Community Detection in General Hypergraph via Graph Embedding
This addresses the problem of identifying communities in hypergraph networks for researchers and practitioners dealing with complex relational data, representing an incremental improvement over existing methods.
The authors tackled community detection in hypergraph networks with multi-way interactions by proposing a method that augments non-uniform hypergraphs into uniform ones and embeds them in low-dimensional space, achieving asymptotic consistency in both community detection and hypergraph estimation as supported by numerical experiments.
Conventional network data has largely focused on pairwise interactions between two entities, yet multi-way interactions among multiple entities have been frequently observed in real-life hypergraph networks. In this article, we propose a novel method for detecting community structure in general hypergraph networks, uniform or non-uniform. The proposed method introduces a null vertex to augment a non-uniform hypergraph into a uniform multi-hypergraph, and then embeds the multi-hypergraph in a low-dimensional vector space such that vertices within the same community are close to each other. The resultant optimization task can be efficiently tackled by an alternative updating scheme. The asymptotic consistencies of the proposed method are established in terms of both community detection and hypergraph estimation, which are also supported by numerical experiments on some synthetic and real-life hypergraph networks.