[Paper Review] Subgraph Matching Kernels for Attributed Graphs

Nils M. Kriege, Petra Mutzel|arXiv (Cornell University)|Jun 27, 2012

Advanced Graph Neural Networks19 references139 citations

TL;DR

This paper introduces subgraph matching kernels for attributed graphs, leveraging structure-preserving bijections between subgraphs and a flexible scoring scheme that compares vertex and edge attributes using kernel functions. The method generalizes existing graph kernels and achieves strong performance on real-world graph classification tasks via a clique-based algorithm on graph products, outperforming prior approaches on benchmark datasets.

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.

Motivation & Objective

• To address the limitation of existing graph kernels that cannot effectively handle attributed graphs with rich node and edge features.
• To develop a kernel method that captures structural and attribute similarities in graphs through subgraph matchings.
• To generalize known graph kernels by incorporating flexible attribute comparison via kernel functions.
• To design an efficient algorithm for computing the kernel using graph product and clique detection.
• To empirically validate the approach on real-world graph classification tasks.

Proposed method

• Proposes a subgraph matching kernel based on structure-preserving bijections between subgraphs of two attributed graphs.
• Introduces a scoring scheme that compares vertex and edge attributes using kernel functions, enabling flexible similarity measurement.
• Maps the subgraph matching problem to finding cliques in the product graph of two input graphs, leveraging a classical result by Levi (1973).
• Employs a graph-theoretical algorithm to compute the kernel efficiently by enumerating maximal cliques in the product graph.
• Uses a weighted kernel formulation where scores are aggregated over all valid subgraph matchings, weighted by attribute similarity.
• Applies the kernel in a kernelized learning framework for graph classification tasks.

Experimental results

Research questions

• RQ1 Can subgraph matching kernels effectively capture both structural and attribute similarities in attributed graphs?
• RQ2 How does the proposed kernel compare to existing common subgraph-based kernels in terms of performance on attributed graphs?
• RQ3 Can the subgraph matching kernel be efficiently computed using graph product and clique detection techniques?
• RQ4 Does the flexible attribute scoring scheme improve classification accuracy on real-world attributed graph datasets?
• RQ5 To what extent does the kernel generalize known graph kernel methods?

Key findings

• The proposed subgraph matching kernel achieves state-of-the-art performance on real-world attributed graph classification benchmarks.
• The method successfully generalizes several known graph kernels by incorporating attribute similarity through kernel functions.
• The algorithm based on graph product and clique detection enables efficient computation of the kernel, despite the NP-hard nature of subgraph isomorphism.
• The flexible scoring scheme for attributes significantly improves classification accuracy compared to methods that ignore attribute information.
• Empirical results on benchmark datasets demonstrate consistent improvements over prior approaches, especially in capturing complex attribute interactions.
• The kernel is robust across diverse real-world graph structures and attribute types, validating its generalization capability.