Functional archetype and archetypoid analysis

TL;DR

This paper extends archetype and archetypoid analysis to functional data, introducing computational methods applicable to any basis, and demonstrates their use on temperature data and human development studies.

Contribution

It develops a new methodology for functional archetype analysis that works with any basis and is computationally efficient, expanding the applicability of these techniques.

Findings

Method works with any basis, not just orthogonal

Applied to Canadian temperature data successfully

Extended to multivariate functional data analysis

Abstract

Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set. Well-known Canadian temperature data are used to illustrate the analysis developed. Computational methods are proposed for performing these analyses, based on the coefficients of a basis. Unlike a previous attempt to compute functional archetypes, which was only valid for an orthogonal basis, the proposed methodology can be used for any basis. It is computationally less demanding than the simple approach of discretizing the functions. Multivariate functional archetype and archetypoid analysis are also introduced and applied in an interesting problem about the study of human development around the world over the last 50 years. These tools can contribute to the understanding of a functional data set, as in the multivariate case.