Unsupervised Alignment of Hypergraphs with Different Scales

Abstract

People usually interact in groups, and such groups may appear on different platforms. For instance, people often create various group chats on messaging apps (e.g., Facebook Messenger and WhatsApp) to communicate with families, friends, or colleagues. How do we identify the same people across the two platforms based on the information about the groups? This gives rise to the hypergraph alignment problem, whose objective is to find the correspondences between the sets of nodes of two hypergraphs. In a hypergraph, a node represents a person, and each hyperedge represents a group of several people. In addition, the two sets of hyperedges in the two hypergraphs can vary significantly in scales as people may use different apps at different time periods. In this work, we propose and tackle the problem of unsupervised hypergraph alignment. Given two hypergraphs with potentially different scales and without any side information or prior ground-truth correspondences, we develop HyperAlign, a learning framework, to find node correspondences across the two hypergraphs. HyperAlign directly addresses each challenge of the problem. In particular, it (a) extracts node features from the hypergraph topology, (b) employs contrastive learning, as a "supervised pseudo-alignment'' task to pre-train the learning model (c) applies topological augmentation to help a generative adversarial network to align the two embedding spaces from the two hypergraphs. The purpose of augmentation is to add virtual hyperedges from one hypergraph in order to the other to resolve the scale difference and share information across the two hypergraphs. Our extensive experiments on 12 real-world datasets demonstrate the significant and consistent superiority of HyperAlign over the baseline approaches.