Community Detection in General Hypergraph Via Graph Embedding
提出一种新方法，通过引入空顶点将非均匀超图转化为均匀多超图，再嵌入低维向量空间来检测社区结构，适用于均匀和非均匀超图网络。
Conventional network data have 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 nonuniform 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. Supplementary materials for this article are available online.