  Representation learning on networks offers a powerful alternative to the oft
painstaking process of manual feature engineering, and as a result, has enjoyed
considerable success in recent years. However, all the existing representation
learning methods are based on the first-order network (FON), that is, the
network that only captures the pairwise interactions between the nodes. As a
result, these methods may fail to incorporate non-Markovian higher-order
dependencies in the network. Thus, the embeddings that are generated may not
accurately represent of the underlying phenomena in a network, resulting in
inferior performance in different inductive or transductive learning tasks. To
address this challenge, this paper presents HONEM, a higher-order network
embedding method that captures the non-Markovian higher-order dependencies in a
network. HONEM is specifically designed for the higher-order network structure
(HON) and outperforms other state-of-the-art methods in node classification,
network re-construction, link prediction, and visualization for networks that
contain non-Markovian higher-order dependencies.
