Bagging Voronoi classifiers for clustering spatial functional data

Abstract

We propose a bagging strategy based on random Voronoi tessellations for the exploration of geo-referenced functional data, suitable for different purposes (e.g., classification, regression, dimensional reduction, …). Urged by an application to environmental data contained in the Surface Solar Energy database, we focus in particular on the problem of clustering functional data indexed by the sites of a spatial finite lattice. We thus illustrate our strategy by implementing a specific algorithm whose rationale is to (i) replace the original data set with a reduced one, composed by local representatives of neighborhoods covering the entire investigated area; (ii) analyze the local representatives; (iii) repeat the previous analysis many times for different reduced data sets associated to randomly generated different sets of neighborhoods, thus obtaining many different weak formulations of the analysis; (iv) finally, bag together the weak analyses to obtain a conclusive strong analysis. Through an extensive simulation study, we show that this new procedure – which does not require an explicit model for spatial dependence – is statistically and computationally efficient.