Theorems on Positive Data: On the Uniqueness of NMF

Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
January 2008
Computational Intelligence & Neuroscience;2008 Supplement, Special section p1
Academic Journal
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.


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