Talk by Nicolas Gillis (University of Mons) 

Given a nonnegative matrix X and a factorization rank r, nonnegative matrix factorization (NMF) approximates the matrix X as the product of a nonnegative matrix W with r columns and a nonnegative matrix H with r rows. NMF has become a standard linear dimensionality reduction technique in data mining and machine learning. In this talk, we address the issue of non-uniqueness of NMF decompositions, also known as the identifiability issue, which is crucial in many applications. We discuss three key NMF models that allow us to obtain unique NMFs, namely, separable NMF, minimum-volume NMF, and sparse NMF. We also discuss how the factors (W,H) in such models can be computed. We illustrate these results on facial feature extraction, blind hyperspectral unmixing, and topic modeling.