Hypergraph Learning for Unsupervised Graph Alignment via Optimal Transport

Unsupervised graph alignment aims to find corresponding nodes across different graphs without supervision. Existing methods usually leverage the graph structure to aggregate features of nodes to find relations between nodes. However, the graph structure is inherently limited in pairwise relations between nodes without considering higher-order dependencies among multiple nodes. In this paper, we take advantage of the hypergraph structure to characterize higher-order structural information among nodes for better graph alignment. Specifically, we propose an optimal transport model to learn a hypergraph to capture complex relations among nodes, so that the nodes involved in one hyperedge can be adaptively based on local geometric information. In addition, inspired by the Dirichlet energy function of a hypergraph, we further refine our model to enhance the consistency between structural and feature information in each hyperedge. After that, we jointly leverage graphs and hypergraphs to extract structural and feature information to better model the relations between nodes, which is used to find node correspondences across graphs. We conduct experiments on several benchmark datasets with different settings, and the results demonstrate the effectiveness of our proposed method.