Inexact Block Coordinate Descent Methods For Symmetric Nonnegative Matrix Factorization

TL;DR

This paper introduces inexact block coordinate descent algorithms for symmetric nonnegative matrix factorization, offering scalable solutions with guaranteed convergence and improved performance for large-scale data clustering.

Contribution

It proposes novel inexact block coordinate descent methods for SNMF, enabling efficient serial and parallel algorithms with convergence guarantees.

Findings

Algorithms are effective on large-scale SNMF problems.

Proposed methods outperform recent state-of-the-art algorithms.

Guarantee stationary convergence for the algorithms.

Abstract

Symmetric nonnegative matrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix factorization technique and have better ability of clustering nonlinearly separable data. In this paper, we focus on the algorithmic aspect of the SNMF problem and propose simple inexact block coordinate decent methods to address the problem, leading to both serial and parallel algorithms. The proposed algorithms have guaranteed stationary convergence and can efficiently handle large-scale and/or sparse SNMF problems. Extensive simulations verify the effectiveness of the proposed algorithms compared to recent state-of-the-art algorithms.