A structure similarity based adaptive sampling method for time-dependent graph embedding

Time-dependent graphs have been well researched in a wealth of fields, such as road network, bioinformatics network. Unlike in static graphs, relations among nodes will change by time in time-dependent graphs, which causes some for such special properties as temporal reachability and node dynamic local structure. And, for different kinds of time-dependent graphs, activity frequency of nodes may be greatly different. These properties should be taken into consideration while embedding nodes in time-dependent graphs into vectors for further research. So, in this work, we study the problem of time-dependent graph embedding and propose a structure similarity based adaptive sampling method, called ATDGEB (Adaptive Time-Dependent Graph Embedding), which aims to encode different kinds of time-dependent graph nodes into vectors based on node's local structure and their special properties. Specifically, we first design a new method based on node's local structure to compute visit probability between nodes, and then propose an adaptive clustering method for solving the problem that nodes’ active frequency is greatly different in different types of time-dependent graph. Meanwhile to get the walk paths as soon as possible, we design a novel walk strategy to get node's walk paths. The sampled nodes in walk process will be stored in bidirectional multi-tree. Once the walk process is finished, we can get node's walk path by reversely travelling​ the multi-tree from leaf nodes in the tree. Sufficient experiments conducted on real datasets demonstrate that our method outperforms the existing embedding methods with respect to node clustering, reachability prediction, and link prediction.