Regularized Projection Matrix Approximation with Applications to Community Detection

TL;DR

This paper presents a novel regularized projection matrix approximation framework that improves community detection by incorporating penalty functions and optimizing on the Stiefel manifold, with proven convergence and superior clustering results.

Contribution

It introduces a new regularized projection matrix approximation method with tailored penalties, optimization on the Stiefel manifold, and theoretical convergence analysis, advancing community detection techniques.

Findings

Outperforms existing methods in clustering accuracy

Convergence of ADMM is theoretically established

Effective on both synthetic and real-world datasets

Abstract

This paper introduces a regularized projection matrix approximation framework designed to recover cluster information from the affinity matrix. The model is formulated as a projection approximation problem, incorporating an entry-wise penalty function. We investigate three distinct penalty functions, each specifically tailored to address bounded, positive, and sparse scenarios. To solve this problem, we propose direct optimization on the Stiefel manifold, utilizing the Cayley transformation along with the Alternating Direction Method of Multipliers (ADMM) algorithm. Additionally, we provide a theoretical analysis that establishes the convergence properties of ADMM, demonstrating that the convergence point satisfies the KKT conditions of the original problem. Numerical experiments conducted on both synthetic and real-world datasets reveal that our regularized projection matrix approximation approach significantly outperforms state-of-the-art methods in clustering performance.