Multi-scale Wasserstein Shortest-path Filtration Kernels on Graphs

The traditional shortest-path graph kernel (SP) is one of the most popular graph kernels. It decomposes graphs into shortest paths and computes their frequencies in each graph. However, SP has two main challenges: Firstly, the triplet representation of the shortest path loses information. Secondly, SP compares graphs without considering the multiple different scales of the graph structure which is common in real-world graphs, e.g., the chain-, ring-, and star-structures in social networks. To overcome these two challenges, we develop a novel shortest-path graph kernel called the Multi-scale Wasserstein Shortest-Path Filtration graph kernel (MWSPF). It uses a BFS tree of a certain depth rooted at each vertex to restrict the maximum length of the shortest path considering the small world property. It considers the labels of all the vertices in the shortest path. To facilitate the comparison of graphs at multiple different scales, it augments graphs from both the aspects of the vertex and the graph structure. The distribution (frequency) of the shortest path changes across augmented graphs and the Wasserstein distance is employed to track the changes. We conduct experiments on various benchmark graph datasets to evaluate MWSPF's performance. MWSPF is superior to the state-of-the-art on most datasets.