Constrained variable clustering and the best basis problem in functional data analysis

Fabrice Rossi (1) , Yves Lechevallier (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 AxIS - Usage-centered design, analysis and improvement of information systems

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.

Keywords: functional data; variable clustering; best basis

Domains: Other Statistics [stat.ML]; Machine Learning [cs.LG]

Fabrice Rossi, Yves Lechevallier. Constrained variable clustering and the best basis problem in functional data analysis. Bernard Fichet, Domenico Piccolo, Rosanna Verde and Maurizio Vichi. Classification and Multivariate Analysis for Complex Data Structures, Springer Berlin Heidelberg, pp.435-444, 2011, Studies in Classification, Data Analysis, and Knowledge Organization, ⟨10.1007/978-3-642-13312-1_46⟩. ⟨hal-00656675⟩