Dynamical classification of functional data with free knots spline estimation

In this paper we address the problem of clustering a set of functional data. Given a collection of n curves corrupted by noise, we wish simultaneously to estimate and classify them through a generalization of the dynamical clustering algorithm (Diday (1971)). For this purpose we consider a clustering procedure based on the best fitting between the representative function of the cluster and the allocation function of the curve to the different clusters. According to Verde et al. (2001) we propose to represent the clusters by prototypes which are ’mean curves’ computed through a free-knot smoothing spline estimation, where the generic prototype of a cluster is carried out by optimizing a non linear problem. Such solution takes into account a dimensionality and a smoothness constraint of the functions prototype. An application of the proposed procedure has been performed in hydro-geology science context.