Fast communication: Bayesian estimation of the number of principal components

Authors:
Abd-Krim Seghouane;Andrzej Cichocki
Affiliations:
National ICT Australia Limited, Canberra Research Laboratory, Locked Bag 8001, Canberra, ACT 2601, Australia and Research School of Information Sciences and Engineering, Building 115, corner of No ...;Brain Science Institute, RIKEN, Laboratory for Advanced Brian Signal Processing, Wako-shi, Saitama 351-0198, Japan
Venue:
Signal Processing
Year:
2007

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Abstract

Recently, the technique of principal component analysis (PCA) has been expressed as the maximum likelihood solution for a generative latent variable model. A central issue in PCA is choosing the number of principal components to retain. This can be considered as a problem of model selection. In this paper, the probabilistic reformulation of PCA is used as a basis for a Bayesian approach of PCA to derive a model selection criterion for determining the true dimensionality of data. The proposed criterion is similar to the Bayesian Information Criterion, BIC, with a particular goodness of fit term and it is consistent. A simulation example that illustrate its performance for the determination of the number of principal components to be retained is presented.