On the estimation of the latent discriminative subspace in the Fisher-EM algorithm

Abstract : The Fisher-EM algorithm has been recently proposed in [2] for the simultaneous visualization and clustering of high-dimensional data. It is based on a discriminative latent mixture model which fits the data into a latent discriminative subspace with an intrinsic dimension lower than the dimension of the original space. The Fisher-EM algorithm includes an F-step which estimates the projection matrix whose columns span the discriminative latent space. This matrix is estimated via an optimization problem which is solved using a Gram-Schmidt procedure in the original algorithm. Unfortunately, this procedure suffers in some case from numerical instabilities which may result in a deterioration of the visualization quality or the clustering accuracy. Two alternatives for estimating the latent subspace are proposed to overcome this limitation. The optimization problem of the F-step is first recasted as a regression-type problem and then reformulated such that the solution can be approximated with a SVD. Experiments on simulated and real datasets show the improvement of the proposed alternatives for both the visualization and the clustering of data.
Type de document :
Article dans une revue
Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2011, 152 (3), pp.98-115
Liste complète des métadonnées

Littérature citée [20 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00632926
Contributeur : Charles Bouveyron <>
Soumis le : lundi 17 octobre 2011 - 10:09:26
Dernière modification le : jeudi 16 mars 2017 - 01:07:46
Document(s) archivé(s) le : jeudi 15 novembre 2012 - 09:51:37

Fichier

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

Identifiants

  • HAL Id : hal-00632926, version 1

Collections

Citation

Charles Bouveyron, Camille Brunet. On the estimation of the latent discriminative subspace in the Fisher-EM algorithm. Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2011, 152 (3), pp.98-115. 〈hal-00632926〉

Partager

Métriques

Consultations de la notice

366

Téléchargements de fichiers

107