Similarity, separability, and the triangle inequality

An alternative analysis of geometric models of proximity data, based on a feature-matching model, leads to the coincidence hypothesis that the dissimilarity between objects that differ on 2 separable dimensions is larger than predicted from their unidimensional differences on the basis of the triangle inequality and segmental additivity. A series of studies of 2-dimensional stimuli with separable attributes (including house plants, parallelograms, schematic faces, and histograms), using judgments of similarity and dissimilarity, classification, inference, and recognition errors, all support the coincidence hypothesis. The size of the effect is determined by the separability of the stimuli, the transparency of the dimensional structure, and the discriminability of the levels within each dimension. Applications of the coincidence effect to inductive inference are investigated, and its relations to selective attention and spatial density are discussed. It is concluded that the triangle inequality and segmental additivity cannot be jointly satisfied for separable attributes. The implications of this result for multidimensional scaling are discussed. (57 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved).