Optimal Noise Reduction in Dense Mixed-Membership Stochastic Block Models under Diverging Spiked Eigenvalues Condition
This work addresses the challenge of reconstructing community relations in networks with overlapping memberships, which is incremental as it builds on existing MMSB frameworks.
The paper tackles the problem of overlapping community detection in networks by establishing the minimax lower bound on estimation error for the Mixed-Membership Stochastic Block Model and proposing a new estimator that achieves this bound, with theoretical results validated through experiments.
Community detection is one of the most critical problems in modern network science. Its applications can be found in various fields, from protein modeling to social network analysis. Recently, many papers appeared studying the problem of overlapping community detection, where each node of a network may belong to several communities. In this work, we consider Mixed-Membership Stochastic Block Model (MMSB) first proposed by Airoldi et al. MMSB provides quite a general setting for modeling overlapping community structure in graphs. The central question of this paper is to reconstruct relations between communities given an observed network. We compare different approaches and establish the minimax lower bound on the estimation error. Then, we propose a new estimator that matches this lower bound. Theoretical results are proved under fairly general conditions on the considered model. Finally, we illustrate the theory in a series of experiments.