diff --git "a/related_34K/test_related_short_2405.00352v1.json" "b/related_34K/test_related_short_2405.00352v1.json" new file mode 100644--- /dev/null +++ "b/related_34K/test_related_short_2405.00352v1.json" @@ -0,0 +1,1411 @@ +[ + { + "url": "http://arxiv.org/abs/2405.00352v1", + "title": "Transformer-based Reasoning for Learning Evolutionary Chain of Events on Temporal Knowledge Graph", + "abstract": "Temporal Knowledge Graph (TKG) reasoning often involves completing missing\nfactual elements along the timeline. Although existing methods can learn good\nembeddings for each factual element in quadruples by integrating temporal\ninformation, they often fail to infer the evolution of temporal facts. This is\nmainly because of (1) insufficiently exploring the internal structure and\nsemantic relationships within individual quadruples and (2) inadequately\nlearning a unified representation of the contextual and temporal correlations\namong different quadruples. To overcome these limitations, we propose a novel\nTransformer-based reasoning model (dubbed ECEformer) for TKG to learn the\nEvolutionary Chain of Events (ECE). Specifically, we unfold the neighborhood\nsubgraph of an entity node in chronological order, forming an evolutionary\nchain of events as the input for our model. Subsequently, we utilize a\nTransformer encoder to learn the embeddings of intra-quadruples for ECE. We\nthen craft a mixed-context reasoning module based on the multi-layer perceptron\n(MLP) to learn the unified representations of inter-quadruples for ECE while\naccomplishing temporal knowledge reasoning. In addition, to enhance the\ntimeliness of the events, we devise an additional time prediction task to\ncomplete effective temporal information within the learned unified\nrepresentation. Extensive experiments on six benchmark datasets verify the\nstate-of-the-art performance and the effectiveness of our method.", + "authors": "Zhiyu Fang, Shuai-Long Lei, Xiaobin Zhu, Chun Yang, Shi-Xue Zhang, Xu-Cheng Yin, Jingyan Qin", + "published": "2024-05-01", + "updated": "2024-05-01", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI" + ], + "label": "Original Paper", + "paper_cat": "Temporal AND Graph", + "gt": "2.1 Interpolation-based TKGR Interpolation-based TKGR methods estimate missing facts or events by identifying consistent trends within a TKG. Based on the process strategy for temporal information, we categorize them into two types: timestamp-independent and timestamp-specific methods. Timestamp-independent methods treat timestamps as independent units, equivalent to entities or relations, and do not apply additional operations on the timestamps. Generally, these methods [19, 20, 27, 29] directly associate timestamps to the corresponding entities and relations based on the foundation of static KG models. For example, Leblay et al. [20] extended the classic TransE [4] model to TKGR by concatenating timestamp embeddings with relation embeddings. Inspired by BoxE [1], Messner et al. [27] directly introduced timestamp embeddings on its basis. However, timestampindependent methods are usually limited in capturing the temporal information of evolutionary events. Timestamp-specific methods embed the temporal information and learn the evolution of entities and relations via timestamp-specific functions. To effectively utilize the structural and semantic information of the time, they ingeniously designed various time-specific functions, such as diachronic embedding functions [11], time-rotating functions [5, 40], time-hyperplane functions [8, 38, 41, 47], and non-linear embedding functions [12, 17, 22, 35, 39]. Specifically, Goel et al. [11] proposed a diachronic entity embedding function to characterize entities at any timestamp. Chen et al. [5] defined the spatial rotation operation of entities around the time axis. Zhang et al. [47] learned spatial structures interactively between the Euclidean, hyperbolic and hyper-spherical spaces. Han et al. [12] explored evolving entity representations on a mixed curvature manifold using a velocity vector defined in the tangent space at each timestamp. Despite the great efforts made by these studies, they are limited in predicting future events [49]. 2.2 Extrapolation-based TKGR Extrapolation-based TKGR methods predict future facts or events by learning effective embeddings from historical snapshots. As knowledge subgraphs at specific timestamps, historical snapshots inherently contain rich structural and semantic information. Extrapolation methods typically employ deep learning techniques such as Graph Neural Networks (GNNs) [24, 45, 46], Recurrent Neural Networks (RNNs) [16, 21], and Reinforcement Learning (RL) [33, 49] to extract features from historical snapshots. To elaborate further, GNN-based methods are naturally applied to TKGR due to the inherent topological structure of historical snapshots. Schlichtkrull et al. [30] early utilized Graph Convolutional Networks (GCN) to model the multi-relational features of traditional KG. To incorporate the temporal characteristics in TKGs, Jin et al. [16] additionally introduced an RNN-based sub-network specifically for recursively encoding past facts. Li et al. [24] presented the recurrent evolution network based on GCN, which learns the evolutionary representations of entities and relations at each timestamp by modeling the KG sequence recurrently. To handle the large-scale inputs and non-independent and identically distributed data, Deng et al. [9] combined GCN and GRU for simultaneously predicting concurrent events of multiple types and inferring multiple candidate participants. RL-based methods are becoming popular to improve the interpretability of reasoning methods, especially in question-answering tasks. By mimicking the human mechanism of searching for historical information and meticulous reasoning, CluSTeR [23] implements an interpretable prediction for TKGR using a two-stage approach of clue searching and temporal reasoning. DREAM [49] introduces an adaptive reinforcement learning model based on attention mechanism, addressing the challenges in traditional RL-based TKG reasoning, specifically the lack of capturing temporal evolution and semantic dependence jointly and the over-reliance on manually designed rewards. Furthermore, some other types of methods also achieve good performance in TKGR. For example, TLogic [26] introduces an explainable framework based on temporal logical rules, leveraging temporal random walks to provide explanations while maintaining time consistency. Faced with the challenge of predicting future facts for newly emerging entities based on extremely limited observational data, MetaTKGR [37] dynamically adjusts its strategies for sampling and aggregating neighbors from recent facts and introduces a temporal adaptation regularizer to stabilize the meta-temporal reasoning process over time. In summary, extrapolation methods generally process structural and temporal characteristics independently. This approach ignores the intrinsic correlation between structural and temporal information, limiting the capability to extract a unified representation of both features. 2.3 Transformer in Knowledge Graph With the Transformer achieving excellent performance in numerous tasks in natural language processing and computer vision, it has been introduced into knowledge graph tasks. Leveraging the powerful learning capability of Transformers for sequential data structures and contexts, numerous Transformer-based methods [6, 7, 14, 43] have emerged for traditional KGs. For example, Chen et al. [6] proposed two different Transformer blocks for hierarchically learning representations of entities and relations. In addition, some methods also achieve remarkable results in downstream tasks of KGs. Specifically, Hu et al. [13] utilized a Transformer-based framework for encoding the content of neighbors of an entity for entity typing task. Meanwhile, Xu et al. [42] applied it for contextaware rule mining over KG. To serve diverse KG-related tasks, Zhang et al. [48] proposed a uniform knowledge representation and fusion module via structure pretraining and prompt tuning. SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA Fang et al. Transformer enables the exploration of structural associations within each historical snapshot and captures the temporal relationships among different historical snapshots to accomplish link prediction tasks [36]. GHT [32] involves two variants of Transformer and a relational continuous-time encoding function, aiming to mitigate the interference of facts irrelevant to the query and enhancing the capability of the model to learn long-term evolution. To effectively embed the rich information in the query-specific subgraph, SToKE [10] learns joint structural and temporal contextualized knowledge embeddings employing the pre-trained language model. Overview: While the Transformer framework has wide application in traditional KGs, its exploration in the field of TKGR remains relatively limited.", + "pre_questions": [], + "main_content": "INTRODUCTION Knowledge graphs (KGs) store human-summarized prior knowledge in structured data formats and are widely applied in many downstream tasks, such as information retrieval [2], intelligent question answering [3], and recommendation systems [44]. Traditional knowledge graphs employ triples (\ud835\udc60, \ud835\udc5d,\ud835\udc5c) to record each fact or event in the knowledge base, where \ud835\udc60and \ud835\udc5crespectively represent the subject and object entities, and \ud835\udc5ddenotes the logical predicate (or relation) connecting these two entities. e.g., (Barack Obama, presidentOf, USA). However, events in the real world often dynamically evolve over time. To extend the temporal nature of events, Temporal Knowledge Graphs (TKGs) incorporate temporal information into the traditional triples, resulting in quadruples (\ud835\udc60, \ud835\udc5d,\ud835\udc5c,\ud835\udf0f). e.g., (Barack Obama, presidentOf, USA, 2009\u20132017) and (Donald Trump, presidentOf, USA, 2017\u20132021). Completing missing events for specific