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

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)

15. 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)

16. 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

17. RULEX Model

18. RULEX Model

19. RULEX Model

20. 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

21. 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

22. 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

23. ATRIUM Model

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

25. 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

26. Prototype vs. Exception

27. Prototype vs. Exception

28. 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

29. 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

30. 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

31. 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

32. 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

33. Dissociations between Categorization and Similarity Judgment

34. 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