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Bayesian Orthogonal Component Analysis for Sparse Representation

Dobigeon, Nicolas and Tourneret, Jean-Yves Bayesian Orthogonal Component Analysis for Sparse Representation. (2010) IEEE Transactions on Signal Processing, vol. 5 (n° 5). pp. 2675-2685. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2010.2041594

Abstract

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This undercomplete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli–Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A noninformative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on undercomplete dictionary is finally investigated.

Item Type:Article
Additional Information:Thanks to IEEE editor. The definitive version is available at http://www.signalprocessingsociety.org/ The original PDF of the article can be found at Transactions on signal prodessing website : http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Université de Toulouse I-Sciences Sociales - UT1
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
French research institutions > Centre National de la Recherche Scientifique - CNRS
Université de Toulouse > Université de Toulouse II-Le Mirail - UTM
Laboratory name:
Statistics:download
Deposited By: Nicolas DOBIGEON

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