Representation of functional data in neural networks

Authors:
Fabrice Rossi;Nicolas Delannay;Brieuc Conan-Guez;Michel Verleysen
Affiliations:
Projet AxIS, INRIA-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France and CEREMADE, UMR CNRS 7534, Université Paris-IX Dauphine, Place du Maréchal ...;Université catholique de Louvain DICE-Machine Learning Group Place du levant 3, 1348 Louvain-la-Neuve, Belgium;Projet AxIS, INRIA-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France;Université catholique de Louvain DICE-Machine Learning Group Place du levant 3, 1348 Louvain-la-Neuve, Belgium
Venue:
Neurocomputing
Year:
2005

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Abstract

Functional data analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice; usually a regular or irregular sampling is known. For this reason, some processing is needed in order to benefit from the smooth character of functional data in the analysis methods. This paper shows how to extend the radial-basis function networks (RBFN) and multi-layer perceptron (MLP) models to functional data inputs, in particular when the latter are known through lists of input-output pairs. Various possibilities for functional processing are discussed, including the projection on smooth bases, functional principal component analysis, functional centering and reduction, and the use of differential operators. It is shown how to incorporate these functional processing into the RBFN and MLP models. The functional approach is illustrated on a benchmark of spectrometric data analysis.