this, we introduce a novel framework, Multi-modal\nTemporal Relation Graph Learning (MTRGL). MTRGL combines time series data and\ndiscrete features into a temporal graph and employs a memory-based temporal\ngraph neural network. This approach reframes temporal correlation\nidentification as a temporal graph link prediction task, which has shown\nempirical success. Our experiments on real-world datasets confirm the superior\nperformance of MTRGL, emphasizing its promise in refining automated pair\ntrading strategies.",
+                    "authors": "Junwei Su, Shan Wu, Jinhui Li",
+                    "published": "2024-01-25",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "econ.GN",
+                        "q-fin.EC",
+                        "q-fin.TR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.07993v2",
+                    "title": "RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion",
+                    "abstract": "Temporal factors are tied to the growth of facts in realistic applications,\nsuch as the progress of diseases and the development of political situation,\ntherefore, research on Temporal Knowledge Graph (TKG) attracks much attention.\nIn TKG, relation patterns inherent with temporality are required to be studied\nfor representation learning and reasoning across temporal facts. However,\nexisting methods can hardly model temporal relation patterns, nor can capture\nthe intrinsic connections between relations when evolving over time, lacking of\ninterpretability. In this paper, we propose a novel temporal modeling method\nwhich represents temporal entities as Rotations in Quaternion Vector Space\n(RotateQVS) and relations as complex vectors in Hamilton's quaternion space. We\ndemonstrate our method can model key patterns of relations in TKG, such as\nsymmetry, asymmetry, inverse, and can further capture time-evolved relations by\ntheory. Empirically, we show that our method can boost the performance of link\nprediction tasks over four temporal knowledge graph benchmarks.",
+                    "authors": "Kai Chen, Ye Wang, Yitong Li, Aiping Li",
+                    "published": "2022-03-15",
+                    "updated": "2022-03-17",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2205.14269v1",
+                    "title": "Temporal graph patterns by timed automata",
+                    "abstract": "Temporal graphs represent graph evolution over time, and have been receiving\nconsiderable research attention. Work on expressing temporal graph patterns or\ndiscovering temporal motifs typically assumes relatively simple temporal\nconstraints, such as journeys or, more generally, existential constraints,\npossibly with finite delays. In this paper we propose to use timed automata to\nexpress temporal constraints, leading to a general and powerful notion of\ntemporal basic graph pattern (BGP). The new difficulty is the evaluation of the\ntemporal constraint on a large set of matchings. An important benefit of timed\nautomata is that they support an iterative state assignment, which can be\nuseful for early detection of matches and pruning of non-matches. We introduce\nalgorithms to retrieve all instances of a temporal BGP match in a graph, and\npresent results of an extensive experimental evaluation, demonstrating\ninteresting performance trade-offs. We show that an on-demand algorithm that\nprocesses total matchings incrementally over time is preferable when dealing\nwith cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and\nwhen connectivity of partial matchings can be guaranteed, the best performance\nis achieved by maintaining partial matchings over time and allowing automaton\nevaluation to be fully incremental.",
+                    "authors": "Amir Pouya Aghasadeghi, Jan Van den Bussche, Julia Stoyanovich",
+                    "published": "2022-05-27",
+                    "updated": "2022-05-27",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                }
+            ],
+            [
+                {
+                    "url": "http://arxiv.org/abs/2310.15722v1",
+                    "title": "Re-Temp: Relation-Aware Temporal Representation Learning for Temporal Knowledge Graph Completion",
+                    "abstract": "Temporal Knowledge Graph Completion (TKGC) under the extrapolation setting\naims to predict the missing entity from a fact in the future, posing a\nchallenge that aligns more closely with real-world prediction problems.\nExisting research mostly encodes entities and relations using sequential graph\nneural networks applied to recent snapshots. However, these approaches tend to\noverlook the ability to skip irrelevant snapshots according to entity-related\nrelations in the query and disregard the importance of explicit temporal\ninformation. To address this, we propose our model, Re-Temp (Relation-Aware\nTemporal Representation Learning), which leverages explicit temporal embedding\nas input and incorporates skip information flow after each timestamp to skip\nunnecessary information for prediction. Additionally, we introduce a two-phase\nforward propagation method to prevent information leakage. Through the\nevaluation on six TKGC (extrapolation) datasets, we demonstrate that our model\noutperforms all eight recent state-of-the-art models by a significant margin.",
+                    "authors": "Kunze Wang, Soyeon Caren Han, Josiah Poon",
+                    "published": "2023-10-24",
+                    "updated": "2023-10-24",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "label": "Original Paper",
+                    "paper_cat": "Temporal AND Graph",
+                    "gt": "KGC models normally adopt an encoder-decoder framework(Hamilton et al., 2017), where the encoder generates the embedding of entities and relations and the score function plays as a decoder. Most of the existing works extend the static KGC models into TKGC models by introducing temporal information. 2.1 TKGC(Interpolation) To integrate the temporal information in the decoder, TTransE(Jiang et al., 2016) extends TransE(Bordes et al., 2013) with the summation of an extra timestamp embedding, and ConT(Ma et al., 2019) extends Tucker(Bala\u017eevi\u00b4 c et al., 2019) by replacing the learnable weight with the timestamp embedding. Some methods also focus on combining temporal information in the encoder: TADistMult(Garcia-Duran et al., 2018) encodes the temporal information into relation embedding by using LSTM, while DE-SimplE(Goel et al., 2020) encodes a diachronic entity embedding with temporal information. with decoders as DistMult and 1Code available at: https://github.com/adlnlp/re-temp Table 1: Summary of TKGC(extrapolation) models and our proposed model. The column\u2018Temporal\u2019 presents the trend of the approach to how the temporal information is used, and the column \u2018Query\u2019 shows the summary of the approach to how the model utilises query. Method Core idea Temporal Query RE-NET(Jin et al., 2020) estimate the future graph distribution implicit N/A CyGNet(Zhu et al., 2021) identify facts with repetition explicit repetitive queries xERTE(Han et al., 2020) sample subgraph according to query implicit query-related subgraph REGCN(Li et al., 2021) relation-GCN + GRU implicit N/A TANGO(Han et al., 2021) neural ODE on continuous-time reasoning implicit N/A TITER(Sun et al., 2021) path-based reinforcement learning implicit query-related path CEN(Li et al., 2022a) ensemble model with different history lengths implicit N/A HiSMatch(Li et al., 2022b) two separated encoders for entity and query information implicit repetitive queries Re-Temp (Ours) skip irrelevant information according to entity-related relations both query-related skip information flow SimplE(Yang et al., 2015; Kazemi and Poole, 2018) accordingly. These models produced relatively lower performance on TKGC under the extrapolation setting tasks since they are unable to capture unseen temporal information. 2.2 TKGC(extrapolation) For the last few years, more attention has been paid to TKGC tasks under the extrapolation setting. GNNs are typically used as the encoder: RENET(Jin et al., 2020) applies sequential neighbourhood aggregators such as R-GCN(Schlichtkrull et al., 2018) to get the distribution of the target timestamp snapshot, REGCN(Li et al., 2021) adopts CompGCN(Vashishth et al., 2020) at each timestamp and GRU for sequential information. CEN(Li et al., 2022a) uses an ensemble model of sequential GNNs with different history lengths, TANGO(Han et al., 2021) solves Neural Ordinary Equations and makes it as the input of a MultiRelational GCN, and HiSMatch(Li et al., 2022b) builds two GNN encoders modelling the sequential candidate graph and query-related subgraphs separately and combines the representation from both sides into a matching function. Meanwhile, some methods do not follow the traditional encoder and decoder framework. xERTE(Han et al., 2020) extracts subgraph according to queries, CyGNet(Zhu et al., 2021) identifies the candidates with repetition, and TITer(Sun et al., 2021) uses reinforcement learning methods to search for the temporal evidence chain for prediction. To conclude, RE-NET, REGCN, and CEN adopt the entity evolvement information, while xERTE, CyGNet and TITer focus on the query. HiSMatch combines these two types of information with two separate encoders. However, none of the previous works encoded sequential and query-related information in one precise encoder. In addition to this, none of these methods considers explicit temporal information, except for CyGNet, which generates an independent timestamp vector but does not encode it into the entity or relation. Table 1 presents the summary of TKGC(extrapolation) models and emphasises the contribution of our proposed model.",
+                    "pre_questions": [],
+                    "main_content": "Introduction A Knowledge Graph (KG) is a graph-structure database, composed of facts represented by triplets in the form of (Subject Entity, Relation, Object Entity) such as (Alice, Is a Friend of, Bob). In this graph, entities serve as nodes, and relations are depicted as direct edges connecting the nodes. However, facts in a KG are not static but undergo continuous updates over time. To incorporate temporal information into the KG, Temporal Knowledge Graphs (TKGs) are introduced. TKGs add the extra temporal information of each fact and extend each triple with a timestamp as a quadruplet (Subject Entity, Relation, Object Entity, Timestamp). A TKG can be represented as a sequence of snapshots, \u2217Corresponding author. caren.han@sydney.edu.au Figure 1: A case study of temporal knowledge graph completion under the extrapolation setting where each snapshot represents a static knowledge graph for one specific timestamp. Temporal Knowledge Graph Completion (TKGC) aims to predict the missing entity from a query (Subject Entity, Relation, ?, Timestamp) or (?, Relation, Object Entity, Timestamp). TKGC is difficult and even large-scale pre-trained language models such as ChatGPT(OpenAI, 2022) are prone to making factual errors(Borji, 2023). There are two main settings: interpolation and extrapolation setting. TKGC under the interpolation setting completes the facts in history, while TKGC under the extrapolation setting predicts facts at future timestamps. In this paper, we focus on TKGC in the extrapolation setting, which is more challenging and requires further improvement(Jin et al., 2020). Enormous attention has been focused on static KGC problems, and numerous models have been employed to encode entities and relations. However, a key question remains: how can a static KGC model be extended to incorporate temporal inforarXiv:2310.15722v1  [cs.CL]  24 Oct 2023 mation for TKGC tasks? Recent works(Jin et al., 2020; Li et al., 2021, 2022a,b) have utilised sequential Graph Neural Networks (GNNs) to the previous snapshots for encoding the entities and relations. Then, they use a static score function as the decoder to assess the score of each candidate. Sequential GNNs are used because the facts shown in recent history can be helpful when making predictions in the future. An example is shown in Figure 1, the previous facts (Kim Jong-Un, criticize, United States) three days before and (Kim Jong-Un, Make Statement, Donald Trump) one day before may imply (Donald Trump, Threaten with administrative sanction, Kim Jong-Un) today. Since no explicit timestamp value is used, we can call it \u201cimplicit temporal information\u201d. However, to effectively encode the timestamp, the temporal information, two additional considerations arise: First, explicit temporal information is crucial. For instance, the validity score of (Donald Trump, Threaten with administrative sanction, Kim Jong-un) may differ between 2018 and 2023 as Donald Trump was the president in 2018 but not in 2023, affecting his ability to threaten another nation with administrative sanctions in 2023. The nature of entities can change over time, necessitating the consideration of explicit temporal information to encode time-dependent factors. Second, not all the facts in the recent history are relevant. Given historical facts (Kim Jong-un, criticize, United States, 2018-08-01),(Donald Trump, Make a visit, Switzerland, 2018-08-02) and (Kim Jong-un, Make Statement, Donald Trump, 2018-0803), when calculating the score of (Donald Trump, Threaten with administrative sanction, Kim Jongun, 2018-08-01), the second quadruplet visiting Switzerland does not contribute to the prediction of the relation between Donald Trump and Kim Jong-un since Switzerland is neutral. In such case, the model should find a way to skip the irrelevant snapshots based on the entity-related relation in the query. Therefore, an optimal TKGC model should consider (1) explicit temporal information and (2) implicit temporal information with skipping irrelevant snapshots by considering the query. In this paper, we propose Re-Temp, an innovative TKGC model designed for extrapolation settings that incorporates relation-aware temporal representation learning. The encoder of Re-Temp utilises explicit temporal embedding for each entity, combining static and dynamic embedding. Within the encoder, a sequential GNN is employed to capture the implicit temporal information with a skip information flow applied after each timestamp, taking into account the entity-related relation in the query. The main contributions of this paper can be summarised as follows: \u2022 We introduce Re-Temp, a precise TKGC model that leverages both explicit and implicit temporal information, incorporates a relationaware skip information flow to exclude irrelevant information and adopts a two-phase forward propagation method to prevent information leakage1. \u2022 We compare our Re-Temp against eight stateof-the-art baseline models from recent years using six publicly available TKGC datasets under the extrapolation setting. Our experimental results demonstrate that Re-Temp outperforms all of the baselines significantly. \u2022 We conduct a detailed case study and statistical analysis to illustrate the distinct characteristics of each dataset and provide an explanation based on our experimental findings. The overall architecture of Re-Temp can be found in Figure 2. Section 3.1 describes the notations of a TKGC task. The input of the model is represented by a combination of static and dynamic entity embedding, in Section 3.2, showing explicit temporal information. The encoder in Section 3.3 uses a sequential multi-relational GNN to learn implicit temporal information and after each timestamp, a relation-aware skip information flow mechanism is applied to retain the necessary information for prediction. The ConvTransE decoder together with the loss function is introduced in Section 3.4. To avoid information leaking, we apply a two-phase forward propagation method in Section 3.5. 3.1 Problem Formulation To denote the set of entities, relations, timestamps and facts, E, R, T and F are selected. A temporal knowledge graph G can be treated as |T | sequential snapshots, G = {G0, G1, ..., GT }, where Gt = {E, R, Ft} is a directed multi-relational graph at timestamp t. For each fact, a quadruplet is represented as (es, r, eo, t), where es, eo \u2208E are the subject and object entities, r \u2208R represents the relation and t \u2208T is the timestamp. The target of the temporal knowledge graph completion under the extrapolation setting is that for a query q, predicting (es, r, ?, tq) or (?, r, eo, tq) given previous snapshots {G0, G1, ..., Gtq\u22121}. Normally, the inverse of each quadruplet is added to the dataset, making all subject entity prediction probFigure 2: Illustration of Encoding and Decoding process in Re-Temp with history length as 3. For a query q, the input vector is heq tq\u22123. The encoder with relation-aware skip information flow learns the entity and relation representation heq tq and hrq. Then the decoder measures the score of all the candidates. lem (?, r, eo, tq) into object entity prediction problem (eo, r\u22121, ?, tq). 3.2 Explicit Temporal Representation For sequential snapshots with length k, let heq tq\u2212k \u2208 R1\u00d7d denotes the input embedding of the subject entity eq from query q, and d is the dimension of the input. In order to encode the explicit temporal information, we concatenated two kinds of input embedding; static and dynamic embedding. The static embedding reveals the nature of an entity that does not change through time, while the dynamic part reveals the time-dependent information. Inspired by ATiSE(Xu et al., 2020), the dynamic embedding is decomposed into the trend component and seasonal component, and the trend component can be represented as a linear transformation on t while the seasonal component should be a periodical function of t. Thus, we model the dynamic temporal embedding at timestamp t by the summation of trend embedding weq,0t and seasonal embedding sin(2\u03c0weq,1t). After concatenation with the static embedding, a feed-forward layer is applied. Formally, the input of the encoder heq tq\u2212k is derived by: heq,S tq\u2212k = heq,S (1) heq,D tq\u2212k = weq,0(tq\u2212k)+sin(2\u03c0weq,1(tq\u2212k)) (2) heq tq\u2212k = Wtmp(heq,S tq\u2212k \u2295heq,D tq\u2212k) (3) where heq,S tq\u2212k in Equation 1 and heq,D tq\u2212k in Equation 2 denote the static and dynamic embedding for subject entity eq at timestamp tq \u2212k, \u2295denotes the concatenation, and heq,s, weq,0, weq,1, Wtmp are learnable parameters. The major difference between our explicit temporal representation and ATiSE lies in the fact that employing a learnable feed-forward layer to concatenate the dynamic embedding and static embedding, enables the model to determine the extent to which it should utilise information from each embedding rather than simply utilising both. Relation embedding hr can simply be extracted from a static embedding lookup table since we do not expect the relation\u2019s nature to evolve through time. 3.3 Relation-Aware Skip Information Flow In order to handle implicit temporal information, we use a sequential GNN-based encoder with a new relation-aware skip information flow mechanism. Following recent work(Li et al., 2021, 2022a,b), we adopt a variant of CompGCN(Vashishth et al., 2020) at each timestamp to model the multirelational snapshot, outputting the entity embedding he and the relation embedding hr. The details of CompGCN are shown in Appendix A.1. Not all snapshots in the recent history are useful in predicting query q, hence, a relation-aware skip information flow is applied. Two things are considered: (1) Skip connection is used for filtering out the unnecessary information from each timestamp. (2) Relation-aware attention mechanism helps to determine whether some information should be filtered. Thus, after getting the output of CompGCN, they will be weighted-summed up with previous timestamps input to partially skip the irrelevant snapshots. The weights of the weighted sum are calculated by considering both the entity and the entity-related relation in the query. Formally, for an entity eq, the relation associated with eq should be considered. To capture the entity-related relation information, mean pooling is applied on all relation embedding associated with eq at timestamp tq. The representation obtained Table 2: Statistics Details of Benchmark Dataset ICEWS14 ICEWS18 ICEWS05-15 ICEWS14* GDELT WIKI # Entities 7,128 23,033 10,094 7,128 7,691 12,554 # Relations 230 256 251 230 240 24 # Facts 89,730 468,558 461,329 90,730 2,277,405 669,934 # Snapshots 365 304 4,017 365 2,976 232 # Snapshots in Train/Val/Test set 304/30/31 240/30/34 3,243/404/370 262/52/51 2,304/288/384 211/11/10 # Facts per Snapshot 245.8 1541.3 32.2 248.6 765.3 2887.6 Time Interval 1 day 1 day 1 day 1 day 15 mins 1 year Total Time Range 1 year 0.83 years 11 years 1 year 0.54 years 232 years from mean pooling will serve as a reference vector to help the model determine the information to keep or skip. Then, this average relation embedding will be summed with all m previous timestamps one by one, followed by a feedforward layer. This calculation can also be treated as additive attention. After getting the attention weights \u03b2eq j , the weighted sum using these attention weights is applied on the current CompGCN output heq,L ti and all m previous timestamp inputs. The detailed calculation shows as follows: heq r,tq = 1 |Req tq | X r\u2208R eq tq hr (4) attneq j = ( 0 j = 0 Wa(heq ti\u2212j + heq r,tq) j \u2208[1, m] (5) \u03b2eq j = softmax(attneq j ), j \u2208[0, m] (6) heq ti+1 = \u03b2eq 0 heq,L ti + m X j=1 \u03b2eq j heq ti\u2212j (7) Note that the output of each timestamp is also the input of the next timestamp. Equation 4 shows the entity-associated relation embedding and Req tq denotes the relation set which connects with entity eq at timestamp tq. Equation 5 and 6 denotes the attention score and weight calculation where Wa is learnable. By applying the relation-aware skip information flow, our model is capable of skipping irrelevant snapshots by considering the target query relations. 3.4 Decoder ConvTransE(Shang et al., 2019) is widely used in both static KGC(Malaviya et al., 2020) and TKGC(Li et al., 2022b) as the score function, and ours is no exception. After getting the score of each candidate using ConvTransE, we train the model as a classification problem and the loss function for each query shows as follows: L = \u2212 X ec\u2208E zclog(s(eq, rq, ec, tq)) (8) and zc will be 1 if correctly classified, otherwise, it is 0. The training target is to minimise the total loss for all queries. Appendix A.2 introduces the details of ConvTransE. 3.5 Two-Phase Propagation There is a potential information leakage problem by applying the relation-aware information flow mechanism. Suppose a query in the test set is (A, r, B, t), after adding the inverse of quadruplets, (B, r\u22121, A, t) will be in the test set. When applying the encoder, with the relation-aware skip information flow, A and B will contain the information of r and r\u22121 accordingly. Therefore, when making predictions on (A, r, ?, t) and calculating the score by dot product A and all candidates, there is a chance that the information of r in A can meet the information of r\u22121 in B. Since r and r\u22121 are paired, the model might find a shortcut to determine B is the right answer for (A, r, ?, t). This information leakage will result in unreasonably high performance during evaluation. To avoid such information leakage, we propose a two-phase forward propagation method. We divide the dataset into two subsets: the original set and the inverse set. The inverse set is the set of inverse quadruplets. The snapshot graph in the history will be built on the whole set, while during forward propagation, the original set and inverse set are used separately. The output of the original set and the inverse set will be collected for loss calculation or performance evaluation. 4 Experiments 4.1 Experiment Setup Datasets We evaluated our model on six widelyused TKG datasets: ICEWS14(Li et al., 2021), ICEWS18(Jin et al., 2020), ICEWS05-15(Han et al., 2020), ICEWS14*(Han et al., 2020), GDELT(Jin et al., 2020), and WIKI(Leblay and Chekol, 2018). The overall statistics of each dataset are presented in Table 2. All datasets are split into the Training, Validation and Test sets in chronological order. For example, the timestamps in ICEWS14 are from 1st to 304th, from 305th to 334th and from 335th to 365th for training, validation and test set accordingly. \u2022 ICEWS14, ICEWS18, ICEWS05-15, ICEWS14* are extracted from Integrated Crisis Early Warning System which is a database system recording political events. 14, 18, 05-15 represent the year of the dataset(2014, 2018, 2005-2015), and ICEWS14* uses a different split compared with ICEWS14. The time interval of ICEWS is 1 day. A sample from ICEWS datasets is (John_Kerry, Host_a_visit, Benjamin_Netanyahu, 2014-0101) \u2022 GDELT is also a political event temporal knowledge graph dataset from the Global Database of Events, Language, and Tone(Leetaru and Schrodt). Compared with ICEWS datasets, its time interval is only 15 minutes and GDELT is collected from a wider variety of sources. (Minist, Return, Nigeria, 0) is a sample in GDELT. \u2022 WIKI is from Wikidata, an open knowledge base and not limited to political events. The temporal representation in the facts from Wikidata is not a single date/year but a range. For example, the fact (Wang Shu, educated at, Southeast University) is valid from 1981 to 1988. To represent a such range, WIKI generates eight quadruplets across eight snapshots during 1981-1988. All the datasets are consistent with their intended use. Baselines Our Re-Temp is compared with TKGC models under the extrapolation setting. Eight models from recent years are selected as baselines: RE-NET(Jin et al., 2020), RE-GCN(Li et al., 2021), CyGNet(Zhu et al., 2021), xERTE(Han et al., 2020), TITer(Sun et al., 2021), TANGO(Han et al., 2021), CEN(Li et al., 2022a), and HiSMatch(Li et al., 2022b). Models that are designed for static KG completion or TKGC under the interpolation setting tasks are not compared since they naturally perform badly in TKGC under the extrapolation setting tasks. Hyperparameter Following the previous works(Li et al., 2022a,b), the dimension of the input is set to 200, which is also the hidden dimension of the graph model and decoder hidden dimension. The number of graph neural network layers is 2 and the dropout rate is set to 0.2. Adam(Kingma and Ba, 2015) with a learning rate of 1e-3 is used for optimisation. The model is trained on the training set with a maximum of 30 epochs and we stop training when the validation performance doesn\u2019t improve in 5 consecutive epochs. Then, the test set is evaluated using the trained model. Evaluation Metrics Following the previous works(Han et al., 2020; Zhu et al., 2021; Li et al., 2022b), we employ widely used evaluation metrics, Mean Reciprocal Rank(MRR), hits@1, hits@3, and hits@10, which is explained in Appendix B.2. We adopt the way of filtering out the quadruplets occurring at the query time, followed by Sun et al. (2021); Han et al. (2021), and we report the fivetimes running average result. 4.2 Performance Comparison We use a history length of 3 for ICES14, ICEWS18, ICEWS05-15, ICEWS14* and GDELT, while 1 for WIKI. The influence of history length is discussed in Section 4.3. Table 3 presents the performance comparison of all baseline models. Our model, Re-Temp, outperforms significantly almost all the baseline models on all datasets, indicating the superiority of our Re-Temp model. In detail, three points can be observed: Firstly, HiSMatch(Li et al., 2022b) achieved the second-highest performance on most of the datasets by considering both the query subgraph and entity subgraph. The concept considering both query and entity of HiSMatch is similar to our relationaware attention mechanism in the skip information flow. However, HiSMatch only builds the query subgraph using the exact same relation of the query, which ignores the potential similarity between relations. For example, in ICEWS14, when making a prediction on (A, provide_aid, ?, tq), relation \u2018provide_aid\u2019 and \u2018provide_military_aid\u2019 share similarities, but HisMatch only considers the entity with \u2018provide_military_aid\u2019 in the recent history while our method uses the embedding of relation Table 3: Performance(%) with Baseline models. The highest value is bold and the second highest is underlined. Model ICEWS14 ICEWS18 ICEWS05-15 MRR hits@1 hits@3 hits@10 MRR hits@1 hits@3 hits@10 MRR hits@1 hits@3 hits@10 RE-NET(Jin et al., 2020) 37.01 27.02 39.66 54.85 29.02 20.03 33.14 48.60 44.03 34.43 49.03 64.03 CyGNet(Zhu et al., 2021) 35.02 25.72 39.06 53.50 25.03 16.03 29.28 43.42 37.03 27.01 42.23 56.98 xERTE(Han et al., 2020) 40.12 32.11 44.73 56.25 29.31 21.03 33.51 46.48 46.62 37.84 52.31 63.92 REGCN(Li et al., 2021) 41.50 30.86 46.60 62.47 30.55 20.00 34.73 51.46 46.41 35.17 52.76 67.64 TANGO(Han et al., 2021) 30.12 23.03 35.48 52.32 28.97 19.51 32.61 47.51 42.86 32.72 48.14 62.34 TITer(Sun et al., 2021) 41.73 32.74 46.46 58.44 29.96 22.06 33.41 44.92 47.78 38.05 53.11 65.93 CEN(Li et al., 2022a) 42.20 32.08 47.46 61.31 31.50 21.70 35.44 50.59 45.97 35.56 51.45 66.14 HiSMatch(Li et al., 2022b) 46.42 35.91 51.63 66.84 33.99 23.91 37.90 53.94 52.85 42.01 59.05 73.28 Re-Temp (Ours) 48.04 37.32 53.60 68.90 35.82 25.02 40.36 57.30 56.30 45.49 62.80 77.17 Model ICEWS14* GDELT WIKI MRR hits@1 hits@3 hits@10 MRR hits@1 hits@3 hits@10 MRR hits@1 hits@3 hits@10 RE-NET(Jin et al., 2020) 38.28 28.68 41.43 54.52 19.63 12.39 21.03 34.02 49.66 46.98 51.23 53.49 CyGNet(Zhu et al., 2021) 33.13 24.16 37.02 51.23 18.98 12.32 20.56 33.89 43.78 39.02 46.12 51.92 xERTE(Han et al., 2020) 40.77 32.65 45.71 57.29 18.07 12.31 20.05 30.32 71.16 68.03 76.15 78.99 REGCN(Li et al., 2021) 41.79 31.55 46.67 61.53 19.31 11.99 20.61 33.59 77.58 73.72 80.39 83.69 TANGO(Han et al., 2021) 26.35 17.33 29.27 44.32 18.03 12.36 19.96 29.31 51.15 49.65 52.26 53.44 TITer(Sun et al., 2021) 41.76 32.69 46.35 58.46 17.02 11.23 19.81 26.92 75.51 72.98 77.51 79.32 CEN(Li et al., 2022a) 40.78 31.26 45.26 59.16 19.89 12.61 21.16 34.09 77.65 73.86 80.69 84.00 HiSMatch(Li et al., 2022b) 45.82 35.84 50.79 65.08 22.01 14.45 23.80 36.61 78.07 73.89 81.32 84.65 Re-Temp (Ours) 46.40 35.86 51.69 67.12 25.05 15.70 27.14 44.16 78.51 74.80 81.33 84.50 Table 4: Cases from WIKI Dataset about Lionel Messi from Year 2003 to Year 2005. Subject Entity Relation Object Entity Year Lionel Messi residence Barcelona 2003 Lionel Messi member of sports team FC Barcelona C 2003 Lionel Messi residence Barcelona 2004 Lionel Messi member of sports team FC Barcelona C 2004 Lionel Messi member of sports team FC Barcelona Atl\u00e8tic 2004 Lionel Messi residence Barcelona 2005 Lionel Messi member of sports team Argentina national football team 2005 to calculate the attention weights, making it general for different types of relations that are close in the embedding space and outperforming HiSMatch. Meanwhile, HiSMatch builds two separate encoders and fuses the output for the decoder while our model only applies one encoder for better information alignment. Secondly, among four ICEWS datasets, our model achieves more improvement on ICEWS0515. As shown in Table 2, the snapshots in ICEWS05-15 are sparser than others, showing the ability of our model to learn sequential information with less data. Thirdly, our model only achieves a comparable performance with HiSMatch on WIKI, which might result from the nature of this dataset. Table 4 lists some cases of facts about Lionel Messi in WIKI. Suppose giving the quadruplets from 2003 and 2004, it is relatively easy to predict (Lionel Messi, residence, ?, 2005) based on his previous residence, however, it is almost impossible to have Figure 3: MRR(%) change of Re-Temp with the history lengths. The x-axis is the history length and the y-axis is the MRR(%) change compared with history length 3. a correct prediction on (Lionel Messi, residence, ? , 2005) since the previous snapshots don\u2019t provide enough information on Argentina national football team. This is an issue in WIKI: the predictions are either too easy (using the previous facts), or too difficult (even humans can not make a correct prediction without any external knowledge). Thus, a relatively better model is not enough to generate an undoubtful better performance on WIKI, and our model and some previous baseline models (CEN, HiSMatch) share similar results on this dataset. 4.3 Impact of history length To study the impact of history length on different datasets, experiments with different history lengths are conducted. The default value of history length is 3 and the MRR changes in percentage are shown Table 5: The MRR(%) result of the ablation test of Re-Temp. The highest value is bold. Model ICEWS14 ICEWS18 ICEWS05-15 ICEWS14* GDELT WIKI Re-Temp 48.04 35.82 56.30 46.40 25.05 78.51 dynamic 47.52 35.33 55.12 45.89 24.85 76.04 relation_aware 39.93 30.56 44.95 38.75 19.92 78.14 skip 36.56 28.07 43.80 36.30 18.61 79.60 Figure 4: Proportion(%) of quadruplets shown in exact one timestamp before for each dataset. The x-axis is the name of the dataset and the y-axis is the proportion(%). in Figure 3 with history lengths from 1 to 5. Two major points can be noticed: (1) On most of the datasets (ICEWS14, ICEWS18, ICEWS05-15, ICEWS14*, and GDELT), a larger history length results in a higher MRR. Where the history length is small, enlarging the history length can substantially enhance performance. However, when the history length surpasses three, the degree of improvement becomes marginal. This aligns with the expectations that the recent several snapshots can help with inference, while in a long history, the irrelevant information does not contribute to the performance. By considering the model performance and calculation complexity, history length = 3 is selected as the final model for these datasets. (2) An exception occurs on WIKI, where the model achieves the best performance when history length = 1. To investigate the factors, a detailed statistical analysis of the datasets is conducted. Table 4 in Section 4.2 shows some sample queries in WIKI, where some facts are the same as the facts at previous timestamps, the reason lies in that for a fact (s,r,o,t1 tn), WIKI generates the same quadruplets across the time range from t1 to tn. Figure 4 shows the proportion of the quadruplets at tq shown in the previous timestamp tq \u22121 for all timestamps in the test set on each dataset. 85.68% samples in the WIKI show in the one timestamp before, while fewer than 15% samples in ICEWS14, ICEWS18, ICEWS05-15, ICEWS14*, GDELT are from the previous timestamp. The same quadruplets shown across different timestamps in WIKI result in similar snapshots(graphs) at different timestamps. When a larger history length is applied, multiple graph neural network models applied on multiple similar graphs will be approximated to applying a multiple layers GNN model on one graph, which leads to the over-smoothing issue in a deep GNN(Li et al., 2018). Therefore, a large history length may decrease model performance on WIKI. 4.4 Ablation Study Table 5 presents the ablation study of different components of our model. Impact of explicit temporal embedding To evaluate the efficiency of the explicit temporal representation, we remove the dynamic embedding from the explicit temporal input, resulting in only the static embedding of each entity left. For all six benchmark datasets, removing dynamic embedding leads to worse performance. Compared with the performance drop in ICEWS14, ICEWS18, ICEWS14* and GDELT, it is clear that the MRR decreases more in WIKI and ICEWS05-15. The reason is that the total time range in these two datasets is large (232 years and 11 years), and the entity information can evolve over a long period, which can be captured by explicit temporal embedding. Impact of relation-aware skip information flow To demonstrate how the relation-aware skip information flow contributes to the model performance, two ablation tests are conducted. (1)\u2018relation_aware\u2019 means that when calculating the attention score in skip information flow, the entityrelated relation is omitted, formally, the attention score is Equation 5 is changed to:attneq j = Wa(heq ti\u2212j), j \u2208[1, m]. (2)\u2018-skip\u2019 means removing the whole skip information flow, making the input of each timestamp the last timestamp the output: heq ti+1 = heq,L ti . The model performance drops heavily if no relation-aware attention mechanism is applied, Table 6: MRR(%) of our model with different ensemble methods. The highest value is bold. Ensemble Model ICEWS14 ICEWS18 ICEWS05-15 ICEWS14* GDELT Re-Temp 48.04 35.82 56.30 46.40 25.05 Ensemble (avg pooling) 48.58 36.16 56.72 46.56 25.04 Ensemble (max pooling) 48.69 36.38 56.69 47.06 25.06 Ensemble (min pooling) 47.55 35.72 55.58 46.23 25.03 showing the vital importance of the relation-aware attention mechanism. We can conclude that the entity-related relation information actually helps the model to select necessary information. In most cases, removing the skip connection worsens the model performance compared with only removing the relation-aware attention mechanism. Compared with \u2018-relation_aware\u2019 setting, the models under the \u2018-skip\u2019 setting learn from all the recent snapshots for prediction, leading to the involvement of irrelevant information during prediction. However, WIKI shows better performance under this setting, even compared with our original ReTemp model. The reason might be the same as that discussed in Section 4.3: More than 80% of facts in the WIKI show in the previous timestamp, and a graph model applied on the previous timestamp can easily capture that repetitive information for prediction. 4.5 Ensemble Modelling Evaluation CEN(Li et al., 2022a) builds an ensemble model with different history lengths. Inspired by this, we test our model under an ensemble setting. For a model with a history length of k, suppose the score vector of all candidates for query q is sq k, a pooling method is applied on {sq 1, sq 2, ..., sq k} to get the final score. Three different pooling methods are applied. Table 6 shows the MRR(%) results of our model under the ensemble setting. We applied the history lengths from one (1), and the maximum history length is set to three (3) as previously defined. We did not include the experiments on WIKI since the optimal history length is one (1), and no models with smaller history lengths can be used. First of all, our model can benefit under the ensemble setting on four of the datasets (ICEWS14, ICEWS18, ICEWS05-15, ICEWS14*), but only achieve similar performance on GDELT compared with the original Re-Temp model (25.05%). Considering the history length influence shown in Figure 3, the model achieves similar results with different history lengths. Therefore, models with different history lengths on GDELT might be similar making the ensemble models less effective. However, ICEWS datasets are history-length sensitive, and ensemble models can benefit from different models of different history lengths. In addition to this, max pooling usually achieves the best performance as the ensemble method while min pooling will worsen the performance. 5 Conclusion We introduced Re-Temp, which integrates both explicit and implicit temporal information and applies a relation-aware skip information flow to adopt after each timestamp to remove unnecessary information for prediction by taking the entity-related relation in the query into consideration. The experimental results on six TKGC datasets present the superiority of our model, compared with eight baseline models. We also conduct a statistical analysis of the datasets to show the different nature between WIKI and other datasets. It is hoped that Re-temp presents insight into the importance of the relation in the query and both types of temporal information. 6 Limitations Re-Temp still follows Knowledge Graph Completion encoder-decoder framework(Hamilton et al., 2017) while more frameworks can be explored. The graph model at each timestamp and the decoder score function follow the same methods widely used by other models. Since we have shown that the explicit temporal embedding and the skip information flow contribute to model performance, more work can be done by combining these concepts into the graph model and score function, for example, combining the entity-related relation into the graph model at each timestamp to selectively propagate between nodes, or combining the explicit temporal embedding into the decoder score function. Also, like most TKGC models, Re-Temp can not handle new entities that do not show in the training data. More methods integrating the text description can be explored(Lv et al., 2022)."
