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Multi-scale Wasserstein Shortest-path Filtration Kernels on Graphs. (arXiv:2206.00979v3 [cs.LG] UPDATED)

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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.

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