An algebraic approch to similarity and categorisation

Mehdi Dastani and Bipin Indurkhya

Abstract We extend Leeuwenberg's Structural Information Theory (SIT) to an algebraic framework, where domain-dependant operators are allowed to become part of perceptualgestalts. Using the SIT notation of information load, we provide a structural notion of similarity and categorisation. We introduce two complexity measures, namely descriptor complexity and member complexity, which drive categorisation to opposite extremes, and propose a simple additive function to find the optimum balance between the two. We remark on how context effect in similarity and categorisation can be modelled in our approach. Finally, we examine some implications of our work for empirical work on categorisation and similarity.