  Mixed membership community detection is a challenging problem. In this paper,
to detect mixed memberships, we propose a new method Mixed-SLIM which is a
spectral clustering method on the symmetrized Laplacian inverse matrix under
the degree-corrected mixed membership model. We provide theoretical bounds for
the estimation error on the proposed algorithm and its regularized version
under mild conditions. Meanwhile, we provide some extensions of the proposed
method to deal with large networks in practice. These Mixed-SLIM methods
outperform state-of-art methods in simulations and substantial empirical
datasets for both community detection and mixed membership community detection
problems.
