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Exemplar-based accounts of “multiple system” phenomena in perceptual categorization

Exemplar-based accounts of “multiple system” phenomena in perceptual categorization. R. M. Nosofsky and M. K. Johansen Presented by Chris Fagan. Background. Most theorizing in perceptual classification has lead to models involving multiple categorization systems

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Exemplar-based accounts of “multiple system” phenomena in perceptual categorization

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  1. Exemplar-based accounts of “multiple system” phenomena in perceptual categorization R. M. Nosofsky and M. K. Johansen Presented by Chris Fagan

  2. Background • Most theorizing in perceptual classification has lead to models involving multiple categorization systems • Typically, one system computes rules and prototypes, and the second relies on specific exemplars and complex decision boundaries • So, what’s wrong with this?

  3. Background • First, the models are flexible and loosely-defined, so they may unduly resist falsification • Second, the principle of parsimony calls for a single system with fewer free parameters Occam >>

  4. Background • Exemplar models: categories are represented by storage of individual exemplars and objects are classified based on similarity to these • Successful at explaining relations between categorization and other fundamental cognitive processes • Object identification, old-new recognition memory, problem solving

  5. Model Overview • Generalized Context Model (GCM), Ashby & Maddox, 1993; Nosofsky, 1984, 1986, 1991 • Uses multidimensional scaling

  6. Model Overview • Exemplars presented in multidimensional psychological space • Similarity between them is a decreasing function of their distance • Observers often learn to distribute attention across dimensions so as to optimize overall performance

  7. Model Overview • The probability that item i is classified into Category J is given by: • Sijdenotes similarity of item i to exemplar j and the index j € J denotes that the sum is over all exemplars j belonging to category J.

  8. Model Overview • The probability that item i is classified into Category J is given by: A critical assumption is that similarity is a context-dependent relation, rather than an invariant one

  9. Model Overview • The distance between exemplars is computed by the Minkowski power-model formula, where r defines the distance metric of the space, and the wm parameters model the degree of attention given to each dimension

  10. Model Overview • The distance between exemplars is assumed to be a nonlinearly decreasing function of their distance, as given by… • …where c is an overall scaling or sensitivity parameter, and the value p gives the form of the similarity gradient.

  11. Model overview

  12. Accounts of the Phenomena

  13. Bias toward verbal rules • Study by Ashby et al. (1998) • COVIS model (competion between a verbal and implicit system) believed to predict results better than GCM (specifically referenced by the authors)

  14. RULEX Classification Model • Nosofksy, Palmeri, and McKinley (1994) • Model states that people learn to classify objects by forming simple logical rules along single dimensions, and storing the occasional exceptions to these rules. • Example of model is given in the form of classic category structure used by Medin and Shaffer (1978)

  15. RULEX Model • Stimuli vary along 4 binary-valued dimensions • 5 Category A exemplars, 4 Category B exemplars, 7 transfer stimuli • Logical value 1 on each dimension indicates Category A, and logical value 2 indicates Category B, with no necessary and jointly sufficient feature sets for either

  16. RULEX Model

  17. RULEX Model

  18. RULEX Model

  19. RULEX Model • GCM exemplar models that allow for individual-subject variation in attention weighting can account for the data • Variation in distribution-of-generalization data reported in original study is poorer than originally believed as a diagnostic of rule use and multiple categorization systems

  20. ATRIUM Model • Erickson and Kruschke (1998) • Hybrid connectionist model for categorization; encorporates both rule- and exemplar-based representations • Consists of single-dimensional decision boundaries, exemplar module for differentiating exemplars and categories, and a gating mechanism to link the two

  21. ATRIUM Model • Predicts that exemplar module will contribute to classification judgments primarily for stimuli similar to learned exceptions • Rule module predicted to dominate in other cases

  22. ATRIUM Model

  23. ATRIUM Model • Replication supports hypothesis that single-system exemplar model can sufficiently account for data

  24. Prototype vs. Exception • Smith, Murray, and Minda (1997; Smith and Minda, 1998) • Mixed prototype-plus-exemplar model of categorization • Prototypes abstracted during early category learning or with highly coherent categories • Exemplars used to supplement prototype abstractions

  25. Prototype vs. Exception

  26. Prototype vs. Exception

  27. Prototype vs. Exception • For some subjects and stages of learning, the exemplar model provides roughly the same fit as prototype model • Generally, however, the exemplar model provides a better explanation for the data

  28. Dissociations between Categorization and Similarity Judgment • Rips (1989), Rips and Collins (1993) • Participants imagined 3” object, decided if it was: • more similar to a quarter or a pizza • belonging to the category quarter or pizza • Similarity group judged it more similar to quarter • Categorization group placed it in pizza category

  29. Dissociations between Categorization and Similarity Judgment • It is theorized that the 3” object is classified as a “pizza” (B) because the size range in the category is highly variable, whereas that of “quarter” is not

  30. Dissociations between Categorization and Similarity Judgment • This poses a challenge to the single-system model, but this can be reconciled by allowing for differing sensitivity parameters for similarity computations in the low- and high-variability conditions • Variable sensitivity parameters allow observers to optimize percentage of correct classifications

  31. Dissociations between Categorization and Similarity Judgment • A follow-up study examined histogram classification of temperature measurements (Rips and Collins, 1993) • A similar dissociation between similarity and categorization judgments was found • This can still be explained in terms of the single-system model, given the assumptions: • Histogram frequency counts translate directly into stored copies of exemplars • Configuration of exemplars in psychological space corresponds directly to physical layout of figure • Category-likelihood judgment is monotonically related to summed similarity of value to histogram exemplar

  32. Dissociations between Categorization and Similarity Judgment

  33. Conclusion • The single-system exemplar model can adequately predict results of studies originally designed with more-complex multiple-system models • The single-system model is more parsimonious • The single-system model is, however, not always better, and sometimes can fail to account for certain patterns in data • The model has potential for application in study higher-level cognitive tasks, such as inference

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