timestamps in TKGs via Temporal Knowledge Graph Reasoning (TKGR) has recently attracted growing attention from both academic and industrial communities. For example, the missing element Barack Obama in the quadruple query (?, president of, USA, 2009\u20132017) can be predicted via TKGR. Existing TKGR methods can be broadly categorized into two types according to the temporal scope of link prediction, arXiv:2405.00352v1 [cs.AI] 1 May 2024 SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA Fang et al. America Barack Obama George Bush France Donald Trump president of, [2017, 2021] president of, [2009, 2017] visit to, 2009 succeded, 2017 visit to, 2017 visit to, 2002 succeded, 2009 president of, [2001, 2009] \uff1f America Barack Obama George Bush France Donald Trump president of, [2017, 2021] president of, [2009, 2017] visit to, 2009 succeded, 2017 visit to, 2017 visit to, 2002 succeded, 2009 president of, [2001, 2009] \uff1f (a) 2001 \u2026 2009 George Bush visit to USA president of Barack Obama succeded \u2026 2001 \u2026 2009 George Bush visit to USA president of Barack Obama succeded \u2026 ECEformer Unified Representation Entity Set Timestamp Set Link Prediction Time Prediction Link Prediction Time Prediction ECEformer Unified Representation Entity Set Timestamp Set Link Prediction Time Prediction (b) Figure 1: Illustration of the overall concept of our method. Part (a) displays a subgraph of TKG, which includes facts related to three U.S. Presidents. Part (b) illustrates our motivation for the ECEformer to learn a unified representation from an evolutionary chain of events, thereby simultaneously addressing link and time prediction tasks. i.e., interpolation and extrapolation [16]. The former focuses on completing unknown knowledge in the past, whereas the latter concentrates on estimating unknown knowledge in the future. Concretely, interpolation reasoning methods aim to effectively integrate temporal information into the evolutionary trajectory of events. They typically utilize geographic and geometric information to model the relationships among elements within individual quadruples. Accordingly, HyTE [8] employs a translation-based strategy [4] to measure the distance between entities and relations in the customized hyperplane, where each timestamp is associated with a corresponding hyperplane. Inspised by BoxE [1], BoxTE [27] additionally incorporates temporal information embedded through the relation-specific transition matrix within the foundational boxtype relation modeling. TGeomE [41], a geometric algebra-based embedding approach, performs 4th-order tensor factorization and applies linear temporal regularization for time representation learning. These methods impose a rigid prior on KGs, relying solely on geometric modeling and geographic measurements. However, they ignore the implicit semantic information, failing to fully capture the complex graph structure and relational context. Therefore, it is necessary to sufficiently explore the internal structure and semantic relationships within individual quadruples (Limitation I). On the other hand, extrapolation reasoning methods aim to effectively leverage the query-associated historical information [36]. They generally utilize Graph Neural Network (GNN) models to capture structural characteristics within each snapshot and leverage Recurrent Neural Networks (RNNs) to explore the evolutionary characteristics across timestamps. Accordingly, RE-Net [16] employs a multi-relational graph aggregator to capture the graph structure and an RNN-based encoder to capture temporal dependencies. RE-GCN [24] leverages a relation-aware Graph Convolution Network (GCN) to capture the structural dependencies for the evolution unit and simultaneously captures the sequential patterns of all facts in parallel using gate recurrent components. RPC [25] mines the information underlying the relational correlations and periodic patterns via two correspondence units: one is based on a relational GCN, and the other is based on Gated Recurrent Units (GRUs). However, this phased processing strategy can easily degrade the accuracy of predicting future events due to incorrect historical information. Therefore, it is necessary to adaptively correct the interference of incorrect historical information on prediction accuracy by learning a unified representation of the contextual and temporal correlations among different quadruples (Limitation II). Given a subgraph of TKG (as shown in Figure 1a), interpolation methods utilize geographical information to maximize structural differences between different quadruples. However, this type of approaches cannot effectively utilize semantic information in reasoning. Moreover, learning discriminative and powerful representations for each item within a quadruple is challenging, especially in modeling timestamps. For instance, differentiating between (Barack Obama, visitTo, France, 2009) and (Donald Trump, visitTo, France, 2017) necessitates precise characterizations of different names and timestamps. Although extrapolation methods consider neighborhood information, independently processing structural and temporal characteristics can lead to confusion in reasoning. For instance, under the timestamps of 2009 and 2017, the structure of Barack Obama and Donald Trump with USA and France is consistent. Hence, the model can naturally infer the structure of George Bush with USA and France in 2001 should be consistent with the structure of Barack Obama and Donald Trump, which contradicts the facts. From this key observation, we believe that designing an end-to-end network for learning a unified representation rich in information from temporal subgraph inputs will enhance the performance of TKGR. This network adaptively extracts both intra-quadruple and inter-quadruple, together with temporal information. According to the aforementioned analysis, we propose an innovative end-to-end Transformer-based network to learn the evolutionary chain of events (dubbed ECEformer) for TKGR. Figure 1b illustrates the motivation of our method. To easily illustrate the structural and contextual relationship between the query node and the adjacent nodes, we form an evolutionary chain of events (ECE) by extracting query-specific neighbors from the subgraph. Subsequently, our proposed Transformer-based model learns the unified representation for the ECE via two novel modules, namely, ECE Representation Learning (ECER) and Mixed-Context Knowledge Reasoning (MCKR). Specifically, to overcome Limitation I, ECER employs a Transformer-based encoder to embed each event in the ECE, such as (USA, president of, 2001) corresponding to a specific query George Bush. To overcome Limitation II, MCKR induces the embeddings of each event and enhances interaction within and between quadruples via crafting an MLP-based information mixing layer. In addition, to enhance the timeliness of the events, we devise an additional time prediction task to imbue effective temporal information within the learned unified representation. Transformer-based Reasoning for Learning Evolutionary Chain of Events on Temporal Knowledge Graph SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA In summary, our main contributions are three-fold: \u2022 We propose an innovative temporal knowledge graph reasoning method, namely ECEformer. Experimental results verify the state-of-the-art performance of our method on six publicly available datasets. Proposing a Transformer-based encoder for ECE representapublicly available datasets. \u2022 Proposing a Transformer-based encoder for ECE representation learning (ECER) aims to explore the internal structure and semantic relationships within individual quadruples. Proposing an MLP-based layer for Mixed-Context Knowland semantic relationships within individual quadruples. \u2022 Proposing an MLP-based layer for Mixed-Context Knowledge Reasoning (MCKR) aims to learn a unified representation of the contextual and temporal correlations among different quadruples. Note that TKG G = (E, R, T, Q) denotes a directed multi-relation graph with timestamped edges between entities, where E \u2208R| E|\u00d7\ud835\udc51, R \u2208R|R|\u00d7\ud835\udc51, and T \u2208R| T|\u00d7\ud835\udc51are the set of entities, relations and timestamps, respectively. Q = {(\ud835\udc60, \ud835\udc5d,\ud835\udc5c,\ud835\udf0f) | \ud835\udc60, \ud835\udc5c\u2208E, \ud835\udc5d\u2208R,\ud835\udf0f\u2208T } is a set of quadruples in G, where \ud835\udc60, \ud835\udc5c, \ud835\udc5dand \ud835\udf0fare a subject entity, an object entity, the relation between them, and a timestamp, respectively. For the link prediction task, we infer the missing object entity by converting (\ud835\udc60, \ud835\udc5d, ?,\ud835\udf0f). Similarly, we infer the missing subject entity by converting (\ud835\udc5c, \ud835\udc5d\u22121, ?,\ud835\udf0f), where we employ a reciprocal predicate \ud835\udc5d\u22121 to distinguish this case. Evolutionary Chain of Events. The evolutionary chain of events (ECE) transforms structural and temporal contexts related to the query-specific neighborhood subgraph into a structured knowledge sequence. Specifically, for the query (\ud835\udc60, \ud835\udc5d, ?,\ud835\udf0f), ECE is conceptualized as a singly linked list C = {\ud835\udc360,\ud835\udc361, \u00b7 \u00b7 \u00b7 ,\ud835\udc36\ud835\udc58}, comprising a chronologically arranged collection of events relevant to the subject \ud835\udc60of the query. Notably, each \ud835\udc36represents an event related to \ud835\udc60, depicted by a triplet (\ud835\udc52, \ud835\udc5d,\ud835\udf0f), where \ud835\udc360 signifies the query and \ud835\udc36\ud835\udc58denotes adjacent facts, \ud835\udc58being the maximum adjacency count, \ud835\udc52can serve as either the subject entity or the object entity. For example, for the query (George Bush, visitTo, ?, 2002) as shown in Figure 1a, the ECE can be formulated as: C ={(George Bush, visitTo, 2002), (USA, presidentOf, 2001), (Barack Obama, succeded, 2009)}. The formal expression is illustrated in Figure 1b. Hence, Our ECE can structurally represent both intra-quadruples and inter-quadruples. By encapsulating the dynamic evolution of entities and their interrelations within the event chain, the ECE can capture the historical and current events related to the subject entity. 