Convexity is a Fundamental Feature of Efficient Semantic Compression in Probability Spaces.

Abstract

This thesis investigates the relationship between convexity and efficient communication using a probabilistic communication model applied to color space. It builds on previous work investigating the plausibility and potential source(s) of Gardenf ̈or's proposed semantic universal: that all subsets of color space affiliated with a particular color term are convex sets. The analysis undertaken in this project makes two major contributions to the existing literature. • First, this project establish a new metric which defines a quantitative measure of convexity that can be applied to probabilistic communication models. • Second, it demonstrates that convexity is an essential feature of efficient color-naming systems, where efficiency is determined with respect to a trade-off between accuracy and complexity. Furthermore, this project demonstrates that convexity is a more significant predictor of communication efficiency than either accuracy or complexity.