SIGMA: A Structural Inconsistency Reducing Graph Matching Algorithm

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.