Knowledge partitioning in categorization: Boundary conditions

Knowledge partitioning refers to the notion that knowledge can be held in independent and nonoverlapping parcels. Partitioned knowledge may cause people to make contradictory decisions for identical problems in different circumstances. We report two experiments that explored the boundary conditions of knowledge partitioning in categorization. The studies examined whether or not people would partition their knowledge (1) when categorization rules were or were not verbalizable and (2) when the to-be-categorized stimuli comprised perceptually separable or integral dimensions. When learning difficulty was controlled, partitioning occurred across all combinations of verbalizability and integrality/separability, underscoring the generality of knowledge partitioning. Partitioning was absent only when the task was rapidly learned and people reached a high level of proficiency, suggesting that task difficulty plays a critical role in the emergence of partitioned knowledge.     

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.     

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.     

Cue abstraction and exemplar memory in categorization

In this article, the authors compare 3 generic models of the cognitive processes in a categorization task. The cue abstraction model implies abstraction in training of explicit cue-criterion relations that are mentally integrated to form a judgment, the lexicographic heuristic uses only the most valid cue, and the exemplar-based model relies on retrieval of exemplars. The results from 2 experiments showed that, in lieu of the lexicographic heuristic, most participants spontaneously integrate cues. In contrast to single-system views, exemplar memory appeared to dominate when the feedback was poor, but when the feedback was rich enough to allow the participants to discern the task structure, it was exploited for abstraction of explicit cue-criterion relations.     

The origin of exemplar effects in rule-driven categorization

S. W. Allen and L. R. Brooks (1991) have shown that exemplar memory can affect categorization even when participants are provided with a classification rule. G. Regehr and L. R. Brooks (1993) argued that stimuli must be individuated for such effects to occur. In this study, the authors further analyze the conditions that yield exemplar effects in this rule application paradigm. The results of Experiments 1-3 show that interchangeable attributes, which are not part of the rule, influence categorization only when attention is explicitly drawn on them. Experiment 4 shows that exemplar effects can occur in an incidental learning condition, whether stimulus individuation is preserved or not. The authors conclude that the influence of exemplar learning in rule-driven categorization stems from the attributes specified in the rule or in the instructions, not from the stimulus gestalts.     

Contrast and assimilation in categorization and exemplar production

We studied contrast and assimilation in three tasks: an exemplar-production task, a categorization task, and a combined categorization-then-production task. On each trial of the first task, subjects produced a circle when prompted with a category label. In the second task, they classified lines that differed in length into one of four categories. On each trial of the combined task, they classified two lines and then produced a line when prompted by a category label. All three tasks converged on the same conclusion: subjects' representation of the categories (measured in pixels in the production tasks and by the direction of errors in classification) shifted systematically from trial to trial. When successive stimuli were from the same category, the representation of that category was pulled toward the exemplar from the previous trial. When successive stimuli were from different categories, the representations of the neighbouring categories were pushed from the category of the initial stimulus. We conclude that accounts of categorization and identification must accommodate both assimilation and contrast as a function of trial-to-trial shifts in representation.     

Context-gated knowledge partitioning in categorization

According to the knowledge partitioning framework, people sometimes master complex tasks by creating multiple independent parcels of partial knowledge. Research has shown that knowledge parcels may contain mutually contradictory information, and that each parcel may be used without regard to knowledge that is demonstrably present in other parcels. This article reports 4 experiments that investigated knowledge partitioning in categorization. When component boundaries of a complex categorization were identified by a context cue, a significant proportion of participants learned partial and independent categorization strategies that were chosen on the basis of context. For those participants, a strategy used in one context was unaffected by knowledge demonstrably present in other contexts, suggesting that knowledge partitioning in categorization can be complete.     

Comparing categorization models

Four experiments are presented that competitively test rule- and exemplar-based models of human categorization behavior. Participants classified stimuli that varied on a unidimensional axis into 2 categories. The stimuli did not consistently belong to a category; instead, they were probabilistically assigned. By manipulating these assignment probabilities, it was possible to produce stimuli for which exemplar- and rule-based explanations made qualitatively different predictions. F. G. Ashby and J. T. Townsend's (1986) rule-based general recognition theory provided a better account of the data than R. M. Nosofsky's (1986) exemplar-based generalized context model in conditions in which the to-be-classified stimuli were relatively confusable. However, generalized context model provided a better account when the stimuli were relatively few and distinct. These findings are consistent with multiple process accounts of categorization and demonstrate that stimulus confusion is a determining factor as 10 which process mediates categorization.     

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.     

Knowledge partitioning: Context-dependent use of expertise

Although exceptional performance is a defining attribute of expertise, experts sometimes exhibit striking errors and performance limitations. This article reports two experiments in which experts predicted the spread of bush fires, a domain characterized by complex but well-understood physical dynamics. Although accuracy was typically high, large errors were observed when two primary predictor variables were in opposition. In a second study, the experts' behavior--in contrast to that of novices--was additionally shown to depend on problem context. In one context, experts again committed errors, whereas in another, equally domain-relevant context, the correct predictions were made. Critically, when comparing performance across contexts, completely opposing predictions were made under identical physical conditions. We therefore suggest that expertise may comprise separate, and sometimes even mutually exclusive, components of knowledge.     

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.     

