Spatio-Functional data Analysis: clustering methods for models discovering

In this paper we propose two clustering strategies for spatially referenced functional data. Both are model based approaches since a functional linear model is supposed to generate the elements of each cluster. A first proposal considers the problem of clustering curves that are realization of a random stochastic process. In this case functional sub-processes are discovered and their generative models are estimated in optimal unsampled locations of the space. A second one achieves simultaneously an optimal partition of the data and functional linear models which incorporate the spatial interaction among different functional variable in each cluster.