  Archetypal analysis represents a set of observations as convex combinations
of pure patterns, or archetypes. The original geometric formulation of finding
archetypes by approximating the convex hull of the observations assumes them to
be real valued. This, unfortunately, is not compatible with many practical
situations. In this paper we revisit archetypal analysis from the basic
principles, and propose a probabilistic framework that accommodates other
observation types such as integers, binary, and probability vectors. We
corroborate the proposed methodology with convincing real-world applications on
finding archetypal winter tourists based on binary survey data, archetypal
disaster-affected countries based on disaster count data, and document
archetypes based on term-frequency data. We also present an appropriate
visualization tool to summarize archetypal analysis solution better.
