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Title: Community detection for hypergraph networks via regularized tensor power iteration Authors:  Dong Xia - Hong Kong University of Science and Technology (Hong Kong) [presenting]
Abstract: To date, social network analysis has been largely focused on pairwise interactions. The study of higher-order interactions, via a hypergraph network, brings in new insights. We study community detection in a hypergraph network. We propose a new method for community detection that operates directly on the hypergraph. At the heart of our method is a regularized higher-order orthogonal iteration (reg-HOOI) algorithm that computes an approximate low-rank decomposition of the network adjacency tensor. Compared with existing tensor decomposition methods such as HOSVD and vanilla HOOI, reg-HOOI yields better performance, especially when the hypergraph is sparse. Given the output of tensor decomposition, we then generalize the community detection method SCORE from graph networks to hypergraph networks. We call our new method Tensor-SCORE. In theory, we introduce a degree-corrected block model for hypergraphs (hDCBM), and show that Tensor-SCORE yields consistent community detection for a wide range of network sparsity and degree heterogeneity. We apply our method to several real hypergraph networks which yield encouraging results. It suggests that exploring higher-order interactions provides additional information not seen in graph representations.