Toward a unified theory of similarity and recognition.

Abstract

A new theory of similarity, rooted in the detection and recognition literatures, is developed. The general recognition theory assumes that the perceptual effect of a stimulus is random but that on any single trial it can be represented as a point in a multidimensional space. Similarity is a function of the overlap of perceptual distributions. It is shown that the general recognition theory contains Euclidean distance models of similarity as a special case but that unlike them, it is not constrained by any distance axioms. Three experiments are reported that test the empirical validity of the theory. In these experiments the general recognition theory accounts for similarity data as well as the currently popular similarity theories do, and it accounts for identification data as well as the longstanding champion identification model does. The concept of similarity is of fundamental importance in psychology. Not only is there a vast literature concerned directly with the interpretation of subjective similarity judgments (e.g., as in multidimensional scaling) but the concept also plays a crucial but less direct role in the modeling of many psychophysical tasks. This is particularly true in the case of pattern and form recognition. It is frequently assumed that the greater the similarity between a pair of stimuli, the more likely one will be confused with the other in a recognition task (e.g., Luce, 1963; Shepard, 1964; Tversky & Gati, 1982). Yet despite the potentially close relationship between the two, there have been only a few attempts at developing theories that unify the similarity and recognition literatures. Most attempts to link the two have used a distance-based similarity measure to predict the confusions in recognition experiments (Appelman & Mayzner, 1982; Getty, Swets, & Swets, 1980; Getty, Swets, Swets, & Green, 1979; Nakatani, 1972; Nosofsky, 1984, 1985b, 1986; Shepard, 1957, 1958b). It is now widely suspected, however, that standard distance-based similarity measures do not provide an adequate account of perceived similarity (e.g., Krumhansl, 1978; Tversky, 1977). Our approach takes the opposite tack. We begin with a very powerful and general theory of recognition and use it to derive a new similarity measure, which successfully accounts for a wide variety of similarity results in both the recognition and the similarity literatures. The theory, which we call the general recognition theory, is rooted in the detection and recognition literatures and, in fact, is a multivariate generalization of signal-detection