A hybrid model of categorization

Category learning is often modeled as either an exemplar-based or a rule-based process. This paper shows that both strategies can be combined in a cognitive architecture that was developed to model other task domains. Variations on the exemplar-based random walk (EBRW) model of Nosofsky and Palmeri (1997b) and the rule-plus-exception (RULEX) rule-based model of Nosofsky, Palmeri, and McKinley (1994) were implemented in the ACT-R cognitive architecture. The architecture allows the two strategies to be mixed to produce classification behavior. The combined system reproduces latency, learning, and generalization data from three category-learning experiments--Nosofsky and Palmeri (1997b), Nosofsky et al., and Erickson and Kruschke (1998). It is concluded that EBRW and ACT-R have different but equivalent means of incorporating similarity and practice. In addition, ACT-R brings a theory of strategy selection that enables the exemplar and the rule-based strategies to be mixed.     

Single versus multiple systems of category learning: Reply to Nosofsky and Kruschke (2002)

Nosofsky and Kruschke (2002) argued that the singlesystem ALCOVE model (Kruschke, 1992) can account for the dual-task category learning data reported by Waldron and Ashby (2001). In our reply, we argue that Nosofsky and Kruschke overstated the ability of ALCOVE to account for the Waldron and Ashby results. In fact, ALCOVE has difficulty with these data, and we show that the only versions of ALCOVE that actually fit the Waldron and Ashby accuracy data make incorrect predictions about other previously unreported features of that experiment. We also show that the dual-system COVIS model (Ashby, Alfonso-Reese, Turken, & Waldron, 1998) naturally predicts these results.     

Rule-based extrapolation: A continuing challenge for exemplar models

Erickson and Kruschke (1998, 2002) demonstrated that in rule-plus-exception categorization, people generalize category knowledge by extrapolating in a rule-like fashion, even when they are presented with a novel stimulus that is most similar to a known exception. Although exemplar models have been found to be deficient in explaining rule-based extrapolation, Rodrigues and Murre (2007) offered a variation of an exemplar model that was better able to account for such performance. Here, we present the results of a new rule-plus-exception experiment that yields rule-like extrapolation similar to that of previous experiments, and yet the data are not accounted for by Rodrigues and Murre's augmented exemplar model. Further, a hybrid rule-and-exemplar model is shown to better describe the data. Thus, we maintain that rule-plus-exception categorization continues to be a challenge for exemplar-only models.     

Measures of similarity in models of categorization

This paper concerns the use of similarities based on geometric distance in models of categorization. Two problematic implications of such similarities are outlined. First, in a comparison between two stimuli, geometric distance implies that matching features are not taken into account. Second, missing features are assumed not to exist. Only nonmatching features enter into calculations of similarity. A new model is constructed that is based on the ALCOVE model (Kruschke, 1992), but it uses a feature-matching similarity measure (see, e.g., Tversky, 1977) rather than a geometric one. It is an on-line model in the sense that both dimensions and exemplars are constructed during the categorization process. The model accounts better than ALCOVE does for data with missing features (Experiments 1 and 2) and at least as well as ALCOVE for a data set without missing features (Nosofsky, Kruschke, & McKinley, 1992). This suggests that, at least for some stimulus materials, similarity in categorization is more akin to a feature-matching procedure than to geometric distance calculation.     

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.     

Rules-plus-exception tasks: A problem for exemplar models?

Erickson and Kruschke (2002b) have shown that human subjects generalize category knowledge in a rule-like fashion when exposed to a rule-plus-exception categorization task. This result has remained a challenge to exemplar models of category learning. We show that these models can account for such performance, if they are augmented with exemplar-specific specificity or exemplar-specific attention. This result, however, is only achieved if the choice rule that converts evidence for competing categories into probabilities is sensitive to small differences between evidence values close to 0. Exemplar-specific attention provided the best overall approximation of the data. Exemplar-specific specificity provided a slightly worse approximation, but it predicted better the rule-like generalization pattern observed.     

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.     

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.     

Information-accumulation theory of speeded categorization

A process model of perceptual categorization is presented, in which it is assumed that the earliest stages of categorization involve gradual accumulation of information about object features. The model provides a joint account of categorization choice proportions and response times by assuming that the probability that the information-accumulation process stops at a given time after stimulus presentation is a function of the stimulus information that has been acquired. The model provides an accurate account of categorization response times for integral-dimension stimuli and for separable-dimension stimuli, and it also explains effects of response deadlines and exemplar frequency.     

