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.

翻译：混合成员社区检测是一个具有挑战性的问题。本文针对混合成员检测，提出了一种新方法Mixed-SLIM，该方法是在度修正混合成员模型下，对对称拉普拉斯逆矩阵进行谱聚类。我们在温和条件下，为所提算法及其正则化版本的估计误差提供了理论界。同时，我们给出了所提方法的一些扩展，以处理实际中的大规模网络。在社区检测和混合成员社区检测问题的模拟实验和大量经验数据集上，这些Mixed-SLIM方法均优于现有最先进方法。