  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.
