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Simultaneous model-based clustering and visualization in the Fisher discriminative subspace
Bouveyron C., Brunet C.
http://hal-paris1.archives-ouvertes.fr/hal-00492406
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Mathématiques/Statistiques
Statistiques/Théorie
Simultaneous model-based clustering and visualization in the Fisher discriminative subspace
Charles Bouveyron () 1, Camille Brunet 2
1 :  Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
http://samm.univ-paris1.fr/
Université Paris I - Panthéon-Sorbonne
Centre Pierre Mendès France 90 Rue de Tolbiac - 75634 Paris Cedex 13
France
2 :  Informatique, Biologie Intégrative et Systèmes Complexes (IBISC)
http://www.ibisc.univ-evry.fr/
CNRS : FRE3190 – Université d'Evry-Val d'Essonne
40,rue du pelvoux, Courcouronnes 91020 EVRY CEDEX
France
Clustering in high-dimensional spaces is nowadays a recurrent problem in many scientific domains but remains a difficult task from both the clustering accuracy and the result understanding points of view. This paper presents a discriminative latent mixture (DLM) model which fits the data in a latent orthonormal discriminative subspace with an intrinsic dimension lower than the dimension of the original space. By constraining model parameters within and between groups, a family of 12 parsimonious DLM models is exhibited which allows to fit onto various situations. An estimation algorithm, called the Fisher-EM algorithm, is also proposed for estimating both the mixture parameters and the discriminative subspace. Experiments on simulated and real datasets show that the proposed approach performs better than existing clustering methods while providing a useful representation of the clustered data. The method is as well applied to the clustering of mass spectrometry data.
Anglais

High-dimensional clustering – Model-based clustering – Discriminative subspace – Fisher criterion – Visualization – Parsimonious models.

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