Non-Negative Matrix Factorization Test Cases

TL;DR

This paper proposes specific test cases for non-negative matrix factorization algorithms, derived from matrices with known factorizations, to evaluate and compare different NMF algorithms effectively.

Contribution

It introduces a set of test matrices with exact factorizations to benchmark and validate NMF algorithms, addressing the challenge of testing due to algorithmic variability.

Findings

Different NMF algorithms produce similar results on the proposed test cases.

Test cases can serve as benchmarks for existing and new NMF algorithms.

Methodology for applying test cases in practical algorithm evaluation.

Abstract

Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms, and the somewhat subjective nature of the problem, there is no clear "correct answer" to any particular NMF problem, and as a result, it can be hard to test new algorithms. This paper suggests some test cases for NMF algorithms derived from matrices with enumerable exact non-negative factorizations and perturbations of these matrices. Three algorithms using widely divergent approaches to NMF all give similar solutions over these test cases, suggesting that these test cases could be used as test cases for implementations of these existing NMF algorithms as well as potentially new NMF algorithms. This paper also describes how the proposed test cases could be used in practice.