Exemplar and prototype models revisited: response strategies,selective attention,and stimulus generalization

J. D. Smith and colleagues (J. P. Minda & J. D. Smith, 2001; J. D. Smith & J. P. Minda, 1998,2000; J. D. Smith, M. J. Murray, & J. P. Minda, 1997) presented evidence that they claimed challenged the 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.     

Prototype and exemplar accounts of category learning and attentional allocation: a reassessment

In a recent article. J. P. Minda and J. D. Smith (2002; see record 2002-00620-002) argued that an exemplar model provided worse quantitative fits than an alternative prototype model to individual subject data from the classic D. L. Medin and M. M. Schaffer (1978) 5/4 categorization paradigm. In addition, they argued that the exemplar model achieved its fits by making untenable assumptions regarding how observers distribute their attention. In this article, we demonstrate that when the models are equated in terms of their response-rule flexibility, the exemplar model provides a substantially better account of the categorization data than does a prototype or mixed model. In addition, we point to shortcomings in the attention-allocation analyses conducted by J. P. Minda and J. D. Smith (2002). When these shortcomings are corrected, we find no evidence that challenges the attention-allocation assumptions of the exemplar model.     

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.     

Exemplar representation without generalization? Comment on Smith and Minda's (2000) "Thirty categorization results in search of a model"

J. D. Smith and J. P. Minda (2000) conducted a meta-analysis of 30 data sets reported in the classification literature that involved use of the "5-4" category structure introduced by D. L. Medin and M. M. Schaffer (1978). The meta-analysis was aimed at investigating exemplar and elaborated prototype models of categorization. In this commentary, the author argues that the meta-analysis is misleading because it includes many data sets from experimental designs that are inappropriate for distinguishing the models. Often, the designs involved manipulations in which the actual 5-4 structure was not, in reality, tested, voiding the predictions of the models. The commentary also clarifies various aspects of the workings of the exemplar-based context model. Finally, concerns are raised that the all-or-none exemplar processes that form part of Smith and Minda's (2000) elaborated prototype models are implausible and lacking in generality.     

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。     

Thirty-something categorization results explained: selective attention, eyetracking, and models of category learning

An eyetracking study testing D. L. Medin and M. M. Schaffer's (1978) 5-4 category structure was conducted. Over 30 studies have shown that the exemplar-based generalized context model (GCM) usually provides a better quantitative account of 5-4 learning data as compared with the prototype model. However, J. D. Smith and J. P. Minda (2000) argued that the GCM is a psychologically implausible account of 5-4 learning because it implies suboptimal attention weights. To test this claim, the authors recorded undergraduates' eye movements while the students learned the 5-4 category structure. Eye fixations matched the attention weights estimated by the GCM but not those of the prototype model. This result confirms that the GCM is a realistic model of the processes involved in learning the 5-4 structure and that learners do not always optimize attention, as commonly supposed. The conditions under which learners are likely to optimize attention during category learning are discussed.     

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.     

Prototypes in category learning: the effects of category size, category structure, and stimulus complexity

Although research in categorization has sometimes been motivated by prototype theory, recent studies have favored exemplar theory. However, some of these studies focused on small, poorly differentiated categories composed of simple, 4-dimensional stimuli. Some analyzed the aggregate data of entire groups. Some compared powerful multiplicative exemplar models to less powerful additive prototype models. Here, comparable prototype and exemplar models were fit to individual-participant data in 4 experiments that sampled category sets varying in size, level of category structure, and stimulus complexity (dimensionality). The prototype model always fit the observed data better than the exemplar model did. Prototype-based processes seemed especially relevant when participants learned categories that were larger or contained more complex stimuli.     

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.     

Generalization and similarity in exemplar models of categorization: Insights from machine learning

Exemplar theories of categorization depend on similarity for explaining subjects’ ability to generalize to new stimuli. A major criticism of exemplar theories concerns their lack of abstraction mechanisms and thus, seemingly, of generalization ability. Here, we use insights from machine learning to demonstrate that exemplar models can actually generalize very well. Kernel methods in machine learning are akin to exemplar models and are very successful in real-world applications. Their generalization performance depends crucially on the chosen similarity measure. Although similarity plays an important role in describing generalization behavior, it is not the only factor that controls generalization performance. In machine learning, kernel methods are often combined with regularization techniques in order to ensure good generalization. These same techniques are easily incorporated in exemplar models. We show that the generalized context model (Nosofsky, 1986) and ALCOVE (Kruschke, 1992) are closely related to a statistical model called kernel logistic regression. We argue that generalization is central to the enterprise of understanding categorization behavior, and we suggest some ways in which insights from machine learning can offer guidance.     

