Clustering Spatially Correlated Functional Data

Abstract

In this paper we discuss and compare two clustering strategies: a hierarchical clustering and a dynamic clustering method for spatially correlated functional data. Both the approaches aim to obtain clusters which are internally homogeneous in terms of their spatial correlation structure. With this scope they incorporate the spatial information into the clustering process by considering, in a different manner, a measure of spatial association ables to emphasize the average spatial dependence among curves: the trace-variogram function. IntroductionThe study of techniques for spatial functional data has recently attracted the interest of the functional data analysis research community due to the fact that many real applications manage data observed in the space that change continuously with respect to time. It is the case when samples of functions are observed in different sites of a region (the so called spatially correlated functional data) or when these functions are observed over a discrete set of time points (temporally correlated functional data). Recent contributions in this framework deal with different topics (see .In this paper we focus on clustering. The purpose of clustering methods in the spatial functional framework is to find subgroups of spatial homogeneous curves. To the best of our knowledge, very few clustering methods incorporating spatial