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

International audienceFunctional 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

A functional approach to variable selection in spectrometric problems

In spectrometric problems, objects are characterized by high-resolution spectra that correspond to hundreds to thousands of variables. In this context, even fast variable selection methods lead to high computational load. However, spectra are generally smooth and can therefore be accurately approximated by splines. In this paper, we propose to use a B-spline expansion as a pre-processing step before variable selection, in which original variables are replaced by coefficients of the B-spline expansions. Using a simple leave-one-out procedure, the optimal number of B-spline coefficients can be found efficiently. As there is generally an order of magnitude less coefficients than original spectral variables, selecting optimal coefficients is faster than selecting variables. Moreover, a B-spline coefficient depends only on a limited range of original variables: this preserves interpretability of the selected variables. We demonstrate the interest of the proposed method on real-world data