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.

haracterized by descriptions of each module and how each serves in those tasks for which it is best suited. However, these theories often do not emphasize how modules interact in producing responses and in learning. In this article we will develop a modular theory of categorization that follows from two distinct accounts of this behavior. The first account is that of rule-based theories of categorization. These theories emerge from a philosophical tradition in which concepts and categorization are described in terms of definitional rules. For example, if a living thing has a wide, flat tail and constructs dams by cutting down trees with its This work was supported by Indiana University Cognitive Science Program Fellowships and by NIMH ResearchTraining Grant PHS-T32-MH19879-03 to Erickson, and in part by NIMH FIRST Award 1-R29-MH51572-01 to Kruschke. This research was reported as a poster at the 1996 Cognitive Science Society Conference in San Diego, CA. We than

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-

structure. Perceptual classification learning experiments were conducted in which presentation frequencies of individual exemplars were manipulated. The exemplars had varying degrees of similarity to members of the target and contrast categories. Classification accuracy and typicality ratings increased for exemplars presented with high frequency and for members of the target category that were similar to the high-frequency exemplars. Typicality decreased for members of the contrast category that were similar to the high-frequency exemplars. A frequency-sensitive similarity-to-exemplars model provided a good quantitative account of the classification learning and typicality data. The interactive relations among similarity, frequency, and categorization are considered in the General Discussion. Among the most well-established findings in the categorization literature is that categories have "graded structures"

A scheme for recognizing 3D objects from single 2D images is introduced. The scheme proceeds in two stages. In the first stage, the categorization stage, the image is compared to prototype objects. For each prototype, the view that most resembles the image is recovered, and, if the view is found to be similar to the image, the class identity of the object is determined. In the second stage, the identification stage, the observed object is compared to the individual models of its class, where classes are expected to contain objects with relatively similar shapes. For each model, a view that matches the image is sought.

A continuum between purely isolated and purely interrelated concepts is described. A concept is interrelated to the extent that it is influenced by other concepts. Methods for manipulating and identiying a concept's degree of interrelatedness are introduced. Relatively isolated concepts are empirically identified by a relatively large use of nondiagnostic features, and by better categorization performance for a concept's prototype than for a caricature of the concept. Relatively interrelated concepts are identified by minimal use of nondiagnostic features, and by better categorization performance for a caricature than a prototype. A concept is likely to be relatively isolated when: subjects are instructed to create images for their concepts rather than find discriminating features, concepts are given unrelated labels, and the categories that are displayed alternate rarely between trials. The entire set of manipulations and measurements supports a graded distinction between isolated and interrelated concepts. The distinction is applied to current models of category learning, and a connectionist framework for interpreting the empirical results is presented. Modern research on concept representation and learning has evolved from two traditions. One tradition connects concept acquisition with language in general and word learning in specific (Lakoff, 1986; Saussure, 1915/1959). Concepts are approximately equated with single words or phrases. In this tradition, for example, evidence that a child has acquired the adult concept of dog comes from the child's use of the word "dog" to designate dogs. The other tradition connects concept acquisition with object recognition (Biederman, 1987). From this perspective, concept learning involves learning to correctly cate...

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Human concept learning presents a version of the classic problem of induction, which is made particularly difficult by the combination of two requirements: the need to learn from a rich (i.e. nested and overlapping) vocabulary of possible concepts and the need to be able to generalize concepts reasonably from only a few positive examples. I begin this thesis by considering a simple number concept game as a concrete illustration of this ability. On this task, human learners can with reasonable confidence lock in on one out of a billion billion billion logically possible concepts, after seeing only four positive examples of the concept, and can generalize informatively after seeing just a single example. Neither of the two classic approaches to inductive inference -- hypothesis testing in a constrained space of possible rules and computing similarity to the observed examples -- can provide a complete picture of how people generalize concepts in even this simple setting. This thesis prop...

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.

The variability in the interpretation of reciprocal expressions has been extensively addressed in the literature and received detailed semantic accounts. After pointing out a central empirical limitation of previous logical accounts of reciprocity, we argue that these approaches suffer from inadequacies due to ignoring typicality