Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density.

Abstract

In a recent article, Tversky questioned the application of geometric models to similarity data and proposed an alternative set-theoretic approach. He suggested that geometric models are inappropriate because the similarity data may violate the metric assumptions underlying such models. In addition, he demonstrated that the stimulus context and the nature of the experimental task can affect the similarity relations. The present article suggests that a geometric approach may be compatible with these effects if the traditional multidimensional scaling model is augmented by the assumption that spatial density in the configuration has an effect on the similarity measure. A distance-densi ty model is outlined that assumes that similarity is a function of both interpoint distance and the spatial density of other stimulus points in the surrounding region of the metric space. The proposed relationship between similarity and spatial density is supported by empirical evidence. The distance-density model is shown to be able to account for violations of the metric axioms and certain context and task effects. A number of other issues are discussed with respect to geometric and set-theoretic models of similarity.