Similarity and entropy

Abstract

Given a set of objects, and given a set of properties and the values of the properties as they are applied to each of the objects, we wish to determine how similar the members of any subset of the objects are to each other. Such a similarity represents a redundancy among the objects in the subset. Knowledge of the similarity reduces ignorance as to which members of the full set are in the subset. This is a reduction in entropy which can serve as a measure of the similarity within the subset. Such a measure has the advantage that it takes into account any dependencies which may exist among the given properties. In this respect it differs from other proposed measures.