3.2 Overview of ECEformer As an innovative end-to-end Transformer-based network, ECEformer learns the evolutionary chain of events (ECE) for TKGR. This work defines the subgraph composed of adjacent nodes that evolve over time along with the query entity as the evolutionary chain of events (ECE). Different from existing Transformer-based models, ECEformer crafts specific modules for handling intra-quadruples and inter-quadruples, respectively. As for intra-quadruples, ECE representation learning (ECER) based on a Transformer encoder is designed to explore the internal structure and semantic relationship within individual quadruples from the input ECE. On the other hand, as for the inter-quadruples, mixed-context knowledge reasoning (MCKR) involves a novel information mixing layer, and the iterative transposition mechanism is designed to explore the contextual and temporal correlations among different quadruples. The architecture of ECEformer is shown in Figure 2, and more details will be illustrated in the following sections. 3.3 Learning Representation for Evolutionary Chain of Events The first key to effectively learning ECE lies in the comprehensive extraction and analysis of each triplet corresponding to the sub-nodes on the ECE. Every constituent node of the ECE stores a historical event associated with the central entity, necessitating an investigation into its inherent structural and temporal characteristics. Inspired by the effectiveness of the Transformer architecture in learning inter-data dependencies, we introduce an ECER module utilizing a Transformer encoder that distills the embedding of each triplet. The details are shown in Figure 2c. Specifically, ECER consists of \ud835\udc41core units, each consisting of alternating layers of multi-head attention (MHA), layer normalization (LN), and MLP-based feed-forward (FF). Among them, both MHA and FF are followed by a LN accompanied by the residual connection (RC). The FF contains two layers with the GELU non-linear activation function. This process can be formulated as: \ud835\udc66= \ud835\udc59\u25e6\ud835\udc5f\u25e6\ud835\udc53\u25e6\ud835\udc59\u25e6\ud835\udc5f\u25e6\u210e(\ud835\udc65;\ud835\udc4a\u210e,\ud835\udc4a\ud835\udc59,\ud835\udc4a\ud835\udc53), (1) denote MHA function with weight, LN function \u25e6\u25e6\u25e6\u25e6\u25e6() where \u210e,\ud835\udc59and \ud835\udc53denote MHA function with weight\ud835\udc4a\u210e, LN function with weight \ud835\udc4a\ud835\udc59, and FF function with weight \ud835\udc4a\ud835\udc53, respectively. \ud835\udc5f denotes the RC function, which performs an operation that directly combines the input with the output of the intermediate layer. \ud835\udc65 denotes the input sequence. \ud835\udc66denotes the output embedding. \u25e6 denotes the composite function operator. Note that the MHA relies on the scaled dot-product attention mechanism to learn semantic interactions between the current token and all tokens within the sequence, thereby thoroughly exploring the structural and semantic information within individual events. Additionally, by directly inputting timestamps as tokens into ECER, the model can semantically extract temporal information within individual events. Given a query \ud835\udc5e(\ud835\udc60, \ud835\udc5d, ?,\ud835\udf0f) and its ECE C\ud835\udc5e, we treat each component within the branch of ECE as an individual token, sequentially unfolding the chain structure based on temporal order. This process yields a new input, as illustrated in Figure 2a. For each triplet on every branch of the ECE, we append a special token, i.e., [\ud835\udc36\ud835\udc3f\ud835\udc46]. Subsequently, we employ the concatenation of semantic embeddings \ud835\udc38and positional embeddings \ud835\udc43in the embedding space to represent each input token, as illustrated in Figure 2b. This process can be formulated as: \ud835\udc38\ud835\udc56 \ud835\udc56\ud835\udc5b\ud835\udc5d= \ud835\udc38\ud835\udc56+ \ud835\udc43\ud835\udc57, {\ud835\udc56\u2208E \u222aR \u222aT, \ud835\udc57\u2208[0, 1, 2, 3]} , (2) where \ud835\udc38\ud835\udc56 \ud835\udc56\ud835\udc5b\ud835\udc5ddenotes \ud835\udc56\u2212\ud835\udc61\u210etoken in the input sequence, \ud835\udc38\ud835\udc56denotes the feature embedding of \ud835\udc56\u2212\ud835\udc61\u210etoken, and \ud835\udc43\ud835\udc57denotes the position embedding. These embeddings are iteratively fed into the ECER module F\ud835\udc38\ud835\udc36\ud835\udc38\ud835\udc45: R4\u00d7\ud835\udc51\u2192R\ud835\udc51. Eventually, the output consists of intermediate embeddings \ud835\udc38\ud835\udc56 \ud835\udc61\ud835\udc5f\ud835\udc56\ud835\udc5d\ud835\udc59\ud835\udc52,\ud835\udc56= 0, 1, \u00b7 \u00b7 \u00b7 ,\ud835\udc58, which represent the structural and semantic information implied in the triples corresponding to each branch. Transformer-based Reasoning for Learning Evolutionary Chain of Events on Temporal Knowledge Graph SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA 2001 \u2026 2009 George Bush visit to USA president of Barack Obama succeded \u2026 2001 \u2026 2009 George Bush visit to USA president of Barack Obama succeded \u2026 (a) Input triples of ECE (b) Embeddingh space USA president of 2001 USA president of 2001 Barack Obama succeded 2009 Barack Obama succeded 2009 George Bush visit to [MASK] George Bush visit to [MASK] \u2026 \u2026 \u2026 + + + + + + + + + + + + ECE Representation Learning (ECER) Mixed-Context Knowledge Reasoning (MCKR) Global Average Pooling Timestamp Set Unified Representation Entity Set Link Prediction Time Prediction (c) Core unit in ECER (d) Core unit in MCKR Layer Norm Transposition Channel MLP Patch MLP Layer Norm Transposition Layer Norm Transposition Channel MLP Patch MLP Layer Norm Transposition Multi-Head Attention Add & Norm Feed Forward Add & Norm Multi-Head Attention Add & Norm Feed Forward Add & Norm Transformer-based Core unit Transformer-based Core unit Transformer-based Core unit \u2026 \u2026 \u2026 MLP-based Core unit Figure 2: The architecture of the proposed ECEformer. Given an evolutionary chain of events, ECEformer obtains input sequences (detailed in (a)) from each branch of the chain and converts each token into a concatenation of semantic embeddings \ud835\udc38and positional embeddings \ud835\udc43(detailed in (b)). Subsequently, these branch embeddings \ud835\udc38\ud835\udc61\ud835\udc5f\ud835\udc56\ud835\udc5d\ud835\udc59\ud835\udc52are derived by the ECER, which is based on the Transformer encoder (detailed in (c)). The contextual information from different branch embeddings is then inductively processed by the MLP-based MCKR (detailed in (d)), culminating in a unified representation. 3.4 Mixed-Context Knowledge Reasoning After encoding through the ECER, the embedded representations have effectively abstracted the relevant information of individual events. We introduce the query-specific contextual information to further enhance the accuracy of reasoning. Inspired by [34], we introduce the MLP-based MCKR module to learn the multidimensional information interaction of the inputs by leveraging two mixing strategies. The details are illustrated in Figure 2d. Different from the single event input in ECER, the MCKR module processes the sequence of 1 + \ud835\udc58embedding representations of ECE. This forms a two-dimensional real-valued input matrix M \u2208R(1+\ud835\udc58)\u00d7\ud835\udc51. The MCKR consists of \ud835\udc40core units, each consisting of two key mixing layers: the channel MLP and the patch MLP. Additionally, each mixing unit is preceded by a layer normalization and a transposition layer. The channel MLP operates on the columns of M, mapping each column from R1+\ud835\udc58to R1+\ud835\udc58. It aims to facilitate information interaction across different event embeddings within the same feature dimension. Conversely, the patch MLP operates on the rows of M, mapping each row from R\ud835\udc51to R\ud835\udc51. It aims to facilitate information interaction within the same event embedding across different feature dimensions. This process can be formulated as: \u00a4 M\u2217,\ud835\udc56= \ud835\udc40\u2217,\ud835\udc56+\ud835\udc4a2\ud835\udf0e(\ud835\udc4a1Norm(M)\u2217,\ud835\udc56), for \ud835\udc56= 1, 2, \u00b7 \u00b7 \u00b7 ,\ud835\udc51 (3) \u00a5 M\ud835\udc57,\u2217= \u00a4 M\ud835\udc57,\u2217+\ud835\udc4a4\ud835\udf0e(\ud835\udc4a3Norm( \u00a4 M)\ud835\udc57,\u2217), for \ud835\udc57= 1, 2, \u00b7 \u00b7 \u00b7 ,\ud835\udc58+ 1 (4) where \ud835\udf0eis the non-linear activation function (GELU). Each MLP block in MCKR contains two fully-connected layers,\ud835\udc4a1 and\ud835\udc4a2 are hidden weights in the channel MLP,\ud835\udc4a3 and\ud835\udc4a4 are hidden weights in the patch MLP. Following the methodology outlined in [34], our MCKR employs the same parameter to translate every column (row) for channel MLP (patch MLP). This parameter sharing mechanism endows the network with positional invariance, enhancing its ability to proficiently process sequential data. Moreover, this approach also circumvents the substantial increase in model complexity that typically accompanies dimensional augmentation. Subsequently, we leverage a global average pooling layer to distill the mixed-context \u00a5 \ud835\udc40, which can be formulated as: U\ud835\udc38\ud835\udc36\ud835\udc38= GlobalAvgPool( \u00a5 \ud835\udc40), (5) where U\ud835\udc38\ud835\udc36\ud835\udc38denotes the unified representation of ECE. Given a quadruple with either the subject or the object missing, the task of link prediction can be accomplished by computing the similarity between U\ud835\udc38\ud835\udc36\ud835\udc38and all candidate entities. Link prediction can be mathematically formulated as: \ud835\udc5d(\ud835\udc52\ud835\udc54\ud835\udc61|\ud835\udc5e) = \ud835\udc46\ud835\udc5c\ud835\udc53\ud835\udc61\ud835\udc5a\ud835\udc4e\ud835\udc65(\ud835\udc46\ud835\udc56\ud835\udc5a(U\ud835\udc38\ud835\udc36\ud835\udc38, E)), (6) SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA Fang et al. Table 1: Statistics of the Experimental Datasets. Dataset |E| |R| |T| Time \ud835\udc41\ud835\udc61\ud835\udc5f\ud835\udc4e\ud835\udc56\ud835\udc5b \ud835\udc41\ud835\udc63\ud835\udc4e\ud835\udc59\ud835\udc56\ud835\udc51 \ud835\udc41\ud835\udc61\ud835\udc52\ud835\udc60\ud835\udc61 GDELT 500 20 366 15 mins 2,735,685 341,961 341,961 ICEWS05-15 10,488 251 4,017 24 hours 386,962 46,092 46,2775 ICEWS18 23,033 256 7,272 24 hours 373,018 45,995 49,545 ICEWS14 7,128 230 365 24 hours 63,685 13,823 13,222 YAGO11K 10,623 10 73 1 year 16,406 2,050 2,051 Wikidata12K 12,554 24 84 1 year 32,497 4,062 4,062 where \ud835\udc46\ud835\udc56\ud835\udc5adenotes the similarity function between U\ud835\udc38\ud835\udc36\ud835\udc38and a candidate entity, \ud835\udc5edenotes the predicted result, obtained by selecting the \ud835\udc61\ud835\udc5c\ud835\udc5d\u22121 entity based on similarity scores. \ud835\udc5d(\ud835\udc52\ud835\udc54\ud835\udc61|\ud835\udc5e) denotes the occurrence probability that \ud835\udc5eis the target entity \ud835\udc52\ud835\udc54\ud835\udc61. 