Title: Some consistent results for the kernel-based Bayes classifier for functional data with values in a submanifolds
Authors: Anne Francoise Yao - Universite Clermont Auvergne/LMBP (France) [presenting]
Pamela Llop - Facultad de Ingenieria Quimica, UNL-CONICET (Argentina)
Chafik Samir - UCA-LMBP/CNRS (France)
Papa Mbaye - University Clermont Auvergne (France)
Abstract: The problem of classification for functional data which lies in a finite-dimensional submanifold of a Hilbert space $H$ is considered. We discuss the choice of the kernel which is a central issue in this setting and study the consistency of the corresponding kernel-based Bayes classifier based on $n$ independent copies $(X_i,Y_i)$ of the couple of variables $(X,Y)$ where $X$ belongs to a $d$ submanifold of $H$. We motivate the practical interest of such a classifier through some applications. Basically, because we deal with functional data, the classification problem requires achieving several issues as finding a suitable representation. Then, through the applications, we illustrate the behavior of the Bayes classifier of interest, based on several representations, including the $L_2$ representation as well as spherical (normalization of the functional data) representation.