Constrained Variable Clustering and the Best Basis Problem in Functional Data Analysis

Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simplification of the functions that reduces the redundancy induced by the regularity. In this paper we propose to use a clustering approach that targets variables rather than individual to design a piecewise constant representation of a set of functions. The contiguity constraint induced by the functional nature of the variables allows a polynomial complexity algorithm to give the optimal solution.

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Notes

Acknowledgments

The authors thank the anonymous reviewer for the detailed and constructive comments that have significantly improved this paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institut Télécom, Télécom ParisTech, LTCI – UMR CNRS 5141ParisFrance
  2. 2.Projet AxIS, INRIA Paris RocquencourtDomaine de Voluceau, RocquencourtLe Chesnay CedexFrance

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