  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
edge-independent vertex weights (EIVWs), without considering hypergraphs with
edge-dependent vertex weights (EDVWs) that have more modeling power. To
compensate for this, we present General Hypergraph Spectral Convolution (GHSC),
a general learning framework that not only handles 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, and protein learning demonstrate the
state-of-the-art performance of the proposed framework.
