Theoretical and practical considerations on the convergence properties of the Fisher-EM algorithm

Abstract : The Fisher-EM algorithm has been recently proposed in (Bouveyron2011) for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a latent discriminative subspace with a low intrinsic dimension. Although the Fisher-EM algorithm is based on the EM algorithm, it does not respect at a first glance all conditions of the EM convergence theory. Its convergence toward a maximum of the likelihood is therefore questionable. The aim of this work is two folds. Firstly, the convergence of the Fisher-EM algorithm is studied from the theoretical point of view. It is in particular proved that the algorithm converges under weak conditions in the general case. Secondly, the convergence of the Fisher-EM algorithm is considered from the practical point of view. It is shown that the Fisher's criterion can be used as stopping criterion for the algorithm to improve the clustering accuracy. It is also shown that the Fisher-EM algorithm converges faster than both the EM and CEM algorithm.
Type de document :
Article dans une revue
Journal of Multivariate Analysis, Elsevier, 2012, 109, pp.29-41. 〈10.1016/j.jmva.2012.02.012〉
Liste complète des métadonnées

Littérature citée [18 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00633744
Contributeur : Charles Bouveyron <>
Soumis le : mercredi 19 octobre 2011 - 12:09:30
Dernière modification le : jeudi 16 mars 2017 - 01:07:48
Document(s) archivé(s) le : vendredi 20 janvier 2012 - 10:26:54

Fichier

convergenceFEM.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Charles Bouveyron, Camille Brunet. Theoretical and practical considerations on the convergence properties of the Fisher-EM algorithm. Journal of Multivariate Analysis, Elsevier, 2012, 109, pp.29-41. 〈10.1016/j.jmva.2012.02.012〉. 〈hal-00633744〉

Partager

Métriques

Consultations de
la notice

362

Téléchargements du document

412