Concept Learning And Representation Research Paper

Models of concept learning have adopted one of three contrasting views concerning category representation. In prototype theories, the concept learning process is assumed to yield an abstract representation corresponding to the central tendency of the category exemplars on each of the dimensions of variation. In exemplar models, the concept is simply the set of mental representations of all of the category exemplars that have been previously observed, with each instance assumed to be stored as a separate trace. And in decision rule models, the learner is assumed to construct a boundary or rule in psychological space which partitions it into different category regions. These different perspectives, and some of the evidence supporting each of them, are considered in turn. Next, the role of selective attention in categorization, and the way in which the different models deal with selective attention, is discussed. Evidence that categorization may be controlled by multiple mechanisms is evaluated, and finally the fine-scale dynamics (i.e., time course) and some aspects of the neuropsychology of categorization are reviewed.

1. Prototype Theories

Prototype theories make a simple assumption about concept representation, namely that the concept is represented as the ‘ideal’ or ‘average’ category exemplar. Thus, representations of specific category exemplars do not influence classification. Numerous forms have been suggested for the (probabilistic) response rule; here we describe one common example. Assume that the probability that stimulus i is classified in category J, P(R_J/S_i), is given by the equation:

where b_J (0 ≤b_J ≤ 1, Σb_J = 1) represents the bias towards making category response J and s_iPJ is the similarity between exemplar i and the prototype of category J. The idea is that classification depends on the similarity between exemplar i and the category J prototype relative to i’s similarity to the proto-types of all other categories. Similarity is usually measured with multidimensional scaling methods.

One piece of evidence favoring prototype models is that a previously unseen prototype may in some circumstances be classified with higher accuracy in the test phase than the actual training stimuli. Moreover, compared to the training stimuli, the prototype may be particularly resistant to forgetting (Homa et al. 1981). Despite this, and notwithstanding their at-tractive simplicity, there is an abundance of evidence against prototype models of concept learning, at least within the domain of perceptual classification. Prototype models have often been shown to provide poorer fits than other models to large sets of classification data, they make a number of predictions that have been falsified, and they fail to account for a number of well-established phenomena (see Nosofsky 1992 for a thorough review).

2. Exemplar Theories

Although it may seem implausible that classification is mediated by a ‘chorus’ of category exemplars, there is an enormous body of evidence consistent with the idea that a trace is created in memory for each category member that is observed and that the effects of individual exemplars on later classification are long lasting. For example, judging whether a letter string is a word or a nonword is influenced by a single prior encounter with that string, and this influence can persist for many days and can be specific to the exact surface form (e.g., font) of the string (Tenpenny 1995). The best-developed formal instance-based model of concept learning is Nosofsky’s Generalized Context Model (GCM). In the GCM, P(R_J /S_i), is given by the equation:

where s_ij is the similarity between exemplars i and j and, as before, b_J represents the bias towards making category response J. The idea is that classification depends on the summed similarity between i and each of the members of category J, relative to i’s similarity to the exemplars of all other categories. As in prototype models, similarity is usually measured using multidimensional scaling methods.

A sizable amount of evidence supports exemplar models such as the GCM (Nosofsky 1992). These models have been shown not only to provide excellent fits to parametric data sets but also to predict a number of qualitative phenomena. For example, they predict that a previously unseen prototype may in some circumstances be classified with higher accuracy in the test phase than the actual training stimuli, and that classification of test items may sometimes be almost completely unrelated to recognition of the same items.

There is also more direct evidence of preservation of the training exemplars in memory. Thomas (1998) first trained participants in a two-dimensional classification task in which values on the dimensions were highly correlated across exemplars. Next, participants were shown stimuli that possessed only one of the dimensions, together with the appropriate category label, and asked to predict the value of the stimulus on the other dimension. Consistent with exemplar theories, Thomas found that many participants were able to perform this task accurately, predicting values for the missing dimension consistent with the correlation observed across the exemplars during training. This implies that they retained quite detailed information about the conjunctions or correlations of feature values across exemplars. Many theories in which information about specific training exemplars is discarded (e.g., prototype theory) would be unable to account for this finding.

The major difficulties faced by exemplar models are that they do not fully reproduce individual differences in the distributions of responses across test stimuli (Nosofsky et al. 1994) and they do not account for certain base-rate effects in categorization (Nosofsky et al. 1992). We will also see below that some further data obtained by Thomas (1998) are very problematic for exemplar theories.

