Recognition vs. classification of ill-defined category exemplars

In Experiment 1, subjects were trained on three ill-defined categories represented by 4, 8, and 12 exemplars. Learning was followed by either a classification test on old, new, and random exemplars or a recognition test in which each learning exemplar was presented with two foils, both equidistant to the learning exemplar, but one more similar to the category prototype than the other. In Experiment 2, category size was manipulated between subjects, followed by the recognition test. Recognition data indicated that increasing the number of learning exemplars did not increase the total amount of exemplar information retained for each category. In addition, the more prototypical foil was incorrectly recognized more often than the less prototypical foil. Classification data replicated previous findings that increasing category size in learning enhances classification of new exemplars. The results were interpreted in terms of the relative amounts of categorical and idiosyncratic information that were retained from the original learning stimuli. It was proposed that categorical information can become a more dominant determinant of performance as category size increases.     

Speeded classification in a probabilistic category structure: contrasting exemplar-retrieval, decision-boundary, and prototype models

Speeded perceptual classification experiments were conducted to distinguish among the predictions of exemplar-retrieval, decision-boundary, and prototype models. The key manipulation was that across conditions, individual stimuli received either probabilistic or deterministic category feedback. Regardless of the probabilistic feedback, however, an ideal observer would always classify the stimuli by using an identical linear decision boundary. Subjects classified the probabilistic stimuli with lower accuracy and longer response times than they classified the deterministic stimuli. These results are in accord with the predictions of the exemplar model and challenge the predictions of the prototype and decision-boundary models.     

Representation at different levels in a conceptual hierarchy

The present study examines the influence of hierarchical level on category representation. Three computational models of representation – an exemplar model, a prototype model and an ideal representation model – were evaluated in their ability to account for the typicality gradient of categories at two hierarchical levels in the conceptual domain of clothes. The domain contains 20 subordinate categories (e.g., trousers, stockings and underwear) and an encompassing superordinate category (CLOTHES). The models were evaluated both in terms of their ability to fit the empirical data and their generalizability through marginal likelihood. The hierarchical level was found to clearly influence the type of representation: For concepts at the subordinate level, exemplar representations were supported. At the superordinate level, however, an ideal representation was overwhelmingly preferred over exemplar and prototype representations. This finding contributes to the increasingly dominant view that the human conceptual apparatus adopts both exemplar representations and more abstract representations, contradicting unitary approaches to categorization.     

Distinguishing prototype-based and exemplar-based processes in dot-pattern category learning

The authors contrast exemplar-based and prototype-based processes in dot-pattern categorization. In Experiments 1A and 1B, participants provided similarity ratings of dot-distortion pairs that were distortions of the same originating prototype. The results show that comparisons to training exemplars surrounding the prototype create flat typicality gradients within a category and small prototype-enhancement effects, whereas comparisons to a prototype center create steep typicality gradients within a category and large prototype-enhancement effects. Thus, prototype and exemplar theories make different predictions regarding common versions of the dot-distortion task. Experiment 2 tested these different predictions by having participants learn dot-pattern categories. The steep typicality gradients, the large prototype effects, and the superior fit of prototype models suggest that participants refer to-be-categorized items to a representation near the category's center (the prototype), and not to the training exemplars that surround the prototype.     

6岁儿童的类别学习能力:类别表征、注意和分类策略

探讨了6岁儿童的类别学习能力、类别表征和分类策略。62名儿童参加了实验,实验1采用了"5/4模型"类别结构,实验2采用了"3/3类别结构"。结果发现:6岁儿童已经具备了一定的类别学习能力;相对于原型表征,6岁儿童更倾向于进行样例表征;6岁儿童在注意上具有定位在高典型性特征维度上的能力,但不具备定位在区分性特征维度上的能力;在类别学习策略上主要采用单维度分类策略和规则加例外的分类策略。     

The modulating influence of category size on the classification of exception patterns

Generalization gradients to exception patterns and the category prototype were investigated in two experiments. In Experiment 1, participants first learned categories of large size that contained a single exception pattern, followed by a transfer test containing new instances that had a manipulated similarity relationship to the exception or a nonexception training pattern as well as distortions of the prototype. The results demonstrated transfer gradients tracked the prototype category rather than the feedback category of the exception category. In Experiment 2, transfer performance was investigated for categories varying in size (5, 10, 20), partially crossed with the number of exception patterns (1, 2, 4). Here, the generalization gradients tracked the feedback category of the training instance when category size was small but tracked the prototype category when category size was large. The benefits of increased category size still emerged, even with proportionality of exception patterns held constant. These, and other outcomes, were consistent with a mixed model of classification, in which exemplar influences were dominant with small-sized categories and/or high error rates, and prototype influences were dominant with larger sized categories.     

