Functional archetype and archetypoid analysis
This provides incremental improvements for researchers analyzing functional data in fields like climate or social sciences.
The authors extended archetype and archetypoid analysis to functional data, proposing computational methods that work with any basis and are less demanding than discretization, and applied these to temperature and human development datasets.
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.