Clustering spatio-functional data: a method based on a nonparametric variogram estimation for functional data

In this paper we propose an extended version of a model-based strategy for clustering spatio-functional data. The original proposed method considers the problem of clustering curves that are realization of a random stochastic process and aims to discover functional sub-processes and their generating models in unsampled location of the space. The estimates of these model implies a fitting of the trace-variogram function for each cluster that is done by ordinary least squares or weighted least squares. In this paper we propose a more general estimator for the variogram function that is a kernel estimator. It is a more general weighted average than the classical estimator and it is robust in the sense that nearst-neighbour parameter selection is distribution free.