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Intrinsic Dimension Estimation by Maximum Likelihood in Probabilistic PCA

Charles Bouveyron 1, 2 Gilles Celeux 3 Stephane Girard 4
3 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
4 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : A central issue in dimension reduction is choosing a sensible number of dimensions to be retained. This work demonstrates the asymptotic consistency of the maximum likelihood criterion for determining the intrinsic dimension of a dataset in a 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 as well the limits of the maximum likelihood criterion and recommends in specific situations the use of the AIC criterion.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00440372
Contributor : Charles Bouveyron <>
Submitted on : Thursday, December 10, 2009 - 2:54:34 PM
Last modification on : Tuesday, February 9, 2021 - 3:20:19 PM
Long-term archiving on: : Thursday, June 17, 2010 - 9:30:18 PM

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  • HAL Id : hal-00440372, version 1

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Charles Bouveyron, Gilles Celeux, Stephane Girard. Intrinsic Dimension Estimation by Maximum Likelihood in Probabilistic PCA. 2009. ⟨hal-00440372v1⟩

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