Non-negative matrix factorization test cases

摘要

Non-negative matrix factorization (NMF) is a problem 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. In this paper, we suggest some test cases for NMF algorithms derived from matrices with enumerable exact non-negative factorizations and perturbations of these matrices. We show that three algorithms using widely divergent approaches to NMF all give similar solutions over these test cases, so they can be used as benchmarks for new algorithms. We also describe how the proposed test cases ought to be used.