The modulating influence of category size on the classification of exception patterns

Generalization gradients to exception patterns and the category prototype were investigated in two experiments. In Experiment 1, participants first learned categories of large size that contained a single exception pattern, followed by a transfer test containing new instances that had a manipulated similarity relationship to the exception or a nonexception training pattern as well as distortions of the prototype. The results demonstrated transfer gradients tracked the prototype category rather than the feedback category of the exception category. In Experiment 2, transfer performance was investigated for categories varying in size (5, 10, 20), partially crossed with the number of exception patterns (1, 2, 4). Here, the generalization gradients tracked the feedback category of the training instance when category size was small but tracked the prototype category when category size was large. The benefits of increased category size still emerged, even with proportionality of exception patterns held constant. These, and other outcomes, were consistent with a mixed model of classification, in which exemplar influences were dominant with small-sized categories and/or high error rates, and prototype influences were dominant with larger sized categories.     

知道与不知道要学多少：类别学习中样例量的预期作用

采用“5/4模型”类别结构探讨了类别学习中样例量的预期作用。设置了两种学习条件(“知道样例量”和“不知道样例量”), 分别探讨两种学习条件下的学习效率、学习策略以及所形成的类别表征。106名大学生参加了实验, 结果表明：在类别学习中, 样例量的预期作用显著, 知道样例量组的学习效率高于不知道样例量组; 样例量的预期作用对类别学习效率的影响是通过影响学习过程中使用的策略来实现的; 样例量的预期作用不影响两种学习条件的学习后形成的类别表征, 且两种学习条件的被试自始至终表现出样例学习的表征模式。     

Dissimilarity is used as evidence of category membership in multidimensional perceptual categorization: a test of the similarity-dissimilarity generalized context model

In exemplar models of categorization, the similarity between an exemplar and category members constitutes evidence that the exemplar belongs to the category. We test the possibility that the dissimilarity to members of competing categories also contributes to this evidence. Data were collected from two 2-dimensional perceptual categorization experiments, one with lines varying in orientation and length and the other with coloured patches varying in saturation and brightness. Model fits of the similarity-dissimilarity generalized context model were used to compare a model where only similarity was used with a model where both similarity and dissimilarity were used. For the majority of participants the similarity-dissimilarity model provided both a significantly better fit and better generalization, suggesting that people do also use dissimilarity as evidence.     

Exemplars, prototypes, and the flexibility of classification models

J. P. Minda and J. D. Smith (2001) showed that a prototype model outperforms an exemplar model, especially in larger categories or categories that contained more complex stimuli. R. M. Nosofsky and S. R. Zaki (2002) showed that an exemplar model with a response-scaling mechanism outperforms a prototype model. The authors of the current study investigated whether excessive model flexibility could explain these results. Using cross-validation, the authors demonstrated that both the prototype model and the exemplar model with a response-scaling mechanism suffered from overfilling in the linearly separable category structure. The results illustrate the need to make sure that the best-fitting model is not chasing error variance instead of variance attributed to the cognitive process it is supposed to model.     

Classification response times in probabilistic rule-based category structures: Contrasting exemplar-retrieval and decision-boundary models

Experiments were conducted to contrast the predictions from exemplar models and rule-based decisionboundary models of perceptual classification. Observers classified multidimensional stimuli into categories that could be described in terms of easily verbalized logical rules. The critical manipulation was that some pairs of stimuli received probabilistic feedback, whereas other control pairs received deterministic feedback. Despite the probabilistic feedback, the probabilistic pairs and the deterministic pairs were the same distance from idealobserver, rule-based decision boundaries. Across two experiments with varying category structures, observers classified the probabilistic pairs with slower response times (RTs) and lower accuracies than the comparison deterministic pairs. The effects were relatively long term, extending into test blocks in which all feedback was withheld. The results were as predicted by exemplar models, but challenged models that posit that RT is a function solely of the distance of a stimulus from rule-based boundaries. The studies add considerable generality to previous ones and suggest that, even in domains involving rule-based category structures, exemplar-retrieval processes play a significant role. Supplemental materials related to this article may be downloaded from http:// mc.psychonomic-journals.org/content/supplemental.     

Combining exemplar-based category representations and connectionist learning rules.

Adaptive network and exemplar-similarity models were compared on their ability to predict category learning and transfer data. An exemplar-based network (Kruschke, 1990a, 1990b, 1992) that combines key aspects of both modeling approaches was also tested. The exemplar-based network incorporates an exemplar-based category representation in which exemplars become associated to categories through the same error-driven, interactive learning rules that are assumed in standard adaptive networks. Experiment 1, which partially replicated and extended the probabilistic classification learning paradigm of Gluck and Bower (1988a), demonstrated the importance of an error-driven learning rule. Experiment 2, which extended the classification learning paradigm of Medin and Schaffer (1978) that discriminated between exemplar and prototype models, demonstrated the importance of an exemplar-based category representation. Only the exemplar-based network accounted for all the major qualitative phenomena; it also achieved good quantitative predictions of the learning and transfer data in both experiments.     

Exemplar theory's predicted typicality gradient can be tested and disconfirmed

One of exemplar theory's central predictions concerns the shape of typicality gradients. The typicality gradient it predicts is a consequence of its exemplar–based comparisons and appears no matter how the theory is evaluated. However, this predicted typicality gradient does not fit the empirical typicality gradients obtained in an influential version of the dot–distortion category task, and this is true even when the exemplar model is made more flexible and mathematically powerful. Thus, exemplar theory is disconfirmed in this domain of categorization. In contrast, prototype theories are consistent with the empirically obtained typicality gradients.     

