Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs

As a powerful tool for modeling complex relationships, hypergraphs are gaining popularity from the graph learning community. However, commonly used frameworks in deep hypergraph learning focus on hypergraphs with \textit{edge-independent vertex weights}(EIVWs), without considering hypergraphs with \textit{edge-dependent vertex weights} (EDVWs) that have more modeling power. To compensate for this, in this paper, we present General Hypergraph Spectral Convolution(GHSC), a general learning framework that not only can handle EDVW and EIVW hypergraphs, but more importantly, enables theoretically explicitly utilizing the existing powerful Graph Convolutional Neural Networks (GCNNs) such that largely ease the design of Hypergraph Neural Networks. In this framework, the graph Laplacian of the given undirected GCNNs is replaced with a unified hypergraph Laplacian that incorporates vertex weight information from a random walk perspective by equating our defined generalized hypergraphs with simple undirected graphs. Extensive experiments from various domains including social network analysis, visual objective classification, protein learning demonstrate that the proposed framework can achieve state-of-the-art performance.