The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds. A new set-theoretical approach to similarity is developed in which objects are represented as collections of features, and similarity is described as a featurematching process. Specifically, a set of qualitative assumptions is shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features. Several predictions of the contrast model are tested in studies of similarity with both semantic and perceptual stimuli. The model is used to uncover, analyze, and explain a variety of empirical phenomena such as the role of common and distinctive features, the relations between judgments of similarity and difference, the presence of asymmetric similarities, and the effects of context on judgments of similarity. The contrast model generalizes standard representations of similarity data in terms of clusters and trees. It is also used to analyze the relations of prototypicality and family resemblance. 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. 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) Similarity or dissimilarity data appear in different forms: ratings of pairs, sorting of objects, communality between associations, This paper benefited from fruitful discussions with
One of the first researchers dealing with the asymmetric approach in data analysis was A. Tversky, who questioned the geometric representation of similarity REF .
Features of similarity.
Psychological Review
Mathematics