On the foundations of similarity in information access

Although computing similarity is one of the fundamental challenges of Information Access tasks, the notion of similarity in this context is not yet completely understood from a formal, axiomatic perspective. In this paper we show how axiomatic explanations of similarity from other fields (Tversky’s axioms from the point of view of cognitive sciences, and metric spaces from the point of view of algebra) do not completely fit the notion of similarity function in Information Access problems, and we propose a new set of formal constraints for similarity functions. Based on these formal constraints, we introduce a new parameterized similarity function, the information contrast model (ICM), which generalizes both pointwise mutual information and Tversky’s linear contrast model. Unlike previous similarity models, ICM satisfies the proposed formal constraints for a certain range of values of its parameters.