Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization

TL;DR

This paper introduces efficient coordinate descent algorithms for symmetric nonnegative matrix factorization, enabling scalable clustering and data analysis on large, sparse datasets with competitive performance.

Contribution

The paper presents novel coordinate descent schemes specifically designed for symNMF, improving efficiency and scalability over existing methods.

Findings

Methods perform well on synthetic data

Algorithms handle large, sparse matrices effectively

Outperform recent state-of-the-art approaches

Abstract

Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymNMF can be used for data analysis and in particular for various clustering tasks. In this paper, we propose simple and very efficient coordinate descent schemes to solve this problem, and that can handle large and sparse input matrices. The effectiveness of our methods is illustrated on synthetic and real-world data sets, and we show that they perform favorably compared to recent state-of-the-art methods.