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Theorems on positive data: on the uniqueness of NMF.

Laurberg, H, Christensen, MG, Plumbley, MD, Hansen, LK and Jensen, SH (2008) Theorems on positive data: on the uniqueness of NMF. Comput Intell Neurosci.

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Abstract

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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering > Centre for Vision Speech and Signal Processing
Authors :
AuthorsEmailORCID
Laurberg, HUNSPECIFIEDUNSPECIFIED
Christensen, MGUNSPECIFIEDUNSPECIFIED
Plumbley, MDUNSPECIFIEDUNSPECIFIED
Hansen, LKUNSPECIFIEDUNSPECIFIED
Jensen, SHUNSPECIFIEDUNSPECIFIED
Date : 2008
Identification Number : 10.1155/2008/764206
Related URLs :
Additional Information : 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
Depositing User : Symplectic Elements
Date Deposited : 23 Sep 2015 17:48
Last Modified : 23 Sep 2015 17:48
URI: http://epubs.surrey.ac.uk/id/eprint/808459

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