A fast epigraph and hypograph-based approach for clustering functional data

Abstract

Clustering techniques for multivariate data are useful tools in Statistics that have been fully studied in the literature. However, there is limited literature on clustering methodologies for functional data. Our proposal consists of a clustering procedure for functional data using techniques for clustering multivariate data. The idea is to reduce a functional data problem into a multivariate one by applying the epigraph and hypograph indexes to the original curves and to their first and/or second derivatives. All the information given by the functional data is therefore transformed to the multivariate context, being informative enough for the usual multivariate clustering techniques to be efficient. The performance of this new methodology is evaluated through a simulation study and is also illustrated through real data sets. The results are compared to some other clustering procedures for functional data.