Hierarchical clustering of spatially correlated functional data

Classification problems of functional data arise naturally in many applications. Several approaches have been considered for solving the problem of finding groups based on functional data. In this paper we are interested in detecting groups when the functional data are spatially correlated. Our methodology allows to find spatially homogeneous groups of sites when the observations at each sampling location consist of samples of random functions. In univariable and multivariable geostatistics various methods of incorporating spatial information into the clustering analysis have been considered. Here we extend these methods to the functional context in order to fulfill the task of clustering spatially correlated curves. In our approach we initially use basis functions to smooth the observed data and then we weight the dissimilarity matrix among curves by either the trace-variogram or the multivariable variogram calculated with the coefficients of the basis functions. As an illustration the methodology is applied to a real data set corresponding to average daily temperatures measured at 35 Canadian weather stations.