Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA

Authors:
Charles Bouveyron;Gilles Celeux;Stéphane Girard
Affiliations:
Laboratoire SAMM, EA 4543, University Paris 1 Panthéon-Sorbonne, 90 rue de Tolbiac, 75013 Paris, France;Select, Inria Saclay-íle de France, Dept. de mathématiques, Université Paris-Sud, 91405 Orsay Cedex, France;Mistis, Inria Rhône-Alpes & LJK, Inovalléée, 655, av. de l'Europe, Montbonnot, 38334 Saint-Ismier Cedex, France
Venue:
Pattern Recognition Letters
Year:
2011

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Abstract

A central issue in dimension reduction is choosing a sensible number of dimensions to be retained. This work demonstrates the surprising result of the asymptotic consistency of the maximum likelihood criterion for determining the intrinsic dimension of a dataset in an isotropic version of probabilistic principal component analysis (PPCA). Numerical experiments on simulated and real datasets show that the maximum likelihood criterion can actually be used in practice and outperforms existing intrinsic dimension selection criteria in various situations. This paper exhibits and outlines the limits of the maximum likelihood criterion. It leads to recommend the use of the AIC criterion in specific situations. A useful application of this work would be the automatic selection of intrinsic dimensions in mixtures of isotropic PPCA for classification.