Theorems on Positive Data: On the Uniqueness of NMF-Reference-Cited by-同舟云学术

Theorems on Positive Data: On the Uniqueness of NMF

Published:2008 Issue: Volume:2008 Page:1-9
ISSN:1687-5265
Container-title:Computational Intelligence and Neuroscience
language:en
Short-container-title:Computational Intelligence and Neuroscience

Author:

Laurberg Hans¹,Christensen Mads Græsbøll¹,Plumbley Mark D.²,Hansen Lars Kai³,Jensen Søren Holdt¹

Affiliation:

1. Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg, Denmark

2. Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London E1 4NS, UK

3. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800 Lyngby, Denmark

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.

Funder

Danish Technical Research Council

Publisher

Hindawi Limited

Subject

General Mathematics,General Medicine,General Neuroscience,General Computer Science

Link

http://downloads.hindawi.com/journals/cin/2008/764206.pdf

Reference12 articles.

1. Learning the parts of objects by non-negative matrix factorization

2. Algorithms and applications for approximate nonnegative matrix factorization

3. Rank Factorization of Nonnegative Matrices

4. Rank Factorization of Nonnegative Matrices (A. Berman)

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