DeepNM: Incremental Graph Matching Based on Sinkhorn Similarity

Yikuan Xia, Jiazun Chen, Xinchi Li, Jun Gao

Abstract: Graph matching is a critical task with diverse real-world applications. Current cutting-edge methodologies incorporate GNN (Graph Neural Network) combined with incremental anchor refinement, calculating the matching similarity directly via node embeddings. However, the direct similarity computation based on aggregated embeddings from GNN may obscure the distinctiveness of nodes within a localized region. In addition, the possible wrongly added anchor pairs in the iterations and the lack of capturing the relationships to anchors may further affect the performance. In order to tackle these challenges, this paper proposes a method named DeepNM, which attempts to find node matching based on their neighbors’ similarities. Specifically, DeepNM introduces a Sinkhorn-based similarity on a node’s neighborhood’s embeddings, which serves as both a training loss and a matching metric tailored to the graph matching problem. Additionally, we demonstrate that the Sinkhorn-based similarity, which relies on common neighbor statistics, is highly resilient to inaccurately identified anchor pairs within the context of incremental graph matching. Our comprehensive experiments on synthetic and real-world datasets demonstrate that DeepNM, compatible with the incremental graph matching paradigm, excels particularly well at matching graphs where common neighbors provide good matches. Applying the DeepNM pipeline to real social networks results in a 6% improvement, and applying the Sinkhorn similarity on knowledge graphs results in an average improvement of 1.7% over the best baseline.

External IDs:dblp:journals/tkde/XiaCLG25