+                },
+                {
+                    "url": "http://arxiv.org/abs/1807.00228v2",
+                    "title": "Embedding Models for Episodic Knowledge Graphs",
+                    "abstract": "In recent years a number of large-scale triple-oriented knowledge graphs have\nbeen generated and various models have been proposed to perform learning in\nthose graphs. Most knowledge graphs are static and reflect the world in its\ncurrent state. In reality, of course, the state of the world is changing: a\nhealthy person becomes diagnosed with a disease and a new president is\ninaugurated. In this paper, we extend models for static knowledge graphs to\ntemporal knowledge graphs. This enables us to store episodic data and to\ngeneralize to new facts (inductive learning). We generalize leading learning\nmodels for static knowledge graphs (i.e., Tucker, RESCAL, HolE, ComplEx,\nDistMult) to temporal knowledge graphs. In particular, we introduce a new\ntensor model, ConT, with superior generalization performance. The performances\nof all proposed models are analyzed on two different datasets: the Global\nDatabase of Events, Language, and Tone (GDELT) and the database for Integrated\nConflict Early Warning System (ICEWS). We argue that temporal knowledge graph\nembeddings might be models also for cognitive episodic memory (facts we\nremember and can recollect) and that a semantic memory (current facts we know)\ncan be generated from episodic memory by a marginalization operation. We\nvalidate this episodic-to-semantic projection hypothesis with the ICEWS\ndataset.",
+                    "authors": "Yunpu Ma, Volker Tresp, Erik Daxberger",
+                    "published": "2018-06-30",
+                    "updated": "2018-12-03",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.IR",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1809.03202v1",
+                    "title": "Learning Sequence Encoders for Temporal Knowledge Graph Completion",
+                    "abstract": "Research on link prediction in knowledge graphs has mainly focused on static\nmulti-relational data. In this work we consider temporal knowledge graphs where\nrelations between entities may only hold for a time interval or a specific\npoint in time. In line with previous work on static knowledge graphs, we\npropose to address this problem by learning latent entity and relation type\nrepresentations. To incorporate temporal information, we utilize recurrent\nneural networks to learn time-aware representations of relation types which can\nbe used in conjunction with existing latent factorization methods. The proposed\napproach is shown to be robust to common challenges in real-world KGs: the\nsparsity and heterogeneity of temporal expressions. Experiments show the\nbenefits of our approach on four temporal KGs. The data sets are available\nunder a permissive BSD-3 license 1.",
+                    "authors": "Alberto Garc\u00eda-Dur\u00e1n, Sebastijan Duman\u010di\u0107, Mathias Niepert",
+                    "published": "2018-09-10",
+                    "updated": "2018-09-10",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2210.09708v1",
+                    "title": "HiSMatch: Historical Structure Matching based Temporal Knowledge Graph Reasoning",
+                    "abstract": "A Temporal Knowledge Graph (TKG) is a sequence of KGs with respective\ntimestamps, which adopts quadruples in the form of (\\emph{subject},\n\\emph{relation}, \\emph{object}, \\emph{timestamp}) to describe dynamic facts.\nTKG reasoning has facilitated many real-world applications via answering such\nqueries as (\\emph{query entity}, \\emph{query relation}, \\emph{?}, \\emph{future\ntimestamp}) about future. This is actually a matching task between a query and\ncandidate entities based on their historical structures, which reflect\nbehavioral trends of the entities at different timestamps. In addition, recent\nKGs provide background knowledge of all the entities, which is also helpful for\nthe matching. Thus, in this paper, we propose the \\textbf{Hi}storical\n\\textbf{S}tructure \\textbf{Match}ing (\\textbf{HiSMatch}) model. It applies two\nstructure encoders to capture the semantic information contained in the\nhistorical structures of the query and candidate entities. Besides, it adopts\nanother encoder to integrate the background knowledge into the model. TKG\nreasoning experiments on six benchmark datasets demonstrate the significant\nimprovement of the proposed HiSMatch model, with up to 5.6\\% performance\nimprovement in MRR, compared to the state-of-the-art baselines.",
+                    "authors": "Zixuan Li, Zhongni Hou, Saiping Guan, Xiaolong Jin, Weihua Peng, Long Bai, Yajuan Lyu, Wei Li, Jiafeng Guo, Xueqi Cheng",
+                    "published": "2022-10-18",
+                    "updated": "2022-10-18",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2109.04101v1",
+                    "title": "TimeTraveler: Reinforcement Learning for Temporal Knowledge Graph Forecasting",
+                    "abstract": "Temporal knowledge graph (TKG) reasoning is a crucial task that has gained\nincreasing research interest in recent years. Most existing methods focus on\nreasoning at past timestamps to complete the missing facts, and there are only\na few works of reasoning on known TKGs to forecast future facts. Compared with\nthe completion task, the forecasting task is more difficult that faces two main\nchallenges: (1) how to effectively model the time information to handle future\ntimestamps? (2) how to make inductive inference to handle previously unseen\nentities that emerge over time? To address these challenges, we propose the\nfirst reinforcement learning method for forecasting. Specifically, the agent\ntravels on historical knowledge graph snapshots to search for the answer. Our\nmethod defines a relative time encoding function to capture the timespan\ninformation, and we design a novel time-shaped reward based on Dirichlet\ndistribution to guide the model learning. Furthermore, we propose a novel\nrepresentation method for unseen entities to improve the inductive inference\nability of the model. We evaluate our method for this link prediction task at\nfuture timestamps. Extensive experiments on four benchmark datasets demonstrate\nsubstantial performance improvement meanwhile with higher explainability, less\ncalculation, and fewer parameters when compared with existing state-of-the-art\nmethods.",
+                    "authors": "Haohai Sun, Jialun Zhong, Yunpu Ma, Zhen Han, Kun He",
+                    "published": "2021-09-09",
+                    "updated": "2021-09-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.06103v4",
+                    "title": "Modeling Relational Data with Graph Convolutional Networks",
+                    "abstract": "Knowledge graphs enable a wide variety of applications, including question\nanswering and information retrieval. Despite the great effort invested in their\ncreation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata)\nremain incomplete. We introduce Relational Graph Convolutional Networks\n(R-GCNs) and apply them to two standard knowledge base completion tasks: Link\nprediction (recovery of missing facts, i.e. subject-predicate-object triples)\nand entity classification (recovery of missing entity attributes). R-GCNs are\nrelated to a recent class of neural networks operating on graphs, and are\ndeveloped specifically to deal with the highly multi-relational data\ncharacteristic of realistic knowledge bases. We demonstrate the effectiveness\nof R-GCNs as a stand-alone model for entity classification. We further show\nthat factorization models for link prediction such as DistMult can be\nsignificantly improved by enriching them with an encoder model to accumulate\nevidence over multiple inference steps in the relational graph, demonstrating a\nlarge improvement of 29.8% on FB15k-237 over a decoder-only baseline.",
+                    "authors": "Michael Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, Max Welling",
+                    "published": "2017-03-17",
+                    "updated": "2017-10-26",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.AI",
+                        "cs.DB",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08492v2",
+                    "title": "Learning from History: Modeling Temporal Knowledge Graphs with Sequential Copy-Generation Networks",
+                    "abstract": "Large knowledge graphs often grow to store temporal facts that model the\ndynamic relations or interactions of entities along the timeline. Since such\ntemporal knowledge graphs often suffer from incompleteness, it is important to\ndevelop time-aware representation learning models that help to infer the\nmissing temporal facts. While the temporal facts are typically evolving, it is\nobserved that many facts often show a repeated pattern along the timeline, such\nas economic crises and diplomatic activities. This observation indicates that a\nmodel could potentially learn much from the known facts appeared in history. To\nthis end, we propose a new representation learning model for temporal knowledge\ngraphs, namely CyGNet, based on a novel timeaware copy-generation mechanism.\nCyGNet is not only able to predict future facts from the whole entity\nvocabulary, but also capable of identifying facts with repetition and\naccordingly predicting such future facts with reference to the known facts in\nthe past. We evaluate the proposed method on the knowledge graph completion\ntask using five benchmark datasets. Extensive experiments demonstrate the\neffectiveness of CyGNet for predicting future facts with repetition as well as\nde novo fact prediction.",
+                    "authors": "Cunchao Zhu, Muhao Chen, Changjun Fan, Guangquan Cheng, Yan Zhan",
+                    "published": "2020-12-15",
+                    "updated": "2021-03-05",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1911.03082v2",
+                    "title": "Composition-based Multi-Relational Graph Convolutional Networks",
+                    "abstract": "Graph Convolutional Networks (GCNs) have recently been shown to be quite\nsuccessful in modeling graph-structured data. However, the primary focus has\nbeen on handling simple undirected graphs. Multi-relational graphs are a more\ngeneral and prevalent form of graphs where each edge has a label and direction\nassociated with it. Most of the existing approaches to handle such graphs\nsuffer from over-parameterization and are restricted to learning\nrepresentations of nodes only. In this paper, we propose CompGCN, a novel Graph\nConvolutional framework which jointly embeds both nodes and relations in a\nrelational graph. CompGCN leverages a variety of entity-relation composition\noperations from Knowledge Graph Embedding techniques and scales with the number\nof relations. It also generalizes several of the existing multi-relational GCN\nmethods. We evaluate our proposed method on multiple tasks such as node\nclassification, link prediction, and graph classification, and achieve\ndemonstrably superior results. We make the source code of CompGCN available to\nfoster reproducible research.",
+                    "authors": "Shikhar Vashishth, Soumya Sanyal, Vikram Nitin, Partha Talukdar",
+                    "published": "2019-11-08",
+                    "updated": "2020-01-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1802.04868v2",
+                    "title": "SimplE Embedding for Link Prediction in Knowledge Graphs",
+                    "abstract": "Knowledge graphs contain knowledge about the world and provide a structured\nrepresentation of this knowledge. Current knowledge graphs contain only a small\nsubset of what is true in the world. Link prediction approaches aim at\npredicting new links for a knowledge graph given the existing links among the\nentities. Tensor factorization approaches have proved promising for such link\nprediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is\namong the first tensor factorization approaches. CP generally performs poorly\nfor link prediction as it learns two independent embedding vectors for each\nentity, whereas they are really tied. We present a simple enhancement of CP\n(which we call SimplE) to allow the two embeddings of each entity to be learned\ndependently. The complexity of SimplE grows linearly with the size of\nembeddings. The embeddings learned through SimplE are interpretable, and\ncertain types of background knowledge can be incorporated into these embeddings\nthrough weight tying. We prove SimplE is fully expressive and derive a bound on\nthe size of its embeddings for full expressivity. We show empirically that,\ndespite its simplicity, SimplE outperforms several state-of-the-art tensor\nfactorization techniques. SimplE's code is available on GitHub at\nhttps://github.com/Mehran-k/SimplE.",
+                    "authors": "Seyed Mehran Kazemi, David Poole",
+                    "published": "2018-02-13",
+                    "updated": "2018-10-26",
+                    "primary_cat": "stat.ML",
+                    "cats": [
+                        "stat.ML",
+                        "cs.LG"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1907.03143v1",
+                    "title": "Diachronic Embedding for Temporal Knowledge Graph Completion",
+                    "abstract": "Knowledge graphs (KGs) typically contain temporal facts indicating\nrelationships among entities at different times. Due to their incompleteness,\nseveral approaches have been proposed to infer new facts for a KG based on the\nexisting ones-a problem known as KG completion. KG embedding approaches have\nproved effective for KG completion, however, they have been developed mostly\nfor static KGs. Developing temporal KG embedding models is an increasingly\nimportant problem. In this paper, we build novel models for temporal KG\ncompletion through equipping static models with a diachronic entity embedding\nfunction which provides the characteristics of entities at any point in time.\nThis is in contrast to the existing temporal KG embedding approaches where only\nstatic entity features are provided. The proposed embedding function is\nmodel-agnostic and can be potentially combined with any static model. We prove\nthat combining it with SimplE, a recent model for static KG embedding, results\nin a fully expressive model for temporal KG completion. Our experiments\nindicate the superiority of our proposal compared to existing baselines.",
+                    "authors": "Rishab Goel, Seyed Mehran Kazemi, Marcus Brubaker, Pascal Poupart",
+                    "published": "2019-07-06",
+                    "updated": "2019-07-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.05530v4",
+                    "title": "Recurrent Event Network: Autoregressive Structure Inference over Temporal Knowledge Graphs",
+                    "abstract": "Knowledge graph reasoning is a critical task in natural language processing.\nThe task becomes more challenging on temporal knowledge graphs, where each fact\nis associated with a timestamp. Most existing methods focus on reasoning at\npast timestamps and they are not able to predict facts happening in the future.\nThis paper proposes Recurrent Event Network (RE-NET), a novel autoregressive\narchitecture for predicting future interactions. The occurrence of a fact\n(event) is modeled as a probability distribution conditioned on temporal\nsequences of past knowledge graphs. Specifically, our RE-NET employs a\nrecurrent event encoder to encode past facts and uses a neighborhood aggregator\nto model the connection of facts at the same timestamp. Future facts can then\nbe inferred in a sequential manner based on the two modules. We evaluate our\nproposed method via link prediction at future times on five public datasets.\nThrough extensive experiments, we demonstrate the strength of RENET, especially\non multi-step inference over future timestamps, and achieve state-of-the-art\nperformance on all five datasets. Code and data can be found at\nhttps://github.com/INK-USC/RE-Net.",
+                    "authors": "Woojeong Jin, Meng Qu, Xisen Jin, Xiang Ren",
+                    "published": "2019-04-11",
+                    "updated": "2020-10-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.CL",
+                        "stat.ML"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.07782v2",
+                    "title": "Complex Evolutional Pattern Learning for Temporal Knowledge Graph Reasoning",
+                    "abstract": "A Temporal Knowledge Graph (TKG) is a sequence of KGs corresponding to\ndifferent timestamps. TKG reasoning aims to predict potential facts in the\nfuture given the historical KG sequences. One key of this task is to mine and\nunderstand evolutional patterns of facts from these sequences. The evolutional\npatterns are complex in two aspects, length-diversity and time-variability.\nExisting models for TKG reasoning focus on modeling fact sequences of a fixed\nlength, which cannot discover complex evolutional patterns that vary in length.\nFurthermore, these models are all trained offline, which cannot well adapt to\nthe changes of evolutional patterns from then on. Thus, we propose a new model,\ncalled Complex Evolutional Network (CEN), which uses a length-aware\nConvolutional Neural Network (CNN) to handle evolutional patterns of different\nlengths via an easy-to-difficult curriculum learning strategy. Besides, we\npropose to learn the model under the online setting so that it can adapt to the\nchanges of evolutional patterns over time. Extensive experiments demonstrate\nthat CEN obtains substantial performance improvement under both the traditional\noffline and the proposed online settings.",
+                    "authors": "Zixuan Li, Saiping Guan, Xiaolong Jin, Weihua Peng, Yajuan Lyu, Yong Zhu, Long Bai, Wei Li, Jiafeng Guo, Xueqi Cheng",
+                    "published": "2022-03-15",
+                    "updated": "2022-03-20",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2104.10353v1",
+                    "title": "Temporal Knowledge Graph Reasoning Based on Evolutional Representation Learning",
+                    "abstract": "Knowledge Graph (KG) reasoning that predicts missing facts for incomplete KGs\nhas been widely explored. However, reasoning over Temporal KG (TKG) that\npredicts facts in the future is still far from resolved. The key to predict\nfuture facts is to thoroughly understand the historical facts. A TKG is\nactually a sequence of KGs corresponding to different timestamps, where all\nconcurrent facts in each KG exhibit structural dependencies and temporally\nadjacent facts carry informative sequential patterns. To capture these\nproperties effectively and efficiently, we propose a novel Recurrent Evolution\nnetwork based on Graph Convolution Network (GCN), called RE-GCN, which learns\nthe evolutional representations of entities and relations at each timestamp by\nmodeling the KG sequence recurrently. Specifically, for the evolution unit, a\nrelation-aware GCN is leveraged to capture the structural dependencies within\nthe KG at each timestamp. In order to capture the sequential patterns of all\nfacts in parallel, the historical KG sequence is modeled auto-regressively by\nthe gate recurrent components. Moreover, the static properties of entities such\nas entity types, are also incorporated via a static graph constraint component\nto obtain better entity representations. Fact prediction at future timestamps\ncan then be realized based on the evolutional entity and relation\nrepresentations. Extensive experiments demonstrate that the RE-GCN model\nobtains substantial performance and efficiency improvement for the temporal\nreasoning tasks on six benchmark datasets. Especially, it achieves up to\n11.46\\% improvement in MRR for entity prediction with up to 82 times speedup\ncomparing to the state-of-the-art baseline.",
+                    "authors": "Zixuan Li, Xiaolong Jin, Wei Li, Saiping Guan, Jiafeng Guo, Huawei Shen, Yuanzhuo Wang, Xueqi Cheng",
+                    "published": "2021-04-21",
+                    "updated": "2021-04-21",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI"
+                    ],
+                    "label": "Related Work"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.15862v1",
+                    "title": "Restless Temporal Path Parameterized Above Lower Bounds",
+                    "abstract": "Reachability questions are one of the most fundamental algorithmic primitives\nin temporal graphs -- graphs whose edge set changes over discrete time steps. A\ncore problem here is the NP-hard Short Restless Temporal Path: given a temporal\ngraph $\\mathcal G$, two distinct vertices $s$ and $z$, and two numbers $\\delta$\nand $k$, is there a $\\delta$-restless temporal $s$-$z$ path of length at most\n$k$? A temporal path is a path whose edges appear in chronological order and a\ntemporal path is $\\delta$-restless if two consecutive path edges appear at most\n$\\delta$ time steps apart from each other. Among others, this problem has\napplications in neuroscience and epidemiology. While Short Restless Temporal\nPath is known to be computationally hard, e.g., it is NP-hard for only three\ntime steps and W[1]-hard when parameterized by the feedback vertex number of\nthe underlying graph, it is fixed-parameter tractable when parameterized by the\npath length $k$. We improve on this by showing that Short Restless Temporal\nPath can be solved in (randomized) $4^{k-d}|\\mathcal G|^{O(1)}$ time, where $d$\nis the minimum length of a temporal $s$-$z$ path.",
+                    "authors": "Philipp Zschoche",
+                    "published": "2022-03-29",
+                    "updated": "2022-03-29",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.05653v1",
+                    "title": "Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition",
+                    "abstract": "Accurate spatial-temporal traffic flow forecasting is essential for helping\ntraffic managers to take control measures and drivers to choose the optimal\ntravel routes. Recently, graph convolutional networks (GCNs) have been widely\nused in traffic flow prediction owing to their powerful ability to capture\nspatial-temporal dependencies. The design of the spatial-temporal graph\nadjacency matrix is a key to the success of GCNs, and it is still an open\nquestion. This paper proposes reconstructing the binary adjacency matrix via\ntensor decomposition, and a traffic flow forecasting method is proposed. First,\nwe reformulate the spatial-temporal fusion graph adjacency matrix into a\nthree-way adjacency tensor. Then, we reconstructed the adjacency tensor via\nTucker decomposition, wherein more informative and global spatial-temporal\ndependencies are encoded. Finally, a Spatial-temporal Synchronous Graph\nConvolutional module for localized spatial-temporal correlations learning and a\nDilated Convolution module for global correlations learning are assembled to\naggregate and learn the comprehensive spatial-temporal dependencies of the road\nnetwork. Experimental results on four open-access datasets demonstrate that the\nproposed model outperforms state-of-the-art approaches in terms of the\nprediction performance and computational cost.",
+                    "authors": "Qin Li, Xuan Yang, Yong Wang, Yuankai Wu, Deqiang He",
+                    "published": "2022-12-12",
+                    "updated": "2022-12-12",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.05631v2",
+                    "title": "ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling",
+                    "abstract": "The spatio-temporal graph learning is becoming an increasingly important\nobject of graph study. Many application domains involve highly dynamic graphs\nwhere temporal information is crucial, e.g. traffic networks and financial\ntransaction graphs. Despite the constant progress made on learning structured\ndata, there is still a lack of effective means to extract dynamic complex\nfeatures from spatio-temporal structures. Particularly, conventional models\nsuch as convolutional networks or recurrent neural networks are incapable of\nrevealing the temporal patterns in short or long terms and exploring the\nspatial properties in local or global scope from spatio-temporal graphs\nsimultaneously. To tackle this problem, we design a novel multi-scale\narchitecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series\nmodeling. In this U-shaped network, a paired sampling operation is proposed in\nspacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in\nspatial from its deterministic partition while abstracts multi-resolution\ntemporal dependencies through dilated recurrent skip connections; based on\nprevious settings in the downsampling, the unpooling (ST-Unpool) restores the\noriginal structure of spatio-temporal graphs and resumes regular intervals\nwithin graph sequences. Experiments on spatio-temporal prediction tasks\ndemonstrate that our model effectively captures comprehensive features in\nmultiple scales and achieves substantial improvements over mainstream methods\non several real-world datasets.",
+                    "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+                    "published": "2019-03-13",
+                    "updated": "2021-06-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.16078v2",
+                    "title": "Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs",
+                    "abstract": "We present the Evolving Graph Fourier Transform (EFT), the first invertible\nspectral transform that captures evolving representations on temporal graphs.\nWe motivate our work by the inadequacy of existing methods for capturing the\nevolving graph spectra, which are also computationally expensive due to the\ntemporal aspect along with the graph vertex domain. We view the problem as an\noptimization over the Laplacian of the continuous time dynamic graph.\nAdditionally, we propose pseudo-spectrum relaxations that decompose the\ntransformation process, making it highly computationally efficient. The EFT\nmethod adeptly captures the evolving graph's structural and positional\nproperties, making it effective for downstream tasks on evolving graphs. Hence,\nas a reference implementation, we develop a simple neural model induced with\nEFT for capturing evolving graph spectra. We empirically validate our\ntheoretical findings on a number of large-scale and standard temporal graph\nbenchmarks and demonstrate that our model achieves state-of-the-art\nperformance.",
+                    "authors": "Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Manish Singh, Toyotaro Suzumura",
+                    "published": "2024-02-25",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.14199v2",
+                    "title": "MTRGL:Effective Temporal Correlation Discerning through Multi-modal Temporal Relational Graph Learning",
+                    "abstract": "In this study, we explore the synergy of deep learning and financial market\napplications, focusing on pair trading. This market-neutral strategy is\nintegral to quantitative finance and is apt for advanced deep-learning\ntechniques. A pivotal challenge in pair trading is discerning temporal\ncorrelations among entities, necessitating the integration of diverse data\nmodalities. Addressing this, we introduce a novel framework, Multi-modal\nTemporal Relation Graph Learning (MTRGL). MTRGL combines time series data and\ndiscrete features into a temporal graph and employs a memory-based temporal\ngraph neural network. This approach reframes temporal correlation\nidentification as a temporal graph link prediction task, which has shown\nempirical success. Our experiments on real-world datasets confirm the superior\nperformance of MTRGL, emphasizing its promise in refining automated pair\ntrading strategies.",
+                    "authors": "Junwei Su, Shan Wu, Jinhui Li",
+                    "published": "2024-01-25",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "econ.GN",
+                        "q-fin.EC",
+                        "q-fin.TR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2208.10364v3",
+                    "title": "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks",
+                    "abstract": "Recent years have seen a surge in research on dynamic graph representation\nlearning, which aims to model temporal graphs that are dynamic and evolving\nconstantly over time. However, current work typically models graph dynamics\nwith recurrent neural networks (RNNs), making them suffer seriously from\ncomputation and memory overheads on large temporal graphs. So far, scalability\nof dynamic graph representation learning on large temporal graphs remains one\nof the major challenges. In this paper, we present a scalable framework, namely\nSpikeNet, to efficiently capture the temporal and structural patterns of\ntemporal graphs. We explore a new direction in that we can capture the evolving\ndynamics of temporal graphs with spiking neural networks (SNNs) instead of\nRNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics\nas spike trains of neuron populations and enable spike-based propagation in an\nefficient way. Experiments on three large real-world temporal graph datasets\ndemonstrate that SpikeNet outperforms strong baselines on the temporal node\nclassification task with lower computational costs. Particularly, SpikeNet\ngeneralizes to a large temporal graph (2.7M nodes and 13.9M edges) with\nsignificantly fewer parameters and computation overheads.Our code is publicly\navailable at \\url{https://github.com/EdisonLeeeee/SpikeNet}.",
+                    "authors": "Jintang Li, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, Changhua Meng",
+                    "published": "2022-08-15",
+                    "updated": "2023-05-18",
+                    "primary_cat": "cs.NE",
+                    "cats": [
+                        "cs.NE",
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1509.08960v1",
+                    "title": "Storing and Analyzing Historical Graph Data at Scale",
+                    "abstract": "The work on large-scale graph analytics to date has largely focused on the\nstudy of static properties of graph snapshots. However, a static view of\ninteractions between entities is often an oversimplification of several complex\nphenomena like the spread of epidemics, information diffusion, formation of\nonline communities}, and so on. Being able to find temporal interaction\npatterns, visualize the evolution of graph properties, or even simply compare\nthem across time, adds significant value in reasoning over graphs. However,\nbecause of lack of underlying data management support, an analyst today has to\nmanually navigate the added temporal complexity of dealing with large evolving\ngraphs. In this paper, we present a system, called Historical Graph Store, that\nenables users to store large volumes of historical graph data and to express\nand run complex temporal graph analytical tasks against that data. It consists\nof two key components: a Temporal Graph Index (TGI), that compactly stores\nlarge volumes of historical graph evolution data in a partitioned and\ndistributed fashion; it provides support for retrieving snapshots of the graph\nas of any timepoint in the past or evolution histories of individual nodes or\nneighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for\nexpressing complex temporal analytical tasks and for executing them in an\nefficient and scalable manner. Our experiments demonstrate our system's\nefficient storage, retrieval and analytics across a wide variety of queries on\nlarge volumes of historical graph data.",
+                    "authors": "Udayan Khurana, Amol Deshpande",
+                    "published": "2015-09-29",
+                    "updated": "2015-09-29",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.02212v1",
+                    "title": "Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by\nattaching the time scope. Existing temporal knowledge graph question answering\n(TKGQA) models solely approach simple questions, owing to the prior assumption\nthat each question only contains a single temporal fact with explicit/implicit\ntemporal constraints. Hence, they perform poorly on questions which own\nmultiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint\n\\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts\n\\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly\nreasoning multiple temporal facts for accurately answering \\emph{complex}\ntemporal questions. Specifically, JMFRN first retrieves question-related\ntemporal facts from TKG for each entity of the given complex question. For\njoint reasoning, we design two different attention (\\ie entity-aware and\ntime-aware) modules, which are suitable for universal settings, to aggregate\nentities and timestamps information of retrieved facts. Moreover, to filter\nincorrect type answers, we introduce an additional answer type discrimination\ntask. Extensive experiments demonstrate our proposed method significantly\noutperforms the state-of-art on the well-known complex temporal question\nbenchmark TimeQuestions.",
+                    "authors": "Rikui Huang, Wei Wei, Xiaoye Qu, Wenfeng Xie, Xianling Mao, Dangyang Chen",
+                    "published": "2024-01-04",
+                    "updated": "2024-01-04",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.07117v1",
+                    "title": "On inefficiently connecting temporal networks",
+                    "abstract": "A temporal graph can be represented by a graph with an edge labelling, such\nthat an edge is present in the network if and only if the edge is assigned the\ncorresponding time label. A journey is a labelled path in a temporal graph such\nthat labels on successive edges of the path are increasing, and if all vertices\nadmit journeys to all other vertices, the temporal graph is temporally\nconnected. A temporal spanner is a sublabelling of the temporal graph such that\ntemporal connectivity is maintained. The study of temporal spanners has raised\ninterest since the early 2000's. Essentially two types of studies have been\nconducted: the positive side where families of temporal graphs are shown to\n(deterministically or stochastically) admit sparse temporal spanners, and the\nnegative side where constructions of temporal graphs with no sparse spanners\nare of importance. Often such studies considered temporal graphs with happy or\nsimple labellings, which associate exactly one label per edge. In this paper,\nwe focus on the negative side and consider proper labellings, where multiple\nlabels per edge are allowed. More precisely, we aim to construct dense\ntemporally connected graphs such that all labels are necessary for temporal\nconnectivity. Our contributions are multiple: we present the first labellings\nmaximizing a local density measure; exact or asymptotically tight results for\nbasic graph families, which are then extended to larger graph families; an\nextension of an efficient temporal graph labelling generator; and overall\ndenser labellings than previous work even when restricted to happy labellings.",
+                    "authors": "Esteban Christiann, Eric Sanlaville, Jason Schoeters",
+                    "published": "2023-12-12",
+                    "updated": "2023-12-12",
+                    "primary_cat": "cs.CC",
+                    "cats": [
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1706.09480v1",
+                    "title": "A Temporal Tree Decomposition for Generating Temporal Graphs",
+                    "abstract": "Discovering the underlying structures present in large real world graphs is a\nfundamental scientific problem. Recent work at the intersection of formal\nlanguage theory and graph theory has found that a Hyperedge Replacement Grammar\n(HRG) can be extracted from a tree decomposition of any graph. This HRG can be\nused to generate new graphs that share properties that are similar to the\noriginal graph. Because the extracted HRG is directly dependent on the shape\nand contents of the of tree decomposition, it is unlikely that informative\ngraph-processes are actually being captured with the extraction algorithm. To\naddress this problem, the current work presents a new extraction algorithm\ncalled temporal HRG (tHRG) that learns HRG production rules from a temporal\ntree decomposition of the graph. We observe problems with the assumptions that\nare made in a temporal HRG model. In experiments on large real world networks,\nwe show and provide reasoning as to why tHRG does not perform as well as HRG\nand other graph generators.",
+                    "authors": "Corey Pennycuff, Salvador Aguinaga, Tim Weninger",
+                    "published": "2017-06-28",
+                    "updated": "2017-06-28",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.12587v1",
+                    "title": "TGLib: An Open-Source Library for Temporal Graph Analysis",
+                    "abstract": "We initiate an open-source library for the efficient analysis of temporal\ngraphs. We consider one of the standard models of dynamic networks in which\neach edge has a discrete timestamp and transition time. Recently there has been\na massive interest in analyzing such temporal graphs. Common computational data\nmining and analysis tasks include the computation of temporal distances,\ncentrality measures, and network statistics like topological overlap,\nburstiness, or temporal diameter. To fulfill the increasing demand for\nefficient and easy-to-use implementations of temporal graph algorithms, we\nintroduce the open-source library TGLib, which integrates efficient data\nstructures and algorithms for temporal graph analysis. TGLib is highly\nefficient and versatile, providing simple and convenient C++ and Python\ninterfaces, targeting computer scientists, practitioners, students, and the\n(temporal) network research community.",
+                    "authors": "Lutz Oettershagen, Petra Mutzel",
+                    "published": "2022-09-26",
+                    "updated": "2022-09-26",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2108.08719v5",
+                    "title": "Temporal Graph Functional Dependencies [Extended Version]",
+                    "abstract": "Data dependencies have been extended to graphs to characterize topological\nand value constraints. Existing data dependencies are defined to capture\ninconsistencies in static graphs. Nevertheless, inconsistencies may occur over\nevolving graphs and only for certain time periods. The need for capturing such\ninconsistencies in temporal graphs is evident in anomaly detection and\npredictive dynamic network analysis. This paper introduces a class of data\ndependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs\ngeneralize functional dependencies to temporal graphs as a sequence of graph\nsnapshots that are induced by time intervals, and enforce both topological\nconstraints and attribute value dependencies that must be satisfied by these\nsnapshots. (1) We establish the complexity results for the satisfiability and\nimplication problems of TGFDs. (2) We propose a sound and complete\naxiomatization system for TGFDs. (3) We also present efficient parallel\nalgorithms to detect inconsistencies in temporal graphs as violations of TGFDs.\nThe algorithm exploits data and temporal locality induced by time intervals,\nand uses incremental pattern matching and load balancing strategies to enable\nfeasible error detection in large temporal graphs. Using real datasets, we\nexperimentally verify that our algorithms achieve lower runtimes compared to\nexisting baselines, while improving the accuracy over error detection using\nexisting graph data constraints, e.g., GFDs and GTARs with 55% and 74% gain in\nF1-score, respectively.",
+                    "authors": "Morteza Alipourlangouri, Adam Mansfield, Fei Chiang, Yinghui Wu",
+                    "published": "2021-08-19",
+                    "updated": "2022-07-26",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1805.06836v2",
+                    "title": "Deleting edges to restrict the size of an epidemic in temporal networks",
+                    "abstract": "Spreading processes on graphs are a natural model for a wide variety of\nreal-world phenomena, including information spread over social networks and\nbiological diseases spreading over contact networks. Often, the networks over\nwhich these processes spread are dynamic in nature, and can be modeled with\ntemporal graphs. Here, we study the problem of deleting edges from a given\ntemporal graph in order to reduce the number of vertices (temporally) reachable\nfrom a given starting point. This could be used to control the spread of a\ndisease, rumour, etc. in a temporal graph. In particular, our aim is to find a\ntemporal subgraph in which a process starting at any single vertex can be\ntransferred to only a limited number of other vertices using a\ntemporally-feasible path. We introduce a natural edge-deletion problem for\ntemporal graphs and provide positive and negative results on its computational\ncomplexity and approximability.",
+                    "authors": "Jessica Enright, Kitty Meeks, George B. Mertzios, Viktor Zamaraev",
+                    "published": "2018-05-17",
+                    "updated": "2021-02-11",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1306.0493v1",
+                    "title": "Graph Metrics for Temporal Networks",
+                    "abstract": "Temporal networks, i.e., networks in which the interactions among a set of\nelementary units change over time, can be modelled in terms of time-varying\ngraphs, which are time-ordered sequences of graphs over a set of nodes. In such\ngraphs, the concepts of node adjacency and reachability crucially depend on the\nexact temporal ordering of the links. Consequently, all the concepts and\nmetrics proposed and used for the characterisation of static complex networks\nhave to be redefined or appropriately extended to time-varying graphs, in order\nto take into account the effects of time ordering on causality. In this chapter\nwe discuss how to represent temporal networks and we review the definitions of\nwalks, paths, connectedness and connected components valid for graphs in which\nthe links fluctuate over time. We then focus on temporal node-node distance,\nand we discuss how to characterise link persistence and the temporal\nsmall-world behaviour in this class of networks. Finally, we discuss the\nextension of classic centrality measures, including closeness, betweenness and\nspectral centrality, to the case of time-varying graphs, and we review the work\non temporal motifs analysis and the definition of modularity for temporal\ngraphs.",
+                    "authors": "Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, Vito Latora",
+                    "published": "2013-06-03",
+                    "updated": "2013-06-03",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.04962v1",
+                    "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering",
+                    "abstract": "Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.",
+                    "authors": "Meng Liu, Ke Liang, Yue Liu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-06-08",
+                    "updated": "2023-06-08",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.13183v1",
+                    "title": "Resolving Sets in Temporal Graphs",
+                    "abstract": "A $\\textit{resolving set}$ $R$ in a graph $G$ is a set of vertices such that\nevery vertex of $G$ is uniquely identified by its distances to the vertices of\n$R$. Introduced in the 1970s, this concept has been since then extensively\nstudied from both combinatorial and algorithmic point of view. We propose a\ngeneralization of the concept of resolving sets to temporal graphs, i.e.,\ngraphs with edge sets that change over discrete time-steps. In this setting,\nthe $\\textit{temporal distance}$ from $u$ to $v$ is the earliest possible\ntime-step at which a journey with strictly increasing time-steps on edges\nleaving $u$ reaches $v$, i.e., the first time-step at which $v$ could receive a\nmessage broadcast from $u$. A $\\textit{temporal resolving set}$ of a temporal\ngraph $\\mathcal{G}$ is a subset $R$ of its vertices such that every vertex of\n$\\mathcal{G}$ is uniquely identified by its temporal distances from vertices of\n$R$.\n  We study the problem of finding a minimum-size temporal resolving set, and\nshow that it is NP-complete even on very restricted graph classes and with\nstrong constraints on the time-steps: temporal complete graphs where every edge\nappears in either time-step 1 or 2, temporal trees where every edge appears in\nat most two consecutive time-steps, and even temporal subdivided stars where\nevery edge appears in at most two (not necessarily consecutive) time-steps. On\nthe other hand, we give polynomial-time algorithms for temporal paths and\ntemporal stars where every edge appears in exactly one time-step, and give a\ncombinatorial analysis and algorithms for several temporal graph classes where\nthe edges appear in periodic time-steps.",
+                    "authors": "Jan Bok, Antoine Dailly, Tuomo Lehtil\u00e4",
+                    "published": "2024-03-19",
+                    "updated": "2024-03-19",
+                    "primary_cat": "math.CO",
+                    "cats": [
+                        "math.CO",
+                        "cs.DM",
+                        "cs.DS",
+                        "05C69, 68Rxx"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.07491v3",
+                    "title": "Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment",