3. Decision-Bound Models

In decision-bound or rule-based models, concepts are represented as regions in psychological space. A rule or boundary demarcates the dividing line between one category and another. In their most general form, decision-bound models can assume any mathematical form for these boundaries, but in practice most researchers have assumed that people can only learn ‘simple’ boundaries, and have therefore attempted to study the plausibility of special cases in which they are constrained to be linear or quadratic. Another reason for studying these particular forms is that the optimal boundary for discriminating between two bivariate normal distributions is either linear or quadratic, and it is reasonable to speculate that many natural categories are multivariate normal. The theory then assumes that, in a two-category situation, if a stimulus (or, more accurately, the percept of the stimulus) falls on one side of the boundary the participant assigns it to the corresponding category and if it falls on the other side it is assigned to the other category. Importantly, the distance of the stimulus from the boundary is assumed to be irrelevant as far as P(RJ Si) is concerned. In that sense, categorization is assumed to be deterministic.

Decision-bound models have proved difficult to discriminate empirically from exemplar-based models such as the GCM—indeed, under some circumstances they are formally equivalent (Ashby and Maddox 1993). Decision-bound models are favored by data from non-normally distributed categories (Maddox and Ashby 1993) and by evidence that participants in some circumstances do not retain information about specific training exemplars. One compelling example was obtained by Thomas (1998) in the study described previously. Although many participants in Thomas’ study were able to predict one dimension value on the basis of another in stimuli drawn from categories with correlated dimensional values, others were quite un- able to do this and instead responded by essentially giving the mean value of the missing dimension, despite the fact that they had learned the initial classification. This strongly suggests that during the course of category learning they had extracted a decision bound and discarded information about the specific training exemplars.

Alternatively, there is rather little evidence, even in one-dimensional perceptual categorization tasks, that participants use all-or-none cutoffs as decision-bound theory predicts (Kalish and Kruschke 1997).

4. Selective Attention In Concept Learning

It has been recognized for many years that concept learning increases the amount of attention paid to stimulus dimensions that are relevant for solving a classification problem and decreases the amount paid to irrelevant ones. Goldstone (1994), for example, found that perceptual discrimination of highly confusable stimuli in a same–different judgment task in-creased as a result of category learning if the stimuli were assigned to different categories whereas, at least in some cases, it decreased if the stimuli were assigned to the same category.

In the GCM, this process of selective attention is accommodated by assuming that the similarity between a test item and category exemplars stored in memory is a function of their separation in psychological space, and that this space can be stretched or shrunk (thus altering the similarities) along orthogonal dimensions as a consequence of selective attention. A similar process can be incorporated into prototype theories. Nosofsky and his colleagues (e.g., McKinley and Nosofsky 1996) have now provided abundant evidence on the one hand that this process of selectively weighting the dimensions of stimulus variation in the generation of category decisions is essential in fitting categorization data within the exemplar-based framework.

On the other hand, decision-bound models have been paradoxically successful at fitting categorization data without needing to assume an explicit selective attention process. On this theory, the structure of the classification problem affects the placement of the decision boundary, but no additional notion of selective attention to stimulus dimensions is necessary. It is perhaps unclear how decision-bound theories would explain results such as those of Goldstone, which provide direct evidence for changes in the perceived similarities of stimuli as a consequence of category learning, but selective attention does not seem to be required for predicting categorization responses per se.

One possible resolution is based on the distinction between selective attention as a perceptual or as a decisional process. The former sees attention as directly altering the perceptual representation of a stimulus, while the latter assumes that attention operates later in the processing stream, perhaps weighting certain features of the stimulus more heavily than others in making a classification decision. Whereas Goldstone’s data provide strong support for selective attention affecting the perceptual representation of stimuli, direct evidence for an influence on decisional processes—as assumed in the GCM—is currently lacking. Therefore there is scope for decision-bound models to dispense with selective attention as a decisional process so long as some dispensation is made for it to operate perceptually, for example via changes in the variances of stimulus percepts on the different dimensions. For further discussion, see Maddox and Ashby (1998).

5. Hybrid Models

An obvious possibility suggested by the evaluation of exemplar and decision-bound models is that people can use different categorization strategies in different circumstances, and indeed there is now a wealth of evidence in support of this conjecture. For example, Johnstone and Shanks (2001) asked participants to classify letter strings as either ‘grammatical’ or ‘un-grammatical’ after exposing them to strings, all of which were consistent with a complex rule. With incidental training conditions, classification was con-trolled purely by featural similarity of studied exemplars, but with explicit ‘code-breaking’ training conditions, classification of exactly the same items was controlled by the complex rule and was unrelated to similarity of studied exemplars. Erickson and Kruschke (1998) review the growing body of evidence for this ‘multiple-mechanism’ view of category learning and representation.

