FUNCTIONAL SUPERVISED CLASSIFICATION WITH WAVELETS

Alain Berlinet (1) , Gérard Biau (2) , Laurent Rouviere (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LSTA - Laboratoire de Statistique Théorique et Appliquée
3 IRMAR - Institut de Recherche Mathématique de Rennes

Let X be a random variable taking values in a Hilbert space and let Y be a random label with values in {0, 1}. Given a collection of classification rules and a learning sample of independent copies of the pair (X, Y ), it is shown how to select optimally and consistently a classifier. As a general strategy, the learning sample observations are first expanded on a wavelet basis and the overall infinite dimension is reduced to a finite one via a suitable data-dependent thresholding. Then, a finite-dimensional classification rule is performed on the non-zero coefficients. Both the dimension and the classifier are automatically selected by data-splitting and empirical risk minimization. Applications of this technique to a signal discrimination problem involving speech recordings and simulated data are presented.

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Alain Berlinet, Gérard Biau, Laurent Rouviere. FUNCTIONAL SUPERVISED CLASSIFICATION WITH WAVELETS. Annales de l'ISUP, 2008, 52, pp.19. ⟨hal-00459437v1⟩