Adaptive Expansion for Hypergraph Learning

Hypergraph, with its powerful ability to capture higher-order relationships, has gained significant attention recently. Consequently, many hypergraph representation learning methods have emerged to model the complex relationships among hypergraphs. In general, these methods leverage classic expansion methods to convert hypergraphs into weighted or bipartite graphs, and further employ message passing mechanisms to model the complex structures within hypergraphs. However, classical expansion methods are designed in straightforward manners with fixed edge weights, resulting in information loss or redundancy. In light of this, we design a novel clique expansion-based Adaptive Expansion method called AdE to adaptively expand hypergraphs into weighted graphs that preserve the higher-order structure information. Specifically, we introduce a novel Global Simulation Network to select two representative nodes for adaptively symbolizing each hyperedge and connect the rest of the nodes within the same hyperedge to the corresponding selected nodes. Afterward, we design a distance-aware kernel function, dynamically adjusting edge weights to ensure similar nodes within a hyperedge are connected with larger weights. Extensive theoretical justifications and empirical experiments over seven benchmark hypergraph datasets demonstrate that AdE has excellent rationality, generalization, and effectiveness compared to classic expansion models.