Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization

TL;DR

This paper investigates how different initializations affect the convergence and accuracy of nonnegative matrix factorization algorithms, especially those based on alternating least squares, and discusses convergence criteria.

Contribution

It introduces two new ALS-based NMF algorithms and compares six initialization methods, providing insights into their impact on convergence and solution quality.

Findings

New ALS algorithms improve convergence speed

Initialization choice significantly affects results

Guidelines for selecting convergence criteria

Abstract

It is well known that good initializations can improve the speed and accuracy of the solutions of many nonnegative matrix factorization (NMF) algorithms. Many NMF algorithms are sensitive with respect to the initialization of W or H or both. This is especially true of algorithms of the alternating least squares (ALS) type, including the two new ALS algorithms that we present in this paper. We compare the results of six initialization procedures (two standard and four new) on our ALS algorithms. Lastly, we discuss the practical issue of choosing an appropriate convergence criterion.