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Capturing structural similarity has been a hot topic in the field of network embedding (NE) recently due to its great help in understanding node functions and behaviors. However, existing works have paid very much attention to learning structures on homogeneous networks, while the related study on heterogeneous networks is still void. In this article, we try to take the first step for representation learning on heterostructures, which is very challenging due to their highly diverse combinations of node types and underlying structures. To effectively distinguish diverse heterostructures, we first propose a theoretically guaranteed technique called heterogeneous anonymous walk (HAW) and give two more applicable variants. Then, we devise the HAW embedding (HAWE) and its variants in a data-driven manner to circumvent using an extremely large number of possible walks and train embeddings by predicting occurring walks in the neighborhood of each node. Finally, we design and apply extensive and illustrative experiments on synthetic and real-world networks to build a benchmark on heterostructure learning and evaluate the effectiveness of our methods. The results demonstrate our methods achieve outstanding performance compared with both homogeneous and heterogeneous classic methods and can be applied on large-scale networks.

A variety of methods have been proposed for modeling and mining dynamic complex networks, in which the topological structure varies with time. As the most popular and successful network model, the stochastic block model (SBM) has been extended and applied to community detection, link prediction, anomaly detection, and evolution analysis of dynamic networks. However, all current models based on the SBM for modeling dynamic networks are designed at the community level, assuming that nodes in each community have the same dynamic behavior, which usually results in poor performance on temporal community detection and loses the modeling of node abnormal behavior. To solve the above-mentioned problem, this article proposes a hierarchical Bayesian dynamic SBM (HB-DSBM) for modeling the node-level and community-level dynamic behavior in a dynamic network synchronously. Based on the SBM, we introduce a hierarchical Dirichlet generative mechanism to associate the global community evolution with the microscopic transition behavior of nodes near-perfectly and generate the observed links across the dynamic networks. Meanwhile, an effective variational inference algorithm is developed and we can easy to infer the communities and dynamic behaviors of the nodes. Furthermore, with the two-level evolution behaviors, it can identify nodes or communities with abnormal behavior. Experiments on simulated and real-world networks demonstrate that HB-DSBM has achieved state-of-the-art performance on community detection and evolution. In addition, abnormal evolutionary behavior and events on dynamic networks can be effectively identified by our model.