Representing functional data in reproducing Kernel Hilbert Spaces with applications to clustering and classification

Javier González and Alberto Muñoz

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: Functional data are difficult to manage for many traditional statistical techniques given their very high (or intrinsically infinite) dimensionality. The reason is that functional data are essentially functions and most algorithms are designed to work with (low) finite-dimensional vectors. Within this context we propose techniques to obtain finitedimensional representations of functional data. The key idea is to consider each functional curve as a point in a general function space and then project these points onto a Reproducing Kernel Hilbert Space with the aid of Regularization theory. In this work we describe the projection method, analyze its theoretical properties and propose a model selection procedure to select appropriate Reproducing Kernel Hilbert spaces to project the functional data.

Keywords: Functional; data; Reproducing; Kernel; Hilbert; Spaces; Regularization; theory (search for similar items in EconPapers)
Date: 2010-05
New Economics Papers: this item is included in nep-ecm
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