Multi-scale Wasserstein Shortest-path Graph Kernels for Graph Classification

TL;DR

This paper introduces MWSP, a novel multi-scale Wasserstein shortest-path graph kernel that effectively compares graphs at multiple scales and considers substructure distributions, achieving state-of-the-art results.

Contribution

The paper proposes MWSP, a new graph kernel combining multi-scale shortest-path features with Wasserstein distance to improve graph comparison performance.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Effectively captures multi-scale graph structures.

Considers distributions of shortest paths in similarity computation.

Abstract

Graph kernels are conventional methods for computing graph similarities. However, the existing R-convolution graph kernels cannot resolve both of the two challenges: 1) Comparing graphs at multiple different scales, and 2) Considering the distributions of substructures when computing the kernel matrix. These two challenges limit their performances. To mitigate both of the two challenges, we propose a novel graph kernel called the Multi-scale Wasserstein Shortest-Path graph kernel (MWSP), at the heart of which is the multi-scale shortest-path node feature map, of which each element denotes the number of occurrences of the shortest path around a node. The shortest path is represented by the concatenation of all the labels of nodes in it. Since the shortest-path node feature map can only compare graphs at local scales, we incorporate into it the multiple different scales of the graph structure, which are captured by the truncated BFS trees of different depths rooted at each node in a graph. We use the Wasserstein distance to compute the similarity between the multi-scale shortest-path node feature maps of two graphs, considering the distributions of shortest paths. We empirically validate MWSP on various benchmark graph datasets and demonstrate that it achieves state-of-the-art performance on most datasets.