Community Detection in General Hypergraph Via Graph Embedding

• 成果类型: Article
• 署名作者: Zhen, Yaoming; Wang, Junhui
• 署名单位: City University of Hong Kong
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2002157
• 发表日期: 2023
• 页码: 1620-1629
• 关键词: Consistency; networks; tensor; DECOMPOSITION

摘要

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.