Representing functional data in reproducing Kernel Hilbert Spaces with applications to clustering and classification
AbstractFunctional 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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws102713.
Date of creation: May 2010
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Functional data; Reproducing; Kernel Hilbert Spaces; Regularization theory;
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