Fuzzy prototypes: From a cognitive view to a machine learning principle

Abstract. Cognitive psychology works have shown that the cognitive representa-tion of categories is based on a typicality notion: all objects of a category do not have the same representativeness, some are more characteristic or more typical than others, and better exemplify their category. Categories are then defined in terms of prototypes, i.e. in terms of their most typical elements. Furthermore, these works showed that an object is all the more typical of its category as it shares many fea-tures with the other members of the category and few features with the members of other categories. In this paper, we propose to profit from these principles in a machine learning framework: a formalization of the previous cognitive notions is presented, leading to a prototype building method that makes it possible to characterize data sets taking into account both common and discriminative features. Algorithms exploiting these prototypes to perform tasks such as classification or clustering are then presented. The formalization is based on the computation of typicality degrees that measure the representativeness of each data point. These typicality degrees are then exploite