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Bayesian Inference for Nonnegative Matrix Factorisation Models

We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximu...

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Detalles Bibliográficos
Autor principal: Cemgil, Ali Taylan
Formato: Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2009
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2688815/
https://www.ncbi.nlm.nih.gov/pubmed/19536273
http://dx.doi.org/10.1155/2009/785152
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author Cemgil, Ali Taylan
author_facet Cemgil, Ali Taylan
author_sort Cemgil, Ali Taylan
collection PubMed
description We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction.
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spelling pubmed-26888152009-06-17 Bayesian Inference for Nonnegative Matrix Factorisation Models Cemgil, Ali Taylan Comput Intell Neurosci Research Article We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction. Hindawi Publishing Corporation 2009 2009-05-27 /pmc/articles/PMC2688815/ /pubmed/19536273 http://dx.doi.org/10.1155/2009/785152 Text en Copyright © 2009 Ali Taylan Cemgil. 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
Cemgil, Ali Taylan
Bayesian Inference for Nonnegative Matrix Factorisation Models
title Bayesian Inference for Nonnegative Matrix Factorisation Models
title_full Bayesian Inference for Nonnegative Matrix Factorisation Models
title_fullStr Bayesian Inference for Nonnegative Matrix Factorisation Models
title_full_unstemmed Bayesian Inference for Nonnegative Matrix Factorisation Models
title_short Bayesian Inference for Nonnegative Matrix Factorisation Models
title_sort bayesian inference for nonnegative matrix factorisation models
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2688815/
https://www.ncbi.nlm.nih.gov/pubmed/19536273
http://dx.doi.org/10.1155/2009/785152
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