Abstract

Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimulus and response generalization in learning, it is employed to explain errors in memory and pattern recognition, and it is central to the analysis of connotative meaning. Similarity or dissimilarity data appear in di¤erent forms: ratings of pairs, sorting of objects, communality between associations, errors of substitution, and correlation between occurrences. Analyses of these data attempt to explain the observed similarity relations and to capture the underlying structure of the objects under study. The theoretical analysis of similarity relations has been dominated by geometric models. These models represent objects as points in some coordinate space such that the observed dissimilarities between objects correspond to the metric distances between the respective points. Practically all analyses of proximity data have been metric in nature, although some (e.g., hierarchical clustering) yield tree-like structures rather than dimensionally organized spaces. However, most theoretical and empirical analyses of similarity assume that objects can be adequately represented as points in some coordinate space and that dissimilarity behaves like a metric distance function. Both dimensional and metric assumptions are open to question. It has been argued by many authors that dimensional representations are appropriate for certain stimuli (e.g., colors, tones) but not for others. It seems more appropriate to represent faces, countries, or personalities in terms of many qualitative features than in terms of a few quantitative dimensions. The assessment of similarity between such stimuli, therefore, may be better described as a comparison of features rather than as the computation of metric distance between points. A metric distance function, d, is a scale that assigns to every pair of points a nonnegative number, called their distance, in accord with the following three axioms: Minimality: dða; bÞ b dða; aÞ ¼ 0: Symmetry: dða; bÞ ¼ dðb; aÞ: The triangle inequality: dða; bÞ þ dðb; cÞ b dða; cÞ: To evaluate the adequacy of the geometric approach, let us examine the validity of the metric axioms when d is regarded as a measure of dissimilarity. The minimality axiom implies that the similarity between an object and itself is the same for all