Subgraph Matching Kernels for Attributed Graphs

TL;DR

This paper introduces subgraph matching kernels for attributed graphs, enabling flexible scoring of subgraph mappings and generalizing existing kernels, with an efficient algorithm and promising experimental results.

Contribution

It presents a novel graph kernel based on subgraph matchings that handles attributed graphs and generalizes previous kernels with an efficient computation method.

Findings

Effective classification results on real-world attributed graphs

The kernel generalizes several known graph kernels

The proposed algorithm is computationally feasible

Abstract

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by a flexible scoring scheme comparing vertex and edge attributes by kernels. We show that subgraph matching kernels generalize several known kernels. To compute the kernel we propose a graph-theoretical algorithm inspired by a classical relation between common subgraphs of two graphs and cliques in their product graph observed by Levi (1973). Encouraging experimental results on a classification task of real-world graphs are presented.