HyperGCN: A New Method For Training Graph Convolutional Networks on Hypergraphs

In many real-world networks such as co-authorship, co-citation, etc., relationships are complex and go beyond pairwise associations. Hypergraphs provide a flexible and natural modeling tool to model such complex relationships. The obvious existence of such complex relationships in many real-world networks naturally motivates the problem of learning with hypergraphs. A popular learning paradigm is hypergraph-based semi-supervised learning (SSL) where the goal is to assign labels to initially unlabelled vertices in a hypergraph. Motivated by the fact that a graph convolutional network (GCN) has been effective for graph-based SSL, we propose HyperGCN, a novel way of training a GCN for SSL on hypergraphs based on tools from sepctral theory of hypergraphs. We demonstrate HyperGCN's effectiveness through detailed experimentation on real-world hypergraphs for SSL and combinatorial optimisation and analyse when it is going to be more effective than state-of-the art baselines. We have made the source code available.