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.

Previously published sets of classification and old-new recognition memory data are reanalyzed within the framework of an exemplar-based generalization model. The key assumption in the model is that, whereas classification decisions are based on the similarity of a probe to exemplars of a target category relative to exemplars of contrast categories, recognition decisions are based on overall summed similarity of a probe to all exemplars. The summed-similarity decision rule is shown to be consistent with a wide variety of recognition memory data obtained in classification learning situations and may provide a unified approach to understanding relations between categorization and recognition. Recently, there has been an upsurge of interest among categorization researchers in exploring relations between classification learning and old-new recognition memory. This interest has been fueled by the exemplar view of category representation, which holds that people base classification decisions on similarity comparisons with stored exemplars (Hintzman, 1986b; Medin & Schaffer, 1978; Nosofsky, 1986).

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-

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

Early theories of categorization assumed that either rules, or prototypes, or exemplars were exclusively used to mentally represent categories of objects. More recently, hybrid theories of categorization have been proposed that variously combine these different forms of category representation. Our research addressed the question of whether there are representational shifts during category learning. We report a series of experiments that tracked how individual subjects generalized their acquired category knowledge to classifying new critical transfer items as a function of learning. Individual differences were observed in the generalization patterns exhibited by subjects, and those generalizations changed systematically with experience. Early in learning, subjects generalized on the basis of single diagnostic dimensions, consistent with the use of simple categorization rules. Later in learning, subjects generalized in a manner consistent with the use of similarity-based exemplar retrieval, attending to multiple stimulus dimensions. Theoretical modeling was used to formally corroborate these empirical observations by comparing fits of rule, prototype, and exemplar models to the observed categorization data. Although we provide strong evidence for shifts in the kind of information used to classify objects as a function of categorization experience, interpreting these results in terms of shifts in representational systems underlying perceptual categorization is a far thornier issue. We provide a discussion of the

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An important element of learning from examples is the extraction of patterns and regularities from data. This paper investigates the structure of patterns in data defined over discrete features, i.e. features with two or more qualitatively distinct values. Any such pattern can be algebraically decomposed into a spectrum of component patterns, each of which is a simpler or more atomic ‘‘regularity.’ ’ Each component regularity involves a certain number of features, referred to as its degree. Regularities of lower degree represent simpler or more coarse patterns in the original pattern, while regularities of higher degree represent finer or more idiosyncratic patterns. The full spectral breakdown of a pattern into component regularities of minimal degree, referred to as its power series, expresses the original pattern in terms of the regular rules or patterns it obeys, amounting to a kind of ‘‘theory’ ’ of the pattern. The number of regularities at various degrees necessary to represent the pattern is tabulated in its power spectrum, which expresses how much of a pattern’s structure can be explained by regularities of various levels of complexity. A weighted mean of the pattern’s spectral power gives a useful numeric summary of its overall complexity, called its algebraic complexity. The basic theory of algebraic decomposition is extended in several ways, including algebraic accounts of the typicality of individual objects within concepts, and estimation of the power series from noisy data. Finally some relations between these algebraic quantities and empirical data are discussed.

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