SIGMA: A Structural Inconsistency Reducing Graph Matching Algorithm

TL;DR

This paper introduces SIGMA, a graph matching algorithm that reduces structural inconsistency using heat diffusion wavelets, improving node alignment accuracy based solely on network topology.

Contribution

The paper proposes a novel structural inconsistency criterion and a graph matching algorithm that leverages heat diffusion wavelets to enhance accuracy without side information.

Findings

SIGMA outperforms state-of-the-art graph matching methods.

It effectively reduces structural inconsistency in node correspondences.

The approach is validated through extensive experiments.

Abstract

Graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. When graph side information is not available, the node correspondence is estimated on the sole basis of network topologies. In this paper, we propose a novel criterion to measure the graph matching accuracy, structural inconsistency (SI), which is defined based on the network topological structure. Specifically, SI incorporates the heat diffusion wavelet to accommodate the multi-hop structure of the graphs. Based on SI, we propose a Structural Inconsistency reducing Graph Matching Algorithm (SIGMA), which improves the alignment scores of node pairs that have low SI values in each iteration. Under suitable assumptions, SIGMA can reduce SI values of true counterparts. Furthermore, we demonstrate that SIGMA can be derived by using a mirror descent method to solve the Gromov-Wasserstein distance with a novel K-hop-structure-based matching costs. Extensive experiments show that our method outperforms state-of-the-art methods.