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A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.

Taslaman, Leo LU and Nilsson, Björn LU (2012) In PLoS ONE 7(11).
Abstract
Non-negative matrix factorization (NMF) condenses high-dimensional data into lower-dimensional models subject to the requirement that data can only be added, never subtracted. However, the NMF problem does not have a unique solution, creating a need for additional constraints (regularization constraints) to promote informative solutions. Regularized NMF problems are more complicated than conventional NMF problems, creating a need for computational methods that incorporate the extra constraints in a reliable way. We developed novel methods for regularized NMF based on block-coordinate descent with proximal point modification and a fast optimization procedure over the alpha simplex. Our framework has important advantages in that it (a)... (More)
Non-negative matrix factorization (NMF) condenses high-dimensional data into lower-dimensional models subject to the requirement that data can only be added, never subtracted. However, the NMF problem does not have a unique solution, creating a need for additional constraints (regularization constraints) to promote informative solutions. Regularized NMF problems are more complicated than conventional NMF problems, creating a need for computational methods that incorporate the extra constraints in a reliable way. We developed novel methods for regularized NMF based on block-coordinate descent with proximal point modification and a fast optimization procedure over the alpha simplex. Our framework has important advantages in that it (a) accommodates for a wide range of regularization terms, including sparsity-inducing terms like the [Formula: see text] penalty, (b) guarantees that the solutions satisfy necessary conditions for optimality, ensuring that the results have well-defined numerical meaning, (c) allows the scale of the solution to be controlled exactly, and (d) is computationally efficient. We illustrate the use of our approach on in the context of gene expression microarray data analysis. The improvements described remedy key limitations of previous proposals, strengthen the theoretical basis of regularized NMF, and facilitate the use of regularized NMF in applications. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
PLoS ONE
volume
7
issue
11
publisher
Public Library of Science
external identifiers
  • wos:000310702400004
  • pmid:23133590
  • scopus:84868326858
ISSN
1932-6203
DOI
10.1371/journal.pone.0046331
language
English
LU publication?
yes
id
7b7e860b-d7c5-4608-9c6a-3df5ac15d5e8 (old id 3219172)
alternative location
http://www.ncbi.nlm.nih.gov/pubmed/23133590?dopt=Abstract
date added to LUP
2012-12-03 12:47:08
date last changed
2017-01-01 06:28:00
@article{7b7e860b-d7c5-4608-9c6a-3df5ac15d5e8,
  abstract     = {Non-negative matrix factorization (NMF) condenses high-dimensional data into lower-dimensional models subject to the requirement that data can only be added, never subtracted. However, the NMF problem does not have a unique solution, creating a need for additional constraints (regularization constraints) to promote informative solutions. Regularized NMF problems are more complicated than conventional NMF problems, creating a need for computational methods that incorporate the extra constraints in a reliable way. We developed novel methods for regularized NMF based on block-coordinate descent with proximal point modification and a fast optimization procedure over the alpha simplex. Our framework has important advantages in that it (a) accommodates for a wide range of regularization terms, including sparsity-inducing terms like the [Formula: see text] penalty, (b) guarantees that the solutions satisfy necessary conditions for optimality, ensuring that the results have well-defined numerical meaning, (c) allows the scale of the solution to be controlled exactly, and (d) is computationally efficient. We illustrate the use of our approach on in the context of gene expression microarray data analysis. The improvements described remedy key limitations of previous proposals, strengthen the theoretical basis of regularized NMF, and facilitate the use of regularized NMF in applications.},
  articleno    = {e46331},
  author       = {Taslaman, Leo and Nilsson, Björn},
  issn         = {1932-6203},
  language     = {eng},
  number       = {11},
  publisher    = {Public Library of Science},
  series       = {PLoS ONE},
  title        = {A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.},
  url          = {http://dx.doi.org/10.1371/journal.pone.0046331},
  volume       = {7},
  year         = {2012},
}