Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration

TL;DR

This paper introduces a novel tensor-based community detection method for hypergraph networks that preserves higher-order interactions, outperforming traditional projection-based approaches, especially in sparse networks.

Contribution

It proposes the reg-HOOI algorithm for tensor decomposition and extends the SCORE method to hypergraphs, providing theoretical guarantees and practical improvements.

Findings

reg-HOOI outperforms HOSVD and vanilla HOOI in sparse hypergraphs

Tensor-SCORE achieves consistent community detection under the hypergraph degree-corrected block model

Application to real hypergraph data shows higher-order interactions add valuable information

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. A popular approach is to project the hypergraph to a graph and then apply community detection methods for graph networks, but we show that this approach may cause unwanted information loss. 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 (Jin, 2015) 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. As a byproduct, we derive the rates of convergence on estimating the principal subspace by reg-HOOI, with different initializations, including the two new initialization methods we propose, a diagonal-removed HOSVD and a randomized graph projection. We apply our method to several real hypergraph networks which yields encouraging results. It suggests that exploring higher-order interactions provides additional information not seen in graph representations.