Finite dimensional representation of functional data with applications

Abstract

Most algorithms in statistics are designed to work with vectors of small or moderate dimension, and the performance of these algorithms decreases when dealing with very high dimensional data as functional data are. In this work we propose a functional analysis technique to obtain appropriate finite-dimensional representations of functional data for pattern recognition purposes. To this aim, we project the available functional data samples onto finite dimensional function spaces generated by the eigenfunctions of suitable Mercer kernels. We demonstrate some theoretical properties of the proposed method and the advantages of the proposed representations in several tasks using simulated and real functional data sets. © Springer-Verlag Berlin Heidelberg 2010.