An Algebraic Approach to Similarity and Categorization

We extend Leeuwenberg's Structural Information Theory (SIT) to an algebraic framework, where domain-dependent operators are allowed to become part of the perceptual gestalts. Using the SIT notion ofìnforma-tion load', we provide a structural notion of similarity and categorization. We introduce two complexity measures , namely descriptor complexity and member complexity , which drive categorization to opposite extremes, and propose a simple additive function to nd an optimum balance between the two. We remark on how context eeect in similarity and categorization can be modeled in our approach. Finally, we examine some implications of our work for the empirical research on categorization and similarity.