+                    "abstract": "Temporal graph learning aims to generate high-quality representations for\ngraph-based tasks with dynamic information, which has recently garnered\nincreasing attention. In contrast to static graphs, temporal graphs are\ntypically organized as node interaction sequences over continuous time rather\nthan an adjacency matrix. Most temporal graph learning methods model current\ninteractions by incorporating historical neighborhood. However, such methods\nonly consider first-order temporal information while disregarding crucial\nhigh-order structural information, resulting in suboptimal performance. To\naddress this issue, we propose a self-supervised method called S2T for temporal\ngraph learning, which extracts both temporal and structural information to\nlearn more informative node representations. Notably, the initial node\nrepresentations combine first-order temporal and high-order structural\ninformation differently to calculate two conditional intensities. An alignment\nloss is then introduced to optimize the node representations, narrowing the gap\nbetween the two intensities and making them more informative. Concretely, in\naddition to modeling temporal information using historical neighbor sequences,\nwe further consider structural knowledge at both local and global levels. At\nthe local level, we generate structural intensity by aggregating features from\nhigh-order neighbor sequences. At the global level, a global representation is\ngenerated based on all nodes to adjust the structural intensity according to\nthe active statuses on different nodes. Extensive experiments demonstrate that\nthe proposed model S2T achieves at most 10.13% performance improvement compared\nwith the state-of-the-art competitors on several datasets.",
+                    "authors": "Meng Liu, Ke Liang, Yawei Zhao, Wenxuan Tu, Sihang Zhou, Xinbiao Gan, Xinwang Liu, Kunlun He",
+                    "published": "2023-02-15",
+                    "updated": "2024-04-28",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1912.03904v1",
+                    "title": "Weighted temporal event graphs",
+                    "abstract": "The times of temporal-network events and their correlations contain\ninformation on the function of the network and they influence dynamical\nprocesses taking place on it. To extract information out of correlated event\ntimes, techniques such as the analysis of temporal motifs have been developed.\nWe discuss a recently-introduced, more general framework that maps\ntemporal-network structure into static graphs while retaining information on\ntime-respecting paths and the time differences between their consequent events.\nThis framework builds on weighted temporal event graphs: directed, acyclic\ngraphs (DAGs) that contain a superposition of all temporal paths. We introduce\nthe reader to the temporal event-graph mapping and associated computational\nmethods and illustrate its use by applying the framework to temporal-network\npercolation.",
+                    "authors": "Jari Saram\u00e4ki, Mikko Kivel\u00e4, M\u00e1rton Karsai",
+                    "published": "2019-12-09",
+                    "updated": "2019-12-09",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/0807.2357v1",
+                    "title": "Temporal Graphs",
+                    "abstract": "We introduce the idea of temporal graphs, a representation that encodes\ntemporal data into graphs while fully retaining the temporal information of the\noriginal data. This representation lets us explore the dynamic temporal\nproperties of data by using existing graph algorithms (such as shortest-path),\nwith no need for data-driven simulations. We also present a number of metrics\nthat can be used to study and explore temporal graphs. Finally, we use temporal\ngraphs to analyse real-world data and present the results of our analysis.",
+                    "authors": "Vassilis Kostakos",
+                    "published": "2008-07-15",
+                    "updated": "2008-07-15",
+                    "primary_cat": "physics.soc-ph",
+                    "cats": [
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1810.06240v4",
+                    "title": "Comparing Temporal Graphs Using Dynamic Time Warping",
+                    "abstract": "Within many real-world networks the links between pairs of nodes change over\ntime. Thus, there has been a recent boom in studying temporal graphs.\nRecognizing patterns in temporal graphs requires a proximity measure to compare\ndifferent temporal graphs. To this end, we propose to study dynamic time\nwarping on temporal graphs. We define the dynamic temporal graph warping\ndistance (dtgw) to determine the dissimilarity of two temporal graphs. Our\nnovel measure is flexible and can be applied in various application domains. We\nshow that computing the dtgw-distance is a challenging (in general) NP-hard\noptimization problem and identify some polynomial-time solvable special cases.\nMoreover, we develop a quadratic programming formulation and an efficient\nheuristic. In experiments on real-word data we show that the heuristic performs\nvery well and that our dtgw-distance performs favorably in de-anonymizing\nnetworks compared to other approaches.",
+                    "authors": "Vincent Froese, Brijnesh Jain, Rolf Niedermeier, Malte Renken",
+                    "published": "2018-10-15",
+                    "updated": "2020-07-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.03363v3",
+                    "title": "Spatio-Temporal Graph Scattering Transform",
+                    "abstract": "Although spatio-temporal graph neural networks have achieved great empirical\nsuccess in handling multiple correlated time series, they may be impractical in\nsome real-world scenarios due to a lack of sufficient high-quality training\ndata. Furthermore, spatio-temporal graph neural networks lack theoretical\ninterpretation. To address these issues, we put forth a novel mathematically\ndesigned framework to analyze spatio-temporal data. Our proposed\nspatio-temporal graph scattering transform (ST-GST) extends traditional\nscattering transforms to the spatio-temporal domain. It performs iterative\napplications of spatio-temporal graph wavelets and nonlinear activation\nfunctions, which can be viewed as a forward pass of spatio-temporal graph\nconvolutional networks without training. Since all the filter coefficients in\nST-GST are mathematically designed, it is promising for the real-world\nscenarios with limited training data, and also allows for a theoretical\nanalysis, which shows that the proposed ST-GST is stable to small perturbations\nof input signals and structures. Finally, our experiments show that i) ST-GST\noutperforms spatio-temporal graph convolutional networks by an increase of 35%\nin accuracy for MSR Action3D dataset; ii) it is better and computationally more\nefficient to design the transform based on separable spatio-temporal graphs\nthan the joint ones; and iii) the nonlinearity in ST-GST is critical to\nempirical performance.",
+                    "authors": "Chao Pan, Siheng Chen, Antonio Ortega",
+                    "published": "2020-12-06",
+                    "updated": "2021-02-09",
+                    "primary_cat": "eess.SP",
+                    "cats": [
+                        "eess.SP",
+                        "cs.AI",
+                        "cs.CV",
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2110.05018v2",
+                    "title": "Time-varying Graph Learning Under Structured Temporal Priors",
+                    "abstract": "This paper endeavors to learn time-varying graphs by using structured\ntemporal priors that assume underlying relations between arbitrary two graphs\nin the graph sequence. Different from many existing chain structure based\nmethods in which the priors like temporal homogeneity can only describe the\nvariations of two consecutive graphs, we propose a structure named\n\\emph{temporal graph} to characterize the underlying real temporal relations.\nUnder this framework, the chain structure is actually a special case of our\ntemporal graph. We further proposed Alternating Direction Method of Multipliers\n(ADMM), a distributed algorithm, to solve the induced optimization problem.\nNumerical experiments demonstrate the superiorities of our method.",
+                    "authors": "Xiang Zhang, Qiao Wang",
+                    "published": "2021-10-11",
+                    "updated": "2022-02-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.SP"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1401.1919v1",
+                    "title": "Temporal Graph Traversals: Definitions, Algorithms, and Applications",
+                    "abstract": "A temporal graph is a graph in which connections between vertices are active\nat specific times, and such temporal information leads to completely new\npatterns and knowledge that are not present in a non-temporal graph. In this\npaper, we study traversal problems in a temporal graph. Graph traversals, such\nas DFS and BFS, are basic operations for processing and studying a graph. While\nboth DFS and BFS are well-known simple concepts, it is non-trivial to adopt the\nsame notions from a non-temporal graph to a temporal graph. We analyze the\ndifficulties of defining temporal graph traversals and propose new definitions\nof DFS and BFS for a temporal graph. We investigate the properties of temporal\nDFS and BFS, and propose efficient algorithms with optimal complexity. In\nparticular, we also study important applications of temporal DFS and BFS. We\nverify the efficiency and importance of our graph traversal algorithms in real\nworld temporal graphs.",
+                    "authors": "Silu Huang, James Cheng, Huanhuan Wu",
+                    "published": "2014-01-09",
+                    "updated": "2014-01-09",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2204.09236v1",
+                    "title": "Scalable Motif Counting for Large-scale Temporal Graphs",
+                    "abstract": "One fundamental problem in temporal graph analysis is to count the\noccurrences of small connected subgraph patterns (i.e., motifs), which benefits\na broad range of real-world applications, such as anomaly detection, structure\nprediction, and network representation learning. However, existing works\nfocused on exacting temporal motif are not scalable to large-scale temporal\ngraph data, due to their heavy computational costs or inherent inadequacy of\nparallelism. In this work, we propose a scalable parallel framework for exactly\ncounting temporal motifs in large-scale temporal graphs. We first categorize\nthe temporal motifs based on their distinct properties, and then design\ncustomized algorithms that offer efficient strategies to exactly count the\nmotif instances of each category. Moreover, our compact data structures, namely\ntriple and quadruple counters, enable our algorithms to directly identify the\ntemporal motif instances of each category, according to edge information and\nthe relationship between edges, therefore significantly improving the counting\nefficiency. Based on the proposed counting algorithms, we design a hierarchical\nparallel framework that features both inter- and intra-node parallel\nstrategies, and fully leverages the multi-threading capacity of modern CPU to\nconcurrently count all temporal motifs. Extensive experiments on sixteen\nreal-world temporal graph datasets demonstrate the superiority and capability\nof our proposed framework for temporal motif counting, achieving up to 538*\nspeedup compared to the state-of-the-art methods. The source code of our method\nis available at: https://github.com/steven-ccq/FAST-temporal-motif.",
+                    "authors": "Zhongqiang Gao, Chuanqi Cheng, Yanwei Yu, Lei Cao, Chao Huang, Junyu Dong",
+                    "published": "2022-04-20",
+                    "updated": "2022-04-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1601.05909v2",
+                    "title": "Efficient Processing of Reachability and Time-Based Path Queries in a Temporal Graph",
+                    "abstract": "A temporal graph is a graph in which vertices communicate with each other at\nspecific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is\nmodeled by an edge from $A$ to $B$ with starting time \"11 a.m.\" and duration \"7\nmins\". Temporal graphs can be used to model many networks with time-related\nactivities, but efficient algorithms for analyzing temporal graphs are severely\ninadequate. We study fundamental problems such as answering reachability and\ntime-based path queries in a temporal graph, and propose an efficient indexing\ntechnique specifically designed for processing these queries in a temporal\ngraph. Our results show that our method is efficient and scalable in both index\nconstruction and query processing.",
+                    "authors": "Huanhuan Wu, Yuzhen Huang, James Cheng, Jinfeng Li, Yiping Ke",
+                    "published": "2016-01-22",
+                    "updated": "2016-01-25",
+                    "primary_cat": "cs.DB",
+                    "cats": [
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.09791v2",
+                    "title": "Temporal Betweenness Centrality on Shortest Paths",
+                    "abstract": "Betweenness centrality measure assesses the importance of nodes in a graph\nand has been used in a variety of contexts. Betweenness centrality has also\nbeen extended to temporal graphs. Temporal graphs have edges that bear labels\naccording to the time of the interactions between the nodes. Betweenness\ncentrality has been extended to the temporal graph settings, and the notion of\npaths has been extended to temporal paths. Recent results by Bu{\\ss} et al. and\nRymar et al. showed that the betweenness centrality of all nodes in a temporal\ngraph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of\ntime units, m the number of temporal edges and n the number of nodes. In this\npaper, we improve the running time analysis of these previous approaches to\ncompute the betweenness centrality of all nodes in a temporal graph. We give an\nalgorithm that runs in O(n m T + n^2 T ).",
+                    "authors": "Mehdi Naima, Matthieu Latapy, Cl\u00e9mence Magnien",
+                    "published": "2023-04-19",
+                    "updated": "2023-06-06",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.08311v1",
+                    "title": "De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs",
+                    "abstract": "We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware\ngraph neural network architecture for time-resolved data on dynamic graphs. Our\napproach accounts for temporal-topological patterns that unfold in the causal\ntopology of dynamic graphs, which is determined by causal walks, i.e.\ntemporally ordered sequences of links by which nodes can influence each other\nover time. Our architecture builds on multiple layers of higher-order De Bruijn\ngraphs, an iterative line graph construction where nodes in a De Bruijn graph\nof order k represent walks of length k-1, while edges represent walks of length\nk. We develop a graph neural network architecture that utilizes De Bruijn\ngraphs to implement a message passing scheme that follows a non-Markovian\ndynamics, which enables us to learn patterns in the causal topology of a\ndynamic graph. Addressing the issue that De Bruijn graphs with different orders\nk can be used to model the same data set, we further apply statistical model\nselection to determine the optimal graph topology to be used for message\npassing. An evaluation in synthetic and empirical data sets suggests that\nDBGNNs can leverage temporal patterns in dynamic graphs, which substantially\nimproves the performance in a supervised node classification task.",
+                    "authors": "Lisi Qarkaxhija, Vincenzo Perri, Ingo Scholtes",
+                    "published": "2022-09-17",
+                    "updated": "2022-09-17",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19508v1",
+                    "title": "Temporal Graph ODEs for Irregularly-Sampled Time Series",
+                    "abstract": "Modern graph representation learning works mostly under the assumption of\ndealing with regularly sampled temporal graph snapshots, which is far from\nrealistic, e.g., social networks and physical systems are characterized by\ncontinuous dynamics and sporadic observations. To address this limitation, we\nintroduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework,\nwhich learns both the temporal and spatial dynamics from graph streams where\nthe intervals between observations are not regularly spaced. We empirically\nvalidate the proposed approach on several graph benchmarks, showing that TG-ODE\ncan achieve state-of-the-art performance in irregular graph stream tasks.",
+                    "authors": "Alessio Gravina, Daniele Zambon, Davide Bacciu, Cesare Alippi",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1904.09610v2",
+                    "title": "Storing and Querying Large-Scale Spatio-Temporal Graphs with High-Throughput Edge Insertions",
+                    "abstract": "Real-world graphs often contain spatio-temporal information and evolve over\ntime. Compared with static graphs, spatio-temporal graphs have very different\ncharacteristics, presenting more significant challenges in data volume, data\nvelocity, and query processing. In this paper, we describe three representative\napplications to understand the features of spatio-temporal graphs. Based on the\ncommonalities of the applications, we define a formal spatio-temporal graph\nmodel, where a graph consists of location vertices, object vertices, and event\nedges. Then we discuss a set of design goals to meet the requirements of the\napplications: (i) supporting up to 10 billion object vertices, 10 million\nlocation vertices, and 100 trillion edges in the graph, (ii) supporting up to 1\ntrillion new edges that are streamed in daily, and (iii) minimizing\ncross-machine communication for query processing. We propose and evaluate PAST,\na framework for efficient PArtitioning and query processing of Spatio-Temporal\ngraphs. Experimental results show that PAST successfully achieves the above\ngoals. It improves query performance by orders of magnitude compared with\nstate-of-the-art solutions, including JanusGraph, Greenplum, Spark and\nST-Hadoop.",
+                    "authors": "Mengsu Ding, Muqiao Yang, Shimin Chen",
+                    "published": "2019-04-21",
+                    "updated": "2020-10-20",
+                    "primary_cat": "cs.DC",
+                    "cats": [
+                        "cs.DC",
+                        "cs.DB"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.05064v1",
+                    "title": "Adaptive Graph Spatial-Temporal Transformer Network for Traffic Flow Forecasting",
+                    "abstract": "Traffic flow forecasting on graphs has real-world applications in many\nfields, such as transportation system and computer networks. Traffic\nforecasting can be highly challenging due to complex spatial-temporal\ncorrelations and non-linear traffic patterns. Existing works mostly model such\nspatial-temporal dependencies by considering spatial correlations and temporal\ncorrelations separately and fail to model the direct spatial-temporal\ncorrelations. Inspired by the recent success of transformers in the graph\ndomain, in this paper, we propose to directly model the cross-spatial-temporal\ncorrelations on the spatial-temporal graph using local multi-head\nself-attentions. To reduce the time complexity, we set the attention receptive\nfield to the spatially neighboring nodes, and we also introduce an adaptive\ngraph to capture the hidden spatial-temporal dependencies. Based on these\nattention mechanisms, we propose a novel Adaptive Graph Spatial-Temporal\nTransformer Network (ASTTN), which stacks multiple spatial-temporal attention\nlayers to apply self-attention on the input graph, followed by linear layers\nfor predictions. Experimental results on public traffic network datasets,\nMETR-LA PEMS-BAY, PeMSD4, and PeMSD7, demonstrate the superior performance of\nour model.",
+                    "authors": "Aosong Feng, Leandros Tassiulas",
+                    "published": "2022-07-09",
+                    "updated": "2022-07-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2106.13517v1",
+                    "title": "Temporal Graph Signal Decomposition",
+                    "abstract": "Temporal graph signals are multivariate time series with individual\ncomponents associated with nodes of a fixed graph structure. Data of this kind\narises in many domains including activity of social network users, sensor\nnetwork readings over time, and time course gene expression within the\ninteraction network of a model organism. Traditional matrix decomposition\nmethods applied to such data fall short of exploiting structural regularities\nencoded in the underlying graph and also in the temporal patterns of the\nsignal. How can we take into account such structure to obtain a succinct and\ninterpretable representation of temporal graph signals?\n  We propose a general, dictionary-based framework for temporal graph signal\ndecomposition (TGSD). The key idea is to learn a low-rank, joint encoding of\nthe data via a combination of graph and time dictionaries. We propose a highly\nscalable decomposition algorithm for both complete and incomplete data, and\ndemonstrate its advantage for matrix decomposition, imputation of missing\nvalues, temporal interpolation, clustering, period estimation, and rank\nestimation in synthetic and real-world data ranging from traffic patterns to\nsocial media activity. Our framework achieves 28% reduction in RMSE compared to\nbaselines for temporal interpolation when as many as 75% of the observations\nare missing. It scales best among baselines taking under 20 seconds on 3.5\nmillion data points and produces the most parsimonious models. To the best of\nour knowledge, TGSD is the first framework to jointly model graph signals by\ntemporal and graph dictionaries.",
+                    "authors": "Maxwell McNeil, Lin Zhang, Petko Bogdanov",
+                    "published": "2021-06-25",
+                    "updated": "2021-06-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2305.10738v3",
+                    "title": "Deep Temporal Graph Clustering",
+                    "abstract": "Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.",
+                    "authors": "Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+                    "published": "2023-05-18",
+                    "updated": "2024-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1812.11244v1",
+                    "title": "Using Compressed Suffix-Arrays for a Compact Representation of Temporal-Graphs",
+                    "abstract": "Temporal graphs represent binary relationships that change along time. They\ncan model the dynamism of, for example, social and communication networks.\nTemporal graphs are defined as sets of contacts that are edges tagged with the\ntemporal intervals when they are active. This work explores the use of the\nCompressed Suffix Array (CSA), a well-known compact and self-indexed data\nstructure in the area of text indexing, to represent large temporal graphs. The\nnew structure, called Temporal Graph CSA (TGCSA), is experimentally compared\nwith the most competitive compact data structures in the state-of-the-art,\nnamely, EDGELOG and CET. The experimental results show that TGCSA obtains a\ngood space-time trade-off. It uses a reasonable space and is efficient for\nsolving complex temporal queries. Furthermore, TGCSA has wider expressive\ncapabilities than EDGELOG and CET, because it is able to represent temporal\ngraphs where contacts on an edge can temporally overlap.",
+                    "authors": "Nieves R. Brisaboa, Diego Caro, Antonio Fari\u00f1a, M. Andrea Rodriguez",
+                    "published": "2018-12-28",
+                    "updated": "2018-12-28",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.02875v1",
+                    "title": "Multi-Task Edge Prediction in Temporally-Dynamic Video Graphs",
+                    "abstract": "Graph neural networks have shown to learn effective node representations,\nenabling node-, link-, and graph-level inference. Conventional graph networks\nassume static relations between nodes, while relations between entities in a\nvideo often evolve over time, with nodes entering and exiting dynamically. In\nsuch temporally-dynamic graphs, a core problem is inferring the future state of\nspatio-temporal edges, which can constitute multiple types of relations. To\naddress this problem, we propose MTD-GNN, a graph network for predicting\ntemporally-dynamic edges for multiple types of relations. We propose a\nfactorized spatio-temporal graph attention layer to learn dynamic node\nrepresentations and present a multi-task edge prediction loss that models\nmultiple relations simultaneously. The proposed architecture operates on top of\nscene graphs that we obtain from videos through object detection and\nspatio-temporal linking. Experimental evaluations on ActionGenome and CLEVRER\nshow that modeling multiple relations in our temporally-dynamic graph network\ncan be mutually beneficial, outperforming existing static and spatio-temporal\ngraph neural networks, as well as state-of-the-art predicate classification\nmethods.",
+                    "authors": "Osman \u00dclger, Julian Wiederer, Mohsen Ghafoorian, Vasileios Belagiannis, Pascal Mettes",
+                    "published": "2022-12-06",
+                    "updated": "2022-12-06",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2209.09677v1",
+                    "title": "A Simple Temporal Information Matching Mechanism for Entity Alignment Between Temporal Knowledge Graphs",
+                    "abstract": "Entity alignment (EA) aims to find entities in different knowledge graphs\n(KGs) that refer to the same object in the real world. Recent studies\nincorporate temporal information to augment the representations of KGs. The\nexisting methods for EA between temporal KGs (TKGs) utilize a time-aware\nattention mechanism to incorporate relational and temporal information into\nentity embeddings. The approaches outperform the previous methods by using\ntemporal information. However, we believe that it is not necessary to learn the\nembeddings of temporal information in KGs since most TKGs have uniform temporal\nrepresentations. Therefore, we propose a simple graph neural network (GNN)\nmodel combined with a temporal information matching mechanism, which achieves\nbetter performance with less time and fewer parameters. Furthermore, since\nalignment seeds are difficult to label in real-world applications, we also\npropose a method to generate unsupervised alignment seeds via the temporal\ninformation of TKG. Extensive experiments on public datasets indicate that our\nsupervised method significantly outperforms the previous methods and the\nunsupervised one has competitive performance.",
+                    "authors": "Li Cai, Xin Mao, Meirong Ma, Hao Yuan, Jianchao Zhu, Man Lan",
+                    "published": "2022-09-20",
+                    "updated": "2022-09-20",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.01928v1",
+                    "title": "Constructing Temporal Dynamic Knowledge Graphs from Interactive Text-based Games",
+                    "abstract": "In natural language processing, interactive text-based games serve as a test\nbed for interactive AI systems. Prior work has proposed to play text-based\ngames by acting based on discrete knowledge graphs constructed by the Discrete\nGraph Updater (DGU) to represent the game state from the natural language\ndescription. While DGU has shown promising results with high interpretability,\nit suffers from lower knowledge graph accuracy due to its lack of temporality\nand limited generalizability to complex environments with objects with the same\nlabel. In order to address DGU's weaknesses while preserving its high\ninterpretability, we propose the Temporal Discrete Graph Updater (TDGU), a\nnovel neural network model that represents dynamic knowledge graphs as a\nsequence of timestamped graph events and models them using a temporal point\nbased graph neural network. Through experiments on the dataset collected from a\ntext-based game TextWorld, we show that TDGU outperforms the baseline DGU. We\nfurther show the importance of temporal information for TDGU's performance\nthrough an ablation study and demonstrate that TDGU has the ability to\ngeneralize to more complex environments with objects with the same label. All\nthe relevant code can be found at\n\\url{https://github.com/yukw777/temporal-discrete-graph-updater}.",
+                    "authors": "Keunwoo Peter Yu",
+                    "published": "2023-11-03",
+                    "updated": "2023-11-03",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.07503v1",
+                    "title": "Temporal Aggregation and Propagation Graph Neural Networks for Dynamic Representation",
+                    "abstract": "Temporal graphs exhibit dynamic interactions between nodes over continuous\ntime, whose topologies evolve with time elapsing.\n  The whole temporal neighborhood of nodes reveals the varying preferences of\nnodes.\n  However, previous works usually generate dynamic representation with limited\nneighbors for simplicity, which results in both inferior performance and high\nlatency of online inference.\n  Therefore, in this paper, we propose a novel method of temporal graph\nconvolution with the whole neighborhood, namely Temporal Aggregation and\nPropagation Graph Neural Networks (TAP-GNN).\n  Specifically, we firstly analyze the computational complexity of the dynamic\nrepresentation problem by unfolding the temporal graph in a message-passing\nparadigm.\n  The expensive complexity motivates us to design the AP (aggregation and\npropagation) block, which significantly reduces the repeated computation of\nhistorical neighbors.\n  The final TAP-GNN supports online inference in the graph stream scenario,\nwhich incorporates the temporal information into node embeddings with a\ntemporal activation function and a projection layer besides several AP blocks.\n  Experimental results on various real-life temporal networks show that our\nproposed TAP-GNN outperforms existing temporal graph methods by a large margin\nin terms of both predictive performance and online inference latency.\n  Our code is available at \\url{https://github.com/doujiang-zheng/TAP-GNN}.",
+                    "authors": "Tongya Zheng, Xinchao Wang, Zunlei Feng, Jie Song, Yunzhi Hao, Mingli Song, Xingen Wang, Xinyu Wang, Chun Chen",
+                    "published": "2023-04-15",
+                    "updated": "2023-04-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.IR"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1811.08366v1",
+                    "title": "Temporal Graph Offset Reconstruction: Towards Temporally Robust Graph Representation Learning",
+                    "abstract": "Graphs are a commonly used construct for representing relationships between\nelements in complex high dimensional datasets. Many real-world phenomenon are\ndynamic in nature, meaning that any graph used to represent them is inherently\ntemporal. However, many of the machine learning models designed to capture\nknowledge about the structure of these graphs ignore this rich temporal\ninformation when creating representations of the graph. This results in models\nwhich do not perform well when used to make predictions about the future state\nof the graph -- especially when the delta between time stamps is not small. In\nthis work, we explore a novel training procedure and an associated unsupervised\nmodel which creates graph representations optimised to predict the future state\nof the graph. We make use of graph convolutional neural networks to encode the\ngraph into a latent representation, which we then use to train our temporal\noffset reconstruction method, inspired by auto-encoders, to predict a later\ntime point -- multiple time steps into the future. Using our method, we\ndemonstrate superior performance for the task of future link prediction\ncompared with none-temporal state-of-the-art baselines. We show our approach to\nbe capable of outperforming non-temporal baselines by 38% on a real world\ndataset.",
+                    "authors": "Stephen Bonner, John Brennan, Ibad Kureshi, Georgios Theodoropoulos, Andrew Stephen McGough, Boguslaw Obara",
+                    "published": "2018-11-20",
+                    "updated": "2018-11-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1703.02852v1",
+                    "title": "Introduction to a Temporal Graph Benchmark",
+                    "abstract": "A temporal graph is a data structure, consisting of nodes and edges in which\nthe edges are associated with time labels. To analyze the temporal graph, the\nfirst step is to find a proper graph dataset/benchmark. While many temporal\ngraph datasets exist online, none could be found that used the interval labels\nin which each edge is associated with a starting and ending time. Therefore we\ncreate a temporal graph data based on Wikipedia reference graph for temporal\nanalysis. This report aims to provide more details of this graph benchmark to\nthose who are interested in using it.",
+                    "authors": "Wouter Ligtenberg, Yulong Pei",
+                    "published": "2017-02-20",
+                    "updated": "2017-02-20",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1903.08889v3",
+                    "title": "Node Embedding over Temporal Graphs",
+                    "abstract": "In this work, we present a method for node embedding in temporal graphs. We\npropose an algorithm that learns the evolution of a temporal graph's nodes and\nedges over time and incorporates this dynamics in a temporal node embedding\nframework for different graph prediction tasks. We present a joint loss\nfunction that creates a temporal embedding of a node by learning to combine its\nhistorical temporal embeddings, such that it optimizes per given task (e.g.,\nlink prediction). The algorithm is initialized using static node embeddings,\nwhich are then aligned over the representations of a node at different time\npoints, and eventually adapted for the given task in a joint optimization. We\nevaluate the effectiveness of our approach over a variety of temporal graphs\nfor the two fundamental tasks of temporal link prediction and multi-label node\nclassification, comparing to competitive baselines and algorithmic\nalternatives. Our algorithm shows performance improvements across many of the\ndatasets and baselines and is found particularly effective for graphs that are\nless cohesive, with a lower clustering coefficient.",
+                    "authors": "Uriel Singer, Ido Guy, Kira Radinsky",
+                    "published": "2019-03-21",
+                    "updated": "2021-05-19",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SI",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.04782v1",
+                    "title": "A Survey on Temporal Knowledge Graph: Representation Learning and Applications",
+                    "abstract": "Knowledge graphs have garnered significant research attention and are widely\nused to enhance downstream applications. However, most current studies mainly\nfocus on static knowledge graphs, whose facts do not change with time, and\ndisregard their dynamic evolution over time. As a result, temporal knowledge\ngraphs have attracted more attention because a large amount of structured\nknowledge exists only within a specific period. Knowledge graph representation\nlearning aims to learn low-dimensional vector embeddings for entities and\nrelations in a knowledge graph. The representation learning of temporal\nknowledge graphs incorporates time information into the standard knowledge\ngraph framework and can model the dynamics of entities and relations over time.\nIn this paper, we conduct a comprehensive survey of temporal knowledge graph\nrepresentation learning and its applications. We begin with an introduction to\nthe definitions, datasets, and evaluation metrics for temporal knowledge graph\nrepresentation learning. Next, we propose a taxonomy based on the core\ntechnologies of temporal knowledge graph representation learning methods, and\nprovide an in-depth analysis of different methods in each category. Finally, we\npresent various downstream applications related to the temporal knowledge\ngraphs. In the end, we conclude the paper and have an outlook on the future\nresearch directions in this area.",
+                    "authors": "Li Cai, Xin Mao, Yuhao Zhou, Zhaoguang Long, Changxu Wu, Man Lan",
+                    "published": "2024-03-02",
+                    "updated": "2024-03-02",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2303.13177v1",
+                    "title": "It is all Connected: A New Graph Formulation for Spatio-Temporal Forecasting",
+                    "abstract": "With an ever-increasing number of sensors in modern society, spatio-temporal\ntime series forecasting has become a de facto tool to make informed decisions\nabout the future. Most spatio-temporal forecasting models typically comprise\ndistinct components that learn spatial and temporal dependencies. A common\nmethodology employs some Graph Neural Network (GNN) to capture relations\nbetween spatial locations, while another network, such as a recurrent neural\nnetwork (RNN), learns temporal correlations. By representing every recorded\nsample as its own node in a graph, rather than all measurements for a\nparticular location as a single node, temporal and spatial information is\nencoded in a similar manner. In this setting, GNNs can now directly learn both\ntemporal and spatial dependencies, jointly, while also alleviating the need for\nadditional temporal networks. Furthermore, the framework does not require\naligned measurements along the temporal dimension, meaning that it also\nnaturally facilitates irregular time series, different sampling frequencies or\nmissing data, without the need for data imputation. To evaluate the proposed\nmethodology, we consider wind speed forecasting as a case study, where our\nproposed framework outperformed other spatio-temporal models using GNNs with\neither Transformer or LSTM networks as temporal update functions.",
+                    "authors": "Lars \u00d8degaard Bentsen, Narada Dilp Warakagoda, Roy Stenbro, Paal Engelstad",
+                    "published": "2023-03-23",
+                    "updated": "2023-03-23",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1502.04579v3",
+                    "title": "The complexity of optimal design of temporally connected graphs",
+                    "abstract": "We study the design of small cost temporally connected graphs, under various\nconstraints. We mainly consider undirected graphs of $n$ vertices, where each\nedge has an associated set of discrete availability instances (labels). A\njourney from vertex $u$ to vertex $v$ is a path from $u$ to $v$ where\nsuccessive path edges have strictly increasing labels. A graph is temporally\nconnected iff there is a $(u,v)$-journey for any pair of vertices $u,v,~u\\not=\nv$. We first give a simple polynomial-time algorithm to check whether a given\ntemporal graph is temporally connected. We then consider the case in which a\ndesigner of temporal graphs can \\emph{freely choose} availability instances for\nall edges and aims for temporal connectivity with very small \\emph{cost}; the\ncost is the total number of availability instances used. We achieve this via a\nsimple polynomial-time procedure which derives designs of cost linear in $n$.\nWe also show that the above procedure is (almost) optimal when the underlying\ngraph is a tree, by proving a lower bound on the cost for any tree. However,\nthere are pragmatic cases where one is not free to design a temporally\nconnected graph anew, but is instead \\emph{given} a temporal graph design with\nthe claim that it is temporally connected, and wishes to make it more\ncost-efficient by removing labels without destroying temporal connectivity\n(redundant labels). Our main technical result is that computing the maximum\nnumber of redundant labels is APX-hard, i.e., there is no PTAS unless $P=NP$.\nOn the positive side, we show that in dense graphs with random edge\navailabilities, there is asymptotically almost surely a very large number of\nredundant labels. A temporal design may, however, be \\emph{minimal}, i.e., no\nredundant labels exist. We show the existence of minimal temporal designs with\nat least $n \\log{n}$ labels.",
+                    "authors": "Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, Paul G. Spirakis",
+                    "published": "2015-02-16",
+                    "updated": "2016-07-06",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.12973v1",
+                    "title": "Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is one of the most fundamental problems in transportation\nscience and artificial intelligence. The key challenge is to effectively model\ncomplex spatial-temporal dependencies and correlations in modern traffic data.\nExisting methods, however, cannot accurately model both long-term and\nshort-term temporal correlations simultaneously, limiting their expressive\npower on complex spatial-temporal patterns. In this paper, we propose a novel\nspatial-temporal neural network framework: Attention-based Spatial-Temporal\nGraph Convolutional Recurrent Network (ASTGCRN), which consists of a graph\nconvolutional recurrent module (GCRN) and a global attention module. In\nparticular, GCRN integrates gated recurrent units and adaptive graph\nconvolutional networks for dynamically learning graph structures and capturing\nspatial dependencies and local temporal relationships. To effectively extract\nglobal temporal dependencies, we design a temporal attention layer and\nimplement it as three independent modules based on multi-head self-attention,\ntransformer, and informer respectively. Extensive experiments on five real\ntraffic datasets have demonstrated the excellent predictive performance of all\nour three models with all their average MAE, RMSE and MAPE across the test\ndatasets lower than the baseline methods.",
+                    "authors": "Haiyang Liu, Chunjiang Zhu, Detian Zhang, Qing Li",
+                    "published": "2023-02-25",
+                    "updated": "2023-02-25",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2311.03897v1",
+                    "title": "Temporal Graph Representation Learning with Adaptive Augmentation Contrastive",
+                    "abstract": "Temporal graph representation learning aims to generate low-dimensional\ndynamic node embeddings to capture temporal information as well as structural\nand property information. Current representation learning methods for temporal\nnetworks often focus on capturing fine-grained information, which may lead to\nthe model capturing random noise instead of essential semantic information.\nWhile graph contrastive learning has shown promise in dealing with noise, it\nonly applies to static graphs or snapshots and may not be suitable for handling\ntime-dependent noise. To alleviate the above challenge, we propose a novel\nTemporal Graph representation learning with Adaptive augmentation Contrastive\n(TGAC) model. The adaptive augmentation on the temporal graph is made by\ncombining prior knowledge with temporal information, and the contrastive\nobjective function is constructed by defining the augmented inter-view contrast\nand intra-view contrast. To complement TGAC, we propose three adaptive\naugmentation strategies that modify topological features to reduce noise from\nthe network. Our extensive experiments on various real networks demonstrate\nthat the proposed model outperforms other temporal graph representation\nlearning methods.",
+                    "authors": "Hongjiang Chen, Pengfei Jiao, Huijun Tang, Huaming Wu",
+                    "published": "2023-11-07",
+                    "updated": "2023-11-07",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08323v2",
+                    "title": "TG-GAN: Continuous-time Temporal Graph Generation with Deep Generative Models",
+                    "abstract": "The recent deep generative models for static graphs that are now being\nactively developed have achieved significant success in areas such as molecule\ndesign. However, many real-world problems involve temporal graphs whose\ntopology and attribute values evolve dynamically over time, including important\napplications such as protein folding, human mobility networks, and social\nnetwork growth. As yet, deep generative models for temporal graphs are not yet\nwell understood and existing techniques for static graphs are not adequate for\ntemporal graphs since they cannot 1) encode and decode continuously-varying\ngraph topology chronologically, 2) enforce validity via temporal constraints,\nor 3) ensure efficiency for information-lossless temporal resolution. To\naddress these challenges, we propose a new model, called ``Temporal Graph\nGenerative Adversarial Network'' (TG-GAN) for continuous-time temporal graph\ngeneration, by modeling the deep generative process for truncated temporal\nrandom walks and their compositions. Specifically, we first propose a novel\ntemporal graph generator that jointly model truncated edge sequences, time\nbudgets, and node attributes, with novel activation functions that enforce\ntemporal validity constraints under recurrent architecture. In addition, a new\ntemporal graph discriminator is proposed, which combines time and node encoding\noperations over a recurrent architecture to distinguish the generated sequences\nfrom the real ones sampled by a newly-developed truncated temporal random walk\nsampler. Extensive experiments on both synthetic and real-world datasets\ndemonstrate TG-GAN significantly outperforms the comparison methods in\nefficiency and effectiveness.",
+                    "authors": "Liming Zhang, Liang Zhao, Shan Qin, Dieter Pfoser",
+                    "published": "2020-05-17",
+                    "updated": "2020-06-09",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.11979v1",
+                    "title": "MTGA: Multi-view Temporal Granularity aligned Aggregation for Event-based Lip-reading",
