Representing functional data using support vector machines

Functional data are difficult to manage for most classical statistical techniques, given the very high (or intrinsically infinite) dimensionality. The reason lies in that functional data are functions and most algorithms are designed to work with low dimensional vectors. In this paper we propose a functional analysis technique to obtain finite-dimensional representations of functional data. The key idea is to consider each functional datum as a point in a general function space and then to project these points onto a Reproducing Kernel Hilbert Space with the aid of a support vector machine. We show some theoretical properties of the method and illustrate its performance in some classification examples.