A unified quantitative approach to modeling subjects ' identification and categorization of multidimensional perceptual stimuli is proposed and tested. Two subjects identified and categorized the same set of perceptually confusable stimuli varying on separable dimensions. The identification data were modeled using Sbepard's (1957) multidimensional scaling-choice framework. This framework was then extended to model the subjects ' categorization performance. The categorization model, which generalizes the context theory of classification developed by Medin and Schaffer (1978), assumes that subjects store category exemplars in memory. Classification decisions are based on the similarity of stimuli to the stored exemplars. It is assumed that the same multidimensional perceptual representation underlies performance in both the identification and Categorization paradigms. However, because of the influence of selective attention, similarity relationships change systematically across the two paradigms. Some support was gained for the hypothesis that subjects distribute attention among component dimensions so as to optimize categorization performance. Evidence was also obtained that subjects may have augmented their category representations with inferred exemplars. Implications of the results for theories of multidimensional scaling and categorization are discussed.

The relationship between subjects ' identification and categorization learning of integral-dimension stimuli was studied within the framework of an exemplar-based generalization model. The model was used to predict subjects ' learning in six different categorization conditions on the basis of data obtained in a single identification learning condition. A crucial assumption in the model is that because of selective attention to component dimensions, similarity relations may change in systematic ways across different experimental contexts. The theoretical analysis provided evidence that, at least under unspeeded conditions, selective attention may play a critical role in determining the identification-categorization relationship for integral stimuli. Evidence was also provided that similarity among exemplars decreased as a function of identification learning. Various alternative classification models, including prototype, multiple-prototype, average distance, and "value-on-dimensions" models, were unable to account for the results. This article seeks to characterize performance relations between the two fundamental classification paradigms of identification and categorization. Whereas in an identification paradigm people identify stimuli as unique items (a one-to-one

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 cur-rently popular similarity theories do, and it accounts for identification data as well as the long-standing "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 cru-cial 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 simi-larity between a pair of stimuli, the more likely one will be con-fused with the other in a recognition task (e.g., Luce, 1963; Shepard, 1964; Tversky & Gati, 1982). Yet despite the poten-tially 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 ex-

Semantic networks produced from human data have statistical properties that cannot be easily captured by spatial representations. We explore a probabilistic approach to semantic representation that explicitly models the probability with which words occur in different contexts, and hence captures the probabilistic relationships between words. We show that this representation has statistical properties consistent with the large-scale structure of semantic networks constructed by humans, and trace the origins of these properties.

Subjects learned to classify perceptual stimuli varying along continuous, separable dimensions into rule-described categories. The categories were designed to contrast the predictions of a selective-attention exemplar model and a simple rule-based model formalizing an economy-ofdescription view. Converging evidence about categorization strategies was obtained by also collecting identification and recognition data and by manipulating strategies via instructions. In free-strategy conditions, the exemplar model generally provided an accurate quantitative account of identification, categorization, and recognition performance, and it allowed for the interrelationship of these paradigms within a unified framework. Analyses of individual subject data also provided some evidence for the use of rules, but in general, the rules seemed to have a great deal in common with exemplar storage processes. Classification and recognition performance for subjects given explicit instructions to use specific rules contrasted dramatically with performance in the free-strategy conditions and could not be predicted by the exemplar model. Markedly different theoretical approaches have been applied to account for the learning and representation of welldefined categories structured according to simple rules and more natural, ill-defined categories (Rosch, 1973; E. E. Smith & Medin, 1981). In the case of well-defined categories, it is generally assumed that people formulate and test hypotheses concerning the "rules " that determine category membership

When ratings of judged similarity or frequencies of stimulus identification are averaged across subjects, the psychological structure ofthe data is fundamentally changed. Regardless of the structure of the individual-subject data, the averaged similarity data will likely be well fit by a standard multidimensional scaling model, and the averaged identification data will likely be well fit by the similarity-choice model. In fact, both models often provide excellent fits to averaged data, even if they fail to fit the data of each individual subject. Thus, a good fit of either model to averaged data cannot be taken as evidence that the model describes the psychological structure that characterizes individual subjects. We hypothesize that these effects are due to the increased symmetry that is a mathematical consequence of the averaging operation. It is common practice to average across subjects when analyzing

In this article, the relation between the identification, similarity judgment, and categorization of multidimensional perceptual stimuli is studied. The theoretical analysis focused on general recognition theory (GRT), which is a multidimensional generalization of signal detection theory. In one application, 2 Ss first identified a set of confusable stimuli and then made judgments of their pairwise similarity. The second application was to Nosofsky's (1985b, 1986) identificationcategorization experiment. In both applications, a GRT model accounted for the identification data better than Luce's (1963) biased-cboice model. The identification results were then used to predict performance in the similarity judgment and categorization conditions. The GRT identification model accurately predicted the similarity judgments under the assumption that Ks allocated attention to the 2 stimulus dimensions differently in the 2 tasks. The categorization data were predicted successfully without appealing to the notion of selective attention. Instead, a simpler GRT model that emphasized the different decision rules used in identification and categorization was adequate. The perceptual processes involved when subjects identify, categorize, or judge the pairwise similarity of multidimensional perceptual stimuli are closely related (e.g., Ashby &

eflecting the importance or precision of dissimilarity # i j . 1. SOURCES OF DISTANCE DATA Dissimilarity information about a set of objects can arise in many different ways. We review some of the more important ones, organized by scientific discipline. 1.1. Geodesy. The most obvious application, perhaps, is in sciences in which distance is measured directly, although generally with error. This happens, for instance, in triangulation in geodesy. We have measurements which are approximately equal to distances, either Euclidean or spherical, depending on the scale of the experiment. In other examples, measured distances are less directly related to physical distances. For example, we could measure airplane or road or train travel distances between different cities. Physical distance is usually not the only factor determining these types of dissimilarities. 1 2 J. DE LEEUW<

predictions of exemplar models and that supported prototype models. In the authors ’ view, this evidence confounded the issue of the nature of the category representation with the type of response rule (probabilistic vs. deterministic) that was used. Also, their designs did not test whether the prototype models correctly predicted generalization performance. The present work demonstrates that an exemplar model that includes a response-scaling mechanism provides a natural account of all of Smith et al.’s experimental results. Furthermore, the exemplar model predicts classification performance better than the prototype models when novel transfer stimuli are included in the experimental designs. A classic issue in cognitive psychology concerns the manner in which people represent categories in memory. According to prototype models (Homa, 1984; Posner & Keele, 1968; Reed, 1972), people represent categories by forming a summary representation that is a central tendency of all of the experienced members of a

Image databases will force us to rethink many of the concepts that led us so far. One of these is matching. We argue that the fundamental operation in a content-indexed image database should not be matching the query against the images in the database in search of a "target" image that best matches the query. The basic operation in query-by-content will be ranking portions of the database with respect to similarity with the query. What kind of similarity measure should be used is a problem we begin exploring in this paper. We let psychological experiments guide us in the quest for a good similarity measure, and devise a measure derived from a set-theoretic measure proposed in the psychological literature, modified by the introduction of fuzzy logic. 1 Introduction What makes a multimedia database di#erent from the databases we have been using until now? Many things, one might say: there are di#erent ways to express a query (a sketch, an image...), a di#erence of several orders of mag...