3.5 Enhancement of Temporal Information Considering that events in TKGs often coincide with specific timestamps, the unified representations learned from link prediction might be trivial solutions facilitated by contextual information. Such representations will introduce spurious correlations, because they only consider entities and relations while neglecting the temporal aspect of events. To address this issue, we propose a marked time prediction task to enhance the exploration of temporal information during the contextualization process. Specifically, we utilize a special token [\ud835\udc40\ud835\udc34\ud835\udc46\ud835\udc3e] to replace the timestamp \ud835\udf0fin the queryspecific branch of ECE. In other words, we transform the \ud835\udc360(\ud835\udc60, \ud835\udc5d,\ud835\udf0f) in ECE to \ud835\udc360(\ud835\udc60, \ud835\udc5d, [\ud835\udc40\ud835\udc34\ud835\udc46\ud835\udc3e]). This direct masking strategy introduces perturbations to the original timestamps, thereby prompting the model to learn contextual information. To promote the model\u2019s capability of understanding temporal information, we train the model using masked inputs to recover the perturbed timestamp. This design can encourage the model to assimilate contextual information and deduce the occurrence time of the query-specific event. The methodology is analogous to link prediction, where we directly utilize the unified representation U\ud835\udc38\ud835\udc36\ud835\udc38to predict the correct timestamp. The prediction probability \ud835\udc5d(\ud835\udf0f\ud835\udc54\ud835\udc61|\ud835\udc5e) can be formulated as: \ud835\udc5d(\ud835\udf0f\ud835\udc54\ud835\udc61|\ud835\udc5e) = \ud835\udc46\ud835\udc5c\ud835\udc53\ud835\udc61\ud835\udc5a\ud835\udc4e\ud835\udc65(\ud835\udc46\ud835\udc56\ud835\udc5a(U\ud835\udc38\ud835\udc36\ud835\udc38, T)), (7) where \ud835\udc5d(\ud835\udf0f\ud835\udc54\ud835\udc61|\ud835\udc5e) denotes the probability that predicted timestamp \ud835\udc5e corresponds to the target timestamp \ud835\udf0f\ud835\udc54\ud835\udc61. 3.6 Training and Optimization For link prediction and time prediction tasks, we employ the crossentropy function to calculate the loss during the training process. The loss function can be formulated as: L = \u2212 \u2211\ufe01 (\ud835\udc60,\ud835\udc5d,\ud835\udc5c,\ud835\udf0f)\u2208G log(\ud835\udc5d(\ud835\udc52\ud835\udc54\ud835\udc61|\ud835\udc5e)) + \ud835\udf06log(\ud835\udc5d(\ud835\udf0f\ud835\udc54\ud835\udc61|\ud835\udc5e)), (8) where (\ud835\udc60, \ud835\udc5d,\ud835\udc5c,\ud835\udf0f) \u2208G represents the historical events in the training set, \ud835\udf06weights the time prediction task. Additionally, for diversifying our training data and reducing memory cost, we implement an ECE sampling strategy similar to the edge dropout regularization [6]. This approach samples only a portion of the neighborhood information of the query subject and filters out the ground truth target entity from the sampled neighborhood information. 4 EXPERIMENTS In this section, the experimental settings are first introduced from four aspects, including datasets, evaluation metrics, compared baselines, and implementation details. Then, we comprehensively analyze the proposed ECEformer also from three aspects, i.e., superiority, effectiveness, and sensitivity. 4.1 Experimental Setup 4.1.1 Datasets and Evaluation Metrics. We evaluate the reasoning performance of our ECEformer on six TKG benchmark datasets, including GDELT, ICEWS05-15, ICEWS18, ICEWS14, YAGO11K, and Wikidata12K. According to [25], we also split the datasets of GDELT and ICEWS05-15/18/14 into train/valid/test by timestamps. According to [8], we split the datasets of YAGO11K and Wikidata12K into train/valid/test by time intervals. The statistical information of datasets is shown in Table 1, in which Time represents time granularity. Two widely used evaluation metrics are adopted to quantify the performance, namely \ud835\udc40\ud835\udc45\ud835\udc45and \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@\ud835\udc58. \ud835\udc40\ud835\udc45\ud835\udc45represents the mean reciprocal rank of the inferred true entity among the queried candidates, and \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@\ud835\udc58measures the proportion of instances where the true entity appears among the top \ud835\udc58 ranked candidates. 4.1.2 Compared Baselines. Considering that different methods are validated on various datasets, we divided our experiments into two groups according to dataset size for a fair comparison. We compared with twenty state-of-the-art (SOTA) models. Specifically, the extrapolation baselines for GDELT, ICEWS05-15, and ICEWS18 consist of RL-based models (TITer [33], TLogic [26], and DREAM [49]), GNN-based models (RE-GCN [24], TiRGN [21], HGLS [46], \ud835\udc3f2TKG [45], and RPC [25]), and Transformer-based models (GHT [32] and SToKE [10]). The interpolation baselines chosen for smaller datasets (ICEWS14, YAGO11K, and Wikidata12K) include TimePlex [15], TeLM [38], TeRo [40], RotateQVS [5], SANe [22], NeuSTIP [31], QDN [35], LCGE [28], TGeomE [41], and HyIE [47]. 4.1.3 Implementation Details. All experiments are conducted on a single NVIDIA RTX A6000. The implementation1 of our model is built upon the open-source framework LibKGE2. The dimension of the input embedding is set to 320. The hidden widths of the feed-forward layer inside ECER and the channel (patch) MLP inside MCKR are set to 1024. The maximum neighborhood of ECE is set to 50. We configure the core unit numbers for ECER and MCKR to be \ud835\udc41= 3 and \ud835\udc40= 6, respectively. The activation function in our network is GELU. We train our model via the Adamax [18] with an initial learning rate of 0.01 and an L2 weight decay rate of 0.01. We employed the warm-up training strategy, wherein the learning rate commenced from zero and increased linearly during the initial 10% of the training steps, followed by a linear decrease throughout the remaining training process. We train the model with a batch size of 512 for a maximum of 300 epochs, employing an early stopping mechanism based on MRR in the validation set. Detailed discussions on the effects of the weight coefficient \ud835\udf06, the number of core units \ud835\udc41and \ud835\udc40are in the subsection Sensitivity Analysis. 1https://github.com/seeyourmind/TKGElib 2https://github.com/uma-pi1/kge Transformer-based Reasoning for Learning Evolutionary Chain of Events on Temporal Knowledge Graph SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA Table 2: Performance of link prediction on GDELT, ICEWS05-15, and ICEWS18. The best results are marked in bold, the second results are marked by underlining. Model GDELT ICEWS05-15 ICEWS18 MRR Hits@1 Hits@3 Hits@10 MRR Hits@1 Hits@3 Hits@10 MRR Hits@1 Hits@3 Hits@10 TITer 18.19 11.52 19.20 31.00 47.60 38.29 52.74 64.86 29.98 22.05 33.46 44.83 TLogic 19.80 12.20 21.70 35.60 46.97 36.21 53.13 67.43 29.82 20.54 33.95 48.53 DREAM 28.10 19.30 31.10 44.70 56.80 47.30 65.10 78.60 39.10 28.00 45.20 62.70 RE-GCN 19.69 12.46 20.93 33.81 48.03 37.33 53.90 68.51 32.62 22.39 36.79 52.68 TiRGN 21.67 13.63 23.27 37.60 49.84 39.07 55.75 70.11 33.58 23.10 37.90 54.20 HGLS 19.04 11.79 33.23 46.21 35.32 67.12 29.32 19.21 49.83 \ud835\udc3f2TKG 20.53 12.89 35.83 57.43 41.86 80.69 33.36 22.15 55.04 RPC 22.41 14.42 24.36 38.33 51.14 39.47 57.11 71.75 34.91 24.34 38.74 55.89 GHT 20.04 12.68 21.37 34.42 41.50 30.79 46.85 62.73 27.40 18.08 30.76 45.76 SToKE 37.10 29.00 39.90 52.50 71.20 60.50 79.00 88.50 ECEformer (Ours) 51.19 38.72 59.41 71.10 77.29 73.11 79.39 85.17 44.80 39.18 46.89 55.31 Table 3: Performance of link prediction task on ICEWS14, YAGO11K, and Wikidata12K. The best results are marked in bold, the second results are marked by underlining. Model ICEWS14 YAGO11K Wikidata12K MRR Hits@1 Hits@3 Hits@10 MRR Hits@1 Hits@3 Hits@10 MRR Hits@1 Hits@3 Hits@10 TimePlex 60.40 51.50 77.11 23.64 16.92 36.71 33.35 22.78 53.20 TeLM 62.50 54.50 67.30 77.40 19.10 12.90 19.40 32.10 33.20 23.10 36.00 54.20 TeRo 56.20 46.80 62.10 73.20 18.70 12.10 19.70 31.90 29.90 19.80 32.90 50.70 RotateQVS 59.10 50.70 64.20 75.40 18.90 12.40 19.90 32.30 SANe 63.80 55.80 68.80 78.20 25.00 18.00 26.60 40.10 43.20 33.10 48.30 64.00 NeuSTIP 25.23 18.45 37.76 34.78 24.38 53.75 QDN 64.30 56.70 68.80 78.40 19.80 13.10 20.10 32.80 LCGE 66.70 58.80 71.40 81.50 42.90 30.40 49.50 67.70 TGeomE 62.90 54.60 68.00 78.00 19.50 13.00 19.60 32.60 33.30 23.20 36.20 54.60 HyIE 63.10 56.30 68.70 78.60 19.10 12.50 20.10 32.60 30.10 19.70 32.80 50.60 ECEformer (Ours) 71.70 67.31 73.60 80.30 25.63 19.48 26.88 37.84 47.81 41.35 49.96 60.35 4.2 Performance Comparison for Superiority We compare our model with 20 SOTA models ranging from 2020 to 2023 on six benchmark datasets. We report the result in Table 2 and Table 3, where the best performances are highlighted in bold, while the second-best are marked by