Constrained variable clustering and the best basis problem in functional data analysis

TL;DR

This paper introduces a clustering method for functional data that simplifies functions into piecewise constant segments, leveraging contiguity constraints for efficient optimal solutions.

Contribution

It proposes a novel variable clustering approach tailored for functional data, optimizing piecewise constant representations with a polynomial complexity algorithm.

Findings

Efficient algorithm for optimal variable clustering in functional data

Reduction of redundancy in functional data representations

Improved data simplification for functional analysis

Abstract

Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simplification of the functions that reduces the redundancy induced by the regularity. In this paper we propose to use a clustering approach that targets variables rather than individual to design a piecewise constant representation of a set of functions. The contiguity constraint induced by the functional nature of the variables allows a polynomial complexity algorithm to give the optimal solution.