Estimating Mixed-Memberships Using the Symmetric Laplacian Inverse Matrix

TL;DR

This paper introduces Mixed-SLIM, a spectral clustering method based on the symmetrized Laplacian inverse matrix, for improved mixed membership community detection with theoretical error bounds and practical extensions.

Contribution

It proposes a novel spectral clustering approach, Mixed-SLIM, with theoretical guarantees and practical extensions for large networks, advancing mixed membership community detection.

Findings

Mixed-SLIM outperforms state-of-the-art methods in simulations.

Theoretical bounds for estimation error are established.

Effective for both community detection and mixed membership problems.

Abstract

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.