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Data-driven penalty calibration: A case studyfor Gaussian mixture model selection

Published online by Cambridge University Press:  05 January 2012

Cathy Maugis  and
Bertrand Michel
Cathy Maugis
Affiliation:
Institut de Mathématiques de Toulouse, INSA de Toulouse, Université de Toulouse, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France. cathy.maugis@insa-toulouse.fr
Bertrand Michel
Affiliation:
Laboratoire de Statistique Théorique et Appliquée, Université Paris 6, 175 rue du Chevaleret, 75013 Paris, France. bertrand.michel@upmc.fr
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Abstract

In the companion paper [C. Maugis and B. Michel,A non asymptotic penalized criterion for Gaussian mixture model selection. ESAIM: P&S15 (2011) 41–68] , a penalized likelihoodcriterion is proposed to select a Gaussian mixture model among aspecific model collection. This criterion depends on unknownconstants which have to be calibrated in practical situations. A“slope heuristics” method is described and experimented to dealwith this practical problem. In a model-based clustering context,the specific form of the considered Gaussian mixtures allows us todetect the noisy variables in order to improve the data clusteringand its interpretation. The behavior of our data-driven criterionis highlighted on simulated datasets, a curve clustering exampleand a genomics application.

Keywords

Slope heuristicsPenalized likelihood criterionModel-based clusteringnoisy variable detection

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 320 - 339
Copyright
© EDP Sciences, SMAI, 2011

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