Title

A Model of Human Categorization and Similarity Based Upon Category Theory

Authors

Michael Healy
Thomas Caudell
Timothy Goldsmith

Document Type

Technical Report

Publication Date

7-1-2008

Abstract

Categorization and the judgement of similarity are fundamental in cognition. We propose that these and other activities are based upon an underlying structure of knowledge, or concept representation, in the brain. Further, we propose that this structure can be represented mathematically in a declarative form via category theory, the mathematical theory of structure. We test the resulting mathematical model in an experiment in which human subjects provide judgements of similarity for pairs of line drawings using a numerical scale to represent degrees of similarity. The resulting numerical similarities are compared with those derived from the category-theoretic model by comparing diagrams. The diagrams represent distributed concept structures underlying the line drawings. To compare with a more conventional analysis technique, we also compare the human judgements with those provided by a two-dimensional feature space model equipped with a distance metric for the line drawings. The results are equally favorable for both models. Because of this and the putative explanatory power of the category-theoretic model, we propose that this model is worthy of further exploration as a mathematical model for cognitive science.

Comments

This report is intended to be read easily by cognitive scientists, neuroscientists interested in cognition, engineers, and scientific investigators in other fields.

Recommended Citation

Healy, Michael; Thomas Caudell; and Timothy Goldsmith. "A Model of Human Categorization and Similarity Based Upon Category Theory." (2008). https://digitalrepository.unm.edu/ece_rpts/28