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Finite Dimensional Representation of Functional Data with Applications

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Classification as a Tool for Research

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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.

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Author information

Authors and Affiliations

  1. Universidad Carlos III de Madrid, c/ Madrid 126, 28903, Getafe, Spain

    Javier González

Authors
  1. Alberto Muñoz
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  2. Javier González
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Corresponding author

Correspondence to Javier González .

Editor information

Editors and Affiliations

  1. LS für BWL, insb. Finanzwirtschaft und, Finanzdienstleistungen, TU Dresden, Helmholtzstr. 10, Dresden, 01062, Germany

    Hermann Locarek-Junge

  2. FG Computergestützte Statistik, Univ. Dortmund, Vogelpothsweg 87, Dortmund, 44227, Germany

    Claus Weihs

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Muñoz, A., González, J. (2010). Finite Dimensional Representation of Functional Data with Applications. In: Locarek-Junge, H., Weihs, C. (eds) Classification as a Tool for Research. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10745-0_16

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