underlining. A noteworthy observation is that our ECEformer significantly outperforms other baseline models across all datasets in terms of \ud835\udc40\ud835\udc45\ud835\udc45and \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@\ud835\udc58. Specifically, ECEformer achieves performance improvements over the second-best models by 14.09%, 6.09%, 5.70%, 5.00%, 0.40%, and 4.61% on \ud835\udc40\ud835\udc45\ud835\udc45, respectively. Additionally, it achieves gains of 9.72%, 12.61%, 11.18%, 8.51%, 1.03%, and 8.25% on \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@1, respectively. This significant margin of improvement demonstrates the superior performance of our ECEformer. In particular, our model exhibits notable performance in four metrics on GDELT: \ud835\udc40\ud835\udc45\ud835\udc45, \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@1, \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@3, and \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@10, achieving respective scores of 51.19%, 38.72%, 59.41%, and 71.10%. Compared with RL-based methods, our ECEformer outperforms DREAM by 23.09% in \ud835\udc40\ud835\udc45\ud835\udc45, by 9.42% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@1, by 28.31% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@3, and by 26.4% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@10, respectively. Compared with GNN-based methods, our ECEformer outperforms RPC by 28.78% in \ud835\udc40\ud835\udc45\ud835\udc45, by 24.30% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@1, by 35.05% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@3, and by 32.77% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@10, respectively. Compared with Transformer-based methods, our ECEformer outperforms SToKE by 14.09% in \ud835\udc40\ud835\udc45\ud835\udc45, by 9.72% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@1, by 19.51% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@3, and by 18.6% in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@10, respectively. This indicates that our model can effectively learn the unified representations from frequently changing historical events in datasets characterized by fine-grained temporal granularity. Based on the comparative results from the ICEWS (i.e., ICEWS05-15/18/14), ECEformer consistently surpasses all the baselines on the \ud835\udc40\ud835\udc45\ud835\udc45, \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@1, and \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@3 metrics. However, it lags behind the second-best model in \ud835\udc3b\ud835\udc56\ud835\udc61\ud835\udc60@10. This situation also occurs in the YAGO11K and Wikidata12K. This suggests that although our model demonstrates high precision in predictions, there is still room for improvement in its recall capability. Besides, compared to other datasets, our method shows a relatively slight performance improvement on YAGO11K. This is attributed to 1) the issue of missing timestamps in the YAGO11K SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA Fang et al. Table 4: Ablation study on different module combinations on ICEWS14 and Wikidata12K. \ud835\udc47\ud835\udc43represents the time prediction task. The best results are marked in bold. Model ICEWS14 Wikidata12K MRR Hits@10 MRR Hits@10 ECER 70.60 80.40 43.49 57.08 ECEformer (w/o TP) 69.4 79.1 46.12 58.54 ECEformer 71.70 80.30 47.81 60.35 dataset, and 2) the NeuSTIP method additionally introduces Allen algebra [31] to refine temporal rules and designs a specialized time prediction evaluation function to capture temporal information. Nevertheless, the performance gain achieved by our method indicates that the proposed masked time prediction task can mitigate challenges arising from low data quality. 4.3 Ablation Study for Effectiveness To analyze the contribution of ECEformer components, we validate them and their variants on the ICEWS14 and Wikidata12K: (1) using only ECER to embed individual query-specific quadruples (without contextual information); (2) combining ECER and MCKR without conducting the time prediction task; (3) combining ECER and MCKR while undertaking the time prediction task (i.e., the complete ECEformer). The detailed results are listed in Table 4. From the results of ECER, we observe that by utilizing the Transformer architecture, our model can surpass most geoinformationbased models (such as TGeomE). This validates our viewpoint, which emphasizes sufficiently exploring the internal structure and semantic relationships within individual quadruples. Comparing the results of the ECER and ECEformer (\ud835\udc64/\ud835\udc5cTP), we observe that incorporating contextual information significantly improves the model\u2019s reasoning accuracy on Wikidata12K. However, this integration within ICEWS14 slightly diminishes performance. Specifically, ECEformer (\ud835\udc64/\ud835\udc5cTP) outperforms ECER by 2.63% on Wikidata12K, but underperforms by 1.20% on ICEWS14 in terms of \ud835\udc40\ud835\udc45\ud835\udc45. This phenomenon is attributed to the finer temporal granularity of ICEWS14 compared to Wikidata12K, where the frequent historical events in the context exacerbate spurious correlations. Without the intervention of the time prediction task, the model is more prone to erroneous estimations. Comparing the results of ECEformer (\ud835\udc64/\ud835\udc5c TP) and ECEformer, we observe consistent performance enhancements on both datasets after executing the time prediction task. This is especially pronounced in ICEWS14, where the implementation of the time prediction task results in a notable augmentation of the \ud835\udc40\ud835\udc45\ud835\udc45, surpassing the performance of the ECER. Specifically, ECEformer outperforms ECER by 1.10%, and it outperforms ECEformer (\ud835\udc64/\ud835\udc5cTP) by 2.30% in terms of \ud835\udc40\ud835\udc45\ud835\udc45. These findings confirm the effectiveness of our proposed temporal information enhancement strategy in prompting the model to leverage temporal information within its context, thereby effectively mitigating the impacts of spurious correlations. Table 5: Sensitivity analysis of ECEformer with different number of unit layers. \ud835\udc41and \ud835\udc40represent the number of ECER units and MCKR units, respectively. \ud835\udc41 \ud835\udc40 ICEWS14 Wikidata12K MRR Hits@10 MRR Hits@10 1x 1 66.30 78.23 47.94 59.33 2x 67.36 78.77 48.08 60.00 3x 66.95 78.79 48.47 60.24 1 1x 66.30 78.23 47.94 59.33 2x 69.01 78.53 48.31 60.19 3x 70.30 79.08 48.19 60.09 1x 2 69.04 79.10 48.37 60.45 2x 69.34 79.03 48.32 60.51 3x 69.36 78.94 48.34 60.61 2 1x 69.04 79.10 48.37 60.45 2x 70.18 78.80 48.22 60.39 3x 70.10 78.19 47.67 59.21 0.5 1.0 1.5 2.0 2.5 ICEWS14 60 65 70 75 80 85 MRR Hits@1 Hits@3 Hits@10 0.5 1.0 1.5 2.0 2.5 Wikidata12K 40 45 50 55 60 65 MRR Hits@1 Hits@3 Hits@10 (a) Weight coefficient \ud835\udf06 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 ICEWS14 60 65 70 75 80 85 MRR Hits@1 Hits@3 Hits@10 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Wikidata12K 35 40 45 50 55 60 MRR Hits@1 Hits@3 Hits@10 (b) Random marking rate \ud835\udefe Figure 3: Sensitivity analysis of weight coefficients \ud835\udf06and random masking rate \ud835\udefeon ICEWS14 and Wikidata12K. 4.4 Sensitivity Analysis As mentioned in Implementation Details, we explore the performance fluctuations of ECEformer caused by the structural control parameters \ud835\udc41and \ud835\udc40, as well as the weight coefficient \ud835\udf06. For structural control parameters \ud835\udc41and \ud835\udc40, we set the base of one parameter to {1, 2}, while the other is adjusted in multiples, specifically to 1\u00d7, 2\u00d7, and 3\u00d7. As shown in Table 5, the results highlight the maximum value in each group in bold. Our observations reveal that different structural settings do introduce perturbations to the model, with the disturbance being relatively minor at \ud835\udc41: \ud835\udc40= 1 : 2. Based on this finding, we configure the architecture of ECEformer as \ud835\udc41= 3 and \ud835\udc40= 6 across all datasets. For the weight coefficient \ud835\udf06, we record the model\u2019s performance across a range of {0.5, 1.0, 1.5, 2.0, 2.5}, and plotted these results in Figure 3a. The performance curve trend suggests that excessively weighting the time prediction task can Transformer-based Reasoning for Learning Evolutionary Chain of Events on Temporal Knowledge Graph SIGIR \u201924, July 14\u201318, 2024, Washington, DC, USA detrimentally affect the link prediction task, thereby reducing overall performance. Therefore, setting the weight coefficient between 0.5 and 1.0 offers a balanced improvement in model performance. In addition, to investigate the impact of the masking mechanism in the time prediction task on model performance, we report the results of each batch of data under varying masking rates, with details as well as illustrated in Figure 3b. Specifically, we employ a fixed masking rate \ud835\udefeduring the training phase, randomly selecting \ud835\udefe\u00d7 batch_size samples per batch to mask their timestamps. We observe that as the masking rate increases, the model performance correspondingly improves. Additionally, compared to Wikidata12K, the performance of ICEWS14 exhibits greater fluctuations with varying masking rates. This observation indicates that datasets with finer temporal granularity are more sensitive to variations in masking rate. Notably, our final model is trained using a fully masked approach. 