Packing: A Geometric Analysis of Feature Selection and Category Formation

This paper presents a geometrical analysis of how local interactions in a large population of categories packed into a feature space create a global structure of feature relevance. The theory is a formal proof that the joint optimization of discrimination and inclusion creates a smooth space of categories such that near categories in the similarity space have similar generalization gradients. Packing theory offers a unified account of several phenomena in human categorization including the differential importance of different features for different kinds of categories, the dissociation between judgments of similarity and judgments of category membership, and children's ability to generalize a category from very few examples.