Archetypal analysis for data-driven prototype identification

Prototypes, as Rosch (1973) defined the term in the cognitive sciences field, are ideal exemplars that summarize and represent groups of objects (or categories) and that are “typical" according to their internal resemblance and external dissimilarity vis-à-vis other groups or categories. In line with the cognitive approach, we propose a data-driven procedure for identifying prototypes that is based on archetypal analysis and compositional data analysis. The procedure presented here exploits the properties of archetypes, both in terms of their external dissimilarity in relation to other points in the data set and in terms of their ability to represent the data through compositions in a simplex in which it is possible to cluster all of the observations. The proposed procedure is useful not only for the usual real data points; it may also be used for interval-valued data, functional data, and relational data, and it provides well-separated and clearly profiled prototypes. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016