Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective

TL;DR

This paper introduces a flexible symmetric matrix factorization approach that relaxes nonnegativity constraints and incorporates regularization to enhance clustering performance, offering a more general framework for various constraints.

Contribution

It proposes a novel, efficient symmetric matrix factorization algorithm with regularization and a general framework for different factor matrix constraints, improving clustering outcomes.

Findings

Enhanced clustering performance with the new regularized factorization method.

Flexible framework accommodating various constraints on factor matrices.

Efficient algorithm applicable to symmetric matrix factorization tasks.

Abstract

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the similarity between data points. Most existing symmetric NMF algorithms require factor matrices to be nonnegative, and only focus on minimizing the gap between similarity matrix and its approximation for clustering, without giving a consideration to other potential regularization terms which can yield better clustering. In this paper, we explore factorizing a symmetric matrix that does not have to be nonnegative, presenting an efficient factorization algorithm with a regularization term to boost the clustering performance. Moreover, a more general framework is proposed to solve symmetric matrix factorization problems with different constraints on the factor matrices.