Similarity-scaling studies of dot-pattern classification and recognition.

Classification performance in the dot-pattern, prototype-distortion paradigm (e.g., Posner & Keele, 1968) was modeled within a multidimensional scaling (MDS) framework. MDS solutions were derived for sets of dot patterns that were generated from prototypes. These MDS solutions were then used in conjunction with exemplar, prototype, and combined models to predict classification and recognition performance. Across 3 experiments, an MDS-based exemplar model accounted for the effects of several fundamental learning variables, including level of distortion of the patterns, category size, delay of transfer phase, and item frequency. Most important, the model quantitatively predicted classification probabilities for individual dot patterns in the sets, not simply general trends of performance. There was little evidence for the existence of a prototype-abstraction process that operated above and beyond pure exemplar-based generalization.     

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。     

观察式学习条件下类别维度与家族相似性类别学习

在观察式学习条件下考察类别维度数量（三维度类别、六维度类别、九维度类别）,类别维度结构（线性分离结构、非线性分离结构）的变化对家族相似性类别学习的影响。结果表明：观察式学习条件下,类别维度数量的变化对样例学习无影响,对特征学习有影响,表现在特征正确再认数量上有差异,但特征再认正确率上无差异;类别维度结构的变化对样例学习有影响,对特征学习无影响,表现在样例正确再认数目上线性结构大于非线性结构。     

Learning nonlinearly separable categories by inference and classification

Previous research suggests that learning categories by classifying new instances highlights information that is useful for discriminating between categories. In contrast, learning categories by making predictive inferences focuses learners on an abstract summary of each category (e.g., the prototype). To test this characterization of classification and inference learning further, the authors evaluated the two learning procedures with nonlinearly separable categories. In contrast to previous research involving cohesive, linearly separable categories, the authors found that it is more difficult to learn nonlinearly separable categories by making inferences about features than it is to learn them by classifying instances. This finding reflects that the prototype of a nonlinearly separable category does not provide a good summary of the category members. The results from this study suggest that having a cohesive category structure is more important for inference than it is for classification.     

Differential forgetting of prototypes and old instances: Simulation by an exemplar-based classification model

A common finding in studies of classification learning is that ability to classify the prototype of a category declines much less over a retention interval than does the ability to classify the previously seen exemplars themselves. We demonstrate here that this finding does not necessarily indicate the existence, in memory, of a representation of the prototype. MINERVA, a computer-simulation model that encodes memory traces only of presented exemplars, was tested on an appropriate task. Differential forgetting of prototypes and old instances was shown by a version of the model that assumed that (1) classification is based on the exemplar trace most similar to the test stimulus and (2) individual properties are lost from the traces over time in an all-or-none fashion. It is suggested that, in general, the key to the prediction of differential forgetting may be the concomitance of forgetting and generalization.     

A Note on Schema and Exemplar Approaches to Motor Skill Representation in Memory

Given the need for a memory representation of well-learned motor skills, a common assumption in motor behavior is that this knowledge is stored in a central, abstracted form. Active production of motor skills has not been used in experimental designs that have provided empirical support for this view of representation, however. Much of the faith in centralized, abstracted forms of memory representation for motor skills is due to the popularity of Schmidt's schema theory, which has adapted the prototype abstraction model from category learning research to the representation of motor skills. Since schema theory was proposed, however, an alternative view that seriously questions the preeminence of the prototype abstraction model for the central representation of knowledge has arisen in the category learning literature. This particular view, termed the specific exemplar model, has led a number of researchers in cognition to develop mixed models that involve both prototypic abstraction and specific exemplar elements. This note, then, identifies what can be perceived as a gap in the empirical knowledge base in motor behavior and discusses the possibility of using the debate about representation for category learning as a stimulus for initiating a similar investigation into the representation of motor skills. A hypothetical specific exemplar model for the memory representation of motor skills is outlined, and possible empirical comparisons between this model and the schema abstraction model are suggested.     

A formal ideal-based account of typicality

Inspired by Barsalou’s (Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 629–654, 1985) proposal that categories can be represented by ideals, we develop and test a computational model, the ideal dimension model (IDM). The IDM is tested in its account of the typicality gradient for 11 superordinate natural language concepts and, using Bayesian model evaluation, contrasted with a standard exemplar model and a central prototype model. The IDM is found to capture typicality better than do the exemplar model and the central tendency prototype model, in terms of both goodness of fit and generalizability. The present findings challenge the dominant view that exemplar representations are most successful and present compelling evidence that superordinate natural language categories can be represented using an abstract summary, in the form of ideal representations. Supplemental appendices for this article can be downloaded from .