5 CONCLUSION In this paper, we address the challenge of completing missing factual elements in TKG reasoning by introducing the ECEformer, a novel end-to-end Transformer-based reasoning model. ECEformer primarily comprises two key components: the evolutionary chain of events representation learning (ECER) and the mixed-context knowledge reasoning (MCKR). The ECER, utilizing the Transformer encoder, thoroughly explores the structural and semantic information of historical events corresponding to each branch in the evolutionary chain of events (ECE). The ECE is composed of neighborhood subgraphs of entity nodes unfolded in chronological order. The MCKR based on MLP relies on the channel and patch mixing strategy to facilitate the learning of contextual information interactions within the ECE. Moreover, an additional time prediction task and a time masking mechanism are employed to force the model to assimilate temporal information from the context. Comparative experiments with state-of-the-art methods validate the superiority of our approach. Furthermore, additional ablation studies demonstrate the effectiveness of each module proposed in our ECEformer. ACKNOWLEDGMENTS This research was supported by National Science and Technology Major Project (2022ZD0119204), National Science Fund for Distinguished Young Scholars (62125601), National Natural Science Foundation of China (62076024, 62172035)." + }, + { + "url": "http://arxiv.org/abs/2308.06512v1", + "title": "HyperFormer: Enhancing Entity and Relation Interaction for Hyper-Relational Knowledge Graph Completion", + "abstract": "Hyper-relational knowledge graphs (HKGs) extend standard knowledge graphs by\nassociating attribute-value qualifiers to triples, which effectively represent\nadditional fine-grained information about its associated triple.\nHyper-relational knowledge graph completion (HKGC) aims at inferring unknown\ntriples while considering its qualifiers. Most existing approaches to HKGC\nexploit a global-level graph structure to encode hyper-relational knowledge\ninto the graph convolution message passing process. However, the addition of\nmulti-hop information might bring noise into the triple prediction process. To\naddress this problem, we propose HyperFormer, a model that considers\nlocal-level sequential information, which encodes the content of the entities,\nrelations and qualifiers of a triple. More precisely, HyperFormer is composed\nof three different modules: an entity neighbor aggregator module allowing to\nintegrate the information of the neighbors of an entity to capture different\nperspectives of it; a relation qualifier aggregator module to integrate\nhyper-relational knowledge into the corresponding relation to refine the\nrepresentation of relational content; a convolution-based bidirectional\ninteraction module based on a convolutional operation, capturing pairwise\nbidirectional interactions of entity-relation, entity-qualifier, and\nrelation-qualifier. realize the depth perception of the content related to the\ncurrent statement. Furthermore, we introduce a Mixture-of-Experts strategy into\nthe feed-forward layers of HyperFormer to strengthen its representation\ncapabilities while reducing the amount of model parameters and computation.\nExtensive experiments on three well-known datasets with four different\nconditions demonstrate HyperFormer's effectiveness. Datasets and code are\navailable at https://github.com/zhiweihu1103/HKGC-HyperFormer.", + "authors": "Zhiwei Hu, V\u00edctor Guti\u00e9rrez-Basulto, Zhiliang Xiang, Ru Li, Jeff Z. Pan", + "published": "2023-08-12", + "updated": "2023-08-12", + "primary_cat": "cs.AI", + "cats": [ + "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/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/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" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2008.12813v2", + "title": "HittER: Hierarchical Transformers for Knowledge Graph Embeddings", + "abstract": "This paper examines the challenging problem of learning representations of\nentities and relations in a complex multi-relational knowledge graph. We\npropose HittER, a Hierarchical Transformer model to jointly learn\nEntity-relation composition and Relational contextualization based on a source\nentity's neighborhood. Our proposed model consists of two different Transformer\nblocks: the bottom block extracts features of each entity-relation pair in the\nlocal neighborhood of the source entity and the top block aggregates the\nrelational information from outputs of the bottom block. We further design a\nmasked entity prediction task to balance information from the relational\ncontext and the source entity itself. Experimental results show that HittER\nachieves new state-of-the-art results on multiple link prediction datasets. We\nadditionally propose a simple approach to integrate HittER into BERT and\ndemonstrate its effectiveness on two Freebase factoid question answering\ndatasets.", + "authors": "Sanxing Chen, Xiaodong Liu, Jianfeng Gao, Jian Jiao, Ruofei Zhang, Yangfeng Ji", + "published": "2020-08-28", + "updated": "2021-10-06", + "primary_cat": "cs.CL", + "cats": [ + "cs.CL", + "cs.LG" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2210.11151v1", + "title": "Transformer-based Entity Typing in Knowledge Graphs", + "abstract": "We investigate the knowledge graph entity typing task which aims at inferring\nplausible entity types. In this paper, we propose a novel Transformer-based\nEntity Typing (TET) approach, effectively encoding the content of neighbors of\nan entity. More precisely, TET is composed of three different mechanisms: a\nlocal transformer allowing to infer missing types of an entity by independently\nencoding the information provided by each of its neighbors; a global\ntransformer aggregating the information of all neighbors of an entity into a\nsingle long sequence to reason about more complex entity types; and a context\ntransformer integrating neighbors content based on their contribution to the\ntype inference through information exchange between neighbor pairs.\nFurthermore, TET uses information about class membership of types to\nsemantically strengthen the representation of an entity. Experiments on two\nreal-world datasets demonstrate the superior performance of TET compared to the\nstate-of-the-art.", + "authors": "Zhiwei Hu, V\u00edctor Guti\u00e9rrez-Basulto, Zhiliang Xiang, Ru Li, Jeff Z. Pan", + "published": "2022-10-20", + "updated": "2022-10-20", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI" + ], + "label": "Related Work" + }, + { + "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" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2303.03922v1", + "title": "Structure Pretraining and Prompt Tuning for Knowledge Graph Transfer", + "abstract": "Knowledge graphs (KG) are essential background knowledge providers in many\ntasks. When designing models for KG-related tasks, one of the key tasks is to\ndevise the Knowledge Representation and Fusion (KRF) module that learns the\nrepresentation of elements from KGs and fuses them with task representations.\nWhile due to the difference of KGs and perspectives to be considered during\nfusion across tasks, duplicate and ad hoc KRF modules design are conducted\namong tasks. In this paper, we propose a novel knowledge graph pretraining\nmodel KGTransformer that could serve as a uniform KRF module in diverse\nKG-related tasks. We pretrain KGTransformer with three self-supervised tasks\nwith sampled sub-graphs as input. For utilization, we propose a general\nprompt-tuning mechanism regarding task data as a triple prompt to allow\nflexible interactions between task KGs and task data. We evaluate pretrained\nKGTransformer on three tasks, triple classification, zero-shot image\nclassification, and question answering. KGTransformer consistently achieves\nbetter results than specifically designed task models. Through experiments, we\njustify that the pretrained KGTransformer could be used off the shelf as a\ngeneral and effective KRF module across KG-related tasks. The code and datasets\nare available at https://github.com/zjukg/KGTransformer.", + "authors": "Wen Zhang, Yushan Zhu, Mingyang Chen, Yuxia Geng, Yufeng Huang, Yajing Xu, Wenting Song, Huajun Chen", + "published": "2023-03-03", + "updated": "2023-03-03", + "primary_cat": "cs.LG", + "cats": [ + "cs.LG", + "cs.AI", + "cs.CL" + ], + "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/2308.02457v1", + "title": "A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects", + "abstract": "Temporal characteristics are prominently evident in a substantial volume of\nknowledge, which underscores the pivotal role of Temporal Knowledge Graphs\n(TKGs) in both academia and industry. However, TKGs often suffer from\nincompleteness for three main reasons: the continuous emergence of new\nknowledge, the weakness of the algorithm for extracting structured information\nfrom unstructured data, and the lack of information in the source dataset.\nThus, the task of Temporal Knowledge Graph Completion (TKGC) has attracted\nincreasing attention, aiming to predict missing items based on the available\ninformation. In this paper, we provide a comprehensive review of TKGC methods\nand their details. Specifically, this paper mainly consists of three\ncomponents, namely, 1)Background, which covers the preliminaries of TKGC\nmethods, loss functions required for training, as well as the dataset and\nevaluation protocol; 2)Interpolation, that estimates and predicts the missing\nelements or set of elements through the relevant available information. It\nfurther categorizes related TKGC methods based on how to process temporal\ninformation; 3)Extrapolation, which typically focuses on continuous TKGs and\npredicts future events, and then classifies all extrapolation methods based on\nthe algorithms they utilize. We further pinpoint the challenges and discuss\nfuture research directions of TKGC.", + "authors": "Jiapu Wang, Boyue Wang, Meikang Qiu, Shirui Pan, Bo Xiong, Heng Liu, Linhao Luo, Tengfei Liu, Yongli Hu, Baocai Yin, Wen Gao", + "published": "2023-08-04", + "updated": "2023-08-04", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2004.04926v1", + "title": "Tensor Decompositions for temporal knowledge base completion", + "abstract": "Most algorithms for representation learning and link prediction in relational\ndata have been designed for static data. However, the data they are applied to\nusually evolves with time, such as friend graphs in social networks or user\ninteractions with items in recommender systems. This is also the case for\nknowledge bases, which contain facts such as (US, has