A natural question which arises is how one might computationally model a multiple-mechanism categorization system, and several attempts have recently been made. Erickson and Kruschke (1998), for example, had some success with a ‘mixture-of-experts’ model which incorporates both an exemplar and a decision-bound module. In this model, an adaptive learning rule (Connectionist Models of Concept Learning) determines the extent to which the final category decision is based on one module or the other, and the weight assigned to each module is an inverse function of the prediction error it generates for that particular classification problem. This sort of modular view of categorization is also supported by recent brain imaging data (Smith et al. 1998).

6. Time Course Of Classification

An important recent development in the study of category learning and representation is the application of exemplar and decision-bound models to the fine-scale dynamics—specifically, the time course—of categorization. Until quite recently, research concentrated almost exclusively on categorization probabilities, but new methodological techniques provide researchers with powerful tools for studying more microscopic aspects of the categorization process.

Two rather different proposals have been advanced to extend exemplar models to deal with this issue (Lamberts, 2000). One approach is to assume that when an item is presented for classification, a race begins to retrieve exemplars from memory. The time to complete the race depends on how similar the stored exemplars are to the test item. When one race is completed, and an exemplar retrieved, a new race commences, and a classification response is only emitted when a random-walk process is driven to one or another decision barrier. The alternative approach is to assume that there is a gradual accumulation of perceptual information about the test stimulus and that similarity to stored exemplars varies during the construction of its representation. On this account, classification at any given moment is governed by Eqn. (2) but the summed similarity term in that equation is dependent on how much information about the test stimulus has been accumulated.

Proponents of decision-bound theory have advanced a rather straightforward hypothesis about the time course of categorization, namely that classification response times depend on distance to the decision bound, with greater distances leading to faster responses.

Attempts to distinguish between these accounts are in their infancy, but each appears to have strong merits. The articles cited in this section provide detailed reviews. Further study of the temporal dynamics of categorization is sure to be a major part of future research.

7. Neuropsychology Of Category Learning And Representation

Neuropsychology raises two important issues concerning categorization. First, there is evidence that the mental representations controlling categorization are functionally and neuraly distinct from those accessed in standard ‘explicit’ tests of memory such as recall and recognition. If this is true, it suggests that models of memory are unlikely to provide any useful input to our understanding of categorization. The main piece of evidence is that amnesic patients suffering from anterograde amnesia seem to behave normally in category learning tasks while being profoundly impaired on tests of recall and recognition (e.g., Squire and Knowlton 1995). For instance, one densely amnesic patient (EP) performed normally in learning to classify dot patterns generated from a prototype, while performing at chance in a recognition test for those patterns. It has been concluded from this that the hippocampus, which controls explicit memory and which is damaged in amnesia, plays no role in category learning.

Recently, however, the conclusion that categorization and memory are functionally and neuraly unconnected has been questioned on the basis of demonstrations that exemplar models such as the GCM can, just like EP, show dissociations between classification and recognition. In Nosofsky and Zaki’s (1998) modeling approach, only a single parameter, the sensitivity parameter, was varied in order to account for a general learning difference between amnesics and controls. This parameter represents the ability to discriminate among distinct exemplars stored in memory, an ability which is plausibly reduced in amnesics as a result of their deteriorated memory capacity. Nosofsky and Zaki showed that decreasing the value of this parameter reduced classification performance only slightly, but reduced recognition performance considerably. Thus, the GCM success-fully accounts for the dissociation between classification and recognition observed by Squire and Knowlton (1995).

Second, there is now a wealth of evidence concerning the brain localization of category knowledge. Brain imaging studies have suggested that knowledge is organized structurally at the neural level. Martin et al. (1996) studied neural organization of conceptual knowledge by presenting normal participants with pictures of animals and tools to name while brain activity was recorded by positron emission tomography (PET). As a control, participants saw nonsense objects. Compared to the control condition, brain activity for the meaningful objects was increased in the ventral temporal lobes bilaterally and in Broca’s area in the left hemisphere. The latter is probably related to word generation. Relative to pictures of tools, pictures of animals produced increased activation in the left medial occipital lobe. Relative to pictures of animals, pictures of tools produced increased activation in the left dorsal temporal lobe and the left premotor region. This premotor area is also activated by imagined hand movements, suggesting that part of the conceptual representation of tools is a specification of the hand movements they afford. Overall, Martin et al.’s results confirm that gross category distinctions are present in the way the brain organizes conceptual knowledge.

For a fuller review of recent psychological and neuroscience research on models of concept learning and representation, see Lamberts and Shanks (1997).

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