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.
翻译:常规网络数据主要侧重于两个实体之间的对称互动,但在实际存在的高射线网络中经常观察到多个实体之间的多路互动。在本条中,我们提出了在一般高射线网络中探测社区结构的新颖方法,无论是统一还是非统一。拟议方法引入了无效的顶点,将非统一的高射线放大为统一的多高射线,然后将多高射线嵌入一个低维矢量空间,使同一社区内的脊椎相互接近。由此产生的优化任务可以通过替代更新计划有效解决。拟议方法的零点构成在社区探测和高射线估计方面都得到了一些合成和实时高射线网络的数字实验的支持。