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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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Formato: | Texto |
Lenguaje: | English |
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Hindawi Publishing Corporation
2009
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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. |
format | Text |
id | pubmed-2688815 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2009 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT cemgilalitaylan bayesianinferencefornonnegativematrixfactorisationmodels |