Theorems on Positive Data: On the Uniqueness of NMF

@article{Laurberg2008TheoremsOP,
  title={Theorems on Positive Data: On the Uniqueness of NMF},
  author={Hans Laurberg and Mads Gr{\ae}sb\oll Christensen and Mark D. Plumbley and Lars Kai Hansen and S\oren Holdt Jensen},
  journal={Computational Intelligence and Neuroscience},
  year={2008},
  volume={2008},
  pages={788 - 791}
}
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… CONTINUE READING
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