Expanding the search for a linear separability constraint on category learning

Formal models of categorization make different predictions about the theoretical importance of linear separability. Prior research, most of which has failed to find support for a linear separability constraint on category learning, has been conducted using tasks that involve learning two categories with a small number of members. The present experiment used four categories with three or nine patterns per category that were either linearly separable or not linearly separable. With overall category structure equivalent across category types, the linearly separable categories were found to be easier to learn than the not linearly separable categories. An analysis of individual participants' data showed that there were more participants operating under a linear separability constraint when learning large categories than when learning small ones. Formal modeling showed that an exemplar model could not account for many of these data. These results are taken to support the existence of multiple processes in categorization.     

Conceptual complexity and the bias/variance tradeoff

In this paper we propose that the conventional dichotomy between exemplar-based and prototype-based models of concept learning is helpfully viewed as an instance of what is known in the statistical learning literature as the bias/variance tradeoff. The bias/variance tradeoff can be thought of as a sliding scale that modulates how closely any learning procedure adheres to its training data. At one end of the scale (high variance), models can entertain very complex hypotheses, allowing them to fit a wide variety of data very closely—but as a result can generalize poorly, a phenomenon called overfitting. At the other end of the scale (high bias), models make relatively simple and inflexible assumptions, and as a result may fit the data poorly, called underfitting. Exemplar and prototype models of category formation are at opposite ends of this scale: prototype models are highly biased, in that they assume a simple, standard conceptual form (the prototype), while exemplar models have very little bias but high variance, allowing them to fit virtually any combination of training data. We investigated human learners’ position on this spectrum by confronting them with category structures at variable levels of intrinsic complexity, ranging from simple prototype-like categories to much more complex multimodal ones. The results show that human learners adopt an intermediate point on the bias/variance continuum, inconsistent with either of the poles occupied by most conventional approaches. We present a simple model that adjusts (regularizes) the complexity of its hypotheses in order to suit the training data, which fits the experimental data better than representative exemplar and prototype models.     

The influence of category representations on exemplar generation

The present study examined the influence of category representations on exemplar generation, which has been neglected in previous category research. An experiment on college students manipulated the category representation of insects in three conditions (prototypes, exemplars, and the hybrid of prototypes and exemplars). Participants were asked to generate as many exemplars as possible. The results demonstrate that category representations affect and constrain exemplar generation. The new findings are as follows. In the prototype and hybrid conditions with the prototype representation, people tend to generate more valid exemplars by using the prototype mutation mechanism, and exemplar generation conforms to the family resemblance structure. Exemplar generation in the hybrid condition is additionally constrained by known exemplars. In the exemplar condition, people tend to generate fewer valid exemplars by using miscellaneous strategies, and their exemplar generation may not conform to the family resemblance structure.     

Refining the visual-cortical hypothesis in category learning

Participants produce steep typicality gradients and large prototype-enhancement effects in dot-distortion category tasks, showing that in these tasks to-be-categorized items are compared to a prototypical representation that is the central tendency of the participant’s exemplar experience. These prototype-abstraction processes have been ascribed to low-level mechanisms in primary visual cortex. Here we asked whether higher-level mechanisms in visual cortex can also sometimes support prototype abstraction. To do so, we compared dot-distortion performance when the stimuli were size constant (allowing some low-level repetition-familiarity to develop for similar shapes) or size variable (defeating repetition-familiarity effects). If prototype formation is only mediated by low-level mechanisms, stimulus-size variability should lessen prototype effects and flatten typicality gradients. Yet prototype effects and typicality gradients were the same under both conditions, whether participants learned the categories explicitly or implicitly and whether they received trial-by-trial reinforcement during transfer tests. These results broaden out the visual-cortical hypothesis because low-level visual areas, featuring retinotopic perceptual representations, would not support robust category learning or prototype-enhancement effects in an environment of pronounced variability in stimulus size. Therefore, higher-level cortical mechanisms evidently can also support prototype formation during categorization.     

Exemplars, prototypes, similarities, and rules in category representation: an example of hierarchical bayesian analysis

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis can provide a unifying explanation of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models.     

Episodic and prototype models of category learning

The question of what processes are involved in the acquisition and representation of categories remains unresolved despite several decades of research. Studies using the well-known prototype distortion task (Posner and Keele in J Exp Psychol 77:353–363, 1968) delineate three candidate models. According to exemplar-based models, we memorize each instance of a category and when asked to decide whether novel items are category members or not, the decision is explicitly based on a similarity comparison with each stored instance. By contrast, prototype models assume that categorization is based on the similarity of the target item to an implicit abstraction of the central tendency or average of previously encountered instances. A third model suggests that the categorization of prototype distortions does not depend on pre-exposure to study exemplars at all and instead reflects properties of the stimuli that are easily learned during the test. The four experiments reported here found evidence that categorization in this task is predicated on the first and third of these models, namely transfer at test and the exemplar-based model. But we found no evidence for the second candidate model that assumed that categorization is based on implicit prototype abstraction.