Estimating network memberships by mixed regularized spectral clustering

Mixed membership community detection is a challenge problem in network analysis. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for short) to estimate the memberships. Mixed-RSC is an extension of the RSC method (Qin and Rohe, 2013) to deal with the mixed membership community detection problem. We show that the algorithm is asymptotically consistent under mild conditions. The approach is successfully applied to a small scale of simulations and substantial empirical networks with encouraging results compared to a number of benchmark methods.