Non-Negative Matrix Factorization Test Cases
This provides a practical testing framework for NMF algorithms, addressing a key challenge in the field, though it is incremental as it builds on existing methods.
The paper tackles the problem of testing non-negative matrix factorization (NMF) algorithms by proposing test cases derived from matrices with exact factorizations and their perturbations, and finds that three diverse algorithms yield similar solutions on these cases.
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.