Theorems on Positive Data: On the Uniqueness of NMF

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 h...

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Detalles Bibliográficos
Autores principales: Laurberg, Hans, Christensen, Mads Græsbøll, Plumbley, Mark D., Hansen, Lars Kai, Jensen, Søren Holdt
Formato: Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2008
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2386872/
https://www.ncbi.nlm.nih.gov/pubmed/18497868
http://dx.doi.org/10.1155/2008/764206
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author Laurberg, Hans
Christensen, Mads Græsbøll
Plumbley, Mark D.
Hansen, Lars Kai
Jensen, Søren Holdt
author_facet Laurberg, Hans
Christensen, Mads Græsbøll
Plumbley, Mark D.
Hansen, Lars Kai
Jensen, Søren Holdt
author_sort Laurberg, Hans
collection PubMed
description 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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spelling pubmed-23868722008-05-22 Theorems on Positive Data: On the Uniqueness of NMF Laurberg, Hans Christensen, Mads Græsbøll Plumbley, Mark D. Hansen, Lars Kai Jensen, Søren Holdt Comput Intell Neurosci Research Article 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. Hindawi Publishing Corporation 2008 2008-03-25 /pmc/articles/PMC2386872/ /pubmed/18497868 http://dx.doi.org/10.1155/2008/764206 Text en Copyright © 2008 Hans Laurberg et al. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Laurberg, Hans
Christensen, Mads Græsbøll
Plumbley, Mark D.
Hansen, Lars Kai
Jensen, Søren Holdt
Theorems on Positive Data: On the Uniqueness of NMF
title Theorems on Positive Data: On the Uniqueness of NMF
title_full Theorems on Positive Data: On the Uniqueness of NMF
title_fullStr Theorems on Positive Data: On the Uniqueness of NMF
title_full_unstemmed Theorems on Positive Data: On the Uniqueness of NMF
title_short Theorems on Positive Data: On the Uniqueness of NMF
title_sort theorems on positive data: on the uniqueness of nmf
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2386872/
https://www.ncbi.nlm.nih.gov/pubmed/18497868
http://dx.doi.org/10.1155/2008/764206
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AT hansenlarskai theoremsonpositivedataontheuniquenessofnmf
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