Classification bayésienne non supervisée de données fonctionnelles

Juery, Damien; Abraham, Christophe; Fontez, Bénédicte

Journal de la société française de statistique, Tome 155 (2014) no. 2, pp. 185-201.

Nous nous intéressons à la classification bayésienne non supervisée de données fonctionnelles. Nous généralisons un modèle de classification de données basé sur le processus de Dirichlet, pour les données fonctionnelles. Contrairement à d’autres articles qui utilisent la dimension finie en projetant les courbes dans des bases de fonctions, ou en considérant les courbes aux temps d’observation, les calculs sont ici réalisés sur les courbes complètes en dimension infinie. Le cadre des espaces de Hilbert à noyau reproduisant nous permet alors d’exprimer les densités, en dimension infinie, des courbes par rapport à une mesure gaussienne. Nous proposons un algorithme généralisant l’algorithme Gibbs with Auxiliary Parameters ( Neal, 2000 ) dans le cas de processus. Les performances sont comparées à celles d’une autre méthode déjà existante, puis discutées.

We are interested in unsupervised bayesian clustering for functional data. We generalize a data clustering model based on the Dirichlet process, to functional data. Contrary to other papers making use of finite dimension, by decomposing curves into arbitrary basis functions, or by considering curves at their observation times, calculations are here realized onto complete curves in infinite dimension. The reproducing kernel Hilbert space theory permits us to derive densities of curves in respect to a gaussian measure. We thus propose a generalization to the algorithm Gibbs with Auxiliary Parameters ( Neal, 2000 ), to the functional case. Performances are compared to those of an already existing method, and then discussed.

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