+                    "abstract": "Lip-reading is to utilize the visual information of the speaker's lip\nmovements to recognize words and sentences. Existing event-based lip-reading\nsolutions integrate different frame rate branches to learn spatio-temporal\nfeatures of varying granularities. However, aggregating events into event\nframes inevitably leads to the loss of fine-grained temporal information within\nframes. To remedy this drawback, we propose a novel framework termed Multi-view\nTemporal Granularity aligned Aggregation (MTGA). Specifically, we first present\na novel event representation method, namely time-segmented voxel graph list,\nwhere the most significant local voxels are temporally connected into a graph\nlist. Then we design a spatio-temporal fusion module based on temporal\ngranularity alignment, where the global spatial features extracted from event\nframes, together with the local relative spatial and temporal features\ncontained in voxel graph list are effectively aligned and integrated. Finally,\nwe design a temporal aggregation module that incorporates positional encoding,\nwhich enables the capture of local absolute spatial and global temporal\ninformation. Experiments demonstrate that our method outperforms both the\nevent-based and video-based lip-reading counterparts. Our code will be publicly\navailable.",
+                    "authors": "Wenhao Zhang, Jun Wang, Yong Luo, Lei Yu, Wei Yu, Zheng He",
+                    "published": "2024-04-18",
+                    "updated": "2024-04-18",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.11886v1",
+                    "title": "Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs",
+                    "abstract": "Temporal bipartite graphs are widely used to denote time-evolving\nrelationships between two disjoint sets of nodes, such as customer-product\ninteractions in E-commerce and user-group memberships in social networks.\nTemporal butterflies, $(2,2)$-bicliques that occur within a short period and in\na prescribed order, are essential in modeling the structural and sequential\npatterns of such graphs. Counting the number of temporal butterflies is thus a\nfundamental task in analyzing temporal bipartite graphs. However, existing\nalgorithms for butterfly counting on static bipartite graphs and motif counting\non temporal unipartite graphs are inefficient for this purpose. In this paper,\nwe present a general framework with three sampling strategies for temporal\nbutterfly counting. Since exact counting can be time-consuming on large graphs,\nour approach alternatively computes approximate estimates accurately and\nefficiently. We also provide analytical bounds on the number of samples each\nstrategy requires to obtain estimates with small relative errors and high\nprobability. We finally evaluate our framework on six real-world datasets and\ndemonstrate its superior accuracy and efficiency compared to several baselines.\nOverall, our proposed framework and sampling strategies provide efficient and\naccurate approaches to approximating temporal butterfly counts on large-scale\ntemporal bipartite graphs.",
+                    "authors": "Jiaxi Pu, Yanhao Wang, Yuchen Li, Xuan Zhou",
+                    "published": "2023-10-18",
+                    "updated": "2023-10-18",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.DB",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2105.12003v1",
+                    "title": "On Finding Separators in Temporal Split and Permutation Graphs",
+                    "abstract": "Removing all connections between two vertices s and z in a graph by removing\na minimum number of vertices is a fundamental problem in algorithmic graph\ntheory. This (s,z)-separation problem is well-known to be polynomial solvable\nand serves as an important primitive in many applications related to network\nconnectivity. We study the NP-hard temporal (s,z)-separation problem on\ntemporal graphs, which are graphs with fixed vertex sets but edge sets that\nchange over discrete time steps. We tackle this problem by restricting the\nlayers (i.e., graphs characterized by edges that are present at a certain point\nin time) to specific graph classes. We restrict the layers of the temporal\ngraphs to be either all split graphs or all permutation graphs (both being\nperfect graph classes) and provide both intractability and tractability\nresults. In particular, we show that in general the problem remains NP-hard\nboth on temporal split and temporal permutation graphs, but we also spot\npromising islands of fixed-parameter tractability particularly based on\nparameterizations that measure the amount of \"change over time\".",
+                    "authors": "Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken",
+                    "published": "2021-05-25",
+                    "updated": "2021-05-25",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2207.10830v1",
+                    "title": "Automated Dilated Spatio-Temporal Synchronous Graph Modeling for Traffic Prediction",
+                    "abstract": "Accurate traffic prediction is a challenging task in intelligent\ntransportation systems because of the complex spatio-temporal dependencies in\ntransportation networks. Many existing works utilize sophisticated temporal\nmodeling approaches to incorporate with graph convolution networks (GCNs) for\ncapturing short-term and long-term spatio-temporal dependencies. However, these\nseparated modules with complicated designs could restrict effectiveness and\nefficiency of spatio-temporal representation learning. Furthermore, most\nprevious works adopt the fixed graph construction methods to characterize the\nglobal spatio-temporal relations, which limits the learning capability of the\nmodel for different time periods and even different data scenarios. To overcome\nthese limitations, we propose an automated dilated spatio-temporal synchronous\ngraph network, named Auto-DSTSGN for traffic prediction. Specifically, we\ndesign an automated dilated spatio-temporal synchronous graph (Auto-DSTSG)\nmodule to capture the short-term and long-term spatio-temporal correlations by\nstacking deeper layers with dilation factors in an increasing order. Further,\nwe propose a graph structure search approach to automatically construct the\nspatio-temporal synchronous graph that can adapt to different data scenarios.\nExtensive experiments on four real-world datasets demonstrate that our model\ncan achieve about 10% improvements compared with the state-of-art methods.\nSource codes are available at https://github.com/jinguangyin/Auto-DSTSGN.",
+                    "authors": "Guangyin Jin, Fuxian Li, Jinlei Zhang, Mudan Wang, Jincai Huang",
+                    "published": "2022-07-22",
+                    "updated": "2022-07-22",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2309.03251v3",
+                    "title": "Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning",
+                    "abstract": "Temporal Knowledge Graph (TKG) is an extension of traditional Knowledge Graph\n(KG) that incorporates the dimension of time. Reasoning on TKGs is a crucial\ntask that aims to predict future facts based on historical occurrences. The key\nchallenge lies in uncovering structural dependencies within historical\nsubgraphs and temporal patterns. Most existing approaches model TKGs relying on\nentity modeling, as nodes in the graph play a crucial role in knowledge\nrepresentation. However, the real-world scenario often involves an extensive\nnumber of entities, with new entities emerging over time. This makes it\nchallenging for entity-dependent methods to cope with extensive volumes of\nentities, and effectively handling newly emerging entities also becomes a\nsignificant challenge. Therefore, we propose Temporal Inductive Path Neural\nNetwork (TiPNN), which models historical information in an entity-independent\nperspective. Specifically, TiPNN adopts a unified graph, namely history\ntemporal graph, to comprehensively capture and encapsulate information from\nhistory. Subsequently, we utilize the defined query-aware temporal paths on a\nhistory temporal graph to model historical path information related to queries\nfor reasoning. Extensive experiments illustrate that the proposed model not\nonly attains significant performance enhancements but also handles inductive\nsettings, while additionally facilitating the provision of reasoning evidence\nthrough history temporal graphs.",
+                    "authors": "Hao Dong, Pengyang Wang, Meng Xiao, Zhiyuan Ning, Pengfei Wang, Yuanchun Zhou",
+                    "published": "2023-09-06",
+                    "updated": "2024-01-25",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.07699v2",
+                    "title": "Time-aware Graph Structure Learning via Sequence Prediction on Temporal Graphs",
+                    "abstract": "Temporal Graph Learning, which aims to model the time-evolving nature of\ngraphs, has gained increasing attention and achieved remarkable performance\nrecently. However, in reality, graph structures are often incomplete and noisy,\nwhich hinders temporal graph networks (TGNs) from learning informative\nrepresentations. Graph contrastive learning uses data augmentation to generate\nplausible variations of existing data and learn robust representations.\nHowever, rule-based augmentation approaches may be suboptimal as they lack\nlearnability and fail to leverage rich information from downstream tasks. To\naddress these issues, we propose a Time-aware Graph Structure Learning (TGSL)\napproach via sequence prediction on temporal graphs, which learns better graph\nstructures for downstream tasks through adding potential temporal edges. In\nparticular, it predicts time-aware context embedding based on previously\nobserved interactions and uses the Gumble-Top-K to select the closest candidate\nedges to this context embedding. Additionally, several candidate sampling\nstrategies are proposed to ensure both efficiency and diversity. Furthermore,\nwe jointly learn the graph structure and TGNs in an end-to-end manner and\nperform inference on the refined graph. Extensive experiments on temporal link\nprediction benchmarks demonstrate that TGSL yields significant gains for the\npopular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive\nlearning methods on temporal graphs. We release the code at\nhttps://github.com/ViktorAxelsen/TGSL.",
+                    "authors": "Haozhen Zhang, Xueting Han, Xi Xiao, Jing Bai",
+                    "published": "2023-06-13",
+                    "updated": "2023-08-15",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.13624v1",
+                    "title": "Towards Linear Spanners in All Temporal Cliques",
+                    "abstract": "Many real-world networks, like transportation networks and social networks,\nare dynamic in the sense that the edge set may change over time, but these\nchanges are known in advance. This behavior is captured by the temporal graphs\nmodel, which has recently become a trending topic in theoretical computer\nscience. A core open problem in the field is to prove the existence of\nlinear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of\ncomplete temporal graphs that ensure all-pairs reachability via temporal paths.\nSo far, the best known result is the existence of temporal spanners with\n$\\mathcal{O}(n\\log n)$ many edges. We present significant progress towards\nproving that linear-size temporal spanners exist in all temporal cliques.\n  We adapt techniques used in previous works and heavily expand and generalize\nthem to provide a simpler and more intuitive proof of the $\\mathcal{O}(n\\log\nn)$ bound. Moreover, we use our novel approach to show that a large class of\ntemporal cliques, called edge-pivot graphs, admit linear-size temporal\nspanners. To contrast this, we investigate other classes of temporal cliques\nthat do not belong to the class of edge-pivot graphs. We introduce two such\ngraph classes and we develop novel techniques for establishing the existence of\nlinear temporal spanners in these graph classes as well.",
+                    "authors": "Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, Armin Wells",
+                    "published": "2024-02-21",
+                    "updated": "2024-02-21",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.00518v1",
+                    "title": "DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting",
+                    "abstract": "Traffic forecasting is essential to intelligent transportation systems, which\nis challenging due to the complicated spatial and temporal dependencies within\na road network. Existing works usually learn spatial and temporal dependencies\nseparately, ignoring the dependencies crossing spatial and temporal dimensions.\nIn this paper, we propose DSTCGCN, a dynamic spatial-temporal cross graph\nconvolution network to learn dynamic spatial and temporal dependencies jointly\nvia graphs for traffic forecasting. Specifically, we introduce a fast Fourier\ntransform (FFT) based attentive selector to choose relevant time steps for each\ntime step based on time-varying traffic data. Given the selected time steps, we\nintroduce a dynamic cross graph construction module, consisting of the spatial\ngraph construction, temporal connection graph construction, and fusion modules,\nto learn dynamic spatial-temporal cross dependencies without pre-defined\npriors. Extensive experiments on six real-world datasets demonstrate that\nDSTCGCN achieves the state-of-the-art performance.",
+                    "authors": "Binqing Wu, Ling Chen",
+                    "published": "2023-07-02",
+                    "updated": "2023-07-02",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.09114v1",
+                    "title": "Relational Temporal Graph Reasoning for Dual-task Dialogue Language Understanding",
+                    "abstract": "Dual-task dialog language understanding aims to tackle two correlative dialog\nlanguage understanding tasks simultaneously via leveraging their inherent\ncorrelations. In this paper, we put forward a new framework, whose core is\nrelational temporal graph reasoning.We propose a speaker-aware temporal graph\n(SATG) and a dual-task relational temporal graph (DRTG) to facilitate\nrelational temporal modeling in dialog understanding and dual-task reasoning.\nBesides, different from previous works that only achieve implicit\nsemantics-level interactions, we propose to model the explicit dependencies via\nintegrating prediction-level interactions. To implement our framework, we first\npropose a novel model Dual-tAsk temporal Relational rEcurrent Reasoning network\n(DARER), which first generates the context-, speaker- and temporal-sensitive\nutterance representations through relational temporal modeling of SATG, then\nconducts recurrent dual-task relational temporal graph reasoning on DRTG, in\nwhich process the estimated label distributions act as key clues in\nprediction-level interactions. And the relational temporal modeling in DARER is\nachieved by relational convolutional networks (RGCNs). Then we further propose\nRelational Temporal Transformer (ReTeFormer), which achieves fine-grained\nrelational temporal modeling via Relation- and Structure-aware Disentangled\nMulti-head Attention. Accordingly, we propose DARER with ReTeFormer (DARER2),\nwhich adopts two variants of ReTeFormer to achieve the relational temporal\nmodeling of SATG and DTRG, respectively. The extensive experiments on different\nscenarios verify that our models outperform state-of-the-art models by a large\nmargin. Remarkably, on the dialog sentiment classification task in the Mastodon\ndataset, DARER and DARER2 gain relative improvements of about 28% and 34% over\nthe previous best model in terms of F1.",
+                    "authors": "Bowen Xing, Ivor W. Tsang",
+                    "published": "2023-06-15",
+                    "updated": "2023-06-15",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1503.00278v1",
+                    "title": "An Introduction to Temporal Graphs: An Algorithmic Perspective",
+                    "abstract": "A \\emph{temporal graph} is, informally speaking, a graph that changes with\ntime. When time is discrete and only the relationships between the\nparticipating entities may change and not the entities themselves, a temporal\ngraph may be viewed as a sequence $G_1,G_2\\ldots,G_l$ of static graphs over the\nsame (static) set of nodes $V$. Though static graphs have been extensively\nstudied, for their temporal generalization we are still far from having a\nconcrete set of structural and algorithmic principles. Recent research shows\nthat many graph properties and problems become radically different and usually\nsubstantially more difficult when an extra time dimension in added to them.\nMoreover, there is already a rich and rapidly growing set of modern systems and\napplications that can be naturally modeled and studied via temporal graphs.\nThis, further motivates the need for the development of a temporal extension of\ngraph theory. We survey here recent results on temporal graphs and temporal\ngraph problems that have appeared in the Computer Science community.",
+                    "authors": "Othon Michail",
+                    "published": "2015-03-01",
+                    "updated": "2015-03-01",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DS",
+                        "05C85, 05C40, 05C38, 05C78, 05C80, 68R10, 68M14, 68M10, 68W25"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.04696v1",
+                    "title": "Nash Equilibria in Reverse Temporal Voronoi Games",
+                    "abstract": "We study Voronoi games on temporal graphs as introduced by Boehmer et al.\n(IJCAI 2021) where two players each select a vertex in a temporal graph with\nthe goal of reaching the other vertices earlier than the other player. In this\nwork, we consider the reverse temporal Voronoi game, that is, a player wants to\nmaximize the number of vertices reaching her earlier than the other player.\nSince temporal distances in temporal graphs are not symmetric in general, this\nyields a different game. We investigate the difference between the two games\nwith respect to the existence of Nash equilibria in various temporal graph\nclasses including temporal trees, cycles, grids, cliques and split graphs. Our\nextensive results show that the two games indeed behave quite differently\ndepending on the considered temporal graph class.",
+                    "authors": "Simeon Pawlowski, Vincent Froese",
+                    "published": "2024-02-07",
+                    "updated": "2024-02-07",
+                    "primary_cat": "cs.GT",
+                    "cats": [
+                        "cs.GT"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.07993v2",
+                    "title": "RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion",
+                    "abstract": "Temporal factors are tied to the growth of facts in realistic applications,\nsuch as the progress of diseases and the development of political situation,\ntherefore, research on Temporal Knowledge Graph (TKG) attracks much attention.\nIn TKG, relation patterns inherent with temporality are required to be studied\nfor representation learning and reasoning across temporal facts. However,\nexisting methods can hardly model temporal relation patterns, nor can capture\nthe intrinsic connections between relations when evolving over time, lacking of\ninterpretability. In this paper, we propose a novel temporal modeling method\nwhich represents temporal entities as Rotations in Quaternion Vector Space\n(RotateQVS) and relations as complex vectors in Hamilton's quaternion space. We\ndemonstrate our method can model key patterns of relations in TKG, such as\nsymmetry, asymmetry, inverse, and can further capture time-evolved relations by\ntheory. Empirically, we show that our method can boost the performance of link\nprediction tasks over four temporal knowledge graph benchmarks.",
+                    "authors": "Kai Chen, Ye Wang, Yitong Li, Aiping Li",
+                    "published": "2022-03-15",
+                    "updated": "2022-03-17",
+                    "primary_cat": "cs.AI",
+                    "cats": [
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2005.08514v2",
+                    "title": "Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction",
+                    "abstract": "Understanding crowd motion dynamics is critical to real-world applications,\ne.g., surveillance systems and autonomous driving. This is challenging because\nit requires effectively modeling the socially aware crowd spatial interaction\nand complex temporal dependencies. We believe attention is the most important\nfactor for trajectory prediction. In this paper, we present STAR, a\nSpatio-Temporal grAph tRansformer framework, which tackles trajectory\nprediction by only attention mechanisms. STAR models intra-graph crowd\ninteraction by TGConv, a novel Transformer-based graph convolution mechanism.\nThe inter-graph temporal dependencies are modeled by separate temporal\nTransformers. STAR captures complex spatio-temporal interactions by\ninterleaving between spatial and temporal Transformers. To calibrate the\ntemporal prediction for the long-lasting effect of disappeared pedestrians, we\nintroduce a read-writable external memory module, consistently being updated by\nthe temporal Transformer. We show that with only attention mechanism, STAR\nachieves state-of-the-art performance on 5 commonly used real-world pedestrian\nprediction datasets.",
+                    "authors": "Cunjun Yu, Xiao Ma, Jiawei Ren, Haiyu Zhao, Shuai Yi",
+                    "published": "2020-05-18",
+                    "updated": "2020-07-24",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.RO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2312.06260v1",
+                    "title": "In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs",
+                    "abstract": "A graph whose edges only appear at certain points in time is called a\ntemporal graph (among other names). These graphs are temporally connected if\nall ordered pairs of vertices are connected by a path that traverses edges in\nchronological order (a temporal path). Reachability in temporal graphs departs\nsignificantly from standard reachability; in particular, it is not transitive,\nwith structural and algorithmic consequences. For instance, temporally\nconnected graphs do not always admit spanning trees, i.e., subsets of edges\nthat form a tree and preserve temporal connectivity among the nodes.\n  In this paper, we revisit fundamental questions about the loss of\nuniversality of spanning trees. To start, we show that deciding if a spanning\ntree exists in a given temporal graph is NP-complete. What could be appropriate\nreplacement for the concept? Beyond having minimum size, spanning trees enjoy\nthe feature of enabling reachability along the same underlying paths in both\ndirections, a pretty uncommon feature in temporal graphs. We explore\nrelaxations in this direction and show that testing the existence of\nbidirectional spanning structures (bi-spanners) is tractable in general. On the\ndown side, finding \\emph{minimum} such structures is NP-hard even in simple\ntemporal graphs. Still, the fact that bidirectionality can be tested\nefficiently may find applications, e.g. for routing and security, and the\ncorresponding primitive that we introduce in the algorithm may be of\nindependent interest.",
+                    "authors": "Arnaud Casteigts, Timoth\u00e9e Corsini",
+                    "published": "2023-12-11",
+                    "updated": "2023-12-11",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "cs.DC",
+                        "68R10, 68W15",
+                        "G.2.2; C.2.4"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2212.01594v1",
+                    "title": "Parameterized temporal exploration problems",
+                    "abstract": "In this paper we study the fixed-parameter tractability of the problem of\ndeciding whether a given temporal graph admits a temporal walk that visits all\nvertices (temporal exploration) or, in some problem variants, a certain subset\nof the vertices. Formally, a temporal graph is a sequence <G_1,...,G_L> of\ngraphs with V(G_t) = V(G) and E(G_t) a subset of E(G) for all t in [L] and some\nunderlying graph G, and a temporal walk is a time-respecting sequence of\nedge-traversals. We consider both the strict variant, in which edges must be\ntraversed in strictly increasing timesteps, and the non-strict variant, in\nwhich an arbitrary number of edges can be traversed in each timestep. For both\nvariants, we give FPT algorithms for the problem of finding a temporal walk\nthat visits a given set X of vertices, parameterized by |X|, and for the\nproblem of finding a temporal walk that visits at least k distinct vertices in\nV(G), parameterized by k. We also show W[2]-hardness for a set version of the\ntemporal exploration problem for both variants. For the non-strict variant, we\ngive an FPT algorithm for the temporal exploration problem parameterized by the\nlifetime of the input graph, and we show that the temporal exploration problem\ncan be solved in polynomial time if the graph in each timestep has at most two\nconnected components.",
+                    "authors": "Thomas Erlebach, Jakob T. Spooner",
+                    "published": "2022-12-03",
+                    "updated": "2022-12-03",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "05C85",
+                        "F.2.2; G.2.2"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2402.03651v1",
+                    "title": "Temporal Graph Analysis with TGX",
+                    "abstract": "Real-world networks, with their evolving relations, are best captured as\ntemporal graphs. However, existing software libraries are largely designed for\nstatic graphs where the dynamic nature of temporal graphs is ignored. Bridging\nthis gap, we introduce TGX, a Python package specially designed for analysis of\ntemporal networks that encompasses an automated pipeline for data loading, data\nprocessing, and analysis of evolving graphs. TGX provides access to eleven\nbuilt-in datasets and eight external Temporal Graph Benchmark (TGB) datasets as\nwell as any novel datasets in the .csv format. Beyond data loading, TGX\nfacilitates data processing functionalities such as discretization of temporal\ngraphs and node subsampling to accelerate working with larger datasets. For\ncomprehensive investigation, TGX offers network analysis by providing a diverse\nset of measures, including average node degree and the evolving number of nodes\nand edges per timestamp. Additionally, the package consolidates meaningful\nvisualization plots indicating the evolution of temporal patterns, such as\nTemporal Edge Appearance (TEA) and Temporal Edge Trafficc (TET) plots. The TGX\npackage is a robust tool for examining the features of temporal graphs and can\nbe used in various areas like studying social networks, citation networks, and\ntracking user interactions. We plan to continuously support and update TGX\nbased on community feedback. TGX is publicly available on:\nhttps://github.com/ComplexData-MILA/TGX.",
+                    "authors": "Razieh Shirzadkhani, Shenyang Huang, Elahe Kooshafar, Reihaneh Rabbany, Farimah Poursafaei",
+                    "published": "2024-02-06",
+                    "updated": "2024-02-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2302.02128v1",
+                    "title": "Interaction Order Prediction for Temporal Graphs",
+                    "abstract": "Link prediction in graphs is a task that has been widely investigated. It has\nbeen applied in various domains such as knowledge graph completion,\ncontent/item recommendation, social network recommendations and so on. The\ninitial focus of most research was on link prediction in static graphs.\nHowever, there has recently been abundant work on modeling temporal graphs, and\nconsequently one of the tasks that has been researched is link prediction in\ntemporal graphs. However, most of the existing work does not focus on the order\nof link formation, and only predicts the existence of links. In this study, we\naim to predict the order of node interactions.",
+                    "authors": "Nayana Bannur, Mashrin Srivastava, Harsha Vardhan",
+                    "published": "2023-02-04",
+                    "updated": "2023-02-04",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.CL",
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2304.05078v1",
+                    "title": "TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification",
+                    "abstract": "Multivariate time series classification (MTSC) is an important data mining\ntask, which can be effectively solved by popular deep learning technology.\nUnfortunately, the existing deep learning-based methods neglect the hidden\ndependencies in different dimensions and also rarely consider the unique\ndynamic features of time series, which lack sufficient feature extraction\ncapability to obtain satisfactory classification accuracy. To address this\nproblem, we propose a novel temporal dynamic graph neural network (TodyNet)\nthat can extract hidden spatio-temporal dependencies without undefined graph\nstructure. It enables information flow among isolated but implicit\ninterdependent variables and captures the associations between different time\nslots by dynamic graph mechanism, which further improves the classification\nperformance of the model. Meanwhile, the hierarchical representations of graphs\ncannot be learned due to the limitation of GNNs. Thus, we also design a\ntemporal graph pooling layer to obtain a global graph-level representation for\ngraph learning with learnable temporal parameters. The dynamic graph, graph\ninformation propagation, and temporal convolution are jointly learned in an\nend-to-end framework. The experiments on 26 UEA benchmark datasets illustrate\nthat the proposed TodyNet outperforms existing deep learning-based methods in\nthe MTSC tasks.",
+                    "authors": "Huaiyuan Liu, Xianzhang Liu, Donghua Yang, Zhiyu Liang, Hongzhi Wang, Yong Cui, Jun Gu",
+                    "published": "2023-04-11",
+                    "updated": "2023-04-11",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.07016v2",
+                    "title": "On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions",
+                    "abstract": "This work formalizes the associational task of predicting node attribute\nevolution in temporal graphs from the perspective of learning equivariant\nrepresentations. We show that node representations in temporal graphs can be\ncast into two distinct frameworks: (a) The most popular approach, which we\ndenote as time-and-graph, where equivariant graph (e.g., GNN) and sequence\n(e.g., RNN) representations are intertwined to represent the temporal evolution\nof node attributes in the graph; and (b) an approach that we denote as\ntime-then-graph, where the sequences describing the node and edge dynamics are\nrepresented first, then fed as node and edge attributes into a static\nequivariant graph representation that comes after. Interestingly, we show that\ntime-then-graph representations have an expressivity advantage over\ntime-and-graph representations when both use component GNNs that are not\nmost-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is\nnot necessarily to obtain state-of-the-art results, our experiments show that\ntime-then-graph methods are capable of achieving better performance and\nefficiency than state-of-the-art time-and-graph methods in some real-world\ntasks, thereby showcasing that the time-then-graph framework is a worthy\naddition to the graph ML toolbox.",
+                    "authors": "Jianfei Gao, Bruno Ribeiro",
+                    "published": "2021-03-12",
+                    "updated": "2023-03-27",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.12843v1",
+                    "title": "An embedding-based distance for temporal graphs",
+                    "abstract": "We define a distance between temporal graphs based on graph embeddings built\nusing time-respecting random walks. We study both the case of matched graphs,\nwhen there exists a known relation between the nodes, and the unmatched case,\nwhen such a relation is unavailable and the graphs may be of different sizes.\nWe illustrate the interest of our distance definition, using both real and\nsynthetic temporal network data, by showing its ability to discriminate between\ngraphs with different structural and temporal properties. Leveraging\nstate-of-the-art machine learning techniques, we propose an efficient\nimplementation of distance computation that is viable for large-scale temporal\ngraphs.",
+                    "authors": "Lorenzo Dall'Amico, Alain Barrat, Ciro Cattuto",
+                    "published": "2024-01-23",
+                    "updated": "2024-01-23",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.LG",
+                        "physics.soc-ph"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2403.09039v1",
+                    "title": "Spatial-temporal Memories Enhanced Graph Autoencoder for Anomaly Detection in Dynamic Graphs",
+                    "abstract": "Anomaly detection in dynamic graphs presents a significant challenge due to\nthe temporal evolution of graph structures and attributes. The conventional\napproaches that tackle this problem typically employ an unsupervised learning\nframework, capturing normality patterns with exclusive normal data during\ntraining and identifying deviations as anomalies during testing. However, these\nmethods face critical drawbacks: they either only depend on proxy tasks for\ngeneral representation without directly pinpointing normal patterns, or they\nneglect to differentiate between spatial and temporal normality patterns,\nleading to diminished efficacy in anomaly detection. To address these\nchallenges, we introduce a novel Spatial-Temporal memories-enhanced graph\nautoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs)\nand gated temporal convolution layers to extract spatial features and temporal\nfeatures, respectively. Then STRIPE incorporates separate spatial and temporal\nmemory networks, which capture and store prototypes of normal patterns, thereby\npreserving the uniqueness of spatial and temporal normality. After that,\nthrough a mutual attention mechanism, these stored patterns are then retrieved\nand integrated with encoded graph embeddings. Finally, the integrated features\nare fed into the decoder to reconstruct the graph streams which serve as the\nproxy task for anomaly detection. This comprehensive approach not only\nminimizes reconstruction errors but also refines the model by emphasizing the\ncompactness and distinctiveness of the embeddings in relation to the nearest\nmemory prototypes. Through extensive testing, STRIPE has demonstrated a\nsuperior capability to discern anomalies by effectively leveraging the distinct\nspatial and temporal dynamics of dynamic graphs, significantly outperforming\nexisting methodologies, with an average improvement of 15.39% on AUC values.",
+                    "authors": "Jie Liu, Xuequn Shang, Xiaolin Han, Wentao Zhang, Hongzhi Yin",
+                    "published": "2024-03-14",
+                    "updated": "2024-03-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.11190v1",
+                    "title": "Using Motif Transitions for Temporal Graph Generation",
+                    "abstract": "Graph generative models are highly important for sharing surrogate data and\nbenchmarking purposes. Real-world complex systems often exhibit dynamic nature,\nwhere the interactions among nodes change over time in the form of a temporal\nnetwork. Most temporal network generation models extend the static graph\ngeneration models by incorporating temporality in the generation process. More\nrecently, temporal motifs are used to generate temporal networks with better\nsuccess. However, existing models are often restricted to a small set of\npredefined motif patterns due to the high computational cost of counting\ntemporal motifs. In this work, we develop a practical temporal graph generator,\nMotif Transition Model (MTM), to generate synthetic temporal networks with\nrealistic global and local features. Our key idea is modeling the arrival of\nnew events as temporal motif transition processes. We first calculate the\ntransition properties from the input graph and then simulate the motif\ntransition processes based on the transition probabilities and transition\nrates. We demonstrate that our model consistently outperforms the baselines\nwith respect to preserving various global and local temporal graph statistics\nand runtime performance.",
+                    "authors": "Penghang Liu, A. Erdem Sar\u0131y\u00fcce",
+                    "published": "2023-06-19",
+                    "updated": "2023-06-19",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2112.08733v1",
+                    "title": "Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast",
+                    "abstract": "Self-supervised learning on graphs has recently drawn a lot of attention due\nto its independence from labels and its robustness in representation. Current\nstudies on this topic mainly use static information such as graph structures\nbut cannot well capture dynamic information such as timestamps of edges.\nRealistic graphs are often dynamic, which means the interaction between nodes\noccurs at a specific time. This paper proposes a self-supervised dynamic graph\nrepresentation learning framework (DySubC), which defines a temporal subgraph\ncontrastive learning task to simultaneously learn the structural and\nevolutional features of a dynamic graph. Specifically, a novel temporal\nsubgraph sampling strategy is firstly proposed, which takes each node of the\ndynamic graph as the central node and uses both neighborhood structures and\nedge timestamps to sample the corresponding temporal subgraph. The subgraph\nrepresentation function is then designed according to the influence of\nneighborhood nodes on the central node after encoding the nodes in each\nsubgraph. Finally, the structural and temporal contrastive loss are defined to\nmaximize the mutual information between node representation and temporal\nsubgraph representation. Experiments on five real-world datasets demonstrate\nthat (1) DySubC performs better than the related baselines including two graph\ncontrastive learning models and four dynamic graph representation learning\nmodels in the downstream link prediction task, and (2) the use of temporal\ninformation can not only sample more effective subgraphs, but also learn better\nrepresentation by temporal contrastive loss.",
+                    "authors": "Linpu Jiang, Ke-Jia Chen, Jingqiang Chen",
+                    "published": "2021-12-16",
+                    "updated": "2021-12-16",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.15894v1",
+                    "title": "A Gated MLP Architecture for Learning Topological Dependencies in Spatio-Temporal Graphs",
+                    "abstract": "Graph Neural Networks (GNNs) and Transformer have been increasingly adopted\nto learn the complex vector representations of spatio-temporal graphs,\ncapturing intricate spatio-temporal dependencies crucial for applications such\nas traffic datasets. Although many existing methods utilize multi-head\nattention mechanisms and message-passing neural networks (MPNNs) to capture\nboth spatial and temporal relations, these approaches encode temporal and\nspatial relations independently, and reflect the graph's topological\ncharacteristics in a limited manner. In this work, we introduce the Cycle to\nMixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial\ninvariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP).\nThe Cy2Mixer is composed of three blocks based on MLPs: A message-passing block\nfor encapsulating spatial information, a cycle message-passing block for\nenriching topological information through cyclic subgraphs, and a temporal\nblock for capturing temporal properties. We bolster the effectiveness of\nCy2Mixer with mathematical evidence emphasizing that our cycle message-passing\nblock is capable of offering differentiated information to the deep learning\nmodel compared to the message-passing block. Furthermore, empirical evaluations\nsubstantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art\nperformances across various traffic benchmark datasets.",
+                    "authors": "Yun Young Choi, Minho Lee, Sun Woo Park, Seunghwan Lee, Joohwan Ko",
+                    "published": "2024-01-29",
+                    "updated": "2024-01-29",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1908.09995v1",
+                    "title": "Temporal Reasoning Graph for Activity Recognition",
+                    "abstract": "Despite great success has been achieved in activity analysis, it still has\nmany challenges. Most existing work in activity recognition pay more attention\nto design efficient architecture or video sampling strategy. However, due to\nthe property of fine-grained action and long term structure in video, activity\nrecognition is expected to reason temporal relation between video sequences. In\nthis paper, we propose an efficient temporal reasoning graph (TRG) to\nsimultaneously capture the appearance features and temporal relation between\nvideo sequences at multiple time scales. Specifically, we construct learnable\ntemporal relation graphs to explore temporal relation on the multi-scale range.\nAdditionally, to facilitate multi-scale temporal relation extraction, we design\na multi-head temporal adjacent matrix to represent multi-kinds of temporal\nrelations. Eventually, a multi-head temporal relation aggregator is proposed to\nextract the semantic meaning of those features convolving through the graphs.\nExtensive experiments are performed on widely-used large-scale datasets, such\nas Something-Something and Charades, and the results show that our model can\nachieve state-of-the-art performance. Further analysis shows that temporal\nrelation reasoning with our TRG can extract discriminative features for\nactivity recognition.",
+                    "authors": "Jingran Zhang, Fumin Shen, Xing Xu, Heng Tao Shen",
+                    "published": "2019-08-27",
+                    "updated": "2019-08-27",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.17110v2",
+                    "title": "LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?",
+                    "abstract": "In an era marked by the increasing adoption of Large Language Models (LLMs)\nfor various tasks, there is a growing focus on exploring LLMs' capabilities in\nhandling web data, particularly graph data. Dynamic graphs, which capture\ntemporal network evolution patterns, are ubiquitous in real-world web data.\nEvaluating LLMs' competence in understanding spatial-temporal information on\ndynamic graphs is essential for their adoption in web applications, which\nremains unexplored in the literature. In this paper, we bridge the gap via\nproposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic\ngraphs, to the best of our knowledge, for the first time. Specifically, we\npropose the LLM4DyG benchmark, which includes nine specially designed tasks\nconsidering the capability evaluation of LLMs from both temporal and spatial\ndimensions. Then, we conduct extensive experiments to analyze the impacts of\ndifferent data generators, data statistics, prompting techniques, and LLMs on\nthe model performance. Finally, we propose Disentangled Spatial-Temporal\nThoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal\nunderstanding abilities. Our main observations are: 1) LLMs have preliminary\nspatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph\ntasks show increasing difficulties for LLMs as the graph size and density\nincrease, while not sensitive to the time span and data generation mechanism,\n3) the proposed DST2 prompting method can help to improve LLMs'\nspatial-temporal understanding abilities on dynamic graphs for most tasks. The\ndata and codes will be open-sourced at publication time.",
+                    "authors": "Zeyang Zhang, Xin Wang, Ziwei Zhang, Haoyang Li, Yijian Qin, Wenwu Zhu",
+                    "published": "2023-10-26",
+                    "updated": "2024-03-08",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2306.01012v1",
+                    "title": "Graph-Level Embedding for Time-Evolving Graphs",
+                    "abstract": "Graph representation learning (also known as network embedding) has been\nextensively researched with varying levels of granularity, ranging from nodes\nto graphs. While most prior work in this area focuses on node-level\nrepresentation, limited research has been conducted on graph-level embedding,\nparticularly for dynamic or temporal networks. However, learning\nlow-dimensional graph-level representations for dynamic networks is critical\nfor various downstream graph retrieval tasks such as temporal graph similarity\nranking, temporal graph isomorphism, and anomaly detection. In this paper, we\npresent a novel method for temporal graph-level embedding that addresses this\ngap. Our approach involves constructing a multilayer graph and using a modified\nrandom walk with temporal backtracking to generate temporal contexts for the\ngraph's nodes. We then train a \"document-level\" language model on these\ncontexts to generate graph-level embeddings. We evaluate our proposed model on\nfive publicly available datasets for the task of temporal graph similarity\nranking, and our model outperforms baseline methods. Our experimental results\ndemonstrate the effectiveness of our method in generating graph-level\nembeddings for dynamic networks.",
+                    "authors": "Lili Wang, Chenghan Huang, Weicheng Ma, Xinyuan Cao, Soroush Vosoughi",
+                    "published": "2023-06-01",
+                    "updated": "2023-06-01",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI",
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.19292v1",
+                    "title": "Fusing Temporal Graphs into Transformers for Time-Sensitive Question Answering",
