Weights and Measures: An Axiomatic Model for Similarity Computations

This paper proposes a formal model for similarity functions, first over arbitrary objects, then over sets and the sorts of weighted sets that are found in text retrieval systems. Using a handful of axioms and constraints, we are able to make statements about the behavior of such functions in reference to set overlap and to noise. The model is then used to analyze, and we hope illuminate, several popular text similarity functions.