Theorems on Positive Data: On the Uniqueness of NMF

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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.
Original languageEnglish
Article number764206
JournalComputational Intelligence and Neuroscience
Volume2008
Pages (from-to)10
ISSN1687-5265
DOIs
Publication statusPublished - 2008

Bibliographical note

Copyright © 2008 Hans Laurberg et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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