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。     

Recognizing distinctive faces: A hybrid-similarity exemplar model account

In recognition memory experiments, Nosofsky and Zaki (2003) found that adding discrete distinctive features to continuous-dimension color stimuli helped participants to identify old items as old (the old-item distinctiveness effect), as well as to identify new items as new. The present study tests the extent to which these results generalize to the domain of face recognition. Two experiments were conducted, one using artificial faces and one using natural faces. Artificial faces were used to test memory for faces with discrete distinctive features while controlling the similarity of the faces themselves on more continuous dimensions. The natural-face experiment used the faces of 40 bald men categorized into three groups (typical, isolated, and distinctive) based on experimental ratings of distinctiveness. In both experiments, there were strong effects of the distinctive features on recognition performance. The data were accounted for reasonably well by a hybrid-similarity version of an exemplar recognition model (Nosofsky and Zaki, 2003), which includes a feature-matching mechanism that can provide boosts to an item's self-similarity.     

Exemplar effects in the context of a categorization rule: Featural and holistic influences

Brooks and colleagues (S. W. Allen & L. R. Brooks, 1991; G. Regehr & L. R. Brooks, 1993) have shown that the classification of transfer stimuli is influenced by their similarity to training stimuli, even when a perfect classification rule is available. It is argued that the original effect obtained by Brooks and colleagues might have resulted from two potential confounding variables. Once these confounds were controlled, the current authors did not replicate Brooks and colleagues' results in Experiment 1. Exemplar effects appeared in Experiment 2 when transfer stimuli were perceptually more similar to training stimuli than in Experiment 1. In Experiment 3, the authors obtained exemplar effects with separated stimuli, a finding that was not predicted by Brooks and colleagues' model. The authors suggest that a close perceptual match between training and transfer stimuli is necessary for the effect to occur, for both integrated and separated stimuli. The nature of this perceptual match, holistic or featural, is 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。     

An extension of the exemplar-based random-walk model to separable-dimension stimuli

An extension of Nosofsky and Palmeri's (Psychol. Rev. 104 (1997a) 266) exemplar-based random-walk (EBRW) model of categorization is presented as a model of the time course of categorization of separable-dimension stimuli. Nosofsky and Palmeri (1997a) assumed that the perceptual encoding of all stimuli was identical. However, in the current model, we assume as in Lamberts (J. Exp. Psychol.: General 124 (1995) 161) that the inclusion of individual stimulus dimensions into the similarity calculations is a stochastic process with the probability of inclusion based on the perceptual salience of the dimensions. Thus, the exemplars that enter into the random-walk change dynamically during the time course of processing. This model is implemented as a Markov chain. Its predictions are compared with alternative models in a speeded categorization experiment with separable-dimension stimuli.     

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.     

Integrating novel dimensions to eliminate category exceptions: when more is less

Category learning can be characterized as a process of discovering the dimensions that represent stimuli efficiently and effectively. Categories that are overlapping when represented in 1 dimensionality may be separate in a higher dimensional cue set. The authors report 2 experiments in which participants were shown an additional cue after learning to use 2 imperfect cues. The results revealed that participants can integrate new information into their categorization cue set. The authors discovered wide individual differences, however, with many participants favoring simpler, but less accurate, cue sets. Some participants demonstrated the ability to discard information previously used when new, more accurate information was introduced. The categorization model RASHNL (J. K. Kruschke & M. K. Johansen, 1999) gave qualitatively accurate fits of the data.     

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.     

An exemplar-retrieval model of speeded same--different judgments

R. M. Nosofsky and T. J. Palmeri's (1997) exemplar-based random-walk (EBRW) model of speeded classification is extended to account for speeded same--different judgments among integral-dimension stimuli. According to the model, an important component process of same--different judgments is that people store individual examples of experienced same and different pairs of objects in memory. These exemplar pairs are retrieved from memory on the basis of how similar they are to a currently presented pair of objects. The retrieved pairs drive a random-walk process for making same--different decisions. The EBRW predicts correctly that same responses are faster for objects lying in isolated than in dense regions of similarity space. The model also predicts correctly effects of same-identity versus same-category instructions and is sensitive to observers' past experiences with specific same and different pairs of objects.     

How many exemplars are used? Explorations with the Rex Leopold I model

The goal of this research is to test the hypothesis that a category is not necessarily represented by all observed exemplars, but by a reduced subset of these exemplars. To test this hypothesis, we made use of a study reported by Nosofsky, Clark, and Shin (1989), and replicated their Experiment 1 in order to gather individual-participant data. Both a full exemplar model and a reduced exemplar model were fit to the data. In general, the fits of the reduced exemplar model were superior to those of the full exemplar model. The results suggest that only a subset of exemplars may be sufficient for category representation.