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

Experiments were conducted in which Ss made classification, recognition, and similarity judgments for 34 schematic faces. A multidimensional scaling (MDS) solution for the faces was derived on the basis of the similarity judgments. This MDS solution was then used in conjunction with an exemplar-similarity model to accurately predict Ss ' classification and recognition judgments. Evidence was provided that Ss allocated attention to the psychological dimensions differentially for classification and recognition. The distribution of attention came close to the ideal-observer distribution for classification, and some tendencies in that direction were observed for recognition. Evidence was also provided for interactive effects of individual exemplar frequencies and similarities on classification and recognition, in accord with the predictions of the exemplar model. Unexpectedly, however, the frequency effects appeared to be larger for classification than for recognition. The purpose of this study was to provide tests of a model for relating perceptual classification performance and oldnew recognition memory. The model under investigation is the context theory of classification proposed by Medin and

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-

this article, we present a model of similarity comparison that makes specific time course predictions, which were tested in three experiments. Before turning to that model, we first outline the need for a consideration of similarity processes

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 &

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Multidimensional scaling models of stimulus domains are widely used as a representational basis for cognitive modeling. These representations associate stimuli with points in a coordinate space that has some predetermined number of dimensions. Although the choice of dimensionality can significantly influence cognitive modeling, it is often made on the basis of unsatisfactory heuristics. To address this problem, a Bayesian approach to dimensionality determination, based on the Bayesian Information Criterion (BIC), is developed using a probabilistic formulation of multidimensional scaling. The BIC approach formalizes the trade-off between data-fit and model complexity implicit in the problem of dimensionality determination and allows for the explicit introduction of information regarding data precision. Monte Carlo simulations are presented that indicate, by using this approach, the determined dimensionality is likely to be accurate if either a significant number of stimuli are considered or a reasonable estimate of precision is available. The approach is demonstrated using an established data set involving the judged pairwise similarities between a set of geometric stimuli. 2001 Academic Press COGNITIVE MODELING AND MULTIDIMENSIONAL SCALING

Data visualizatio n has the poE tialto assist humans in analyzing and co prehending large vo umes o data, andto detect patterns, clusters ando utliers that are n o o vi oq using noq graphical f ms o presentatiot Fo this reas oq data visualizatio ns have an impo rtant ro le to play in a diverse range o applied pro blems, including data explo atio n and mining, info rmatio n retrieval, and intelligence analysis.

v Declaration .................................... ix Acknowledgements................................ xi 1Prelude 1 TheVeryIdeaofRepresentation......................... 2 TypesofSimilarity ................................ 8 IsSimilarityIndeterminate? ........................... 11 TheRoleofSimilarityinCognition....................... 11 Summary&GeneralDiscussion......................... 14 2 Theories of Similarity 17 SimilarityDataSets................................ 17 SpatialRepresentation .............................. 21 FeaturalRepresentation.............................. 31 TreeRepresentation................................ 40 NetworkRepresentation ............................. 47 Alignment-BasedSimilarityModels....................... 48 TransformationalSimilarityModels ....................... 50 Summary&GeneralDiscussion......................... 54 i 3 On Representational Complexity 55 ApproachestoModelSelection ......................... 57 ChoosinganAdditiveClusteringRepresentation ................ 67 ChoosinganAdditiveTreeRepresentation ................... 82 ChoosingaSpatialRepresentation........................ 94 Summary&GeneralDiscussion......................... 95 4 Featural Representation 97 AMenagerieofFeaturalModels......................... 98 ClusteringModels.................................104 GeometricComplexityCriteria..........................106 AlgorithmsforFittingFeaturalModels .....................107 MonteCarloStudyI:DotheAlgorithmsWork? ................109 RepresentationsofKinshipTerms ........................117 MonteCarloStudyII:Complexity........................122 ExperimentI:Faces................................125 ExperimentII:Countries .............................1...