Statistical Archetypal Analysis for Cognitive Categorization

Human knowledge develops through complex relationships between categories. In the era of Big Data, the concept of categorization implies data summa-rization in a limited number of well-separated groups that must be maximally and internally homogeneous at the same time. This proposal exploits archetypal analysis capabilities by finding a set of extreme points that can summarize entire data sets in homogeneous groups. The archetypes are then used to identify the best prototypes according to Rosch’s definition. Finally, in the geometric approach to cognitive science, the Voronoi tessellation based on the prototypes is used to define categorization. An example using a well-known wine dataset by Forina et al. illustrates the procedure.