We investigate the conditions for which nonnegative matrixfactorization (NMF) is unique and introduce severaltheorems which can determine whether the decompositionis in fact unique or not. The theorems are illustrated byseveral examples showing the use of the theorems and theirlimitations. 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 usea stochastic view of NMF to analyze which characterizationof the underlying model will result in an NMF with smallestimation errors.
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