president, B. Obama,\n[2009-2017]) that are valid only at certain points in time. For the problem of\nlink prediction under temporal constraints, i.e., answering queries such as\n(US, has president, ?, 2012), we propose a solution inspired by the canonical\ndecomposition of tensors of order 4. We introduce new regularization schemes\nand present an extension of ComplEx (Trouillon et al., 2016) that achieves\nstate-of-the-art performance. Additionally, we propose a new dataset for\nknowledge base completion constructed from Wikidata, larger than previous\nbenchmarks by an order of magnitude, as a new reference for evaluating temporal\nand non-temporal link prediction methods.", + "authors": "Timoth\u00e9e Lacroix, Guillaume Obozinski, Nicolas Usunier", + "published": "2020-04-10", + "updated": "2020-04-10", + "primary_cat": "stat.ML", + "cats": [ + "stat.ML", + "cs.LG" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2106.00327v1", + "title": "Search from History and Reason for Future: Two-stage Reasoning on Temporal Knowledge Graphs", + "abstract": "Temporal Knowledge Graphs (TKGs) have been developed and used in many\ndifferent areas. Reasoning on TKGs that predicts potential facts (events) in\nthe future brings great challenges to existing models. When facing a prediction\ntask, human beings usually search useful historical information (i.e., clues)\nin their memories and then reason for future meticulously. Inspired by this\nmechanism, we propose CluSTeR to predict future facts in a two-stage manner,\nClue Searching and Temporal Reasoning, accordingly. Specifically, at the clue\nsearching stage, CluSTeR learns a beam search policy via reinforcement learning\n(RL) to induce multiple clues from historical facts. At the temporal reasoning\nstage, it adopts a graph convolution network based sequence method to deduce\nanswers from clues. Experiments on four datasets demonstrate the substantial\nadvantages of CluSTeR compared with the state-of-the-art methods. Moreover, the\nclues found by CluSTeR further provide interpretability for the results.", + "authors": "Zixuan Li, Xiaolong Jin, Saiping Guan, Wei Li, Jiafeng Guo, Yuanzhuo Wang, Xueqi Cheng", + "published": "2021-06-01", + "updated": "2021-06-01", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2007.06267v2", + "title": "BoxE: A Box Embedding Model for Knowledge Base Completion", + "abstract": "Knowledge base completion (KBC) aims to automatically infer missing facts by\nexploiting information already present in a knowledge base (KB). A promising\napproach for KBC is to embed knowledge into latent spaces and make predictions\nfrom learned embeddings. However, existing embedding models are subject to at\nleast one of the following limitations: (1) theoretical inexpressivity, (2)\nlack of support for prominent inference patterns (e.g., hierarchies), (3) lack\nof support for KBC over higher-arity relations, and (4) lack of support for\nincorporating logical rules. Here, we propose a spatio-translational embedding\nmodel, called BoxE, that simultaneously addresses all these limitations. BoxE\nembeds entities as points, and relations as a set of hyper-rectangles (or\nboxes), which spatially characterize basic logical properties. This seemingly\nsimple abstraction yields a fully expressive model offering a natural encoding\nfor many desired logical properties. BoxE can both capture and inject rules\nfrom rich classes of rule languages, going well beyond individual inference\npatterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a\ndetailed experimental analysis, and show that BoxE achieves state-of-the-art\nperformance, both on benchmark knowledge graphs and on more general KBs, and we\nempirically show the power of integrating logical rules.", + "authors": "Ralph Abboud, \u0130smail \u0130lkan Ceylan, Thomas Lukasiewicz, Tommaso Salvatori", + "published": "2020-07-13", + "updated": "2020-10-29", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI", + "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/2010.01029v2", + "title": "TeRo: A Time-aware Knowledge Graph Embedding via Temporal Rotation", + "abstract": "In the last few years, there has been a surge of interest in learning\nrepresentations of entitiesand relations in knowledge graph (KG). However, the\nrecent availability of temporal knowledgegraphs (TKGs) that contain time\ninformation for each fact created the need for reasoning overtime in such TKGs.\nIn this regard, we present a new approach of TKG embedding, TeRo, which defines\nthe temporal evolution of entity embedding as a rotation from the initial time\nto the currenttime in the complex vector space. Specially, for facts involving\ntime intervals, each relation isrepresented as a pair of dual complex\nembeddings to handle the beginning and the end of therelation, respectively. We\nshow our proposed model overcomes the limitations of the existing KG embedding\nmodels and TKG embedding models and has the ability of learning and\ninferringvarious relation patterns over time. Experimental results on four\ndifferent TKGs show that TeRo significantly outperforms existing\nstate-of-the-art models for link prediction. In addition, we analyze the effect\nof time granularity on link prediction over TKGs, which as far as we know\nhasnot been investigated in previous literature.", + "authors": "Chengjin Xu, Mojtaba Nayyeri, Fouad Alkhoury, Hamed Shariat Yazdi, Jens Lehmann", + "published": "2020-10-02", + "updated": "2020-10-24", + "primary_cat": "cs.CL", + "cats": [ + "cs.CL", + "cs.AI", + "cs.LG" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2112.08025v2", + "title": "TLogic: Temporal Logical Rules for Explainable Link Forecasting on Temporal Knowledge Graphs", + "abstract": "Conventional static knowledge graphs model entities in relational data as\nnodes, connected by edges of specific relation types. However, information and\nknowledge evolve continuously, and temporal dynamics emerge, which are expected\nto influence future situations. In temporal knowledge graphs, time information\nis integrated into the graph by equipping each edge with a timestamp or a time\nrange. Embedding-based methods have been introduced for link prediction on\ntemporal knowledge graphs, but they mostly lack explainability and\ncomprehensible reasoning chains. Particularly, they are usually not designed to\ndeal with link forecasting -- event prediction involving future timestamps. We\naddress the task of link forecasting on temporal knowledge graphs and introduce\nTLogic, an explainable framework that is based on temporal logical rules\nextracted via temporal random walks. We compare TLogic with state-of-the-art\nbaselines on three benchmark datasets and show better overall performance while\nour method also provides explanations that preserve time consistency.\nFurthermore, in contrast to most state-of-the-art embedding-based methods,\nTLogic works well in the inductive setting where already learned rules are\ntransferred to related datasets with a common vocabulary.", + "authors": "Yushan Liu, Yunpu Ma, Marcel Hildebrandt, Mitchell Joblin, Volker Tresp", + "published": "2021-12-15", + "updated": "2022-03-09", + "primary_cat": "cs.LG", + "cats": [ + "cs.LG", + "cs.AI" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2202.09464v3", + "title": "Geometric Algebra based Embeddings for Static and Temporal Knowledge Graph Completion", + "abstract": "Recent years, Knowledge Graph Embeddings (KGEs) have shown promising\nperformance on link prediction tasks by mapping the entities and relations from\na Knowledge Graph (KG) into a geometric space and thus have gained increasing\nattentions. In addition, many recent Knowledge Graphs involve evolving data,\ne.g., the fact (\\textit{Obama}, \\textit{PresidentOf}, \\textit{USA}) is valid\nonly from 2009 to 2017. This introduces important challenges for knowledge\nrepresentation learning since such temporal KGs change over time. In this work,\nwe strive to move beyond the complex or hypercomplex space for KGE and propose\na novel geometric algebra based embedding approach, GeomE, which uses\nmultivector representations and the geometric product to model entities and\nrelations. GeomE subsumes several state-of-the-art KGE models and is able to\nmodel diverse relations patterns. On top of this, we extend GeomE to TGeomE for\ntemporal KGE, which performs 4th-order tensor factorization of a temporal KG\nand devises a new linear temporal regularization for time representation\nlearning. Moreover, we study the effect of time granularity on the performance\nof TGeomE models. Experimental results show that our proposed models achieve\nthe state-of-the-art performances on link prediction over four commonly-used\nstatic KG datasets and four well-established temporal KG datasets across\nvarious metrics.", + "authors": "Chengjin Xu, Mojtaba Nayyeri, Yung-Yu Chen, Jens Lehmann", + "published": "2022-02-18", + "updated": "2022-02-25", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2109.08970v1", + "title": "Temporal Knowledge Graph Completion using Box Embeddings", + "abstract": "Knowledge graph completion is the task of inferring missing facts based on\nexisting data in a knowledge graph. Temporal knowledge graph completion (TKGC)\nis an extension of this task to temporal knowledge graphs, where each fact is\nadditionally associated with a time stamp. Current approaches for TKGC\nprimarily build on existing embedding models which are developed for (static)\nknowledge graph completion, and extend these models to incorporate time, where\nthe idea is to learn latent representations for entities, relations, and\ntimestamps and then use the learned representations to predict missing facts at\nvarious time steps. In this paper, we propose BoxTE, a box embedding model for\nTKGC, building on the static knowledge graph embedding model BoxE. We show that\nBoxTE is fully expressive, and possesses strong inductive capacity in the\ntemporal setting. We then empirically evaluate our model and show that it\nachieves state-of-the-art results on several TKGC benchmarks.", + "authors": "Johannes Messner, Ralph