Choice of B-splines with free parameters in the flexible discriminant analysis context

Abstract

Flexible discriminant analysis (FDA) is a general methodology which aims at providing tools for multigroup non linear classification. It consists in a nonparametric version of discriminant analysis by replacing linear regression by any nonparametric regression method. A new option for FDA, consisting in a nonparametric regression method based on B-spline functions, will be introduced. The relevance of the transformation (hence the discrimination) depends on the parameters defining the spline functions: degree, number and location of the knots for each continuous variable. This method called FDA-FKBS (Free Knot B-Splines) allows to determine all these parameters without the necessity of many prior parameters. It is inspired by Reversible Jumps Monte Carlo Markov Chains but the objective function is different and the Bayesian aspect is put aside.