+                    "abstract": "Answering time-sensitive questions from long documents requires temporal\nreasoning over the times in questions and documents. An important open question\nis whether large language models can perform such reasoning solely using a\nprovided text document, or whether they can benefit from additional temporal\ninformation extracted using other systems. We address this research question by\napplying existing temporal information extraction systems to construct temporal\ngraphs of events, times, and temporal relations in questions and documents. We\nthen investigate different approaches for fusing these graphs into Transformer\nmodels. Experimental results show that our proposed approach for fusing\ntemporal graphs into input text substantially enhances the temporal reasoning\ncapabilities of Transformer models with or without fine-tuning. Additionally,\nour proposed method outperforms various graph convolution-based approaches and\nestablishes a new state-of-the-art performance on SituatedQA and three splits\nof TimeQA.",
+                    "authors": "Xin Su, Phillip Howard, Nagib Hakim, Steven Bethard",
+                    "published": "2023-10-30",
+                    "updated": "2023-10-30",
+                    "primary_cat": "cs.CL",
+                    "cats": [
+                        "cs.CL"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2401.11074v1",
+                    "title": "On The Temporal Domain of Differential Equation Inspired Graph Neural Networks",
+                    "abstract": "Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling\ncomplex relationships in graph-structured data. A recent innovation in this\nfield is the family of Differential Equation-Inspired Graph Neural Networks\n(DE-GNNs), which leverage principles from continuous dynamical systems to model\ninformation flow on graphs with built-in properties such as feature smoothing\nor preservation. However, existing DE-GNNs rely on first or second-order\ntemporal dependencies. In this paper, we propose a neural extension to those\npre-defined temporal dependencies. We show that our model, called TDE-GNN, can\ncapture a wide range of temporal dynamics that go beyond typical first or\nsecond-order methods, and provide use cases where existing temporal models are\nchallenged. We demonstrate the benefit of learning the temporal dependencies\nusing our method rather than using pre-defined temporal dynamics on several\ngraph benchmarks.",
+                    "authors": "Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane Sch\u00f6nlieb",
+                    "published": "2024-01-20",
+                    "updated": "2024-01-20",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2307.13250v1",
+                    "title": "Keyword-Aware Relative Spatio-Temporal Graph Networks for Video Question Answering",
+                    "abstract": "The main challenge in video question answering (VideoQA) is to capture and\nunderstand the complex spatial and temporal relations between objects based on\ngiven questions. Existing graph-based methods for VideoQA usually ignore\nkeywords in questions and employ a simple graph to aggregate features without\nconsidering relative relations between objects, which may lead to inferior\nperformance. In this paper, we propose a Keyword-aware Relative Spatio-Temporal\n(KRST) graph network for VideoQA. First, to make question features aware of\nkeywords, we employ an attention mechanism to assign high weights to keywords\nduring question encoding. The keyword-aware question features are then used to\nguide video graph construction. Second, because relations are relative, we\nintegrate the relative relation modeling to better capture the spatio-temporal\ndynamics among object nodes. Moreover, we disentangle the spatio-temporal\nreasoning into an object-level spatial graph and a frame-level temporal graph,\nwhich reduces the impact of spatial and temporal relation reasoning on each\nother. Extensive experiments on the TGIF-QA, MSVD-QA and MSRVTT-QA datasets\ndemonstrate the superiority of our KRST over multiple state-of-the-art methods.",
+                    "authors": "Yi Cheng, Hehe Fan, Dongyun Lin, Ying Sun, Mohan Kankanhalli, Joo-Hwee Lim",
+                    "published": "2023-07-25",
+                    "updated": "2023-07-25",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2101.00820v8",
+                    "title": "Temporal Contrastive Graph Learning for Video Action Recognition and Retrieval",
+                    "abstract": "Attempt to fully discover the temporal diversity and chronological\ncharacteristics for self-supervised video representation learning, this work\ntakes advantage of the temporal dependencies within videos and further proposes\na novel self-supervised method named Temporal Contrastive Graph Learning\n(TCGL). In contrast to the existing methods that ignore modeling elaborate\ntemporal dependencies, our TCGL roots in a hybrid graph contrastive learning\nstrategy to jointly regard the inter-snippet and intra-snippet temporal\ndependencies as self-supervision signals for temporal representation learning.\nTo model multi-scale temporal dependencies, our TCGL integrates the prior\nknowledge about the frame and snippet orders into graph structures, i.e., the\nintra-/inter- snippet temporal contrastive graphs. By randomly removing edges\nand masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL\ncan generate different correlated graph views. Then, specific contrastive\nlearning modules are designed to maximize the agreement between nodes in\ndifferent views. To adaptively learn the global context representation and\nrecalibrate the channel-wise features, we introduce an adaptive video snippet\norder prediction module, which leverages the relational knowledge among video\nsnippets to predict the actual snippet orders. Experimental results demonstrate\nthe superiority of our TCGL over the state-of-the-art methods on large-scale\naction recognition and video retrieval benchmarks.",
+                    "authors": "Yang Liu, Keze Wang, Haoyuan Lan, Liang Lin",
+                    "published": "2021-01-04",
+                    "updated": "2021-03-17",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV",
+                        "cs.LG",
+                        "cs.MM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1711.00963v5",
+                    "title": "The Complexity of Finding Small Separators in Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs with time-stamped edges. We study the problem of\nfinding a small vertex set (the separator) with respect to two designated\nterminal vertices such that the removal of the set eliminates all temporal\npaths connecting one terminal to the other. Herein, we consider two models of\ntemporal paths: paths that pass through arbitrarily many edges per time step\n(non-strict) and paths that pass through at most one edge per time step\n(strict). Regarding the number of time steps of a temporal graph, we show a\ncomplexity dichotomy (NP-hardness versus polynomial-time solvability) for both\nproblem variants. Moreover we prove both problem variants to be NP-complete\neven on temporal graphs whose underlying graph is planar. We further show that,\non temporal graphs with planar underlying graph, if additionally the number of\ntime steps is constant, then the problem variant for strict paths is solvable\nin quasi-linear time. Finally, we introduce and motivate the notion of a\ntemporal core (vertices whose incident edges change over time). We prove that\nthe non-strict variant is fixed-parameter tractable when parameterized by the\nsize of the temporal core, while the strict variant remains NP-complete, even\nfor constant-size temporal cores.",
+                    "authors": "Philipp Zschoche, Till Fluschnik, Hendrik Molter, Rolf Niedermeier",
+                    "published": "2017-11-02",
+                    "updated": "2018-07-25",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS",
+                        "cs.CC",
+                        "cs.DM"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.06411v1",
+                    "title": "On the Size and the Approximability of Minimum Temporally Connected Subgraphs",
+                    "abstract": "We consider temporal graphs with discrete time labels and investigate the\nsize and the approximability of minimum temporally connected spanning\nsubgraphs. We present a family of minimally connected temporal graphs with $n$\nvertices and $\\Omega(n^2)$ edges, thus resolving an open question of (Kempe,\nKleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal\nconnectivity certificates. Next, we consider the problem of computing a minimum\nweight subset of temporal edges that preserve connectivity of a given temporal\ngraph either from a given vertex r (r-MTC problem) or among all vertex pairs\n(MTC problem). We show that the approximability of r-MTC is closely related to\nthe approximability of Directed Steiner Tree and that r-MTC can be solved in\npolynomial time if the underlying graph has bounded treewidth. We also show\nthat the best approximation ratio for MTC is at least $O(2^{\\log^{1-\\epsilon}\nn})$ and at most $O(\\min\\{n^{1+\\epsilon}, (\\Delta M)^{2/3+\\epsilon}\\})$, for\nany constant $\\epsilon > 0$, where $M$ is the number of temporal edges and\n$\\Delta$ is the maximum degree of the underlying graph. Furthermore, we prove\nthat the unweighted version of MTC is APX-hard and that MTC is efficiently\nsolvable in trees and $2$-approximable in cycles.",
+                    "authors": "Kyriakos Axiotis, Dimitris Fotakis",
+                    "published": "2016-02-20",
+                    "updated": "2016-02-20",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2103.10379v1",
+                    "title": "ChronoR: Rotation Based Temporal Knowledge Graph Embedding",
+                    "abstract": "Despite the importance and abundance of temporal knowledge graphs, most of\nthe current research has been focused on reasoning on static graphs. In this\npaper, we study the challenging problem of inference over temporal knowledge\ngraphs. In particular, the task of temporal link prediction. In general, this\nis a difficult task due to data non-stationarity, data heterogeneity, and its\ncomplex temporal dependencies. We propose Chronological Rotation embedding\n(ChronoR), a novel model for learning representations for entities, relations,\nand time. Learning dense representations is frequently used as an efficient and\nversatile method to perform reasoning on knowledge graphs. The proposed model\nlearns a k-dimensional rotation transformation parametrized by relation and\ntime, such that after each fact's head entity is transformed using the\nrotation, it falls near its corresponding tail entity. By using high\ndimensional rotation as its transformation operator, ChronoR captures rich\ninteraction between the temporal and multi-relational characteristics of a\nTemporal Knowledge Graph. Experimentally, we show that ChronoR is able to\noutperform many of the state-of-the-art methods on the benchmark datasets for\ntemporal knowledge graph link prediction.",
+                    "authors": "Ali Sadeghian, Mohammadreza Armandpour, Anthony Colas, Daisy Zhe Wang",
+                    "published": "2021-03-18",
+                    "updated": "2021-03-18",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SC"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2002.08312v2",
+                    "title": "ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks",
+                    "abstract": "Networks are a fundamental and flexible way of representing various complex\nsystems. Many domains such as communication, citation, procurement, biology,\nsocial media, and transportation can be modeled as a set of entities and their\nrelationships. Temporal networks are a specialization of general networks where\nthe temporal evolution of the system is as important to understand as the\nstructure of the entities and relationships. We present the Independent\nTemporal Motif (ITeM) to characterize temporal graphs from different domains.\nThe ITeMs are edge-disjoint temporal motifs that can be used to model the\nstructure and the evolution of the graph. For a given temporal graph, we\nproduce a feature vector of ITeM frequencies and apply this distribution to the\ntask of measuring the similarity of temporal graphs. We show that ITeM has\nhigher accuracy than other motif frequency-based approaches. We define various\nmetrics based on ITeM that reveal salient properties of a temporal network. We\nalso present importance sampling as a method for efficiently estimating the\nITeM counts. We evaluate our approach on both synthetic and real temporal\nnetworks.",
+                    "authors": "Sumit Purohit, Lawrence B. Holder, George Chin",
+                    "published": "2020-02-19",
+                    "updated": "2020-08-06",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2404.19453v1",
+                    "title": "Structural Parameters for Dense Temporal Graphs",
+                    "abstract": "Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.",
+                    "authors": "Jessica Enright, Samuel D. Hand, Laura Larios-Jones, Kitty Meeks",
+                    "published": "2024-04-30",
+                    "updated": "2024-04-30",
+                    "primary_cat": "cs.DM",
+                    "cats": [
+                        "cs.DM",
+                        "math.CO"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2202.01727v2",
+                    "title": "Skeleton-Based Action Segmentation with Multi-Stage Spatial-Temporal Graph Convolutional Neural Networks",
+                    "abstract": "The ability to identify and temporally segment fine-grained actions in motion\ncapture sequences is crucial for applications in human movement analysis.\nMotion capture is typically performed with optical or inertial measurement\nsystems, which encode human movement as a time series of human joint locations\nand orientations or their higher-order representations. State-of-the-art action\nsegmentation approaches use multiple stages of temporal convolutions. The main\nidea is to generate an initial prediction with several layers of temporal\nconvolutions and refine these predictions over multiple stages, also with\ntemporal convolutions. Although these approaches capture long-term temporal\npatterns, the initial predictions do not adequately consider the spatial\nhierarchy among the human joints. To address this limitation, we recently\nintroduced multi-stage spatial-temporal graph convolutional neural networks\n(MS-GCN). Our framework replaces the initial stage of temporal convolutions\nwith spatial graph convolutions and dilated temporal convolutions, which better\nexploit the spatial configuration of the joints and their long-term temporal\ndynamics. Our framework was compared to four strong baselines on five tasks.\nExperimental results demonstrate that our framework is a strong baseline for\nskeleton-based action segmentation.",
+                    "authors": "Benjamin Filtjens, Bart Vanrumste, Peter Slaets",
+                    "published": "2022-02-03",
+                    "updated": "2022-10-09",
+                    "primary_cat": "cs.CV",
+                    "cats": [
+                        "cs.CV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.09641v2",
+                    "title": "Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting",
+                    "abstract": "Spatial-temporal data forecasting of traffic flow is a challenging task\nbecause of complicated spatial dependencies and dynamical trends of temporal\npattern between different roads. Existing frameworks typically utilize given\nspatial adjacency graph and sophisticated mechanisms for modeling spatial and\ntemporal correlations. However, limited representations of given spatial graph\nstructure with incomplete adjacent connections may restrict effective\nspatial-temporal dependencies learning of those models. To overcome those\nlimitations, our paper proposes Spatial-Temporal Fusion Graph Neural Networks\n(STFGNN) for traffic flow forecasting. SFTGNN could effectively learn hidden\nspatial-temporal dependencies by a novel fusion operation of various spatial\nand temporal graphs, which is generated by a data-driven method. Meanwhile, by\nintegrating this fusion graph module and a novel gated convolution module into\na unified layer, SFTGNN could handle long sequences. Experimental results on\nseveral public traffic datasets demonstrate that our method achieves\nstate-of-the-art performance consistently than other baselines.",
+                    "authors": "Mengzhang Li, Zhanxing Zhu",
+                    "published": "2020-12-15",
+                    "updated": "2021-03-06",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.AI"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2310.02606v1",
+                    "title": "Learning adjacency matrix for dynamic graph neural network",
+                    "abstract": "In recent work, [1] introduced the concept of using a Block Adjacency Matrix\n(BA) for the representation of spatio-temporal data. While their method\nsuccessfully concatenated adjacency matrices to encapsulate spatio-temporal\nrelationships in a single graph, it formed a disconnected graph. This\nlimitation hampered the ability of Graph Convolutional Networks (GCNs) to\nperform message passing across nodes belonging to different time steps, as no\ntemporal links were present. To overcome this challenge, we introduce an\nencoder block specifically designed to learn these missing temporal links. The\nencoder block processes the BA and predicts connections between previously\nunconnected subgraphs, resulting in a Spatio-Temporal Block Adjacency Matrix\n(STBAM). This enriched matrix is then fed into a Graph Neural Network (GNN) to\ncapture the complex spatio-temporal topology of the network. Our evaluations on\nbenchmark datasets, surgVisDom and C2D2, demonstrate that our method, with\nslightly higher complexity, achieves superior results compared to\nstate-of-the-art results. Our approach's computational overhead remains\nsignificantly lower than conventional non-graph-based methodologies for\nspatio-temporal data.",
+                    "authors": "Osama Ahmad, Omer Abdul Jalil, Usman Nazir, Murtaza Taj",
+                    "published": "2023-10-04",
+                    "updated": "2023-10-04",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "eess.IV"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/1602.04434v1",
+                    "title": "Frequency Analysis of Temporal Graph Signals",
+                    "abstract": "This letter extends the concept of graph-frequency to graph signals that\nevolve with time. Our goal is to generalize and, in fact, unify the familiar\nconcepts from time- and graph-frequency analysis. To this end, we study a joint\ntemporal and graph Fourier transform (JFT) and demonstrate its attractive\nproperties. We build on our results to create filters which act on the joint\n(temporal and graph) frequency domain, and show how these can be used to\nperform interference cancellation. The proposed algorithms are distributed,\nhave linear complexity, and can approximate any desired joint filtering\nobjective.",
+                    "authors": "Andreas Loukas, Damien Foucard",
+                    "published": "2016-02-14",
+                    "updated": "2016-02-14",
+                    "primary_cat": "cs.LG",
+                    "cats": [
+                        "cs.LG",
+                        "cs.SY",
+                        "stat.ML"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2012.08909v2",
+                    "title": "Maximum 0-1 Timed Matching on Temporal Graphs",
+                    "abstract": "Temporal graphs are graphs where the topology and/or other properties of the\ngraph change with time. They have been used to model applications with temporal\ninformation in various domains. Problems on static graphs become more\nchallenging to solve in temporal graphs because of dynamically changing\ntopology, and many recent works have explored graph problems on temporal\ngraphs. In this paper, we define a type of matching called {\\em 0-1 timed\nmatching} for temporal graphs, and investigate the problem of finding a {\\em\nmaximum 0-1 timed matching} for different classes of temporal graphs. We first\nprove that the problem is NP-Complete for rooted temporal trees when each edge\nis associated with two or more time intervals. We then propose an $O(n \\log n)$\ntime algorithm for the problem on a rooted temporal tree with $n$ nodes when\neach edge is associated with exactly one time interval. The problem is then\nshown to be NP-Complete also for bipartite temporal graphs even when each edge\nis associated with a single time interval and degree of each node is bounded by\na constant $k \\geq 3$. We next investigate approximation algorithms for the\nproblem for temporal graphs where each edge is associated with more than one\ntime intervals. It is first shown that there is no\n$\\frac{1}{n^{1-\\epsilon}}$-factor approximation algorithm for the problem for\nany $\\epsilon > 0$ even on a rooted temporal tree with $n$ nodes unless NP =\nZPP. We then present a $\\frac{5}{2\\mathcal{N}^* + 3}$-factor approximation\nalgorithm for the problem for general temporal graphs where $\\mathcal{N^*}$ is\nthe average number of edges overlapping in time with each edge in the temporal\ngraph. The same algorithm is also a constant-factor approximation algorithm for\ndegree bounded temporal graphs.",
+                    "authors": "Subhrangsu Mandal, Arobinda Gupta",
+                    "published": "2020-12-16",
+                    "updated": "2022-02-01",
+                    "primary_cat": "cs.DS",
+                    "cats": [
+                        "cs.DS"
+                    ],
+                    "category": "Temporal AND Graph"
+                },
+                {
+                    "url": "http://arxiv.org/abs/2203.14303v1",
+                    "title": "TREND: TempoRal Event and Node Dynamics for Graph Representation Learning",
+                    "abstract": "Temporal graph representation learning has drawn significant attention for\nthe prevalence of temporal graphs in the real world. However, most existing\nworks resort to taking discrete snapshots of the temporal graph, or are not\ninductive to deal with new nodes, or do not model the exciting effects which is\nthe ability of events to influence the occurrence of another event. In this\nwork, We propose TREND, a novel framework for temporal graph representation\nlearning, driven by TempoRal Event and Node Dynamics and built upon a Hawkes\nprocess-based graph neural network (GNN). TREND presents a few major\nadvantages: (1) it is inductive due to its GNN architecture; (2) it captures\nthe exciting effects between events by the adoption of the Hawkes process; (3)\nas our main novelty, it captures the individual and collective characteristics\nof events by integrating both event and node dynamics, driving a more precise\nmodeling of the temporal process. Extensive experiments on four real-world\ndatasets demonstrate the effectiveness of our proposed model.",
+                    "authors": "Zhihao Wen, Yuan Fang",
+                    "published": "2022-03-27",
+                    "updated": "2022-03-27",
+                    "primary_cat": "cs.SI",
+                    "cats": [
+                        "cs.SI"
+                    ],
+                    "category": "Temporal AND Graph"
+                }
+            ]
+        ]
+    },
+    {
+        "url": "http://arxiv.org/abs/2112.10154v4",
+        "title": "Dynamic Representation Learning with Temporal Point Processes for Higher-Order Interaction Forecasting",
+        "abstract": "The explosion of digital information and the growing involvement of people in\nsocial networks led to enormous research activity to develop methods that can\nextract meaningful information from interaction data. Commonly, interactions\nare represented by edges in a network or a graph, which implicitly assumes that\nthe interactions are pairwise and static. However, real-world interactions\ndeviate from these assumptions: (i) interactions can be multi-way, involving\nmore than two nodes or individuals (e.g., family relationships, protein\ninteractions), and (ii) interactions can change over a period of time (e.g.,\nchange of opinions and friendship status). While pairwise interactions have\nbeen studied in a dynamic network setting and multi-way interactions have been\nstudied using hypergraphs in static networks, there exists no method, at\npresent, that can predict multi-way interactions or hyperedges in dynamic\nsettings. Existing related methods cannot answer temporal queries like what\ntype of interaction will occur next and when it will occur. This paper proposes\na temporal point process model for hyperedge prediction to address these\nproblems. Our proposed model uses dynamic representation learning techniques\nfor nodes in a neural point process framework to forecast hyperedges. We\npresent several experimental results and set benchmark results. As far as our\nknowledge, this is the first work that uses the temporal point process to\nforecast hyperedges in dynamic networks.",
+        "authors": "Tony Gracious, Ambedkar Dukkipati",
+        "published": "2021-12-19",
+        "updated": "2023-04-01",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.SI"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/1609.03675v4",
+        "title": "Deep Coevolutionary Network: Embedding User and Item Features for Recommendation",
+        "abstract": "Recommender systems often use latent features to explain the behaviors of\nusers and capture the properties of items. As users interact with different\nitems over time, user and item features can influence each other, evolve and\nco-evolve over time. The compatibility of user and item's feature further\ninfluence the future interaction between users and items. Recently, point\nprocess based models have been proposed in the literature aiming to capture the\ntemporally evolving nature of these latent features. However, these models\noften make strong parametric assumptions about the evolution process of the\nuser and item latent features, which may not reflect the reality, and has\nlimited power in expressing the complex and nonlinear dynamics underlying these\nprocesses. To address these limitations, we propose a novel deep coevolutionary\nnetwork model (DeepCoevolve), for learning user and item features based on\ntheir interaction graph. DeepCoevolve use recurrent neural network (RNN) over\nevolving networks to define the intensity function in point processes, which\nallows the model to capture complex mutual influence between users and items,\nand the feature evolution over time. We also develop an efficient procedure for\ntraining the model parameters, and show that the learned models lead to\nsignificant improvements in recommendation and activity prediction compared to\nprevious state-of-the-arts parametric models.",
+        "authors": "Hanjun Dai, Yichen Wang, Rakshit Trivedi, Le Song",
+        "published": "2016-09-13",
+        "updated": "2017-02-28",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.IR"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2003.13432v3",
+        "title": "Graph Hawkes Neural Network for Forecasting on Temporal Knowledge Graphs",
+        "abstract": "The Hawkes process has become a standard method for modeling self-exciting\nevent sequences with different event types. A recent work has generalized the\nHawkes process to a neurally self-modulating multivariate point process, which\nenables the capturing of more complex and realistic impacts of past events on\nfuture events. However, this approach is limited by the number of possible\nevent types, making it impossible to model the dynamics of evolving graph\nsequences, where each possible link between two nodes can be considered as an\nevent type. The number of event types increases even further when links are\ndirectional and labeled. To address this issue, we propose the Graph Hawkes\nNeural Network that can capture the dynamics of evolving graph sequences and\ncan predict the occurrence of a fact in a future time instance. Extensive\nexperiments on large-scale temporal multi-relational databases, such as\ntemporal knowledge graphs, demonstrate the effectiveness of our approach.",
+        "authors": "Zhen Han, Yunpu Ma, Yuyi Wang, Stephan G\u00fcnnemann, Volker Tresp",
+        "published": "2020-03-30",
+        "updated": "2020-06-14",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2104.03528v5",
+        "title": "Neural Temporal Point Processes: A Review",
+        "abstract": "Temporal point processes (TPP) are probabilistic generative models for\ncontinuous-time event sequences. Neural TPPs combine the fundamental ideas from\npoint process literature with deep learning approaches, thus enabling\nconstruction of flexible and efficient models. The topic of neural TPPs has\nattracted significant attention in the recent years, leading to the development\nof numerous new architectures and applications for this class of models. In\nthis review paper we aim to consolidate the existing body of knowledge on\nneural TPPs. Specifically, we focus on important design choices and general\nprinciples for defining neural TPP models. Next, we provide an overview of\napplication areas commonly considered in the literature. We conclude this\nsurvey with the list of open challenges and important directions for future\nwork in the field of neural TPPs.",
+        "authors": "Oleksandr Shchur, Ali Caner T\u00fcrkmen, Tim Januschowski, Stephan G\u00fcnnemann",
+        "published": "2021-04-08",
+        "updated": "2021-08-25",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2006.10637v3",
+        "title": "Temporal Graph Networks for Deep Learning on Dynamic Graphs",
+        "abstract": "Graph Neural Networks (GNNs) have recently become increasingly popular due to\ntheir ability to learn complex systems of relations or interactions arising in\na broad spectrum of problems ranging from biology and particle physics to\nsocial networks and recommendation systems. Despite the plethora of different\nmodels for deep learning on graphs, few approaches have been proposed thus far\nfor dealing with graphs that present some sort of dynamic nature (e.g. evolving\nfeatures or connectivity over time). In this paper, we present Temporal Graph\nNetworks (TGNs), a generic, efficient framework for deep learning on dynamic\ngraphs represented as sequences of timed events. Thanks to a novel combination\nof memory modules and graph-based operators, TGNs are able to significantly\noutperform previous approaches being at the same time more computationally\nefficient. We furthermore show that several previous models for learning on\ndynamic graphs can be cast as specific instances of our framework. We perform a\ndetailed ablation study of different components of our framework and devise the\nbest configuration that achieves state-of-the-art performance on several\ntransductive and inductive prediction tasks for dynamic graphs.",
+        "authors": "Emanuele Rossi, Ben Chamberlain, Fabrizio Frasca, Davide Eynard, Federico Monti, Michael Bronstein",
+        "published": "2020-06-18",
+        "updated": "2020-10-09",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/1908.01207v1",
+        "title": "Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks",
+        "abstract": "Modeling sequential interactions between users and items/products is crucial\nin domains such as e-commerce, social networking, and education. Representation\nlearning presents an attractive opportunity to model the dynamic evolution of\nusers and items, where each user/item can be embedded in a Euclidean space and\nits evolution can be modeled by an embedding trajectory in this space. However,\nexisting dynamic embedding methods generate embeddings only when users take\nactions and do not explicitly model the future trajectory of the user/item in\nthe embedding space. Here we propose JODIE, a coupled recurrent neural network\nmodel that learns the embedding trajectories of users and items. JODIE employs\ntwo recurrent neural networks to update the embedding of a user and an item at\nevery interaction. Crucially, JODIE also models the future embedding trajectory\nof a user/item. To this end, it introduces a novel projection operator that\nlearns to estimate the embedding of the user at any time in the future. These\nestimated embeddings are then used to predict future user-item interactions. To\nmake the method scalable, we develop a t-Batch algorithm that creates\ntime-consistent batches and leads to 9x faster training. We conduct six\nexperiments to validate JODIE on two prediction tasks---future interaction\nprediction and state change prediction---using four real-world datasets. We\nshow that JODIE outperforms six state-of-the-art algorithms in these tasks by\nat least 20% in predicting future interactions and 12% in state change\nprediction.",
+        "authors": "Srijan Kumar, Xikun Zhang, Jure Leskovec",
+        "published": "2019-08-03",
+        "updated": "2019-08-03",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.CY",
+            "cs.LG"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2107.03573v1",
+        "title": "Deep Structural Point Process for Learning Temporal Interaction Networks",
+        "abstract": "This work investigates the problem of learning temporal interaction networks.\nA temporal interaction network consists of a series of chronological\ninteractions between users and items. Previous methods tackle this problem by\nusing different variants of recurrent neural networks to model sequential\ninteractions, which fail to consider the structural information of temporal\ninteraction networks and inevitably lead to sub-optimal results. To this end,\nwe propose a novel Deep Structural Point Process termed as DSPP for learning\ntemporal interaction networks. DSPP simultaneously incorporates the topological\nstructure and long-range dependency structure into our intensity function to\nenhance model expressiveness. To be specific, by using the topological\nstructure as a strong prior, we first design a topological fusion encoder to\nobtain node embeddings. An attentive shift encoder is then developed to learn\nthe long-range dependency structure between users and items in continuous time.\nThe proposed two modules enable our model to capture the user-item correlation\nand dynamic influence in temporal interaction networks. DSPP is evaluated on\nthree real-world datasets for both tasks of item prediction and time\nprediction. Extensive experiments demonstrate that our model achieves\nconsistent and significant improvements over state-of-the-art baselines.",
+        "authors": "Jiangxia Cao, Xixun Lin, Xin Cong, Shu Guo, Hengzhu Tang, Tingwen Liu, Bin Wang",
+        "published": "2021-07-08",
+        "updated": "2021-07-08",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.AI"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2002.07962v1",
+        "title": "Inductive Representation Learning on Temporal Graphs",
+        "abstract": "Inductive representation learning on temporal graphs is an important step\ntoward salable machine learning on real-world dynamic networks. The evolving\nnature of temporal dynamic graphs requires handling new nodes as well as\ncapturing temporal patterns. The node embeddings, which are now functions of\ntime, should represent both the static node features and the evolving\ntopological structures. Moreover, node and topological features can be temporal\nas well, whose patterns the node embeddings should also capture. We propose the\ntemporal graph attention (TGAT) layer to efficiently aggregate\ntemporal-topological neighborhood features as well as to learn the time-feature\ninteractions. For TGAT, we use the self-attention mechanism as building block\nand develop a novel functional time encoding technique based on the classical\nBochner's theorem from harmonic analysis. By stacking TGAT layers, the network\nrecognizes the node embeddings as functions of time and is able to inductively\ninfer embeddings for both new and observed nodes as the graph evolves. The\nproposed approach handles both node classification and link prediction task,\nand can be naturally extended to include the temporal edge features. We\nevaluate our method with transductive and inductive tasks under temporal\nsettings with two benchmark and one industrial dataset. Our TGAT model compares\nfavorably to state-of-the-art baselines as well as the previous temporal graph\nembedding approaches.",
+        "authors": "Da Xu, Chuanwei Ruan, Evren Korpeoglu, Sushant Kumar, Kannan Achan",
+        "published": "2020-02-19",
+        "updated": "2020-02-19",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "label": "Related Work"
+    },
+    {
+        "url": "http://arxiv.org/abs/2105.12003v1",
+        "title": "On Finding Separators in Temporal Split and Permutation Graphs",
+        "abstract": "Removing all connections between two vertices s and z in a graph by removing\na minimum number of vertices is a fundamental problem in algorithmic graph\ntheory. This (s,z)-separation problem is well-known to be polynomial solvable\nand serves as an important primitive in many applications related to network\nconnectivity. We study the NP-hard temporal (s,z)-separation problem on\ntemporal graphs, which are graphs with fixed vertex sets but edge sets that\nchange over discrete time steps. We tackle this problem by restricting the\nlayers (i.e., graphs characterized by edges that are present at a certain point\nin time) to specific graph classes. We restrict the layers of the temporal\ngraphs to be either all split graphs or all permutation graphs (both being\nperfect graph classes) and provide both intractability and tractability\nresults. In particular, we show that in general the problem remains NP-hard\nboth on temporal split and temporal permutation graphs, but we also spot\npromising islands of fixed-parameter tractability particularly based on\nparameterizations that measure the amount of \"change over time\".",
+        "authors": "Nicolas Maack, Hendrik Molter, Rolf Niedermeier, Malte Renken",
+        "published": "2021-05-25",
+        "updated": "2021-05-25",
+        "primary_cat": "cs.DM",
+        "cats": [
+            "cs.DM",
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.14199v2",
+        "title": "MTRGL:Effective Temporal Correlation Discerning through Multi-modal Temporal Relational Graph Learning",
+        "abstract": "In this study, we explore the synergy of deep learning and financial market\napplications, focusing on pair trading. This market-neutral strategy is\nintegral to quantitative finance and is apt for advanced deep-learning\ntechniques. A pivotal challenge in pair trading is discerning temporal\ncorrelations among entities, necessitating the integration of diverse data\nmodalities. Addressing this, we introduce a novel framework, Multi-modal\nTemporal Relation Graph Learning (MTRGL). MTRGL combines time series data and\ndiscrete features into a temporal graph and employs a memory-based temporal\ngraph neural network. This approach reframes temporal correlation\nidentification as a temporal graph link prediction task, which has shown\nempirical success. Our experiments on real-world datasets confirm the superior\nperformance of MTRGL, emphasizing its promise in refining automated pair\ntrading strategies.",
+        "authors": "Junwei Su, Shan Wu, Jinhui Li",
+        "published": "2024-01-25",
+        "updated": "2024-02-06",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "econ.GN",
+            "q-fin.EC",
+            "q-fin.TR"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.09114v1",
+        "title": "Relational Temporal Graph Reasoning for Dual-task Dialogue Language Understanding",
+        "abstract": "Dual-task dialog language understanding aims to tackle two correlative dialog\nlanguage understanding tasks simultaneously via leveraging their inherent\ncorrelations. In this paper, we put forward a new framework, whose core is\nrelational temporal graph reasoning.We propose a speaker-aware temporal graph\n(SATG) and a dual-task relational temporal graph (DRTG) to facilitate\nrelational temporal modeling in dialog understanding and dual-task reasoning.\nBesides, different from previous works that only achieve implicit\nsemantics-level interactions, we propose to model the explicit dependencies via\nintegrating prediction-level interactions. To implement our framework, we first\npropose a novel model Dual-tAsk temporal Relational rEcurrent Reasoning network\n(DARER), which first generates the context-, speaker- and temporal-sensitive\nutterance representations through relational temporal modeling of SATG, then\nconducts recurrent dual-task relational temporal graph reasoning on DRTG, in\nwhich process the estimated label distributions act as key clues in\nprediction-level interactions. And the relational temporal modeling in DARER is\nachieved by relational convolutional networks (RGCNs). Then we further propose\nRelational Temporal Transformer (ReTeFormer), which achieves fine-grained\nrelational temporal modeling via Relation- and Structure-aware Disentangled\nMulti-head Attention. Accordingly, we propose DARER with ReTeFormer (DARER2),\nwhich adopts two variants of ReTeFormer to achieve the relational temporal\nmodeling of SATG and DTRG, respectively. The extensive experiments on different\nscenarios verify that our models outperform state-of-the-art models by a large\nmargin. Remarkably, on the dialog sentiment classification task in the Mastodon\ndataset, DARER and DARER2 gain relative improvements of about 28% and 34% over\nthe previous best model in terms of F1.",
+        "authors": "Bowen Xing, Ivor W. Tsang",
+        "published": "2023-06-15",
+        "updated": "2023-06-15",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1502.04579v3",
+        "title": "The complexity of optimal design of temporally connected graphs",
+        "abstract": "We study the design of small cost temporally connected graphs, under various\nconstraints. We mainly consider undirected graphs of $n$ vertices, where each\nedge has an associated set of discrete availability instances (labels). A\njourney from vertex $u$ to vertex $v$ is a path from $u$ to $v$ where\nsuccessive path edges have strictly increasing labels. A graph is temporally\nconnected iff there is a $(u,v)$-journey for any pair of vertices $u,v,~u\\not=\nv$. We first give a simple polynomial-time algorithm to check whether a given\ntemporal graph is temporally connected. We then consider the case in which a\ndesigner of temporal graphs can \\emph{freely choose} availability instances for\nall edges and aims for temporal connectivity with very small \\emph{cost}; the\ncost is the total number of availability instances used. We achieve this via a\nsimple polynomial-time procedure which derives designs of cost linear in $n$.\nWe also show that the above procedure is (almost) optimal when the underlying\ngraph is a tree, by proving a lower bound on the cost for any tree. However,\nthere are pragmatic cases where one is not free to design a temporally\nconnected graph anew, but is instead \\emph{given} a temporal graph design with\nthe claim that it is temporally connected, and wishes to make it more\ncost-efficient by removing labels without destroying temporal connectivity\n(redundant labels). Our main technical result is that computing the maximum\nnumber of redundant labels is APX-hard, i.e., there is no PTAS unless $P=NP$.\nOn the positive side, we show that in dense graphs with random edge\navailabilities, there is asymptotically almost surely a very large number of\nredundant labels. A temporal design may, however, be \\emph{minimal}, i.e., no\nredundant labels exist. We show the existence of minimal temporal designs with\nat least $n \\log{n}$ labels.",
+        "authors": "Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, Paul G. Spirakis",
+        "published": "2015-02-16",
+        "updated": "2016-07-06",
+        "primary_cat": "cs.DM",
+        "cats": [
+            "cs.DM",
+            "G.2.2"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2008.08282v2",
+        "title": "Multiscale Snapshots: Visual Analysis of Temporal Summaries in Dynamic Graphs",
+        "abstract": "The overview-driven visual analysis of large-scale dynamic graphs poses a\nmajor challenge. We propose Multiscale Snapshots, a visual analytics approach\nto analyze temporal summaries of dynamic graphs at multiple temporal scales.\nFirst, we recursively generate temporal summaries to abstract overlapping\nsequences of graphs into compact snapshots. Second, we apply graph embeddings\nto the snapshots to learn low-dimensional representations of each sequence of\ngraphs to speed up specific analytical tasks (e.g., similarity search). Third,\nwe visualize the evolving data from a coarse to fine-granular snapshots to\nsemi-automatically analyze temporal states, trends, and outliers. The approach\nenables to discover similar temporal summaries (e.g., recurring states),\nreduces the temporal data to speed up automatic analysis, and to explore both\nstructural and temporal properties of a dynamic graph. We demonstrate the\nusefulness of our approach by a quantitative evaluation and the application to\na real-world dataset.",
+        "authors": "Eren Cakmak, Udo Schlegel, Dominik J\u00e4ckle, Daniel Keim, Tobias Schreck",
+        "published": "2020-08-19",
+        "updated": "2020-09-15",
+        "primary_cat": "cs.HC",
+        "cats": [
+            "cs.HC"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2112.08733v1",
+        "title": "Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrast",
