Estimating mixed-memberships using the Symmetric Laplacian Inverse Matrix

Abstract

Community detection has been well studied in network analysis, and one popular technique is spectral clustering which is fast and statistically analyzable for detecting clusters for given networks. But the more realistic case of mixed membership community detection remains a challenge. In this paper, we propose a new spectral clustering method Mixed-SLIM for mixed membership community detection. Mixed-SLIM is designed based on the symmetrized Laplacian inverse matrix (SLIM) (Jing et al. 2021) under the degree-corrected mixed membership (DCMM) model. We show that this algorithm and its regularized version Mixed-SLIM τ are asymptotically consistent under mild conditions. Meanwhile, we provide Mixed-SLIM appro and its regularized version Mixed-SLIM τ appro by approximating the SLIM matrix when dealing with large networks in practice. These four Mixed-SLIM methods outperform state-of-art methods in simulations and substantial empirical datasets for both community detection and mixed membership community detection problems.