  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.
