Multivariate Functional Data Clustering for Spatio-temporal Data

Abstract

We propose a method for clustering functional data obtained at several spatial locations, including unobserved ones, using multivariate longitudinal data. The observed data are transformed into functional data by .tting smooth functions and then the functions at un-observed locations are predicted by the ordinary kriging for functional data. This enables us to predict the data taking the spatial correlation into consideration. Furthermore, we apply the clustering based on the x-means method to the functional data at observed locations and unobserved locations which are predicted via the kriging. The proposed method enables clustering at arbitrary locations regardless of whether the data are observed or unobserved. Numerical experiments and real data analysis show the e.ectiveness of our method.