  Community detection has been well studied in network analysis, and one
popular technique is spectral clustering which is fast and statistically
analyzable for detect-ing 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 {\tau} are asymptotically consistent under mild conditions.
Meanwhile, we provide Mixed-SLIM appro and its regularized version Mixed-SLIM
{\tau}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.

Machine Learning;Machine Learning