+        "abstract": "Self-supervised learning on graphs has recently drawn a lot of attention due\nto its independence from labels and its robustness in representation. Current\nstudies on this topic mainly use static information such as graph structures\nbut cannot well capture dynamic information such as timestamps of edges.\nRealistic graphs are often dynamic, which means the interaction between nodes\noccurs at a specific time. This paper proposes a self-supervised dynamic graph\nrepresentation learning framework (DySubC), which defines a temporal subgraph\ncontrastive learning task to simultaneously learn the structural and\nevolutional features of a dynamic graph. Specifically, a novel temporal\nsubgraph sampling strategy is firstly proposed, which takes each node of the\ndynamic graph as the central node and uses both neighborhood structures and\nedge timestamps to sample the corresponding temporal subgraph. The subgraph\nrepresentation function is then designed according to the influence of\nneighborhood nodes on the central node after encoding the nodes in each\nsubgraph. Finally, the structural and temporal contrastive loss are defined to\nmaximize the mutual information between node representation and temporal\nsubgraph representation. Experiments on five real-world datasets demonstrate\nthat (1) DySubC performs better than the related baselines including two graph\ncontrastive learning models and four dynamic graph representation learning\nmodels in the downstream link prediction task, and (2) the use of temporal\ninformation can not only sample more effective subgraphs, but also learn better\nrepresentation by temporal contrastive loss.",
+        "authors": "Linpu Jiang, Ke-Jia Chen, Jingqiang Chen",
+        "published": "2021-12-16",
+        "updated": "2021-12-16",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2305.10738v3",
+        "title": "Deep Temporal Graph Clustering",
+        "abstract": "Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.",
+        "authors": "Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+        "published": "2023-05-18",
+        "updated": "2024-04-11",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2103.07016v2",
+        "title": "On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions",
+        "abstract": "This work formalizes the associational task of predicting node attribute\nevolution in temporal graphs from the perspective of learning equivariant\nrepresentations. We show that node representations in temporal graphs can be\ncast into two distinct frameworks: (a) The most popular approach, which we\ndenote as time-and-graph, where equivariant graph (e.g., GNN) and sequence\n(e.g., RNN) representations are intertwined to represent the temporal evolution\nof node attributes in the graph; and (b) an approach that we denote as\ntime-then-graph, where the sequences describing the node and edge dynamics are\nrepresented first, then fed as node and edge attributes into a static\nequivariant graph representation that comes after. Interestingly, we show that\ntime-then-graph representations have an expressivity advantage over\ntime-and-graph representations when both use component GNNs that are not\nmost-expressive (e.g., 1-Weisfeiler-Lehman GNNs). Moreover, while our goal is\nnot necessarily to obtain state-of-the-art results, our experiments show that\ntime-then-graph methods are capable of achieving better performance and\nefficiency than state-of-the-art time-and-graph methods in some real-world\ntasks, thereby showcasing that the time-then-graph framework is a worthy\naddition to the graph ML toolbox.",
+        "authors": "Jianfei Gao, Bruno Ribeiro",
+        "published": "2021-03-12",
+        "updated": "2023-03-27",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2312.06260v1",
+        "title": "In search of the lost tree: Hardness and relaxation of spanning trees in temporal graphs",
+        "abstract": "A graph whose edges only appear at certain points in time is called a\ntemporal graph (among other names). These graphs are temporally connected if\nall ordered pairs of vertices are connected by a path that traverses edges in\nchronological order (a temporal path). Reachability in temporal graphs departs\nsignificantly from standard reachability; in particular, it is not transitive,\nwith structural and algorithmic consequences. For instance, temporally\nconnected graphs do not always admit spanning trees, i.e., subsets of edges\nthat form a tree and preserve temporal connectivity among the nodes.\n  In this paper, we revisit fundamental questions about the loss of\nuniversality of spanning trees. To start, we show that deciding if a spanning\ntree exists in a given temporal graph is NP-complete. What could be appropriate\nreplacement for the concept? Beyond having minimum size, spanning trees enjoy\nthe feature of enabling reachability along the same underlying paths in both\ndirections, a pretty uncommon feature in temporal graphs. We explore\nrelaxations in this direction and show that testing the existence of\nbidirectional spanning structures (bi-spanners) is tractable in general. On the\ndown side, finding \\emph{minimum} such structures is NP-hard even in simple\ntemporal graphs. Still, the fact that bidirectionality can be tested\nefficiently may find applications, e.g. for routing and security, and the\ncorresponding primitive that we introduce in the algorithm may be of\nindependent interest.",
+        "authors": "Arnaud Casteigts, Timoth\u00e9e Corsini",
+        "published": "2023-12-11",
+        "updated": "2023-12-11",
+        "primary_cat": "cs.DM",
+        "cats": [
+            "cs.DM",
+            "cs.DC",
+            "68R10, 68W15",
+            "G.2.2; C.2.4"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2312.07117v1",
+        "title": "On inefficiently connecting temporal networks",
+        "abstract": "A temporal graph can be represented by a graph with an edge labelling, such\nthat an edge is present in the network if and only if the edge is assigned the\ncorresponding time label. A journey is a labelled path in a temporal graph such\nthat labels on successive edges of the path are increasing, and if all vertices\nadmit journeys to all other vertices, the temporal graph is temporally\nconnected. A temporal spanner is a sublabelling of the temporal graph such that\ntemporal connectivity is maintained. The study of temporal spanners has raised\ninterest since the early 2000's. Essentially two types of studies have been\nconducted: the positive side where families of temporal graphs are shown to\n(deterministically or stochastically) admit sparse temporal spanners, and the\nnegative side where constructions of temporal graphs with no sparse spanners\nare of importance. Often such studies considered temporal graphs with happy or\nsimple labellings, which associate exactly one label per edge. In this paper,\nwe focus on the negative side and consider proper labellings, where multiple\nlabels per edge are allowed. More precisely, we aim to construct dense\ntemporally connected graphs such that all labels are necessary for temporal\nconnectivity. Our contributions are multiple: we present the first labellings\nmaximizing a local density measure; exact or asymptotically tight results for\nbasic graph families, which are then extended to larger graph families; an\nextension of an efficient temporal graph labelling generator; and overall\ndenser labellings than previous work even when restricted to happy labellings.",
+        "authors": "Esteban Christiann, Eric Sanlaville, Jason Schoeters",
+        "published": "2023-12-12",
+        "updated": "2023-12-12",
+        "primary_cat": "cs.CC",
+        "cats": [
+            "cs.CC",
+            "cs.DM"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2303.13177v1",
+        "title": "It is all Connected: A New Graph Formulation for Spatio-Temporal Forecasting",
+        "abstract": "With an ever-increasing number of sensors in modern society, spatio-temporal\ntime series forecasting has become a de facto tool to make informed decisions\nabout the future. Most spatio-temporal forecasting models typically comprise\ndistinct components that learn spatial and temporal dependencies. A common\nmethodology employs some Graph Neural Network (GNN) to capture relations\nbetween spatial locations, while another network, such as a recurrent neural\nnetwork (RNN), learns temporal correlations. By representing every recorded\nsample as its own node in a graph, rather than all measurements for a\nparticular location as a single node, temporal and spatial information is\nencoded in a similar manner. In this setting, GNNs can now directly learn both\ntemporal and spatial dependencies, jointly, while also alleviating the need for\nadditional temporal networks. Furthermore, the framework does not require\naligned measurements along the temporal dimension, meaning that it also\nnaturally facilitates irregular time series, different sampling frequencies or\nmissing data, without the need for data imputation. To evaluate the proposed\nmethodology, we consider wind speed forecasting as a case study, where our\nproposed framework outperformed other spatio-temporal models using GNNs with\neither Transformer or LSTM networks as temporal update functions.",
+        "authors": "Lars \u00d8degaard Bentsen, Narada Dilp Warakagoda, Roy Stenbro, Paal Engelstad",
+        "published": "2023-03-23",
+        "updated": "2023-03-23",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2101.00820v8",
+        "title": "Temporal Contrastive Graph Learning for Video Action Recognition and Retrieval",
+        "abstract": "Attempt to fully discover the temporal diversity and chronological\ncharacteristics for self-supervised video representation learning, this work\ntakes advantage of the temporal dependencies within videos and further proposes\na novel self-supervised method named Temporal Contrastive Graph Learning\n(TCGL). In contrast to the existing methods that ignore modeling elaborate\ntemporal dependencies, our TCGL roots in a hybrid graph contrastive learning\nstrategy to jointly regard the inter-snippet and intra-snippet temporal\ndependencies as self-supervision signals for temporal representation learning.\nTo model multi-scale temporal dependencies, our TCGL integrates the prior\nknowledge about the frame and snippet orders into graph structures, i.e., the\nintra-/inter- snippet temporal contrastive graphs. By randomly removing edges\nand masking nodes of the intra-snippet graphs or inter-snippet graphs, our TCGL\ncan generate different correlated graph views. Then, specific contrastive\nlearning modules are designed to maximize the agreement between nodes in\ndifferent views. To adaptively learn the global context representation and\nrecalibrate the channel-wise features, we introduce an adaptive video snippet\norder prediction module, which leverages the relational knowledge among video\nsnippets to predict the actual snippet orders. Experimental results demonstrate\nthe superiority of our TCGL over the state-of-the-art methods on large-scale\naction recognition and video retrieval benchmarks.",
+        "authors": "Yang Liu, Keze Wang, Haoyuan Lan, Liang Lin",
+        "published": "2021-01-04",
+        "updated": "2021-03-17",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.LG",
+            "cs.MM"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2311.03897v1",
+        "title": "Temporal Graph Representation Learning with Adaptive Augmentation Contrastive",
+        "abstract": "Temporal graph representation learning aims to generate low-dimensional\ndynamic node embeddings to capture temporal information as well as structural\nand property information. Current representation learning methods for temporal\nnetworks often focus on capturing fine-grained information, which may lead to\nthe model capturing random noise instead of essential semantic information.\nWhile graph contrastive learning has shown promise in dealing with noise, it\nonly applies to static graphs or snapshots and may not be suitable for handling\ntime-dependent noise. To alleviate the above challenge, we propose a novel\nTemporal Graph representation learning with Adaptive augmentation Contrastive\n(TGAC) model. The adaptive augmentation on the temporal graph is made by\ncombining prior knowledge with temporal information, and the contrastive\nobjective function is constructed by defining the augmented inter-view contrast\nand intra-view contrast. To complement TGAC, we propose three adaptive\naugmentation strategies that modify topological features to reduce noise from\nthe network. Our extensive experiments on various real networks demonstrate\nthat the proposed model outperforms other temporal graph representation\nlearning methods.",
+        "authors": "Hongjiang Chen, Pengfei Jiao, Huijun Tang, Huaming Wu",
+        "published": "2023-11-07",
+        "updated": "2023-11-07",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1912.03904v1",
+        "title": "Weighted temporal event graphs",
+        "abstract": "The times of temporal-network events and their correlations contain\ninformation on the function of the network and they influence dynamical\nprocesses taking place on it. To extract information out of correlated event\ntimes, techniques such as the analysis of temporal motifs have been developed.\nWe discuss a recently-introduced, more general framework that maps\ntemporal-network structure into static graphs while retaining information on\ntime-respecting paths and the time differences between their consequent events.\nThis framework builds on weighted temporal event graphs: directed, acyclic\ngraphs (DAGs) that contain a superposition of all temporal paths. We introduce\nthe reader to the temporal event-graph mapping and associated computational\nmethods and illustrate its use by applying the framework to temporal-network\npercolation.",
+        "authors": "Jari Saram\u00e4ki, Mikko Kivel\u00e4, M\u00e1rton Karsai",
+        "published": "2019-12-09",
+        "updated": "2019-12-09",
+        "primary_cat": "physics.soc-ph",
+        "cats": [
+            "physics.soc-ph",
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2304.07503v1",
+        "title": "Temporal Aggregation and Propagation Graph Neural Networks for Dynamic Representation",
+        "abstract": "Temporal graphs exhibit dynamic interactions between nodes over continuous\ntime, whose topologies evolve with time elapsing.\n  The whole temporal neighborhood of nodes reveals the varying preferences of\nnodes.\n  However, previous works usually generate dynamic representation with limited\nneighbors for simplicity, which results in both inferior performance and high\nlatency of online inference.\n  Therefore, in this paper, we propose a novel method of temporal graph\nconvolution with the whole neighborhood, namely Temporal Aggregation and\nPropagation Graph Neural Networks (TAP-GNN).\n  Specifically, we firstly analyze the computational complexity of the dynamic\nrepresentation problem by unfolding the temporal graph in a message-passing\nparadigm.\n  The expensive complexity motivates us to design the AP (aggregation and\npropagation) block, which significantly reduces the repeated computation of\nhistorical neighbors.\n  The final TAP-GNN supports online inference in the graph stream scenario,\nwhich incorporates the temporal information into node embeddings with a\ntemporal activation function and a projection layer besides several AP blocks.\n  Experimental results on various real-life temporal networks show that our\nproposed TAP-GNN outperforms existing temporal graph methods by a large margin\nin terms of both predictive performance and online inference latency.\n  Our code is available at \\url{https://github.com/doujiang-zheng/TAP-GNN}.",
+        "authors": "Tongya Zheng, Xinchao Wang, Zunlei Feng, Jie Song, Yunzhi Hao, Mingli Song, Xingen Wang, Xinyu Wang, Chun Chen",
+        "published": "2023-04-15",
+        "updated": "2023-04-15",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.IR"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2012.08804v1",
+        "title": "Temporal Graph Modeling for Skeleton-based Action Recognition",
+        "abstract": "Graph Convolutional Networks (GCNs), which model skeleton data as graphs,\nhave obtained remarkable performance for skeleton-based action recognition.\nParticularly, the temporal dynamic of skeleton sequence conveys significant\ninformation in the recognition task. For temporal dynamic modeling, GCN-based\nmethods only stack multi-layer 1D local convolutions to extract temporal\nrelations between adjacent time steps. With the repeat of a lot of local\nconvolutions, the key temporal information with non-adjacent temporal distance\nmay be ignored due to the information dilution. Therefore, these methods still\nremain unclear how to fully explore temporal dynamic of skeleton sequence. In\nthis paper, we propose a Temporal Enhanced Graph Convolutional Network (TE-GCN)\nto tackle this limitation. The proposed TE-GCN constructs temporal relation\ngraph to capture complex temporal dynamic. Specifically, the constructed\ntemporal relation graph explicitly builds connections between semantically\nrelated temporal features to model temporal relations between both adjacent and\nnon-adjacent time steps. Meanwhile, to further explore the sufficient temporal\ndynamic, multi-head mechanism is designed to investigate multi-kinds of\ntemporal relations. Extensive experiments are performed on two widely used\nlarge-scale datasets, NTU-60 RGB+D and NTU-120 RGB+D. And experimental results\nshow that the proposed model achieves the state-of-the-art performance by\nmaking contribution to temporal modeling for action recognition.",
+        "authors": "Jianan Li, Xuemei Xie, Zhifu Zhao, Yuhan Cao, Qingzhe Pan, Guangming Shi",
+        "published": "2020-12-16",
+        "updated": "2020-12-16",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV",
+            "cs.GR"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1503.00278v1",
+        "title": "An Introduction to Temporal Graphs: An Algorithmic Perspective",
+        "abstract": "A \\emph{temporal graph} is, informally speaking, a graph that changes with\ntime. When time is discrete and only the relationships between the\nparticipating entities may change and not the entities themselves, a temporal\ngraph may be viewed as a sequence $G_1,G_2\\ldots,G_l$ of static graphs over the\nsame (static) set of nodes $V$. Though static graphs have been extensively\nstudied, for their temporal generalization we are still far from having a\nconcrete set of structural and algorithmic principles. Recent research shows\nthat many graph properties and problems become radically different and usually\nsubstantially more difficult when an extra time dimension in added to them.\nMoreover, there is already a rich and rapidly growing set of modern systems and\napplications that can be naturally modeled and studied via temporal graphs.\nThis, further motivates the need for the development of a temporal extension of\ngraph theory. We survey here recent results on temporal graphs and temporal\ngraph problems that have appeared in the Computer Science community.",
+        "authors": "Othon Michail",
+        "published": "2015-03-01",
+        "updated": "2015-03-01",
+        "primary_cat": "cs.DM",
+        "cats": [
+            "cs.DM",
+            "cs.DS",
+            "05C85, 05C40, 05C38, 05C78, 05C80, 68R10, 68M14, 68M10, 68W25"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1703.02852v1",
+        "title": "Introduction to a Temporal Graph Benchmark",
+        "abstract": "A temporal graph is a data structure, consisting of nodes and edges in which\nthe edges are associated with time labels. To analyze the temporal graph, the\nfirst step is to find a proper graph dataset/benchmark. While many temporal\ngraph datasets exist online, none could be found that used the interval labels\nin which each edge is associated with a starting and ending time. Therefore we\ncreate a temporal graph data based on Wikipedia reference graph for temporal\nanalysis. This report aims to provide more details of this graph benchmark to\nthose who are interested in using it.",
+        "authors": "Wouter Ligtenberg, Yulong Pei",
+        "published": "2017-02-20",
+        "updated": "2017-02-20",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "physics.soc-ph"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2304.09791v2",
+        "title": "Temporal Betweenness Centrality on Shortest Paths",
+        "abstract": "Betweenness centrality measure assesses the importance of nodes in a graph\nand has been used in a variety of contexts. Betweenness centrality has also\nbeen extended to temporal graphs. Temporal graphs have edges that bear labels\naccording to the time of the interactions between the nodes. Betweenness\ncentrality has been extended to the temporal graph settings, and the notion of\npaths has been extended to temporal paths. Recent results by Bu{\\ss} et al. and\nRymar et al. showed that the betweenness centrality of all nodes in a temporal\ngraph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of\ntime units, m the number of temporal edges and n the number of nodes. In this\npaper, we improve the running time analysis of these previous approaches to\ncompute the betweenness centrality of all nodes in a temporal graph. We give an\nalgorithm that runs in O(n m T + n^2 T ).",
+        "authors": "Mehdi Naima, Matthieu Latapy, Cl\u00e9mence Magnien",
+        "published": "2023-04-19",
+        "updated": "2023-06-06",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2302.12973v1",
+        "title": "Attention-based Spatial-Temporal Graph Convolutional Recurrent Networks for Traffic Forecasting",
+        "abstract": "Traffic forecasting is one of the most fundamental problems in transportation\nscience and artificial intelligence. The key challenge is to effectively model\ncomplex spatial-temporal dependencies and correlations in modern traffic data.\nExisting methods, however, cannot accurately model both long-term and\nshort-term temporal correlations simultaneously, limiting their expressive\npower on complex spatial-temporal patterns. In this paper, we propose a novel\nspatial-temporal neural network framework: Attention-based Spatial-Temporal\nGraph Convolutional Recurrent Network (ASTGCRN), which consists of a graph\nconvolutional recurrent module (GCRN) and a global attention module. In\nparticular, GCRN integrates gated recurrent units and adaptive graph\nconvolutional networks for dynamically learning graph structures and capturing\nspatial dependencies and local temporal relationships. To effectively extract\nglobal temporal dependencies, we design a temporal attention layer and\nimplement it as three independent modules based on multi-head self-attention,\ntransformer, and informer respectively. Extensive experiments on five real\ntraffic datasets have demonstrated the excellent predictive performance of all\nour three models with all their average MAE, RMSE and MAPE across the test\ndatasets lower than the baseline methods.",
+        "authors": "Haiyang Liu, Chunjiang Zhu, Detian Zhang, Qing Li",
+        "published": "2023-02-25",
+        "updated": "2023-02-25",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1609.04350v2",
+        "title": "Time-Variant Graph Classification",
+        "abstract": "Graphs are commonly used to represent objects, such as images and text, for\npattern classification. In a dynamic world, an object may continuously evolve\nover time, and so does the graph extracted from the underlying object. These\nchanges in graph structure with respect to the temporal order present a new\nrepresentation of the graph, in which an object corresponds to a set of\ntime-variant graphs. In this paper, we formulate a novel time-variant graph\nclassification task and propose a new graph feature, called a graph-shapelet\npattern, for learning and classifying time-variant graphs. Graph-shapelet\npatterns are compact and discriminative graph transformation subsequences. A\ngraph-shapelet pattern can be regarded as a graphical extension of a shapelet\n-- a class of discriminative features designed for vector-based temporal data\nclassification. To discover graph-shapelet patterns, we propose to convert a\ntime-variant graph sequence into time-series data and use the discovered\nshapelets to find graph transformation subsequences as graph-shapelet patterns.\nBy converting each graph-shapelet pattern into a unique tokenized graph\ntransformation sequence, we can measure the similarity between two\ngraph-shapelet patterns and therefore classify time-variant graphs. Experiments\non both synthetic and real-world data demonstrate the superior performance of\nthe proposed algorithms.",
+        "authors": "Haishuai Wang",
+        "published": "2016-09-14",
+        "updated": "2017-06-12",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2204.09236v1",
+        "title": "Scalable Motif Counting for Large-scale Temporal Graphs",
+        "abstract": "One fundamental problem in temporal graph analysis is to count the\noccurrences of small connected subgraph patterns (i.e., motifs), which benefits\na broad range of real-world applications, such as anomaly detection, structure\nprediction, and network representation learning. However, existing works\nfocused on exacting temporal motif are not scalable to large-scale temporal\ngraph data, due to their heavy computational costs or inherent inadequacy of\nparallelism. In this work, we propose a scalable parallel framework for exactly\ncounting temporal motifs in large-scale temporal graphs. We first categorize\nthe temporal motifs based on their distinct properties, and then design\ncustomized algorithms that offer efficient strategies to exactly count the\nmotif instances of each category. Moreover, our compact data structures, namely\ntriple and quadruple counters, enable our algorithms to directly identify the\ntemporal motif instances of each category, according to edge information and\nthe relationship between edges, therefore significantly improving the counting\nefficiency. Based on the proposed counting algorithms, we design a hierarchical\nparallel framework that features both inter- and intra-node parallel\nstrategies, and fully leverages the multi-threading capacity of modern CPU to\nconcurrently count all temporal motifs. Extensive experiments on sixteen\nreal-world temporal graph datasets demonstrate the superiority and capability\nof our proposed framework for temporal motif counting, achieving up to 538*\nspeedup compared to the state-of-the-art methods. The source code of our method\nis available at: https://github.com/steven-ccq/FAST-temporal-motif.",
+        "authors": "Zhongqiang Gao, Chuanqi Cheng, Yanwei Yu, Lei Cao, Chao Huang, Junyu Dong",
+        "published": "2022-04-20",
+        "updated": "2022-04-20",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/0807.2357v1",
+        "title": "Temporal Graphs",
+        "abstract": "We introduce the idea of temporal graphs, a representation that encodes\ntemporal data into graphs while fully retaining the temporal information of the\noriginal data. This representation lets us explore the dynamic temporal\nproperties of data by using existing graph algorithms (such as shortest-path),\nwith no need for data-driven simulations. We also present a number of metrics\nthat can be used to study and explore temporal graphs. Finally, we use temporal\ngraphs to analyse real-world data and present the results of our analysis.",
+        "authors": "Vassilis Kostakos",
+        "published": "2008-07-15",
+        "updated": "2008-07-15",
+        "primary_cat": "physics.soc-ph",
+        "cats": [
+            "physics.soc-ph"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1310.7898v1",
+        "title": "Moving in temporal graphs with very sparse random availability of edges",
+        "abstract": "In this work we consider temporal graphs, i.e. graphs, each edge of which is\nassigned a set of discrete time-labels drawn from a set of integers. The labels\nof an edge indicate the discrete moments in time at which the edge is\navailable. We also consider temporal paths in a temporal graph, i.e. paths\nwhose edges are assigned a strictly increasing sequence of labels. Furthermore,\nwe assume the uniform case (UNI-CASE), in which every edge of a graph is\nassigned exactly one time label from a set of integers and the time labels\nassigned to the edges of the graph are chosen randomly and independently, with\nthe selection following the uniform distribution. We call uniform random\ntemporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the\nexpected number of temporal paths of a given length in the uniform random\ntemporal clique. We define the term temporal distance of two vertices, which is\nthe arrival time, i.e. the time-label of the last edge, of the temporal path\nthat connects those vertices, which has the smallest arrival time amongst all\ntemporal paths that connect those vertices. We then propose and study two\nstatistical properties of temporal graphs. One is the maximum expected temporal\ndistance which is, as the term indicates, the maximum of all expected temporal\ndistances in the graph. The other one is the temporal diameter which, loosely\nspeaking, is the expectation of the maximum temporal distance in the graph. We\nderive the maximum expected temporal distance of a uniform random temporal star\ngraph as well as an upper bound on both the maximum expected temporal distance\nand the temporal diameter of the normalized version of the uniform random\ntemporal clique, in which the largest time-label available equals the number of\nvertices. Finally, we provide an algorithm that solves an optimization problem\non a specific type of temporal (multi)graphs of two vertices.",
+        "authors": "Paul G. Spirakis, Eleni Ch. Akrida",
+        "published": "2013-10-29",
+        "updated": "2013-10-29",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2205.14269v1",
+        "title": "Temporal graph patterns by timed automata",
+        "abstract": "Temporal graphs represent graph evolution over time, and have been receiving\nconsiderable research attention. Work on expressing temporal graph patterns or\ndiscovering temporal motifs typically assumes relatively simple temporal\nconstraints, such as journeys or, more generally, existential constraints,\npossibly with finite delays. In this paper we propose to use timed automata to\nexpress temporal constraints, leading to a general and powerful notion of\ntemporal basic graph pattern (BGP). The new difficulty is the evaluation of the\ntemporal constraint on a large set of matchings. An important benefit of timed\nautomata is that they support an iterative state assignment, which can be\nuseful for early detection of matches and pruning of non-matches. We introduce\nalgorithms to retrieve all instances of a temporal BGP match in a graph, and\npresent results of an extensive experimental evaluation, demonstrating\ninteresting performance trade-offs. We show that an on-demand algorithm that\nprocesses total matchings incrementally over time is preferable when dealing\nwith cyclic patterns on sparse graphs. On acyclic patterns or dense graphs, and\nwhen connectivity of partial matchings can be guaranteed, the best performance\nis achieved by maintaining partial matchings over time and allowing automaton\nevaluation to be fully incremental.",
+        "authors": "Amir Pouya Aghasadeghi, Jan Van den Bussche, Julia Stoyanovich",
+        "published": "2022-05-27",
+        "updated": "2022-05-27",
+        "primary_cat": "cs.DB",
+        "cats": [
+            "cs.DB"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2311.01928v1",
+        "title": "Constructing Temporal Dynamic Knowledge Graphs from Interactive Text-based Games",
+        "abstract": "In natural language processing, interactive text-based games serve as a test\nbed for interactive AI systems. Prior work has proposed to play text-based\ngames by acting based on discrete knowledge graphs constructed by the Discrete\nGraph Updater (DGU) to represent the game state from the natural language\ndescription. While DGU has shown promising results with high interpretability,\nit suffers from lower knowledge graph accuracy due to its lack of temporality\nand limited generalizability to complex environments with objects with the same\nlabel. In order to address DGU's weaknesses while preserving its high\ninterpretability, we propose the Temporal Discrete Graph Updater (TDGU), a\nnovel neural network model that represents dynamic knowledge graphs as a\nsequence of timestamped graph events and models them using a temporal point\nbased graph neural network. Through experiments on the dataset collected from a\ntext-based game TextWorld, we show that TDGU outperforms the baseline DGU. We\nfurther show the importance of temporal information for TDGU's performance\nthrough an ablation study and demonstrate that TDGU has the ability to\ngeneralize to more complex environments with objects with the same label. All\nthe relevant code can be found at\n\\url{https://github.com/yukw777/temporal-discrete-graph-updater}.",
+        "authors": "Keunwoo Peter Yu",
+        "published": "2023-11-03",
+        "updated": "2023-11-03",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.15894v1",
+        "title": "A Gated MLP Architecture for Learning Topological Dependencies in Spatio-Temporal Graphs",
+        "abstract": "Graph Neural Networks (GNNs) and Transformer have been increasingly adopted\nto learn the complex vector representations of spatio-temporal graphs,\ncapturing intricate spatio-temporal dependencies crucial for applications such\nas traffic datasets. Although many existing methods utilize multi-head\nattention mechanisms and message-passing neural networks (MPNNs) to capture\nboth spatial and temporal relations, these approaches encode temporal and\nspatial relations independently, and reflect the graph's topological\ncharacteristics in a limited manner. In this work, we introduce the Cycle to\nMixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial\ninvariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP).\nThe Cy2Mixer is composed of three blocks based on MLPs: A message-passing block\nfor encapsulating spatial information, a cycle message-passing block for\nenriching topological information through cyclic subgraphs, and a temporal\nblock for capturing temporal properties. We bolster the effectiveness of\nCy2Mixer with mathematical evidence emphasizing that our cycle message-passing\nblock is capable of offering differentiated information to the deep learning\nmodel compared to the message-passing block. Furthermore, empirical evaluations\nsubstantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art\nperformances across various traffic benchmark datasets.",
+        "authors": "Yun Young Choi, Minho Lee, Sun Woo Park, Seunghwan Lee, Joohwan Ko",
+        "published": "2024-01-29",
+        "updated": "2024-01-29",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2403.13183v1",
+        "title": "Resolving Sets in Temporal Graphs",
+        "abstract": "A $\\textit{resolving set}$ $R$ in a graph $G$ is a set of vertices such that\nevery vertex of $G$ is uniquely identified by its distances to the vertices of\n$R$. Introduced in the 1970s, this concept has been since then extensively\nstudied from both combinatorial and algorithmic point of view. We propose a\ngeneralization of the concept of resolving sets to temporal graphs, i.e.,\ngraphs with edge sets that change over discrete time-steps. In this setting,\nthe $\\textit{temporal distance}$ from $u$ to $v$ is the earliest possible\ntime-step at which a journey with strictly increasing time-steps on edges\nleaving $u$ reaches $v$, i.e., the first time-step at which $v$ could receive a\nmessage broadcast from $u$. A $\\textit{temporal resolving set}$ of a temporal\ngraph $\\mathcal{G}$ is a subset $R$ of its vertices such that every vertex of\n$\\mathcal{G}$ is uniquely identified by its temporal distances from vertices of\n$R$.\n  We study the problem of finding a minimum-size temporal resolving set, and\nshow that it is NP-complete even on very restricted graph classes and with\nstrong constraints on the time-steps: temporal complete graphs where every edge\nappears in either time-step 1 or 2, temporal trees where every edge appears in\nat most two consecutive time-steps, and even temporal subdivided stars where\nevery edge appears in at most two (not necessarily consecutive) time-steps. On\nthe other hand, we give polynomial-time algorithms for temporal paths and\ntemporal stars where every edge appears in exactly one time-step, and give a\ncombinatorial analysis and algorithms for several temporal graph classes where\nthe edges appear in periodic time-steps.",
+        "authors": "Jan Bok, Antoine Dailly, Tuomo Lehtil\u00e4",
+        "published": "2024-03-19",
+        "updated": "2024-03-19",
+        "primary_cat": "math.CO",
+        "cats": [
+            "math.CO",
+            "cs.DM",
+            "cs.DS",
+            "05C69, 68Rxx"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2310.19292v1",
+        "title": "Fusing Temporal Graphs into Transformers for Time-Sensitive Question Answering",
+        "abstract": "Answering time-sensitive questions from long documents requires temporal\nreasoning over the times in questions and documents. An important open question\nis whether large language models can perform such reasoning solely using a\nprovided text document, or whether they can benefit from additional temporal\ninformation extracted using other systems. We address this research question by\napplying existing temporal information extraction systems to construct temporal\ngraphs of events, times, and temporal relations in questions and documents. We\nthen investigate different approaches for fusing these graphs into Transformer\nmodels. Experimental results show that our proposed approach for fusing\ntemporal graphs into input text substantially enhances the temporal reasoning\ncapabilities of Transformer models with or without fine-tuning. Additionally,\nour proposed method outperforms various graph convolution-based approaches and\nestablishes a new state-of-the-art performance on SituatedQA and three splits\nof TimeQA.",
+        "authors": "Xin Su, Phillip Howard, Nagib Hakim, Steven Bethard",
+        "published": "2023-10-30",
+        "updated": "2023-10-30",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2111.13684v3",
+        "title": "Spatio-Temporal Joint Graph Convolutional Networks for Traffic Forecasting",
+        "abstract": "Recent studies have shifted their focus towards formulating traffic\nforecasting as a spatio-temporal graph modeling problem. Typically, they\nconstructed a static spatial graph at each time step and then connected each\nnode with itself between adjacent time steps to create a spatio-temporal graph.\nHowever, this approach failed to explicitly reflect the correlations between\ndifferent nodes at different time steps, thus limiting the learning capability\nof graph neural networks. Additionally, those models overlooked the dynamic\nspatio-temporal correlations among nodes by using the same adjacency matrix\nacross different time steps. To address these limitations, we propose a novel\napproach called Spatio-Temporal Joint Graph Convolutional Networks (STJGCN) for\naccurate traffic forecasting on road networks over multiple future time steps.\nSpecifically, our method encompasses the construction of both pre-defined and\nadaptive spatio-temporal joint graphs (STJGs) between any two time steps, which\nrepresent comprehensive and dynamic spatio-temporal correlations. We further\nintroduce dilated causal spatio-temporal joint graph convolution layers on the\nSTJG to capture spatio-temporal dependencies from distinct perspectives with\nmultiple ranges. To aggregate information from different ranges, we propose a\nmulti-range attention mechanism. Finally, we evaluate our approach on five\npublic traffic datasets and experimental results demonstrate that STJGCN is not\nonly computationally efficient but also outperforms 11 state-of-the-art\nbaseline methods.",
+        "authors": "Chuanpan Zheng, Xiaoliang Fan, Shirui Pan, Haibing Jin, Zhaopeng Peng, Zonghan Wu, Cheng Wang, Philip S. Yu",
+        "published": "2021-11-25",
+        "updated": "2023-06-13",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2402.04696v1",
+        "title": "Nash Equilibria in Reverse Temporal Voronoi Games",
+        "abstract": "We study Voronoi games on temporal graphs as introduced by Boehmer et al.\n(IJCAI 2021) where two players each select a vertex in a temporal graph with\nthe goal of reaching the other vertices earlier than the other player. In this\nwork, we consider the reverse temporal Voronoi game, that is, a player wants to\nmaximize the number of vertices reaching her earlier than the other player.\nSince temporal distances in temporal graphs are not symmetric in general, this\nyields a different game. We investigate the difference between the two games\nwith respect to the existence of Nash equilibria in various temporal graph\nclasses including temporal trees, cycles, grids, cliques and split graphs. Our\nextensive results show that the two games indeed behave quite differently\ndepending on the considered temporal graph class.",
+        "authors": "Simeon Pawlowski, Vincent Froese",
+        "published": "2024-02-07",
+        "updated": "2024-02-07",
+        "primary_cat": "cs.GT",
+        "cats": [
+            "cs.GT"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1904.09610v2",
+        "title": "Storing and Querying Large-Scale Spatio-Temporal Graphs with High-Throughput Edge Insertions",
+        "abstract": "Real-world graphs often contain spatio-temporal information and evolve over\ntime. Compared with static graphs, spatio-temporal graphs have very different\ncharacteristics, presenting more significant challenges in data volume, data\nvelocity, and query processing. In this paper, we describe three representative\napplications to understand the features of spatio-temporal graphs. Based on the\ncommonalities of the applications, we define a formal spatio-temporal graph\nmodel, where a graph consists of location vertices, object vertices, and event\nedges. Then we discuss a set of design goals to meet the requirements of the\napplications: (i) supporting up to 10 billion object vertices, 10 million\nlocation vertices, and 100 trillion edges in the graph, (ii) supporting up to 1\ntrillion new edges that are streamed in daily, and (iii) minimizing\ncross-machine communication for query processing. We propose and evaluate PAST,\na framework for efficient PArtitioning and query processing of Spatio-Temporal\ngraphs. Experimental results show that PAST successfully achieves the above\ngoals. It improves query performance by orders of magnitude compared with\nstate-of-the-art solutions, including JanusGraph, Greenplum, Spark and\nST-Hadoop.",
+        "authors": "Mengsu Ding, Muqiao Yang, Shimin Chen",
+        "published": "2019-04-21",
+        "updated": "2020-10-20",
+        "primary_cat": "cs.DC",
+        "cats": [
+            "cs.DC",
+            "cs.DB"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2209.12587v1",
+        "title": "TGLib: An Open-Source Library for Temporal Graph Analysis",
+        "abstract": "We initiate an open-source library for the efficient analysis of temporal\ngraphs. We consider one of the standard models of dynamic networks in which\neach edge has a discrete timestamp and transition time. Recently there has been\na massive interest in analyzing such temporal graphs. Common computational data\nmining and analysis tasks include the computation of temporal distances,\ncentrality measures, and network statistics like topological overlap,\nburstiness, or temporal diameter. To fulfill the increasing demand for\nefficient and easy-to-use implementations of temporal graph algorithms, we\nintroduce the open-source library TGLib, which integrates efficient data\nstructures and algorithms for temporal graph analysis. TGLib is highly\nefficient and versatile, providing simple and convenient C++ and Python\ninterfaces, targeting computer scientists, practitioners, students, and the\n(temporal) network research community.",
+        "authors": "Lutz Oettershagen, Petra Mutzel",
+        "published": "2022-09-26",
+        "updated": "2022-09-26",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1908.09995v1",
+        "title": "Temporal Reasoning Graph for Activity Recognition",
+        "abstract": "Despite great success has been achieved in activity analysis, it still has\nmany challenges. Most existing work in activity recognition pay more attention\nto design efficient architecture or video sampling strategy. However, due to\nthe property of fine-grained action and long term structure in video, activity\nrecognition is expected to reason temporal relation between video sequences. In\nthis paper, we propose an efficient temporal reasoning graph (TRG) to\nsimultaneously capture the appearance features and temporal relation between\nvideo sequences at multiple time scales. Specifically, we construct learnable\ntemporal relation graphs to explore temporal relation on the multi-scale range.\nAdditionally, to facilitate multi-scale temporal relation extraction, we design\na multi-head temporal adjacent matrix to represent multi-kinds of temporal\nrelations. Eventually, a multi-head temporal relation aggregator is proposed to\nextract the semantic meaning of those features convolving through the graphs.\nExtensive experiments are performed on widely-used large-scale datasets, such\nas Something-Something and Charades, and the results show that our model can\nachieve state-of-the-art performance. Further analysis shows that temporal\nrelation reasoning with our TRG can extract discriminative features for\nactivity recognition.",
+        "authors": "Jingran Zhang, Fumin Shen, Xing Xu, Heng Tao Shen",
+        "published": "2019-08-27",
+        "updated": "2019-08-27",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2207.10830v1",
+        "title": "Automated Dilated Spatio-Temporal Synchronous Graph Modeling for Traffic Prediction",
