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

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 constra...

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Autores principales:	Leo Taslaman, Björn Nilsson
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2012
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/801bcbbcc3384ae3a416ec9c3e844900
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spelling	oai:doaj.org-article:801bcbbcc3384ae3a416ec9c3e8449002021-11-18T08:10:12ZA framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.1932-620310.1371/journal.pone.0046331https://doaj.org/article/801bcbbcc3384ae3a416ec9c3e8449002012-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/23133590/?tool=EBIhttps://doaj.org/toc/1932-6203Non-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 L1 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.Leo TaslamanBjörn NilssonPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 7, Iss 11, p e46331 (2012)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Leo Taslaman Björn Nilsson A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
description	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 L1 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.
format	article
author	Leo Taslaman Björn Nilsson
author_facet	Leo Taslaman Björn Nilsson
author_sort	Leo Taslaman
title	A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
title_short	A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
title_full	A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
title_fullStr	A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
title_full_unstemmed	A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
title_sort	framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.
publisher	Public Library of Science (PLoS)
publishDate	2012
url	https://doaj.org/article/801bcbbcc3384ae3a416ec9c3e844900
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A framework for regularized non-negative matrix factorization, with application to the analysis of gene expression data.

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