Limitations of exemplar models of multi-attribute probabilistic inference

Observers were presented with pairs of objects varying along binary-valued attributes and learned to predict which member of each pair had a greater value on a continuously varying criterion variable. The predictions from exemplar models of categorization were contrasted with classic alternative models, including generalized versions of a "take-the-best" model and a weighted-additive model, by testing structures in which interactions between attributes predicted the magnitude of the criterion variable. Under typical training conditions, observers showed little sensitivity to the attribute interactions, thereby challenging the predictions from the exemplar models. In a condition involving highly extended training, observers eventually learned the relations between the attribute interactions and the criterion variable. However, an analysis of the observers' response times for making their paired-comparison decisions also challenged the exemplar model predictions. Instead, it appeared that most observers recoded the interacting attributes into emergent configural cues. They then applied a set of hierarchically organized rules based on the priority of the cues to make their decisions.     

Evolutionary models of color categorization based on discrimination

Specifying the factors that contribute to the universality of color categorization across individuals and cultures is a longstanding and still controversial issue in psychology, linguistics, and anthropology. This article approaches this issue through the simulated evolution of color lexicons. It is shown that the combination of a minimal perceptual psychology of discrimination, simple pragmatic constraints involving communication, and simple learning rules is enough to evolve color-naming systems. Implications of this result for psychological theories of color categorization and the evolution of color-naming systems in human societies are discussed.     

When parameters collide: a warning about categorization models

Similarity-choice (S—C) models of categorization contain two principal mathematical transformations: an exponential-decay similarity function and a choice rule. However, there is a tension between the psychological processes that models emulate and the mathematics they use to do so. To illustrate this, I show that in these models an unappreciated interaction occurs between the mathematical transformations so that the stages of the model essentially cancel each other out. The result is that the model’s output reflects its input linearly. This cancellation phenomenon has potentially serious implications regarding the interpretation and use of S—C models. The phenomenon also raises questions about the simplification and psychological grounding of categorization models. Modelers broadly might benefit from an internal analysis of their models, such as that described here.     

Overconfidence effects in category learning: a comparison of connectionist and exemplar memory models

Exemplar and connectionist models were compared on their ability to predict overconfidence effects in category learning data. In the standard task, participants learned to classify hypothetical patients with particular symptom patterns into disease categories and reported confidence judgments in the form of probabilities. The connectionist model asserts that classifications and confidence are based on the strength of learned associations between symptoms and diseases. The exemplar retrieval model (ERM) proposes that people learn by storing examples and that their judgments are often based on the first example they happen to retrieve. Experiments 1 and 2 established that overconfidence increases when the classification step of the process is bypassed. Experiments 2 and 3 showed that a direct instruction to retrieve many exemplars reduces overconfidence. Only the ERM predicted the major qualitative phenomena exhibited in these experiments.     

Category vs. item learning: Implications for categorization models

A paradigm that required that subjects learn two responses to each of 10 schematic faces was used to study the relative rate of discrimination and generalization learning. One response uniquely identified each face, whereas the second response classified each face as a member of one of two categories. Rapid category learning and slow item learning suggested that category responses were learned on the basis of abstracted information, but item responses depended on the more difficult task of discriminating among patterns. The results are related to categorization models and to task variables that should influence the relative rates of discrimination and generalization learning.     

Response-time tests of logical-rule models of categorization

A recent resurgence in logical-rule theories of categorization has motivated the development of a class of models that predict not only choice probabilities but also categorization response times (RTs; Fifi?, Little, & Nosofsky, 2010). The new models combine mental-architecture and random-walk approaches within an integrated framework and predict detailed RT-distribution data at the level of individual participants and individual stimuli. To date, however, tests of the models have been limited to validation tests in which participants were provided with explicit instructions to adopt particular processing strategies for implementing the rules. In the present research, we test conditions in which categories are learned via induction over training exemplars and in which participants are free to adopt whatever classification strategy they choose. In addition, we explore how variations in stimulus formats, involving either spatially separated or overlapping dimensions, influence processing modes in rule-based classification tasks. In conditions involving spatially separated dimensions, strong evidence is obtained for application of logical-rule strategies operating in a serial-self-terminating processing mode. In conditions involving spatially overlapping dimensions, preliminary evidence is obtained that a mixture of serial and parallel processing underlies the application of rule-based classification strategies. The logical-rule models fare considerably better than major extant alternative models in accounting for the categorization RTs.     

Synonym comprehension and the generality of categorization models

Memory & Cognition - When subjects classify a two-word display as representing the “same” category or two “different” categories, semantic similarity between the words...     

Elemental versus configurai models of categorization in children and adults

In experiment 1, 7-and 8-year-old children learned to classify six features, A–F, as belonging to one of two artificial categories, or to neither category. Feature A and the compound BC were designated as members of Category 1, the compounds DE and EF were members of category 2, while D alone and the compound AB, belonged to neither category. Following successful learning, the participants were asked to rate two groups of test features, ABC and DEF, as likely members of their respective categories. Participants' certainty ratings of the categorization of the compound DEF were greater than for the compound ABC. Experiment 2 replicated the results of experiment 1 with adult participants. These data are at odds with predictions from an elemental associative theory, that suggested by Rescorla and Wagner (1972), which assumes that category judgements are made on the basis of associations between individual features and a category.     

Elemental versus configurai models of categorization in children and adults

In experiment 1, 7-and 8-year-old children learned to classify six features, A–F, as belonging to one of two artificial categories, or to neither category. Feature A and the compound BC were designated as members of Category 1, the compounds DE and EF were members of category 2, while D alone and the compound AB, belonged to neither category. Following successful learning, the participants were asked to rate two groups of test features, ABC and DEF, as likely members of their respective categories. Participants' certainty ratings of the categorization of the compound DEF were greater than for the compound ABC. Experiment 2 replicated the results of experiment 1 with adult participants. These data are at odds with predictions from an elemental associative theory, that suggested by Rescorla and Wagner (1972), which assumes that category judgements are made on the basis of associations between individual features and a category.