A multidimensional stochastic theory of similarity

Abstract

A multidimensional theory of similarity in which the mental representations of stimulus objects are assumed to be drawn from multivariate normal distributions is described. A distance-based similarity function is defined and the expected value of similarity is derived. This theory is the basis for a possible explanation of paradoxical results with highly similar stimuli regarding the form of the similarity function and the distance metric. A stochastic approach to multidimensional scaling based on same-different judgments is demonstrated using artificial and real data sets. The theory of similarity presented is used as a basis for a Thurstonian extension of Shepard's model of identification performance.