+        "abstract": "Accurate traffic prediction is a challenging task in intelligent\ntransportation systems because of the complex spatio-temporal dependencies in\ntransportation networks. Many existing works utilize sophisticated temporal\nmodeling approaches to incorporate with graph convolution networks (GCNs) for\ncapturing short-term and long-term spatio-temporal dependencies. However, these\nseparated modules with complicated designs could restrict effectiveness and\nefficiency of spatio-temporal representation learning. Furthermore, most\nprevious works adopt the fixed graph construction methods to characterize the\nglobal spatio-temporal relations, which limits the learning capability of the\nmodel for different time periods and even different data scenarios. To overcome\nthese limitations, we propose an automated dilated spatio-temporal synchronous\ngraph network, named Auto-DSTSGN for traffic prediction. Specifically, we\ndesign an automated dilated spatio-temporal synchronous graph (Auto-DSTSG)\nmodule to capture the short-term and long-term spatio-temporal correlations by\nstacking deeper layers with dilation factors in an increasing order. Further,\nwe propose a graph structure search approach to automatically construct the\nspatio-temporal synchronous graph that can adapt to different data scenarios.\nExtensive experiments on four real-world datasets demonstrate that our model\ncan achieve about 10% improvements compared with the state-of-art methods.\nSource codes are available at https://github.com/jinguangyin/Auto-DSTSGN.",
+        "authors": "Guangyin Jin, Fuxian Li, Jinlei Zhang, Mudan Wang, Jincai Huang",
+        "published": "2022-07-22",
+        "updated": "2022-07-22",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1805.06836v2",
+        "title": "Deleting edges to restrict the size of an epidemic in temporal networks",
+        "abstract": "Spreading processes on graphs are a natural model for a wide variety of\nreal-world phenomena, including information spread over social networks and\nbiological diseases spreading over contact networks. Often, the networks over\nwhich these processes spread are dynamic in nature, and can be modeled with\ntemporal graphs. Here, we study the problem of deleting edges from a given\ntemporal graph in order to reduce the number of vertices (temporally) reachable\nfrom a given starting point. This could be used to control the spread of a\ndisease, rumour, etc. in a temporal graph. In particular, our aim is to find a\ntemporal subgraph in which a process starting at any single vertex can be\ntransferred to only a limited number of other vertices using a\ntemporally-feasible path. We introduce a natural edge-deletion problem for\ntemporal graphs and provide positive and negative results on its computational\ncomplexity and approximability.",
+        "authors": "Jessica Enright, Kitty Meeks, George B. Mertzios, Viktor Zamaraev",
+        "published": "2018-05-17",
+        "updated": "2021-02-11",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS",
+            "cs.CC"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.02563v1",
+        "title": "Kairos: Efficient Temporal Graph Analytics on a Single Machine",
+        "abstract": "Many important societal problems are naturally modeled as algorithms over\ntemporal graphs. To date, however, most graph processing systems remain\ninefficient as they rely on distributed processing even for graphs that fit\nwell within a commodity server's available storage. In this paper, we introduce\nKairos, a temporal graph analytics system that provides application developers\na framework for efficiently implementing and executing algorithms over temporal\ngraphs on a single machine. Specifically, Kairos relies on fork-join\nparallelism and a highly optimized parallel data structure as core primitives\nto maximize performance of graph processing tasks needed for temporal graph\nanalytics. Furthermore, we introduce the notion of selective indexing and show\nhow it can be used with an efficient index to speedup temporal queries. Our\nexperiments on a 24-core server show that our algorithms obtain good parallel\nspeedups, and are significantly faster than equivalent algorithms in existing\ntemporal graph processing systems: up to 60x against a shared-memory approach,\nand several orders of magnitude when compared with distributed processing of\ngraphs that fit within a single server.",
+        "authors": "Joana M. F. da Trindade, Julian Shun, Samuel Madden, Nesime Tatbul",
+        "published": "2024-01-04",
+        "updated": "2024-01-04",
+        "primary_cat": "cs.DB",
+        "cats": [
+            "cs.DB",
+            "cs.DC",
+            "cs.PF"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2403.04782v1",
+        "title": "A Survey on Temporal Knowledge Graph: Representation Learning and Applications",
+        "abstract": "Knowledge graphs have garnered significant research attention and are widely\nused to enhance downstream applications. However, most current studies mainly\nfocus on static knowledge graphs, whose facts do not change with time, and\ndisregard their dynamic evolution over time. As a result, temporal knowledge\ngraphs have attracted more attention because a large amount of structured\nknowledge exists only within a specific period. Knowledge graph representation\nlearning aims to learn low-dimensional vector embeddings for entities and\nrelations in a knowledge graph. The representation learning of temporal\nknowledge graphs incorporates time information into the standard knowledge\ngraph framework and can model the dynamics of entities and relations over time.\nIn this paper, we conduct a comprehensive survey of temporal knowledge graph\nrepresentation learning and its applications. We begin with an introduction to\nthe definitions, datasets, and evaluation metrics for temporal knowledge graph\nrepresentation learning. Next, we propose a taxonomy based on the core\ntechnologies of temporal knowledge graph representation learning methods, and\nprovide an in-depth analysis of different methods in each category. Finally, we\npresent various downstream applications related to the temporal knowledge\ngraphs. In the end, we conclude the paper and have an outlook on the future\nresearch directions in this area.",
+        "authors": "Li Cai, Xin Mao, Yuhao Zhou, Zhaoguang Long, Changxu Wu, Man Lan",
+        "published": "2024-03-02",
+        "updated": "2024-03-02",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1903.08889v3",
+        "title": "Node Embedding over Temporal Graphs",
+        "abstract": "In this work, we present a method for node embedding in temporal graphs. We\npropose an algorithm that learns the evolution of a temporal graph's nodes and\nedges over time and incorporates this dynamics in a temporal node embedding\nframework for different graph prediction tasks. We present a joint loss\nfunction that creates a temporal embedding of a node by learning to combine its\nhistorical temporal embeddings, such that it optimizes per given task (e.g.,\nlink prediction). The algorithm is initialized using static node embeddings,\nwhich are then aligned over the representations of a node at different time\npoints, and eventually adapted for the given task in a joint optimization. We\nevaluate the effectiveness of our approach over a variety of temporal graphs\nfor the two fundamental tasks of temporal link prediction and multi-label node\nclassification, comparing to competitive baselines and algorithmic\nalternatives. Our algorithm shows performance improvements across many of the\ndatasets and baselines and is found particularly effective for graphs that are\nless cohesive, with a lower clustering coefficient.",
+        "authors": "Uriel Singer, Ido Guy, Kira Radinsky",
+        "published": "2019-03-21",
+        "updated": "2021-05-19",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.SI",
+            "stat.ML"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2203.15862v1",
+        "title": "Restless Temporal Path Parameterized Above Lower Bounds",
+        "abstract": "Reachability questions are one of the most fundamental algorithmic primitives\nin temporal graphs -- graphs whose edge set changes over discrete time steps. A\ncore problem here is the NP-hard Short Restless Temporal Path: given a temporal\ngraph $\\mathcal G$, two distinct vertices $s$ and $z$, and two numbers $\\delta$\nand $k$, is there a $\\delta$-restless temporal $s$-$z$ path of length at most\n$k$? A temporal path is a path whose edges appear in chronological order and a\ntemporal path is $\\delta$-restless if two consecutive path edges appear at most\n$\\delta$ time steps apart from each other. Among others, this problem has\napplications in neuroscience and epidemiology. While Short Restless Temporal\nPath is known to be computationally hard, e.g., it is NP-hard for only three\ntime steps and W[1]-hard when parameterized by the feedback vertex number of\nthe underlying graph, it is fixed-parameter tractable when parameterized by the\npath length $k$. We improve on this by showing that Short Restless Temporal\nPath can be solved in (randomized) $4^{k-d}|\\mathcal G|^{O(1)}$ time, where $d$\nis the minimum length of a temporal $s$-$z$ path.",
+        "authors": "Philipp Zschoche",
+        "published": "2022-03-29",
+        "updated": "2022-03-29",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS",
+            "cs.DM"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2404.19453v1",
+        "title": "Structural Parameters for Dense Temporal Graphs",
+        "abstract": "Temporal graphs provide a useful model for many real-world networks.\nUnfortunately the majority of algorithmic problems we might consider on such\ngraphs are intractable. There has been recent progress in defining structural\nparameters which describe tractable cases by simultaneously restricting the\nunderlying structure and the times at which edges appear in the graph. These\nall rely on the temporal graph being sparse in some sense. We introduce\ntemporal analogues of three increasingly restrictive static graph parameters --\ncliquewidth, modular-width and neighbourhood diversity -- which take small\nvalues for highly structured temporal graphs, even if a large number of edges\nare active at each timestep. The computational problems solvable efficiently\nwhen the temporal cliquewidth of the input graph is bounded form a subset of\nthose solvable efficiently when the temporal modular-width is bounded, which is\nin turn a subset of problems efficiently solvable when the temporal\nneighbourhood diversity is bounded. By considering specific temporal graph\nproblems, we demonstrate that (up to standard complexity theoretic assumptions)\nthese inclusions are strict.",
+        "authors": "Jessica Enright, Samuel D. Hand, Laura Larios-Jones, Kitty Meeks",
+        "published": "2024-04-30",
+        "updated": "2024-04-30",
+        "primary_cat": "cs.DM",
+        "cats": [
+            "cs.DM",
+            "math.CO"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1504.07976v3",
+        "title": "On Temporal Graph Exploration",
+        "abstract": "A temporal graph is a graph in which the edge set can change from one time\nstep to the next. The temporal graph exploration problem TEXP is the problem of\ncomputing a foremost exploration schedule for a temporal graph, i.e., a\ntemporal walk that starts at a given start node, visits all nodes of the graph,\nand has the smallest arrival time. In the first part of the paper, we consider\nonly undirected temporal graphs that are connected at each time step. For such\ntemporal graphs with $n$ nodes, we show that it is \\NP-hard to approximate TEXP\nwith ratio $O(n^{1-\\varepsilon})$ for every $\\varepsilon>0$. We also provide an\nexplicit construction of temporal graphs that require $\\Theta(n^2)$ time steps\nto be explored. In the second part of the paper, we still consider temporal\ngraphs that are connected in each time step, but we assume that the underlying\ngraph (i.e. the graph that contains all edges that are present in the temporal\ngraph in at least one time step) belongs to a specific class of graphs. Among\nother results, we show that temporal graphs can be explored in\n$O(n^{1.5}k^{1.5}\\log n)$ time steps if the underlying graph has treewidth $k$,\nin $O(n^{1.8}\\log n)$ time steps if the underlying graph is planar, and in\n$O(n\\log^3 n)$ time steps if the underlying graph is a $2\\times n$ grid. In the\nthird part of the paper, we consider settings where the graphs in future time\nsteps are not known and the exploration schedule is constructed online. We\nreplace the connectedness assumption by a weaker assumption and show that\n$m$-edge temporal graphs with regularly present edges and with\nprobabilistically present edges can be explored online in $O(m)$ time steps and\n$O(m \\log n)$ time steps with high probability, respectively. We finally show\nthat the latter result can be used to obtain a distributed algorithm for the\ngossiping problem in random temporal graphs.",
+        "authors": "Thomas Erlebach, Michael Hoffmann, Frank Kammer",
+        "published": "2015-04-29",
+        "updated": "2021-03-16",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS",
+            "05C85, 68M14",
+            "C.2.4; F.2.2; G.2.2"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2402.13624v1",
+        "title": "Towards Linear Spanners in All Temporal Cliques",
+        "abstract": "Many real-world networks, like transportation networks and social networks,\nare dynamic in the sense that the edge set may change over time, but these\nchanges are known in advance. This behavior is captured by the temporal graphs\nmodel, which has recently become a trending topic in theoretical computer\nscience. A core open problem in the field is to prove the existence of\nlinear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of\ncomplete temporal graphs that ensure all-pairs reachability via temporal paths.\nSo far, the best known result is the existence of temporal spanners with\n$\\mathcal{O}(n\\log n)$ many edges. We present significant progress towards\nproving that linear-size temporal spanners exist in all temporal cliques.\n  We adapt techniques used in previous works and heavily expand and generalize\nthem to provide a simpler and more intuitive proof of the $\\mathcal{O}(n\\log\nn)$ bound. Moreover, we use our novel approach to show that a large class of\ntemporal cliques, called edge-pivot graphs, admit linear-size temporal\nspanners. To contrast this, we investigate other classes of temporal cliques\nthat do not belong to the class of edge-pivot graphs. We introduce two such\ngraph classes and we develop novel techniques for establishing the existence of\nlinear temporal spanners in these graph classes as well.",
+        "authors": "Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, Armin Wells",
+        "published": "2024-02-21",
+        "updated": "2024-02-21",
+        "primary_cat": "cs.DM",
+        "cats": [
+            "cs.DM",
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.07699v2",
+        "title": "Time-aware Graph Structure Learning via Sequence Prediction on Temporal Graphs",
+        "abstract": "Temporal Graph Learning, which aims to model the time-evolving nature of\ngraphs, has gained increasing attention and achieved remarkable performance\nrecently. However, in reality, graph structures are often incomplete and noisy,\nwhich hinders temporal graph networks (TGNs) from learning informative\nrepresentations. Graph contrastive learning uses data augmentation to generate\nplausible variations of existing data and learn robust representations.\nHowever, rule-based augmentation approaches may be suboptimal as they lack\nlearnability and fail to leverage rich information from downstream tasks. To\naddress these issues, we propose a Time-aware Graph Structure Learning (TGSL)\napproach via sequence prediction on temporal graphs, which learns better graph\nstructures for downstream tasks through adding potential temporal edges. In\nparticular, it predicts time-aware context embedding based on previously\nobserved interactions and uses the Gumble-Top-K to select the closest candidate\nedges to this context embedding. Additionally, several candidate sampling\nstrategies are proposed to ensure both efficiency and diversity. Furthermore,\nwe jointly learn the graph structure and TGNs in an end-to-end manner and\nperform inference on the refined graph. Extensive experiments on temporal link\nprediction benchmarks demonstrate that TGSL yields significant gains for the\npopular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive\nlearning methods on temporal graphs. We release the code at\nhttps://github.com/ViktorAxelsen/TGSL.",
+        "authors": "Haozhen Zhang, Xueting Han, Xi Xiao, Jing Bai",
+        "published": "2023-06-13",
+        "updated": "2023-08-15",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2203.14303v1",
+        "title": "TREND: TempoRal Event and Node Dynamics for Graph Representation Learning",
+        "abstract": "Temporal graph representation learning has drawn significant attention for\nthe prevalence of temporal graphs in the real world. However, most existing\nworks resort to taking discrete snapshots of the temporal graph, or are not\ninductive to deal with new nodes, or do not model the exciting effects which is\nthe ability of events to influence the occurrence of another event. In this\nwork, We propose TREND, a novel framework for temporal graph representation\nlearning, driven by TempoRal Event and Node Dynamics and built upon a Hawkes\nprocess-based graph neural network (GNN). TREND presents a few major\nadvantages: (1) it is inductive due to its GNN architecture; (2) it captures\nthe exciting effects between events by the adoption of the Hawkes process; (3)\nas our main novelty, it captures the individual and collective characteristics\nof events by integrating both event and node dynamics, driving a more precise\nmodeling of the temporal process. Extensive experiments on four real-world\ndatasets demonstrate the effectiveness of our proposed model.",
+        "authors": "Zhihao Wen, Yuan Fang",
+        "published": "2022-03-27",
+        "updated": "2022-03-27",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2309.03251v3",
+        "title": "Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning",
+        "abstract": "Temporal Knowledge Graph (TKG) is an extension of traditional Knowledge Graph\n(KG) that incorporates the dimension of time. Reasoning on TKGs is a crucial\ntask that aims to predict future facts based on historical occurrences. The key\nchallenge lies in uncovering structural dependencies within historical\nsubgraphs and temporal patterns. Most existing approaches model TKGs relying on\nentity modeling, as nodes in the graph play a crucial role in knowledge\nrepresentation. However, the real-world scenario often involves an extensive\nnumber of entities, with new entities emerging over time. This makes it\nchallenging for entity-dependent methods to cope with extensive volumes of\nentities, and effectively handling newly emerging entities also becomes a\nsignificant challenge. Therefore, we propose Temporal Inductive Path Neural\nNetwork (TiPNN), which models historical information in an entity-independent\nperspective. Specifically, TiPNN adopts a unified graph, namely history\ntemporal graph, to comprehensively capture and encapsulate information from\nhistory. Subsequently, we utilize the defined query-aware temporal paths on a\nhistory temporal graph to model historical path information related to queries\nfor reasoning. Extensive experiments illustrate that the proposed model not\nonly attains significant performance enhancements but also handles inductive\nsettings, while additionally facilitating the provision of reasoning evidence\nthrough history temporal graphs.",
+        "authors": "Hao Dong, Pengyang Wang, Meng Xiao, Zhiyuan Ning, Pengfei Wang, Yuanchun Zhou",
+        "published": "2023-09-06",
+        "updated": "2024-01-25",
+        "primary_cat": "cs.AI",
+        "cats": [
+            "cs.AI",
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1207.7103v1",
+        "title": "Temporal Reachability Graphs",
+        "abstract": "While a natural fit for modeling and understanding mobile networks,\ntime-varying graphs remain poorly understood. Indeed, many of the usual\nconcepts of static graphs have no obvious counterpart in time-varying ones. In\nthis paper, we introduce the notion of temporal reachability graphs. A\n(tau,delta)-reachability graph} is a time-varying directed graph derived from\nan existing connectivity graph. An edge exists from one node to another in the\nreachability graph at time t if there exists a journey (i.e., a spatiotemporal\npath) in the connectivity graph from the first node to the second, leaving\nafter t, with a positive edge traversal time tau, and arriving within a maximum\ndelay delta. We make three contributions. First, we develop the theoretical\nframework around temporal reachability graphs. Second, we harness our\ntheoretical findings to propose an algorithm for their efficient computation.\nFinally, we demonstrate the analytic power of the temporal reachability graph\nconcept by applying it to synthetic and real-life datasets. On top of defining\nclear upper bounds on communication capabilities, reachability graphs highlight\nasymmetric communication opportunities and offloading potential.",
+        "authors": "John Whitbeck, Marcelo Dias de Amorim, Vania Conan, Jean-Loup Guillaume",
+        "published": "2012-07-30",
+        "updated": "2012-07-30",
+        "primary_cat": "cs.NI",
+        "cats": [
+            "cs.NI",
+            "C.2.1; F.2.2; G.2.2"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1706.09480v1",
+        "title": "A Temporal Tree Decomposition for Generating Temporal Graphs",
+        "abstract": "Discovering the underlying structures present in large real world graphs is a\nfundamental scientific problem. Recent work at the intersection of formal\nlanguage theory and graph theory has found that a Hyperedge Replacement Grammar\n(HRG) can be extracted from a tree decomposition of any graph. This HRG can be\nused to generate new graphs that share properties that are similar to the\noriginal graph. Because the extracted HRG is directly dependent on the shape\nand contents of the of tree decomposition, it is unlikely that informative\ngraph-processes are actually being captured with the extraction algorithm. To\naddress this problem, the current work presents a new extraction algorithm\ncalled temporal HRG (tHRG) that learns HRG production rules from a temporal\ntree decomposition of the graph. We observe problems with the assumptions that\nare made in a temporal HRG model. In experiments on large real world networks,\nwe show and provide reasoning as to why tHRG does not perform as well as HRG\nand other graph generators.",
+        "authors": "Corey Pennycuff, Salvador Aguinaga, Tim Weninger",
+        "published": "2017-06-28",
+        "updated": "2017-06-28",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2012.09641v2",
+        "title": "Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting",
+        "abstract": "Spatial-temporal data forecasting of traffic flow is a challenging task\nbecause of complicated spatial dependencies and dynamical trends of temporal\npattern between different roads. Existing frameworks typically utilize given\nspatial adjacency graph and sophisticated mechanisms for modeling spatial and\ntemporal correlations. However, limited representations of given spatial graph\nstructure with incomplete adjacent connections may restrict effective\nspatial-temporal dependencies learning of those models. To overcome those\nlimitations, our paper proposes Spatial-Temporal Fusion Graph Neural Networks\n(STFGNN) for traffic flow forecasting. SFTGNN could effectively learn hidden\nspatial-temporal dependencies by a novel fusion operation of various spatial\nand temporal graphs, which is generated by a data-driven method. Meanwhile, by\nintegrating this fusion graph module and a novel gated convolution module into\na unified layer, SFTGNN could handle long sequences. Experimental results on\nseveral public traffic datasets demonstrate that our method achieves\nstate-of-the-art performance consistently than other baselines.",
+        "authors": "Mengzhang Li, Zhanxing Zhu",
+        "published": "2020-12-15",
+        "updated": "2021-03-06",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1602.04434v1",
+        "title": "Frequency Analysis of Temporal Graph Signals",
+        "abstract": "This letter extends the concept of graph-frequency to graph signals that\nevolve with time. Our goal is to generalize and, in fact, unify the familiar\nconcepts from time- and graph-frequency analysis. To this end, we study a joint\ntemporal and graph Fourier transform (JFT) and demonstrate its attractive\nproperties. We build on our results to create filters which act on the joint\n(temporal and graph) frequency domain, and show how these can be used to\nperform interference cancellation. The proposed algorithms are distributed,\nhave linear complexity, and can approximate any desired joint filtering\nobjective.",
+        "authors": "Andreas Loukas, Damien Foucard",
+        "published": "2016-02-14",
+        "updated": "2016-02-14",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.SY",
+            "stat.ML"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.11074v1",
+        "title": "On The Temporal Domain of Differential Equation Inspired Graph Neural Networks",
+        "abstract": "Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling\ncomplex relationships in graph-structured data. A recent innovation in this\nfield is the family of Differential Equation-Inspired Graph Neural Networks\n(DE-GNNs), which leverage principles from continuous dynamical systems to model\ninformation flow on graphs with built-in properties such as feature smoothing\nor preservation. However, existing DE-GNNs rely on first or second-order\ntemporal dependencies. In this paper, we propose a neural extension to those\npre-defined temporal dependencies. We show that our model, called TDE-GNN, can\ncapture a wide range of temporal dynamics that go beyond typical first or\nsecond-order methods, and provide use cases where existing temporal models are\nchallenged. We demonstrate the benefit of learning the temporal dependencies\nusing our method rather than using pre-defined temporal dynamics on several\ngraph benchmarks.",
+        "authors": "Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane Sch\u00f6nlieb",
+        "published": "2024-01-20",
+        "updated": "2024-01-20",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2106.12931v1",
+        "title": "Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting",
+        "abstract": "Spatial-temporal forecasting has attracted tremendous attention in a wide\nrange of applications, and traffic flow prediction is a canonical and typical\nexample. The complex and long-range spatial-temporal correlations of traffic\nflow bring it to a most intractable challenge. Existing works typically utilize\nshallow graph convolution networks (GNNs) and temporal extracting modules to\nmodel spatial and temporal dependencies respectively. However, the\nrepresentation ability of such models is limited due to: (1) shallow GNNs are\nincapable to capture long-range spatial correlations, (2) only spatial\nconnections are considered and a mass of semantic connections are ignored,\nwhich are of great importance for a comprehensive understanding of traffic\nnetworks. To this end, we propose Spatial-Temporal Graph Ordinary Differential\nEquation Networks (STGODE). Specifically, we capture spatial-temporal dynamics\nthrough a tensor-based ordinary differential equation (ODE), as a result,\ndeeper networks can be constructed and spatial-temporal features are utilized\nsynchronously. To understand the network more comprehensively, semantical\nadjacency matrix is considered in our model, and a well-design temporal\ndialated convolution structure is used to capture long term temporal\ndependencies. We evaluate our model on multiple real-world traffic datasets and\nsuperior performance is achieved over state-of-the-art baselines.",
+        "authors": "Zheng Fang, Qingqing Long, Guojie Song, Kunqing Xie",
+        "published": "2021-06-24",
+        "updated": "2021-06-24",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2212.05653v1",
+        "title": "Spatial-temporal traffic modeling with a fusion graph reconstructed by tensor decomposition",
+        "abstract": "Accurate spatial-temporal traffic flow forecasting is essential for helping\ntraffic managers to take control measures and drivers to choose the optimal\ntravel routes. Recently, graph convolutional networks (GCNs) have been widely\nused in traffic flow prediction owing to their powerful ability to capture\nspatial-temporal dependencies. The design of the spatial-temporal graph\nadjacency matrix is a key to the success of GCNs, and it is still an open\nquestion. This paper proposes reconstructing the binary adjacency matrix via\ntensor decomposition, and a traffic flow forecasting method is proposed. First,\nwe reformulate the spatial-temporal fusion graph adjacency matrix into a\nthree-way adjacency tensor. Then, we reconstructed the adjacency tensor via\nTucker decomposition, wherein more informative and global spatial-temporal\ndependencies are encoded. Finally, a Spatial-temporal Synchronous Graph\nConvolutional module for localized spatial-temporal correlations learning and a\nDilated Convolution module for global correlations learning are assembled to\naggregate and learn the comprehensive spatial-temporal dependencies of the road\nnetwork. Experimental results on four open-access datasets demonstrate that the\nproposed model outperforms state-of-the-art approaches in terms of the\nprediction performance and computational cost.",
+        "authors": "Qin Li, Xuan Yang, Yong Wang, Yuankai Wu, Deqiang He",
+        "published": "2022-12-12",
+        "updated": "2022-12-12",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1810.06240v4",
+        "title": "Comparing Temporal Graphs Using Dynamic Time Warping",
+        "abstract": "Within many real-world networks the links between pairs of nodes change over\ntime. Thus, there has been a recent boom in studying temporal graphs.\nRecognizing patterns in temporal graphs requires a proximity measure to compare\ndifferent temporal graphs. To this end, we propose to study dynamic time\nwarping on temporal graphs. We define the dynamic temporal graph warping\ndistance (dtgw) to determine the dissimilarity of two temporal graphs. Our\nnovel measure is flexible and can be applied in various application domains. We\nshow that computing the dtgw-distance is a challenging (in general) NP-hard\noptimization problem and identify some polynomial-time solvable special cases.\nMoreover, we develop a quadratic programming formulation and an efficient\nheuristic. In experiments on real-word data we show that the heuristic performs\nvery well and that our dtgw-distance performs favorably in de-anonymizing\nnetworks compared to other approaches.",
+        "authors": "Vincent Froese, Brijnesh Jain, Rolf Niedermeier, Malte Renken",
+        "published": "2018-10-15",
+        "updated": "2020-07-06",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML",
+            "F.2.2; G.2.2"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2403.09039v1",
+        "title": "Spatial-temporal Memories Enhanced Graph Autoencoder for Anomaly Detection in Dynamic Graphs",
+        "abstract": "Anomaly detection in dynamic graphs presents a significant challenge due to\nthe temporal evolution of graph structures and attributes. The conventional\napproaches that tackle this problem typically employ an unsupervised learning\nframework, capturing normality patterns with exclusive normal data during\ntraining and identifying deviations as anomalies during testing. However, these\nmethods face critical drawbacks: they either only depend on proxy tasks for\ngeneral representation without directly pinpointing normal patterns, or they\nneglect to differentiate between spatial and temporal normality patterns,\nleading to diminished efficacy in anomaly detection. To address these\nchallenges, we introduce a novel Spatial-Temporal memories-enhanced graph\nautoencoder (STRIPE). Initially, STRIPE employs Graph Neural Networks (GNNs)\nand gated temporal convolution layers to extract spatial features and temporal\nfeatures, respectively. Then STRIPE incorporates separate spatial and temporal\nmemory networks, which capture and store prototypes of normal patterns, thereby\npreserving the uniqueness of spatial and temporal normality. After that,\nthrough a mutual attention mechanism, these stored patterns are then retrieved\nand integrated with encoded graph embeddings. Finally, the integrated features\nare fed into the decoder to reconstruct the graph streams which serve as the\nproxy task for anomaly detection. This comprehensive approach not only\nminimizes reconstruction errors but also refines the model by emphasizing the\ncompactness and distinctiveness of the embeddings in relation to the nearest\nmemory prototypes. Through extensive testing, STRIPE has demonstrated a\nsuperior capability to discern anomalies by effectively leveraging the distinct\nspatial and temporal dynamics of dynamic graphs, significantly outperforming\nexisting methodologies, with an average improvement of 15.39% on AUC values.",
+        "authors": "Jie Liu, Xuequn Shang, Xiaolin Han, Wentao Zhang, Hongzhi Yin",
+        "published": "2024-03-14",
+        "updated": "2024-03-14",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2311.04816v1",
+        "title": "MTGER: Multi-view Temporal Graph Enhanced Temporal Reasoning over Time-Involved Document",
+        "abstract": "The facts and time in the document are intricately intertwined, making\ntemporal reasoning over documents challenging. Previous work models time\nimplicitly, making it difficult to handle such complex relationships. To\naddress this issue, we propose MTGER, a novel Multi-view Temporal Graph\nEnhanced Temporal Reasoning framework for temporal reasoning over time-involved\ndocuments. Concretely, MTGER explicitly models the temporal relationships among\nfacts by multi-view temporal graphs. On the one hand, the heterogeneous\ntemporal graphs explicitly model the temporal and discourse relationships among\nfacts; on the other hand, the multi-view mechanism captures both time-focused\nand fact-focused information, allowing the two views to complement each other\nthrough adaptive fusion. To further improve the implicit reasoning capability\nof the model, we design a self-supervised time-comparing objective. Extensive\nexperimental results demonstrate the effectiveness of our method on the TimeQA\nand SituatedQA datasets. Furthermore, MTGER gives more consistent answers under\nquestion perturbations.",
+        "authors": "Zheng Chu, Zekun Wang, Jiafeng Liang, Ming Liu, Bing Qin",
+        "published": "2023-11-08",
+        "updated": "2023-11-08",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2304.05078v1",
+        "title": "TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification",
+        "abstract": "Multivariate time series classification (MTSC) is an important data mining\ntask, which can be effectively solved by popular deep learning technology.\nUnfortunately, the existing deep learning-based methods neglect the hidden\ndependencies in different dimensions and also rarely consider the unique\ndynamic features of time series, which lack sufficient feature extraction\ncapability to obtain satisfactory classification accuracy. To address this\nproblem, we propose a novel temporal dynamic graph neural network (TodyNet)\nthat can extract hidden spatio-temporal dependencies without undefined graph\nstructure. It enables information flow among isolated but implicit\ninterdependent variables and captures the associations between different time\nslots by dynamic graph mechanism, which further improves the classification\nperformance of the model. Meanwhile, the hierarchical representations of graphs\ncannot be learned due to the limitation of GNNs. Thus, we also design a\ntemporal graph pooling layer to obtain a global graph-level representation for\ngraph learning with learnable temporal parameters. The dynamic graph, graph\ninformation propagation, and temporal convolution are jointly learned in an\nend-to-end framework. The experiments on 26 UEA benchmark datasets illustrate\nthat the proposed TodyNet outperforms existing deep learning-based methods in\nthe MTSC tasks.",
+        "authors": "Huaiyuan Liu, Xianzhang Liu, Donghua Yang, Zhiyu Liang, Hongzhi Wang, Yong Cui, Jun Gu",
+        "published": "2023-04-11",
+        "updated": "2023-04-11",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2103.10379v1",
+        "title": "ChronoR: Rotation Based Temporal Knowledge Graph Embedding",
+        "abstract": "Despite the importance and abundance of temporal knowledge graphs, most of\nthe current research has been focused on reasoning on static graphs. In this\npaper, we study the challenging problem of inference over temporal knowledge\ngraphs. In particular, the task of temporal link prediction. In general, this\nis a difficult task due to data non-stationarity, data heterogeneity, and its\ncomplex temporal dependencies. We propose Chronological Rotation embedding\n(ChronoR), a novel model for learning representations for entities, relations,\nand time. Learning dense representations is frequently used as an efficient and\nversatile method to perform reasoning on knowledge graphs. The proposed model\nlearns a k-dimensional rotation transformation parametrized by relation and\ntime, such that after each fact's head entity is transformed using the\nrotation, it falls near its corresponding tail entity. By using high\ndimensional rotation as its transformation operator, ChronoR captures rich\ninteraction between the temporal and multi-relational characteristics of a\nTemporal Knowledge Graph. Experimentally, we show that ChronoR is able to\noutperform many of the state-of-the-art methods on the benchmark datasets for\ntemporal knowledge graph link prediction.",
+        "authors": "Ali Sadeghian, Mohammadreza Armandpour, Anthony Colas, Daisy Zhe Wang",
+        "published": "2021-03-18",
+        "updated": "2021-03-18",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.SC"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1401.1919v1",
+        "title": "Temporal Graph Traversals: Definitions, Algorithms, and Applications",
+        "abstract": "A temporal graph is a graph in which connections between vertices are active\nat specific times, and such temporal information leads to completely new\npatterns and knowledge that are not present in a non-temporal graph. In this\npaper, we study traversal problems in a temporal graph. Graph traversals, such\nas DFS and BFS, are basic operations for processing and studying a graph. While\nboth DFS and BFS are well-known simple concepts, it is non-trivial to adopt the\nsame notions from a non-temporal graph to a temporal graph. We analyze the\ndifficulties of defining temporal graph traversals and propose new definitions\nof DFS and BFS for a temporal graph. We investigate the properties of temporal\nDFS and BFS, and propose efficient algorithms with optimal complexity. In\nparticular, we also study important applications of temporal DFS and BFS. We\nverify the efficiency and importance of our graph traversal algorithms in real\nworld temporal graphs.",
+        "authors": "Silu Huang, James Cheng, Huanhuan Wu",
+        "published": "2014-01-09",
+        "updated": "2014-01-09",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS",
+            "cs.DB"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2404.19508v1",
+        "title": "Temporal Graph ODEs for Irregularly-Sampled Time Series",
+        "abstract": "Modern graph representation learning works mostly under the assumption of\ndealing with regularly sampled temporal graph snapshots, which is far from\nrealistic, e.g., social networks and physical systems are characterized by\ncontinuous dynamics and sporadic observations. To address this limitation, we\nintroduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework,\nwhich learns both the temporal and spatial dynamics from graph streams where\nthe intervals between observations are not regularly spaced. We empirically\nvalidate the proposed approach on several graph benchmarks, showing that TG-ODE\ncan achieve state-of-the-art performance in irregular graph stream tasks.",
+        "authors": "Alessio Gravina, Daniele Zambon, Davide Bacciu, Cesare Alippi",
+        "published": "2024-04-30",
+        "updated": "2024-04-30",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2203.07993v2",
+        "title": "RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion",
+        "abstract": "Temporal factors are tied to the growth of facts in realistic applications,\nsuch as the progress of diseases and the development of political situation,\ntherefore, research on Temporal Knowledge Graph (TKG) attracks much attention.\nIn TKG, relation patterns inherent with temporality are required to be studied\nfor representation learning and reasoning across temporal facts. However,\nexisting methods can hardly model temporal relation patterns, nor can capture\nthe intrinsic connections between relations when evolving over time, lacking of\ninterpretability. In this paper, we propose a novel temporal modeling method\nwhich represents temporal entities as Rotations in Quaternion Vector Space\n(RotateQVS) and relations as complex vectors in Hamilton's quaternion space. We\ndemonstrate our method can model key patterns of relations in TKG, such as\nsymmetry, asymmetry, inverse, and can further capture time-evolved relations by\ntheory. Empirically, we show that our method can boost the performance of link\nprediction tasks over four temporal knowledge graph benchmarks.",
+        "authors": "Kai Chen, Ye Wang, Yitong Li, Aiping Li",
+        "published": "2022-03-15",
+        "updated": "2022-03-17",
+        "primary_cat": "cs.AI",
+        "cats": [
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2307.13250v1",
+        "title": "Keyword-Aware Relative Spatio-Temporal Graph Networks for Video Question Answering",
+        "abstract": "The main challenge in video question answering (VideoQA) is to capture and\nunderstand the complex spatial and temporal relations between objects based on\ngiven questions. Existing graph-based methods for VideoQA usually ignore\nkeywords in questions and employ a simple graph to aggregate features without\nconsidering relative relations between objects, which may lead to inferior\nperformance. In this paper, we propose a Keyword-aware Relative Spatio-Temporal\n(KRST) graph network for VideoQA. First, to make question features aware of\nkeywords, we employ an attention mechanism to assign high weights to keywords\nduring question encoding. The keyword-aware question features are then used to\nguide video graph construction. Second, because relations are relative, we\nintegrate the relative relation modeling to better capture the spatio-temporal\ndynamics among object nodes. Moreover, we disentangle the spatio-temporal\nreasoning into an object-level spatial graph and a frame-level temporal graph,\nwhich reduces the impact of spatial and temporal relation reasoning on each\nother. Extensive experiments on the TGIF-QA, MSVD-QA and MSRVTT-QA datasets\ndemonstrate the superiority of our KRST over multiple state-of-the-art methods.",
+        "authors": "Yi Cheng, Hehe Fan, Dongyun Lin, Ying Sun, Mohan Kankanhalli, Joo-Hwee Lim",
+        "published": "2023-07-25",
+        "updated": "2023-07-25",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2108.08719v5",
+        "title": "Temporal Graph Functional Dependencies [Extended Version]",
+        "abstract": "Data dependencies have been extended to graphs to characterize topological\nand value constraints. Existing data dependencies are defined to capture\ninconsistencies in static graphs. Nevertheless, inconsistencies may occur over\nevolving graphs and only for certain time periods. The need for capturing such\ninconsistencies in temporal graphs is evident in anomaly detection and\npredictive dynamic network analysis. This paper introduces a class of data\ndependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs\ngeneralize functional dependencies to temporal graphs as a sequence of graph\nsnapshots that are induced by time intervals, and enforce both topological\nconstraints and attribute value dependencies that must be satisfied by these\nsnapshots. (1) We establish the complexity results for the satisfiability and\nimplication problems of TGFDs. (2) We propose a sound and complete\naxiomatization system for TGFDs. (3) We also present efficient parallel\nalgorithms to detect inconsistencies in temporal graphs as violations of TGFDs.\nThe algorithm exploits data and temporal locality induced by time intervals,\nand uses incremental pattern matching and load balancing strategies to enable\nfeasible error detection in large temporal graphs. Using real datasets, we\nexperimentally verify that our algorithms achieve lower runtimes compared to\nexisting baselines, while improving the accuracy over error detection using\nexisting graph data constraints, e.g., GFDs and GTARs with 55% and 74% gain in\nF1-score, respectively.",
+        "authors": "Morteza Alipourlangouri, Adam Mansfield, Fei Chiang, Yinghui Wu",
+        "published": "2021-08-19",
+        "updated": "2022-07-26",
+        "primary_cat": "cs.DB",
+        "cats": [
+            "cs.DB"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1509.08960v1",
+        "title": "Storing and Analyzing Historical Graph Data at Scale",
