A Functional Approach to Variable Selection in Spectrometric Problems

Abstract

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.

M. Verleysen is Research Director of the Belgian F.N.R.S. (National Fund for Scientific Research). D. François is funded by a grant from the Belgian F.R.I.A. Parts of this research result from the Belgian Program on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its authors.