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.     

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.     

Comparisons between exemplar similarity and mixed prototype models using a linearly separable category structure

Nosofsky and Zaki (2002) found that an exemplar similarity model provided better accounts of individual subject classification and generalization performance than did a mixed prototype model proposed by Smith and Minda (1998; Minda & Smith, 2001). However, these previous tests used a nonlinearly separable category structure. In the present work, the authors extend the previous findings by demonstrating a superiority for the exemplar generalization model over the mixed prototype model in a case involving a linearly separable structure. Because this structure has numerous features that Minda and Smith argued should be conducive to prototype-based processing, the results pose a significant challenge to the mixed prototype view.     

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.     

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.     

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。     

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.     

Comparing decision bound and exemplar models of categorization

The performance of a decision bound model of categorization (Ashby, J992a; Ashby & Maddox, in press) is compared with the performance of two exemplar models. The first is the generalized context model (e.g., Nosofsky, 1986, 1992) and the second is a recently proposed deterministic exemplar model (Ashby & Maddox, in press), which contains the generalized context model as a special case. When the exemplars from each category were normally distributed and the optimal decision bound was linear, the deterministic exemplar model and the decision bound model provided roughly equivalent accounts of the data. When the optimal decision bound was nonlinear, the decision bound model provided a more accurate account of the data than did either exemplar model. When applied to categorization data collected by Nosofsky (1986, 1989), in which the category exemplars are not normally distributed, the decision bound model provided excellent accounts of the data, in many cases significantly outperforming the exemplar models. The decision bound model was found to be especially successful when(1) single subject analyses were performed, (2) each subject was given relatively extensive training, and (3) the subject's performance was characterized by complex suboptimalities. These results support the hypothesis that the decision bound is of fundamental importance in predicting asymptotic categorization performance and that the decision bound models provide a viable alternative to the currently popular exemplar models of categorization.     

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.     

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.     

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.     

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。     

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.     

The cognitive substrate of subjective probability

The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as prototype similarity, relative likelihood, or evidential support accumulation (ESAM; D. J. Koehler, C. M. White, & R. Grondin, 2003); cue-based relative frequency; and exemplar memory, implemented by probabilities from exemplars (PROBEX; P. Juslin & M. Persson, 2002). Three experiments with different task structures consistently demonstrate that exemplar memory is the best account of the data whereas the results are inconsistent with extant formulations of the representativeness heuristic and cue-based relative frequency.     

Journey to the center of the category: the dissociation in amnesia between categorization and recognition

The authors' theoretical analysis of the dissociation in amnesia between categorization and recognition suggests these conclusions: (a) Comparing to-be-categorized items to a category center or prototype produces strong prototype advantages and steep typicality gradients, whereas comparing to-be-categorized items to the training exemplars that surround the prototype produces weak prototype advantages and flat typicality gradients; (b) participants often show the former pattern, suggesting their use of prototypes; (c) exemplar models account poorly for these categorization data, but prototype models account well for them; and (d) the recognition data suggest that controls use a single-comparison exemplar-memorization process more powerfully than amnesics. By pairing categorization based in prototypes with recognition based in exemplar memorization, the authors support and extend other recent accounts of cognitive performance that intermix prototypes and exemplars, and the authors reinforce traditional interpretations of the categorization-recognition dissociation in amnesia.     

Fruits and vegetables categorized: an application of the generalized context model

In the study reported in this paper, we investigated the categorization of well-known and novel food items in the categories fruits and vegetables. Predictions based on Nosofsky’s (1984, 1986) generalized context model (GCM), on a multiplicative-similarity prototype model, and on an instantiation model as applied in Storms, De Boeck, and Ruts (2001) were compared. Despite suggestions in the literature that prototype models predict categorization from large categories better than exemplar models do, our results showed that the exemplar-based GCM yielded clearly better predictions than did a (multiplicative-similarity) prototype model.     

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 .     

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.