+        "abstract": "The work on large-scale graph analytics to date has largely focused on the\nstudy of static properties of graph snapshots. However, a static view of\ninteractions between entities is often an oversimplification of several complex\nphenomena like the spread of epidemics, information diffusion, formation of\nonline communities}, and so on. Being able to find temporal interaction\npatterns, visualize the evolution of graph properties, or even simply compare\nthem across time, adds significant value in reasoning over graphs. However,\nbecause of lack of underlying data management support, an analyst today has to\nmanually navigate the added temporal complexity of dealing with large evolving\ngraphs. In this paper, we present a system, called Historical Graph Store, that\nenables users to store large volumes of historical graph data and to express\nand run complex temporal graph analytical tasks against that data. It consists\nof two key components: a Temporal Graph Index (TGI), that compactly stores\nlarge volumes of historical graph evolution data in a partitioned and\ndistributed fashion; it provides support for retrieving snapshots of the graph\nas of any timepoint in the past or evolution histories of individual nodes or\nneighborhoods; and a Spark-based Temporal Graph Analysis Framework (TAF), for\nexpressing complex temporal analytical tasks and for executing them in an\nefficient and scalable manner. Our experiments demonstrate our system's\nefficient storage, retrieval and analytics across a wide variety of queries on\nlarge volumes of historical graph data.",
+        "authors": "Udayan Khurana, Amol Deshpande",
+        "published": "2015-09-29",
+        "updated": "2015-09-29",
+        "primary_cat": "cs.DB",
+        "cats": [
+            "cs.DB"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1306.0493v1",
+        "title": "Graph Metrics for Temporal Networks",
+        "abstract": "Temporal networks, i.e., networks in which the interactions among a set of\nelementary units change over time, can be modelled in terms of time-varying\ngraphs, which are time-ordered sequences of graphs over a set of nodes. In such\ngraphs, the concepts of node adjacency and reachability crucially depend on the\nexact temporal ordering of the links. Consequently, all the concepts and\nmetrics proposed and used for the characterisation of static complex networks\nhave to be redefined or appropriately extended to time-varying graphs, in order\nto take into account the effects of time ordering on causality. In this chapter\nwe discuss how to represent temporal networks and we review the definitions of\nwalks, paths, connectedness and connected components valid for graphs in which\nthe links fluctuate over time. We then focus on temporal node-node distance,\nand we discuss how to characterise link persistence and the temporal\nsmall-world behaviour in this class of networks. Finally, we discuss the\nextension of classic centrality measures, including closeness, betweenness and\nspectral centrality, to the case of time-varying graphs, and we review the work\non temporal motifs analysis and the definition of modularity for temporal\ngraphs.",
+        "authors": "Vincenzo Nicosia, John Tang, Cecilia Mascolo, Mirco Musolesi, Giovanni Russo, Vito Latora",
+        "published": "2013-06-03",
+        "updated": "2013-06-03",
+        "primary_cat": "physics.soc-ph",
+        "cats": [
+            "physics.soc-ph",
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2002.08312v2",
+        "title": "ITeM: Independent Temporal Motifs to Summarize and Compare Temporal Networks",
+        "abstract": "Networks are a fundamental and flexible way of representing various complex\nsystems. Many domains such as communication, citation, procurement, biology,\nsocial media, and transportation can be modeled as a set of entities and their\nrelationships. Temporal networks are a specialization of general networks where\nthe temporal evolution of the system is as important to understand as the\nstructure of the entities and relationships. We present the Independent\nTemporal Motif (ITeM) to characterize temporal graphs from different domains.\nThe ITeMs are edge-disjoint temporal motifs that can be used to model the\nstructure and the evolution of the graph. For a given temporal graph, we\nproduce a feature vector of ITeM frequencies and apply this distribution to the\ntask of measuring the similarity of temporal graphs. We show that ITeM has\nhigher accuracy than other motif frequency-based approaches. We define various\nmetrics based on ITeM that reveal salient properties of a temporal network. We\nalso present importance sampling as a method for efficiently estimating the\nITeM counts. We evaluate our approach on both synthetic and real temporal\nnetworks.",
+        "authors": "Sumit Purohit, Lawrence B. Holder, George Chin",
+        "published": "2020-02-19",
+        "updated": "2020-08-06",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2212.02875v1",
+        "title": "Multi-Task Edge Prediction in Temporally-Dynamic Video Graphs",
+        "abstract": "Graph neural networks have shown to learn effective node representations,\nenabling node-, link-, and graph-level inference. Conventional graph networks\nassume static relations between nodes, while relations between entities in a\nvideo often evolve over time, with nodes entering and exiting dynamically. In\nsuch temporally-dynamic graphs, a core problem is inferring the future state of\nspatio-temporal edges, which can constitute multiple types of relations. To\naddress this problem, we propose MTD-GNN, a graph network for predicting\ntemporally-dynamic edges for multiple types of relations. We propose a\nfactorized spatio-temporal graph attention layer to learn dynamic node\nrepresentations and present a multi-task edge prediction loss that models\nmultiple relations simultaneously. The proposed architecture operates on top of\nscene graphs that we obtain from videos through object detection and\nspatio-temporal linking. Experimental evaluations on ActionGenome and CLEVRER\nshow that modeling multiple relations in our temporally-dynamic graph network\ncan be mutually beneficial, outperforming existing static and spatio-temporal\ngraph neural networks, as well as state-of-the-art predicate classification\nmethods.",
+        "authors": "Osman \u00dclger, Julian Wiederer, Mohsen Ghafoorian, Vasileios Belagiannis, Pascal Mettes",
+        "published": "2022-12-06",
+        "updated": "2022-12-06",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1601.05909v2",
+        "title": "Efficient Processing of Reachability and Time-Based Path Queries in a Temporal Graph",
+        "abstract": "A temporal graph is a graph in which vertices communicate with each other at\nspecific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is\nmodeled by an edge from $A$ to $B$ with starting time \"11 a.m.\" and duration \"7\nmins\". Temporal graphs can be used to model many networks with time-related\nactivities, but efficient algorithms for analyzing temporal graphs are severely\ninadequate. We study fundamental problems such as answering reachability and\ntime-based path queries in a temporal graph, and propose an efficient indexing\ntechnique specifically designed for processing these queries in a temporal\ngraph. Our results show that our method is efficient and scalable in both index\nconstruction and query processing.",
+        "authors": "Huanhuan Wu, Yuzhen Huang, James Cheng, Jinfeng Li, Yiping Ke",
+        "published": "2016-01-22",
+        "updated": "2016-01-25",
+        "primary_cat": "cs.DB",
+        "cats": [
+            "cs.DB"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1812.11244v1",
+        "title": "Using Compressed Suffix-Arrays for a Compact Representation of Temporal-Graphs",
+        "abstract": "Temporal graphs represent binary relationships that change along time. They\ncan model the dynamism of, for example, social and communication networks.\nTemporal graphs are defined as sets of contacts that are edges tagged with the\ntemporal intervals when they are active. This work explores the use of the\nCompressed Suffix Array (CSA), a well-known compact and self-indexed data\nstructure in the area of text indexing, to represent large temporal graphs. The\nnew structure, called Temporal Graph CSA (TGCSA), is experimentally compared\nwith the most competitive compact data structures in the state-of-the-art,\nnamely, EDGELOG and CET. The experimental results show that TGCSA obtains a\ngood space-time trade-off. It uses a reasonable space and is efficient for\nsolving complex temporal queries. Furthermore, TGCSA has wider expressive\ncapabilities than EDGELOG and CET, because it is able to represent temporal\ngraphs where contacts on an edge can temporally overlap.",
+        "authors": "Nieves R. Brisaboa, Diego Caro, Antonio Fari\u00f1a, M. Andrea Rodriguez",
+        "published": "2018-12-28",
+        "updated": "2018-12-28",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2208.10364v3",
+        "title": "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks",
+        "abstract": "Recent years have seen a surge in research on dynamic graph representation\nlearning, which aims to model temporal graphs that are dynamic and evolving\nconstantly over time. However, current work typically models graph dynamics\nwith recurrent neural networks (RNNs), making them suffer seriously from\ncomputation and memory overheads on large temporal graphs. So far, scalability\nof dynamic graph representation learning on large temporal graphs remains one\nof the major challenges. In this paper, we present a scalable framework, namely\nSpikeNet, to efficiently capture the temporal and structural patterns of\ntemporal graphs. We explore a new direction in that we can capture the evolving\ndynamics of temporal graphs with spiking neural networks (SNNs) instead of\nRNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics\nas spike trains of neuron populations and enable spike-based propagation in an\nefficient way. Experiments on three large real-world temporal graph datasets\ndemonstrate that SpikeNet outperforms strong baselines on the temporal node\nclassification task with lower computational costs. Particularly, SpikeNet\ngeneralizes to a large temporal graph (2.7M nodes and 13.9M edges) with\nsignificantly fewer parameters and computation overheads.Our code is publicly\navailable at \\url{https://github.com/EdisonLeeeee/SpikeNet}.",
+        "authors": "Jintang Li, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, Changhua Meng",
+        "published": "2022-08-15",
+        "updated": "2023-05-18",
+        "primary_cat": "cs.NE",
+        "cats": [
+            "cs.NE",
+            "cs.AI",
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2212.01594v1",
+        "title": "Parameterized temporal exploration problems",
+        "abstract": "In this paper we study the fixed-parameter tractability of the problem of\ndeciding whether a given temporal graph admits a temporal walk that visits all\nvertices (temporal exploration) or, in some problem variants, a certain subset\nof the vertices. Formally, a temporal graph is a sequence <G_1,...,G_L> of\ngraphs with V(G_t) = V(G) and E(G_t) a subset of E(G) for all t in [L] and some\nunderlying graph G, and a temporal walk is a time-respecting sequence of\nedge-traversals. We consider both the strict variant, in which edges must be\ntraversed in strictly increasing timesteps, and the non-strict variant, in\nwhich an arbitrary number of edges can be traversed in each timestep. For both\nvariants, we give FPT algorithms for the problem of finding a temporal walk\nthat visits a given set X of vertices, parameterized by |X|, and for the\nproblem of finding a temporal walk that visits at least k distinct vertices in\nV(G), parameterized by k. We also show W[2]-hardness for a set version of the\ntemporal exploration problem for both variants. For the non-strict variant, we\ngive an FPT algorithm for the temporal exploration problem parameterized by the\nlifetime of the input graph, and we show that the temporal exploration problem\ncan be solved in polynomial time if the graph in each timestep has at most two\nconnected components.",
+        "authors": "Thomas Erlebach, Jakob T. Spooner",
+        "published": "2022-12-03",
+        "updated": "2022-12-03",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS",
+            "05C85",
+            "F.2.2; G.2.2"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2106.13517v1",
+        "title": "Temporal Graph Signal Decomposition",
+        "abstract": "Temporal graph signals are multivariate time series with individual\ncomponents associated with nodes of a fixed graph structure. Data of this kind\narises in many domains including activity of social network users, sensor\nnetwork readings over time, and time course gene expression within the\ninteraction network of a model organism. Traditional matrix decomposition\nmethods applied to such data fall short of exploiting structural regularities\nencoded in the underlying graph and also in the temporal patterns of the\nsignal. How can we take into account such structure to obtain a succinct and\ninterpretable representation of temporal graph signals?\n  We propose a general, dictionary-based framework for temporal graph signal\ndecomposition (TGSD). The key idea is to learn a low-rank, joint encoding of\nthe data via a combination of graph and time dictionaries. We propose a highly\nscalable decomposition algorithm for both complete and incomplete data, and\ndemonstrate its advantage for matrix decomposition, imputation of missing\nvalues, temporal interpolation, clustering, period estimation, and rank\nestimation in synthetic and real-world data ranging from traffic patterns to\nsocial media activity. Our framework achieves 28% reduction in RMSE compared to\nbaselines for temporal interpolation when as many as 75% of the observations\nare missing. It scales best among baselines taking under 20 seconds on 3.5\nmillion data points and produces the most parsimonious models. To the best of\nour knowledge, TGSD is the first framework to jointly model graph signals by\ntemporal and graph dictionaries.",
+        "authors": "Maxwell McNeil, Lin Zhang, Petko Bogdanov",
+        "published": "2021-06-25",
+        "updated": "2021-06-25",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2012.03363v3",
+        "title": "Spatio-Temporal Graph Scattering Transform",
+        "abstract": "Although spatio-temporal graph neural networks have achieved great empirical\nsuccess in handling multiple correlated time series, they may be impractical in\nsome real-world scenarios due to a lack of sufficient high-quality training\ndata. Furthermore, spatio-temporal graph neural networks lack theoretical\ninterpretation. To address these issues, we put forth a novel mathematically\ndesigned framework to analyze spatio-temporal data. Our proposed\nspatio-temporal graph scattering transform (ST-GST) extends traditional\nscattering transforms to the spatio-temporal domain. It performs iterative\napplications of spatio-temporal graph wavelets and nonlinear activation\nfunctions, which can be viewed as a forward pass of spatio-temporal graph\nconvolutional networks without training. Since all the filter coefficients in\nST-GST are mathematically designed, it is promising for the real-world\nscenarios with limited training data, and also allows for a theoretical\nanalysis, which shows that the proposed ST-GST is stable to small perturbations\nof input signals and structures. Finally, our experiments show that i) ST-GST\noutperforms spatio-temporal graph convolutional networks by an increase of 35%\nin accuracy for MSR Action3D dataset; ii) it is better and computationally more\nefficient to design the transform based on separable spatio-temporal graphs\nthan the joint ones; and iii) the nonlinearity in ST-GST is critical to\nempirical performance.",
+        "authors": "Chao Pan, Siheng Chen, Antonio Ortega",
+        "published": "2020-12-06",
+        "updated": "2021-02-09",
+        "primary_cat": "eess.SP",
+        "cats": [
+            "eess.SP",
+            "cs.AI",
+            "cs.CV",
+            "cs.LG",
+            "eess.IV"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2310.17110v2",
+        "title": "LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?",
+        "abstract": "In an era marked by the increasing adoption of Large Language Models (LLMs)\nfor various tasks, there is a growing focus on exploring LLMs' capabilities in\nhandling web data, particularly graph data. Dynamic graphs, which capture\ntemporal network evolution patterns, are ubiquitous in real-world web data.\nEvaluating LLMs' competence in understanding spatial-temporal information on\ndynamic graphs is essential for their adoption in web applications, which\nremains unexplored in the literature. In this paper, we bridge the gap via\nproposing to evaluate LLMs' spatial-temporal understanding abilities on dynamic\ngraphs, to the best of our knowledge, for the first time. Specifically, we\npropose the LLM4DyG benchmark, which includes nine specially designed tasks\nconsidering the capability evaluation of LLMs from both temporal and spatial\ndimensions. Then, we conduct extensive experiments to analyze the impacts of\ndifferent data generators, data statistics, prompting techniques, and LLMs on\nthe model performance. Finally, we propose Disentangled Spatial-Temporal\nThoughts (DST2) for LLMs on dynamic graphs to enhance LLMs' spatial-temporal\nunderstanding abilities. Our main observations are: 1) LLMs have preliminary\nspatial-temporal understanding abilities on dynamic graphs, 2) Dynamic graph\ntasks show increasing difficulties for LLMs as the graph size and density\nincrease, while not sensitive to the time span and data generation mechanism,\n3) the proposed DST2 prompting method can help to improve LLMs'\nspatial-temporal understanding abilities on dynamic graphs for most tasks. The\ndata and codes will be open-sourced at publication time.",
+        "authors": "Zeyang Zhang, Xin Wang, Ziwei Zhang, Haoyang Li, Yijian Qin, Wenwu Zhu",
+        "published": "2023-10-26",
+        "updated": "2024-03-08",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.04962v1",
+        "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering",
+        "abstract": "Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.",
+        "authors": "Meng Liu, Ke Liang, Yue Liu, Siwei Wang, Sihang Zhou, Xinwang Liu",
+        "published": "2023-06-08",
+        "updated": "2023-06-08",
+        "primary_cat": "cs.AI",
+        "cats": [
+            "cs.AI",
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2005.08323v2",
+        "title": "TG-GAN: Continuous-time Temporal Graph Generation with Deep Generative Models",
+        "abstract": "The recent deep generative models for static graphs that are now being\nactively developed have achieved significant success in areas such as molecule\ndesign. However, many real-world problems involve temporal graphs whose\ntopology and attribute values evolve dynamically over time, including important\napplications such as protein folding, human mobility networks, and social\nnetwork growth. As yet, deep generative models for temporal graphs are not yet\nwell understood and existing techniques for static graphs are not adequate for\ntemporal graphs since they cannot 1) encode and decode continuously-varying\ngraph topology chronologically, 2) enforce validity via temporal constraints,\nor 3) ensure efficiency for information-lossless temporal resolution. To\naddress these challenges, we propose a new model, called ``Temporal Graph\nGenerative Adversarial Network'' (TG-GAN) for continuous-time temporal graph\ngeneration, by modeling the deep generative process for truncated temporal\nrandom walks and their compositions. Specifically, we first propose a novel\ntemporal graph generator that jointly model truncated edge sequences, time\nbudgets, and node attributes, with novel activation functions that enforce\ntemporal validity constraints under recurrent architecture. In addition, a new\ntemporal graph discriminator is proposed, which combines time and node encoding\noperations over a recurrent architecture to distinguish the generated sequences\nfrom the real ones sampled by a newly-developed truncated temporal random walk\nsampler. Extensive experiments on both synthetic and real-world datasets\ndemonstrate TG-GAN significantly outperforms the comparison methods in\nefficiency and effectiveness.",
+        "authors": "Liming Zhang, Liang Zhao, Shan Qin, Dieter Pfoser",
+        "published": "2020-05-17",
+        "updated": "2020-06-09",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2402.03651v1",
+        "title": "Temporal Graph Analysis with TGX",
+        "abstract": "Real-world networks, with their evolving relations, are best captured as\ntemporal graphs. However, existing software libraries are largely designed for\nstatic graphs where the dynamic nature of temporal graphs is ignored. Bridging\nthis gap, we introduce TGX, a Python package specially designed for analysis of\ntemporal networks that encompasses an automated pipeline for data loading, data\nprocessing, and analysis of evolving graphs. TGX provides access to eleven\nbuilt-in datasets and eight external Temporal Graph Benchmark (TGB) datasets as\nwell as any novel datasets in the .csv format. Beyond data loading, TGX\nfacilitates data processing functionalities such as discretization of temporal\ngraphs and node subsampling to accelerate working with larger datasets. For\ncomprehensive investigation, TGX offers network analysis by providing a diverse\nset of measures, including average node degree and the evolving number of nodes\nand edges per timestamp. Additionally, the package consolidates meaningful\nvisualization plots indicating the evolution of temporal patterns, such as\nTemporal Edge Appearance (TEA) and Temporal Edge Trafficc (TET) plots. The TGX\npackage is a robust tool for examining the features of temporal graphs and can\nbe used in various areas like studying social networks, citation networks, and\ntracking user interactions. We plan to continuously support and update TGX\nbased on community feedback. TGX is publicly available on:\nhttps://github.com/ComplexData-MILA/TGX.",
+        "authors": "Razieh Shirzadkhani, Shenyang Huang, Elahe Kooshafar, Reihaneh Rabbany, Farimah Poursafaei",
+        "published": "2024-02-06",
+        "updated": "2024-02-06",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2209.08311v1",
+        "title": "De Bruijn goes Neural: Causality-Aware Graph Neural Networks for Time Series Data on Dynamic Graphs",
+        "abstract": "We introduce De Bruijn Graph Neural Networks (DBGNNs), a novel time-aware\ngraph neural network architecture for time-resolved data on dynamic graphs. Our\napproach accounts for temporal-topological patterns that unfold in the causal\ntopology of dynamic graphs, which is determined by causal walks, i.e.\ntemporally ordered sequences of links by which nodes can influence each other\nover time. Our architecture builds on multiple layers of higher-order De Bruijn\ngraphs, an iterative line graph construction where nodes in a De Bruijn graph\nof order k represent walks of length k-1, while edges represent walks of length\nk. We develop a graph neural network architecture that utilizes De Bruijn\ngraphs to implement a message passing scheme that follows a non-Markovian\ndynamics, which enables us to learn patterns in the causal topology of a\ndynamic graph. Addressing the issue that De Bruijn graphs with different orders\nk can be used to model the same data set, we further apply statistical model\nselection to determine the optimal graph topology to be used for message\npassing. An evaluation in synthetic and empirical data sets suggests that\nDBGNNs can leverage temporal patterns in dynamic graphs, which substantially\nimproves the performance in a supervised node classification task.",
+        "authors": "Lisi Qarkaxhija, Vincenzo Perri, Ingo Scholtes",
+        "published": "2022-09-17",
+        "updated": "2022-09-17",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2012.08909v2",
+        "title": "Maximum 0-1 Timed Matching on Temporal Graphs",
+        "abstract": "Temporal graphs are graphs where the topology and/or other properties of the\ngraph change with time. They have been used to model applications with temporal\ninformation in various domains. Problems on static graphs become more\nchallenging to solve in temporal graphs because of dynamically changing\ntopology, and many recent works have explored graph problems on temporal\ngraphs. In this paper, we define a type of matching called {\\em 0-1 timed\nmatching} for temporal graphs, and investigate the problem of finding a {\\em\nmaximum 0-1 timed matching} for different classes of temporal graphs. We first\nprove that the problem is NP-Complete for rooted temporal trees when each edge\nis associated with two or more time intervals. We then propose an $O(n \\log n)$\ntime algorithm for the problem on a rooted temporal tree with $n$ nodes when\neach edge is associated with exactly one time interval. The problem is then\nshown to be NP-Complete also for bipartite temporal graphs even when each edge\nis associated with a single time interval and degree of each node is bounded by\na constant $k \\geq 3$. We next investigate approximation algorithms for the\nproblem for temporal graphs where each edge is associated with more than one\ntime intervals. It is first shown that there is no\n$\\frac{1}{n^{1-\\epsilon}}$-factor approximation algorithm for the problem for\nany $\\epsilon > 0$ even on a rooted temporal tree with $n$ nodes unless NP =\nZPP. We then present a $\\frac{5}{2\\mathcal{N}^* + 3}$-factor approximation\nalgorithm for the problem for general temporal graphs where $\\mathcal{N^*}$ is\nthe average number of edges overlapping in time with each edge in the temporal\ngraph. The same algorithm is also a constant-factor approximation algorithm for\ndegree bounded temporal graphs.",
+        "authors": "Subhrangsu Mandal, Arobinda Gupta",
+        "published": "2020-12-16",
+        "updated": "2022-02-01",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2110.05018v2",
+        "title": "Time-varying Graph Learning Under Structured Temporal Priors",
+        "abstract": "This paper endeavors to learn time-varying graphs by using structured\ntemporal priors that assume underlying relations between arbitrary two graphs\nin the graph sequence. Different from many existing chain structure based\nmethods in which the priors like temporal homogeneity can only describe the\nvariations of two consecutive graphs, we propose a structure named\n\\emph{temporal graph} to characterize the underlying real temporal relations.\nUnder this framework, the chain structure is actually a special case of our\ntemporal graph. We further proposed Alternating Direction Method of Multipliers\n(ADMM), a distributed algorithm, to solve the induced optimization problem.\nNumerical experiments demonstrate the superiorities of our method.",
+        "authors": "Xiang Zhang, Qiao Wang",
+        "published": "2021-10-11",
+        "updated": "2022-02-23",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "eess.SP"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1602.06411v1",
+        "title": "On the Size and the Approximability of Minimum Temporally Connected Subgraphs",
+        "abstract": "We consider temporal graphs with discrete time labels and investigate the\nsize and the approximability of minimum temporally connected spanning\nsubgraphs. We present a family of minimally connected temporal graphs with $n$\nvertices and $\\Omega(n^2)$ edges, thus resolving an open question of (Kempe,\nKleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal\nconnectivity certificates. Next, we consider the problem of computing a minimum\nweight subset of temporal edges that preserve connectivity of a given temporal\ngraph either from a given vertex r (r-MTC problem) or among all vertex pairs\n(MTC problem). We show that the approximability of r-MTC is closely related to\nthe approximability of Directed Steiner Tree and that r-MTC can be solved in\npolynomial time if the underlying graph has bounded treewidth. We also show\nthat the best approximation ratio for MTC is at least $O(2^{\\log^{1-\\epsilon}\nn})$ and at most $O(\\min\\{n^{1+\\epsilon}, (\\Delta M)^{2/3+\\epsilon}\\})$, for\nany constant $\\epsilon > 0$, where $M$ is the number of temporal edges and\n$\\Delta$ is the maximum degree of the underlying graph. Furthermore, we prove\nthat the unweighted version of MTC is APX-hard and that MTC is efficiently\nsolvable in trees and $2$-approximable in cycles.",
+        "authors": "Kyriakos Axiotis, Dimitris Fotakis",
+        "published": "2016-02-20",
+        "updated": "2016-02-20",
+        "primary_cat": "cs.DS",
+        "cats": [
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2401.02212v1",
+        "title": "Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph",
+        "abstract": "Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by\nattaching the time scope. Existing temporal knowledge graph question answering\n(TKGQA) models solely approach simple questions, owing to the prior assumption\nthat each question only contains a single temporal fact with explicit/implicit\ntemporal constraints. Hence, they perform poorly on questions which own\nmultiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint\n\\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts\n\\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly\nreasoning multiple temporal facts for accurately answering \\emph{complex}\ntemporal questions. Specifically, JMFRN first retrieves question-related\ntemporal facts from TKG for each entity of the given complex question. For\njoint reasoning, we design two different attention (\\ie entity-aware and\ntime-aware) modules, which are suitable for universal settings, to aggregate\nentities and timestamps information of retrieved facts. Moreover, to filter\nincorrect type answers, we introduce an additional answer type discrimination\ntask. Extensive experiments demonstrate our proposed method significantly\noutperforms the state-of-art on the well-known complex temporal question\nbenchmark TimeQuestions.",
+        "authors": "Rikui Huang, Wei Wei, Xiaoye Qu, Wenfeng Xie, Xianling Mao, Dangyang Chen",
+        "published": "2024-01-04",
+        "updated": "2024-01-04",
+        "primary_cat": "cs.CL",
+        "cats": [
+            "cs.CL",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/1903.05631v2",
+        "title": "ST-UNet: A Spatio-Temporal U-Network for Graph-structured Time Series Modeling",
+        "abstract": "The spatio-temporal graph learning is becoming an increasingly important\nobject of graph study. Many application domains involve highly dynamic graphs\nwhere temporal information is crucial, e.g. traffic networks and financial\ntransaction graphs. Despite the constant progress made on learning structured\ndata, there is still a lack of effective means to extract dynamic complex\nfeatures from spatio-temporal structures. Particularly, conventional models\nsuch as convolutional networks or recurrent neural networks are incapable of\nrevealing the temporal patterns in short or long terms and exploring the\nspatial properties in local or global scope from spatio-temporal graphs\nsimultaneously. To tackle this problem, we design a novel multi-scale\narchitecture, Spatio-Temporal U-Net (ST-UNet), for graph-structured time series\nmodeling. In this U-shaped network, a paired sampling operation is proposed in\nspacetime domain accordingly: the pooling (ST-Pool) coarsens the input graph in\nspatial from its deterministic partition while abstracts multi-resolution\ntemporal dependencies through dilated recurrent skip connections; based on\nprevious settings in the downsampling, the unpooling (ST-Unpool) restores the\noriginal structure of spatio-temporal graphs and resumes regular intervals\nwithin graph sequences. Experiments on spatio-temporal prediction tasks\ndemonstrate that our model effectively captures comprehensive features in\nmultiple scales and achieves substantial improvements over mainstream methods\non several real-world datasets.",
+        "authors": "Bing Yu, Haoteng Yin, Zhanxing Zhu",
+        "published": "2019-03-13",
+        "updated": "2021-06-15",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "stat.ML"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2307.00518v1",
+        "title": "DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting",
+        "abstract": "Traffic forecasting is essential to intelligent transportation systems, which\nis challenging due to the complicated spatial and temporal dependencies within\na road network. Existing works usually learn spatial and temporal dependencies\nseparately, ignoring the dependencies crossing spatial and temporal dimensions.\nIn this paper, we propose DSTCGCN, a dynamic spatial-temporal cross graph\nconvolution network to learn dynamic spatial and temporal dependencies jointly\nvia graphs for traffic forecasting. Specifically, we introduce a fast Fourier\ntransform (FFT) based attentive selector to choose relevant time steps for each\ntime step based on time-varying traffic data. Given the selected time steps, we\nintroduce a dynamic cross graph construction module, consisting of the spatial\ngraph construction, temporal connection graph construction, and fusion modules,\nto learn dynamic spatial-temporal cross dependencies without pre-defined\npriors. Extensive experiments on six real-world datasets demonstrate that\nDSTCGCN achieves the state-of-the-art performance.",
+        "authors": "Binqing Wu, Ling Chen",
+        "published": "2023-07-02",
+        "updated": "2023-07-02",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2310.11886v1",
+        "title": "Sampling Algorithms for Butterfly Counting on Temporal Bipartite Graphs",
+        "abstract": "Temporal bipartite graphs are widely used to denote time-evolving\nrelationships between two disjoint sets of nodes, such as customer-product\ninteractions in E-commerce and user-group memberships in social networks.\nTemporal butterflies, $(2,2)$-bicliques that occur within a short period and in\na prescribed order, are essential in modeling the structural and sequential\npatterns of such graphs. Counting the number of temporal butterflies is thus a\nfundamental task in analyzing temporal bipartite graphs. However, existing\nalgorithms for butterfly counting on static bipartite graphs and motif counting\non temporal unipartite graphs are inefficient for this purpose. In this paper,\nwe present a general framework with three sampling strategies for temporal\nbutterfly counting. Since exact counting can be time-consuming on large graphs,\nour approach alternatively computes approximate estimates accurately and\nefficiently. We also provide analytical bounds on the number of samples each\nstrategy requires to obtain estimates with small relative errors and high\nprobability. We finally evaluate our framework on six real-world datasets and\ndemonstrate its superior accuracy and efficiency compared to several baselines.\nOverall, our proposed framework and sampling strategies provide efficient and\naccurate approaches to approximating temporal butterfly counts on large-scale\ntemporal bipartite graphs.",
+        "authors": "Jiaxi Pu, Yanhao Wang, Yuchen Li, Xuan Zhou",
+        "published": "2023-10-18",
+        "updated": "2023-10-18",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.DB",
+            "cs.DS"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2310.02606v1",
+        "title": "Learning adjacency matrix for dynamic graph neural network",
+        "abstract": "In recent work, [1] introduced the concept of using a Block Adjacency Matrix\n(BA) for the representation of spatio-temporal data. While their method\nsuccessfully concatenated adjacency matrices to encapsulate spatio-temporal\nrelationships in a single graph, it formed a disconnected graph. This\nlimitation hampered the ability of Graph Convolutional Networks (GCNs) to\nperform message passing across nodes belonging to different time steps, as no\ntemporal links were present. To overcome this challenge, we introduce an\nencoder block specifically designed to learn these missing temporal links. The\nencoder block processes the BA and predicts connections between previously\nunconnected subgraphs, resulting in a Spatio-Temporal Block Adjacency Matrix\n(STBAM). This enriched matrix is then fed into a Graph Neural Network (GNN) to\ncapture the complex spatio-temporal topology of the network. Our evaluations on\nbenchmark datasets, surgVisDom and C2D2, demonstrate that our method, with\nslightly higher complexity, achieves superior results compared to\nstate-of-the-art results. Our approach's computational overhead remains\nsignificantly lower than conventional non-graph-based methodologies for\nspatio-temporal data.",
+        "authors": "Osama Ahmad, Omer Abdul Jalil, Usman Nazir, Murtaza Taj",
+        "published": "2023-10-04",
+        "updated": "2023-10-04",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "eess.IV"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.01012v1",
+        "title": "Graph-Level Embedding for Time-Evolving Graphs",
+        "abstract": "Graph representation learning (also known as network embedding) has been\nextensively researched with varying levels of granularity, ranging from nodes\nto graphs. While most prior work in this area focuses on node-level\nrepresentation, limited research has been conducted on graph-level embedding,\nparticularly for dynamic or temporal networks. However, learning\nlow-dimensional graph-level representations for dynamic networks is critical\nfor various downstream graph retrieval tasks such as temporal graph similarity\nranking, temporal graph isomorphism, and anomaly detection. In this paper, we\npresent a novel method for temporal graph-level embedding that addresses this\ngap. Our approach involves constructing a multilayer graph and using a modified\nrandom walk with temporal backtracking to generate temporal contexts for the\ngraph's nodes. We then train a \"document-level\" language model on these\ncontexts to generate graph-level embeddings. We evaluate our proposed model on\nfive publicly available datasets for the task of temporal graph similarity\nranking, and our model outperforms baseline methods. Our experimental results\ndemonstrate the effectiveness of our method in generating graph-level\nembeddings for dynamic networks.",
+        "authors": "Lili Wang, Chenghan Huang, Weicheng Ma, Xinyuan Cao, Soroush Vosoughi",
+        "published": "2023-06-01",
+        "updated": "2023-06-01",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI",
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2404.11979v1",
+        "title": "MTGA: Multi-view Temporal Granularity aligned Aggregation for Event-based Lip-reading",
+        "abstract": "Lip-reading is to utilize the visual information of the speaker's lip\nmovements to recognize words and sentences. Existing event-based lip-reading\nsolutions integrate different frame rate branches to learn spatio-temporal\nfeatures of varying granularities. However, aggregating events into event\nframes inevitably leads to the loss of fine-grained temporal information within\nframes. To remedy this drawback, we propose a novel framework termed Multi-view\nTemporal Granularity aligned Aggregation (MTGA). Specifically, we first present\na novel event representation method, namely time-segmented voxel graph list,\nwhere the most significant local voxels are temporally connected into a graph\nlist. Then we design a spatio-temporal fusion module based on temporal\ngranularity alignment, where the global spatial features extracted from event\nframes, together with the local relative spatial and temporal features\ncontained in voxel graph list are effectively aligned and integrated. Finally,\nwe design a temporal aggregation module that incorporates positional encoding,\nwhich enables the capture of local absolute spatial and global temporal\ninformation. Experiments demonstrate that our method outperforms both the\nevent-based and video-based lip-reading counterparts. Our code will be publicly\navailable.",
+        "authors": "Wenhao Zhang, Jun Wang, Yong Luo, Lei Yu, Wei Yu, Zheng He",
+        "published": "2024-04-18",
+        "updated": "2024-04-18",
+        "primary_cat": "cs.CV",
+        "cats": [
+            "cs.CV"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2302.02128v1",
+        "title": "Interaction Order Prediction for Temporal Graphs",
+        "abstract": "Link prediction in graphs is a task that has been widely investigated. It has\nbeen applied in various domains such as knowledge graph completion,\ncontent/item recommendation, social network recommendations and so on. The\ninitial focus of most research was on link prediction in static graphs.\nHowever, there has recently been abundant work on modeling temporal graphs, and\nconsequently one of the tasks that has been researched is link prediction in\ntemporal graphs. However, most of the existing work does not focus on the order\nof link formation, and only predicts the existence of links. In this study, we\naim to predict the order of node interactions.",
+        "authors": "Nayana Bannur, Mashrin Srivastava, Harsha Vardhan",
+        "published": "2023-02-04",
+        "updated": "2023-02-04",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.CL",
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2302.07491v3",
+        "title": "Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment",
+        "abstract": "Temporal graph learning aims to generate high-quality representations for\ngraph-based tasks with dynamic information, which has recently garnered\nincreasing attention. In contrast to static graphs, temporal graphs are\ntypically organized as node interaction sequences over continuous time rather\nthan an adjacency matrix. Most temporal graph learning methods model current\ninteractions by incorporating historical neighborhood. However, such methods\nonly consider first-order temporal information while disregarding crucial\nhigh-order structural information, resulting in suboptimal performance. To\naddress this issue, we propose a self-supervised method called S2T for temporal\ngraph learning, which extracts both temporal and structural information to\nlearn more informative node representations. Notably, the initial node\nrepresentations combine first-order temporal and high-order structural\ninformation differently to calculate two conditional intensities. An alignment\nloss is then introduced to optimize the node representations, narrowing the gap\nbetween the two intensities and making them more informative. Concretely, in\naddition to modeling temporal information using historical neighbor sequences,\nwe further consider structural knowledge at both local and global levels. At\nthe local level, we generate structural intensity by aggregating features from\nhigh-order neighbor sequences. At the global level, a global representation is\ngenerated based on all nodes to adjust the structural intensity according to\nthe active statuses on different nodes. Extensive experiments demonstrate that\nthe proposed model S2T achieves at most 10.13% performance improvement compared\nwith the state-of-the-art competitors on several datasets.",
+        "authors": "Meng Liu, Ke Liang, Yawei Zhao, Wenxuan Tu, Sihang Zhou, Xinbiao Gan, Xinwang Liu, Kunlun He",
+        "published": "2023-02-15",
+        "updated": "2024-04-28",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG",
+            "cs.AI",
+            "cs.SI"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2402.16078v2",
+        "title": "Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs",
+        "abstract": "We present the Evolving Graph Fourier Transform (EFT), the first invertible\nspectral transform that captures evolving representations on temporal graphs.\nWe motivate our work by the inadequacy of existing methods for capturing the\nevolving graph spectra, which are also computationally expensive due to the\ntemporal aspect along with the graph vertex domain. We view the problem as an\noptimization over the Laplacian of the continuous time dynamic graph.\nAdditionally, we propose pseudo-spectrum relaxations that decompose the\ntransformation process, making it highly computationally efficient. The EFT\nmethod adeptly captures the evolving graph's structural and positional\nproperties, making it effective for downstream tasks on evolving graphs. Hence,\nas a reference implementation, we develop a simple neural model induced with\nEFT for capturing evolving graph spectra. We empirically validate our\ntheoretical findings on a number of large-scale and standard temporal graph\nbenchmarks and demonstrate that our model achieves state-of-the-art\nperformance.",
+        "authors": "Anson Bastos, Kuldeep Singh, Abhishek Nadgeri, Manish Singh, Toyotaro Suzumura",
+        "published": "2024-02-25",
+        "updated": "2024-04-18",
+        "primary_cat": "cs.LG",
+        "cats": [
+            "cs.LG"
+        ],
+        "category": "Temporal AND Graph"
+    },
+    {
+        "url": "http://arxiv.org/abs/2306.11190v1",
+        "title": "Using Motif Transitions for Temporal Graph Generation",
+        "abstract": "Graph generative models are highly important for sharing surrogate data and\nbenchmarking purposes. Real-world complex systems often exhibit dynamic nature,\nwhere the interactions among nodes change over time in the form of a temporal\nnetwork. Most temporal network generation models extend the static graph\ngeneration models by incorporating temporality in the generation process. More\nrecently, temporal motifs are used to generate temporal networks with better\nsuccess. However, existing models are often restricted to a small set of\npredefined motif patterns due to the high computational cost of counting\ntemporal motifs. In this work, we develop a practical temporal graph generator,\nMotif Transition Model (MTM), to generate synthetic temporal networks with\nrealistic global and local features. Our key idea is modeling the arrival of\nnew events as temporal motif transition processes. We first calculate the\ntransition properties from the input graph and then simulate the motif\ntransition processes based on the transition probabilities and transition\nrates. We demonstrate that our model consistently outperforms the baselines\nwith respect to preserving various global and local temporal graph statistics\nand runtime performance.",
+        "authors": "Penghang Liu, A. Erdem Sar\u0131y\u00fcce",
+        "published": "2023-06-19",
+        "updated": "2023-06-19",
+        "primary_cat": "cs.SI",
+        "cats": [
+            "cs.SI",
+            "cs.AI"
+        ],
+        "category": "Temporal AND Graph"
+    }
+]
\ No newline at end of file