Un résultat de consistance pour des SVM fonctionnels par interpolation spline

Nathalie Villa (1) , Fabrice Rossi (2)

1 GRIMM - Groupe de Recherche en Mathématiques et Informatique du Mirail
2 AxIS - Usage-centered design, analysis and improvement of information systems

This Note proposes a new methodology for function classification with Support Vector Machine (SVM). Rather than relying on projection on a truncated Hilbert basis as in our previous work, we use an implicit spline interpolation that allows us to compute SVM on the derivatives of the studied functions. To that end, we propose a kernel defined directly on the discretizations of the observed functions. We show that this method is universally consistent.

Mots clés: Functional Data Analysis; Support Vector Machine; Classification; Consistency

Domaines: Statistiques [math.ST]

Nathalie Villa, Fabrice Rossi. Un résultat de consistance pour des SVM fonctionnels par interpolation spline. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2006, 343 (8), pp.555-560. ⟨10.1016/j.crma.2006.09.025⟩. ⟨hal-00144142⟩