Functional clustering via multivariate clustering

TL;DR

This paper introduces a novel clustering method for functional data by transforming it into a multivariate form using epigraph and hypograph indexes, enabling the use of standard multivariate clustering techniques.

Contribution

It proposes a new approach to functional data clustering by reducing it to multivariate clustering through index transformations, which is a novel application of existing techniques.

Findings

Method performs well in simulation studies

Effective on real functional datasets

Outperforms some existing functional clustering methods

Abstract

Clustering techniques applied to multivariate data are a very useful tool in Statistics and have been fully studied in the literature. Nevertheless, these clustering methodologies are less well known when dealing with functional data. Our proposal consists of introducing a clustering procedure for functional data using the very well known techniques for clustering multivariate data. The idea is to reduce a functional data problem to a multivariate data problem by applying the epigraph and the hypograph indexes to the original data and to its first and second derivatives. All the information given by the functional data is therefore transformed to the multivariate context, being sufficiently informative for the usual multivariate clustering techniques to be efficient. The performance of this new methodology is evaluated through a simulation study and it is also illustrated through real data sets.