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Representation of Functional Data in Neural Networks

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Date
2005
Dewey
Probabilités et mathématiques appliquées
Sujet
Functional data analysis; smooth data; projection on smooth bases; irregular sampling; missing data
Journal issue
Neurocomputing
Volume
64
Publication date
2005
Article pages
183--210
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.neucom.2004.11.012
URI
https://basepub.dauphine.fr/handle/123456789/589
Collections
  • CEREMADE : Publications
Metadata
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Author
Conan-Guez, Brieuc
Delannay, Nicolas
Rossi, Fabrice
Verleysen, Michel
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

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