Abboud, \u0130smail \u0130lkan Ceylan", + "published": "2021-09-18", + "updated": "2021-09-18", + "primary_cat": "cs.LG", + "cats": [ + "cs.LG", + "cs.AI" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2011.03984v2", + "title": "DyERNIE: Dynamic Evolution of Riemannian Manifold Embeddings for Temporal Knowledge Graph Completion", + "abstract": "There has recently been increasing interest in learning representations of\ntemporal knowledge graphs (KGs), which record the dynamic relationships between\nentities over time. Temporal KGs often exhibit multiple simultaneous\nnon-Euclidean structures, such as hierarchical and cyclic structures. However,\nexisting embedding approaches for temporal KGs typically learn entity\nrepresentations and their dynamic evolution in the Euclidean space, which might\nnot capture such intrinsic structures very well. To this end, we propose Dy-\nERNIE, a non-Euclidean embedding approach that learns evolving entity\nrepresentations in a product of Riemannian manifolds, where the composed spaces\nare estimated from the sectional curvatures of underlying data. Product\nmanifolds enable our approach to better reflect a wide variety of geometric\nstructures on temporal KGs. Besides, to capture the evolutionary dynamics of\ntemporal KGs, we let the entity representations evolve according to a velocity\nvector defined in the tangent space at each timestamp. We analyze in detail the\ncontribution of geometric spaces to representation learning of temporal KGs and\nevaluate our model on temporal knowledge graph completion tasks. Extensive\nexperiments on three real-world datasets demonstrate significantly improved\nperformance, indicating that the dynamics of multi-relational graph data can be\nmore properly modeled by the evolution of embeddings on Riemannian manifolds.", + "authors": "Zhen Han, Yunpu Ma, Peng Chen, Volker Tresp", + "published": "2020-11-08", + "updated": "2020-12-02", + "primary_cat": "cs.LG", + "cats": [ + "cs.LG", + "cs.AI", + "cs.CL" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/1909.03193v2", + "title": "KG-BERT: BERT for Knowledge Graph Completion", + "abstract": "Knowledge graphs are important resources for many artificial intelligence\ntasks but often suffer from incompleteness. In this work, we propose to use\npre-trained language models for knowledge graph completion. We treat triples in\nknowledge graphs as textual sequences and propose a novel framework named\nKnowledge Graph Bidirectional Encoder Representations from Transformer\n(KG-BERT) to model these triples. Our method takes entity and relation\ndescriptions of a triple as input and computes scoring function of the triple\nwith the KG-BERT language model. Experimental results on multiple benchmark\nknowledge graphs show that our method can achieve state-of-the-art performance\nin triple classification, link prediction and relation prediction tasks.", + "authors": "Liang Yao, Chengsheng Mao, Yuan Luo", + "published": "2019-09-07", + "updated": "2019-09-11", + "primary_cat": "cs.CL", + "cats": [ + "cs.CL", + "cs.AI" + ], + "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/2205.02357v5", + "title": "Hybrid Transformer with Multi-level Fusion for Multimodal Knowledge Graph Completion", + "abstract": "Multimodal Knowledge Graphs (MKGs), which organize visual-text factual\nknowledge, have recently been successfully applied to tasks such as information\nretrieval, question answering, and recommendation system. Since most MKGs are\nfar from complete, extensive knowledge graph completion studies have been\nproposed focusing on the multimodal entity, relation extraction and link\nprediction. However, different tasks and modalities require changes to the\nmodel architecture, and not all images/objects are relevant to text input,\nwhich hinders the applicability to diverse real-world scenarios. In this paper,\nwe propose a hybrid transformer with multi-level fusion to address those\nissues. Specifically, we leverage a hybrid transformer architecture with\nunified input-output for diverse multimodal knowledge graph completion tasks.\nMoreover, we propose multi-level fusion, which integrates visual and text\nrepresentation via coarse-grained prefix-guided interaction and fine-grained\ncorrelation-aware fusion modules. We conduct extensive experiments to validate\nthat our MKGformer can obtain SOTA performance on four datasets of multimodal\nlink prediction, multimodal RE, and multimodal NER. Code is available in\nhttps://github.com/zjunlp/MKGformer.", + "authors": "Xiang Chen, Ningyu Zhang, Lei Li, Shumin Deng, Chuanqi Tan, Changliang Xu, Fei Huang, Luo Si, Huajun Chen", + "published": "2022-05-04", + "updated": "2023-09-18", + "primary_cat": "cs.CL", + "cats": [ + "cs.CL", + "cs.AI", + "cs.CV", + "cs.LG", + "cs.MM" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2304.03984v1", + "title": "DREAM: Adaptive Reinforcement Learning based on Attention Mechanism for Temporal Knowledge Graph Reasoning", + "abstract": "Temporal knowledge graphs (TKGs) model the temporal evolution of events and\nhave recently attracted increasing attention. Since TKGs are intrinsically\nincomplete, it is necessary to reason out missing elements. Although existing\nTKG reasoning methods have the ability to predict missing future events, they\nfail to generate explicit reasoning paths and lack explainability. As\nreinforcement learning (RL) for multi-hop reasoning on traditional knowledge\ngraphs starts showing superior explainability and performance in recent\nadvances, it has opened up opportunities for exploring RL techniques on TKG\nreasoning. However, the performance of RL-based TKG reasoning methods is\nlimited due to: (1) lack of ability to capture temporal evolution and semantic\ndependence jointly; (2) excessive reliance on manually designed rewards. To\novercome these challenges, we propose an adaptive reinforcement learning model\nbased on attention mechanism (DREAM) to predict missing elements in the future.\nSpecifically, the model contains two components: (1) a multi-faceted attention\nrepresentation learning method that captures semantic dependence and temporal\nevolution jointly; (2) an adaptive RL framework that conducts multi-hop\nreasoning by adaptively learning the reward functions. Experimental results\ndemonstrate DREAM outperforms state-of-the-art models on public dataset", + "authors": "Shangfei Zheng, Hongzhi Yin, Tong Chen, Quoc Viet Hung Nguyen, Wei Chen, Lei Zhao", + "published": "2023-04-08", + "updated": "2023-04-08", + "primary_cat": "cs.AI", + "cats": [ + "cs.AI", + "cs.IR" + ], + "label": "Related Work" + }, + { + "url": "http://arxiv.org/abs/2210.08654v1", + "title": "Learning to Sample and Aggregate: Few-shot Reasoning over Temporal Knowledge Graphs", + "abstract": "In this paper, we investigate a realistic but underexplored problem, called\nfew-shot temporal knowledge graph reasoning, that aims to predict future facts\nfor newly emerging entities based on extremely limited observations in evolving\ngraphs. It offers practical value in applications that need to derive instant\nnew knowledge about new entities in temporal knowledge graphs (TKGs) with\nminimal supervision. The challenges mainly come from the few-shot and time\nshift properties of new entities. First, the limited observations associated\nwith them are insufficient for training a model from scratch. Second, the\npotentially dynamic distributions from the initially observable facts to the\nfuture facts ask for explicitly modeling the evolving characteristics of new\nentities. We correspondingly propose a novel Meta Temporal Knowledge Graph\nReasoning (MetaTKGR) framework. Unlike prior work that relies on rigid\nneighborhood aggregation schemes to enhance low-data entity representation,\nMetaTKGR dynamically adjusts the strategies of sampling and aggregating\nneighbors from recent facts for new entities, through temporally supervised\nsignals on future facts as instant feedback. Besides, such a meta temporal\nreasoning procedure goes beyond existing meta-learning paradigms on static\nknowledge graphs that fail to handle temporal adaptation with large entity\nvariance. We further provide a theoretical analysis and propose a temporal\nadaptation regularizer to stabilize the meta temporal reasoning over time.\nEmpirically, extensive experiments on three real-world TKGs demonstrate the\nsuperiority of MetaTKGR over state-of-the-art baselines by a large margin.", + "authors": "Ruijie Wang, Zheng Li, Dachun Sun, Shengzhong Liu, Jinning Li, Bing Yin, Tarek Abdelzaher", + "published": "2022-10-16", + "updated": "2022-10-16", + "primary_cat": "cs.LG", + "cats": [ + "cs.LG", + "cs.AI", + "cs.CL" + ], + "label": "Related Work" + }, + { + "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/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/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/2307.00518v1", + "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/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/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/1602.06411v1", + "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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/2401.02563v1", + "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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/2304.09791v2", + "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/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/2209.09677v1", + "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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/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/2012.08909v2", + "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/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/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/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 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/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/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/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" + } +] \ No newline at end of file