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inria-00369376, version 1
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%% inria-00369376, version 1 %% http://hal.inria.fr/inria-00369376/en/ @inproceedings{TAN:2009:INRIA-00369376:1, title = { {A}utomatic {R}elevance {D}etermination in {N}onnegative {M}atrix {F}actorization}, author = {{T}an, {V}incent {Y}. {F}. and {F}{\'e}votte, {C}{\'e}dric}, abstract = {{N}onnegative matrix factorization ({NMF}) has become a popular technique for data analysis and dimensionality reduction. {H}owever, it is often assumed that the number of latent dimensions (or components) is given. {I}n practice, one must choose a suitable value depending on the data and/or setting. {I}n this paper, we address this important issue by using a {B}ayesian approach to estimate the latent dimensionality, or equivalently, select the model order. {T}his is achieved via automatic relevance determination ({ARD}), a technique that has been employed in {B}ayesian {PCA} and sparse {B}ayesian learning. {W}e show via experiments on synthetic data that our technique is able to recover the correct number of components, while it is also able to recover an effective number of components from real datasets such as the {MIT} {CBCL} datase}, language = {{E}nglish}, affiliation = {{L}aboratory for {I}nformation and {D}ecision {S}ystems - {M}assachusetts {I}nstitute of {T}echnology - {LIDS} - {M}assachusetts {I}nstitute of {T}echnology - {L}aboratoire traitement et communication de l'information - {LTCI} - {CNRS} : {UMR}5141 - {I}nstitut {T}{\'e}l{\'e}com - {T}{\'e}l{\'e}com {P}aris{T}ech }, booktitle = {{SPARS}'09 - {S}ignal {P}rocessing with {A}daptive {S}parse {S}tructured {R}epresentations }, address = {{S}aint {M}alo {U}nited {K}ingdom }, organization = {{I}nria {R}ennes - {B}retagne {A}tlantique }, editor = {{R}{\'e}mi {G}ribonval }, audience = {international }, year = {2009}, URL = {http://hal.inria.fr/inria-00369376/en/}, URL = {http://hal.inria.fr/inria-00369376/PDF/17.pdf}, }
%F inria-00369376, version 1 %0 Conference Proceedings %U http://hal.inria.fr/inria-00369376/en/ %2 INFO:INFO_TS %T Automatic Relevance Determination in Nonnegative Matrix Factorization %A Tan, Vincent Y. F. %A Févotte, Cédric %A Tan, V. Y. F. %A Févotte, C. %A Tan V. Y. F. et al %+ Laboratory for Information and Decision Systems - Massachusetts Institute of Technology - LIDS - Massachusetts Institute of Technology - Laboratoire traitement et communication de l'information - LTCI - CNRS : UMR5141 - Institut Télécom - Télécom ParisTech %X Nonnegative matrix factorization (NMF) has become a popular technique for data analysis and dimensionality reduction. However, it is often assumed that the number of latent dimensions (or components) is given. In practice, one must choose a suitable value depending on the data and/or setting. In this paper, we address this important issue by using a Bayesian approach to estimate the latent dimensionality, or equivalently, select the model order. This is achieved via automatic relevance determination (ARD), a technique that has been employed in Bayesian PCA and sparse Bayesian learning. We show via experiments on synthetic data that our technique is able to recover the correct number of components, while it is also able to recover an effective number of components from real datasets such as the MIT CBCL datase %G English %8 2009 %2 international %B SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations %2 Saint Malo %2 United Kingdom %8 2009-04-06 %2 Inria Rennes - Bretagne Atlantique %E Rémi Gribonval
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