Exemplar based accounts of multiple system phenomena in perceptual categorization
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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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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

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?


Background1

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 >>


Background2

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


Model overview

Model Overview

  • Generalized Context Model (GCM), Ashby & Maddox, 1993; Nosofsky, 1984, 1986, 1991

  • Uses multidimensional scaling


Model overview1

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


Model overview2

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.


Model overview3

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


Model overview4

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


Model overview5

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.


Model overview6

Model overview


Accounts of the phenomena

Accounts of the Phenomena


Bias toward verbal rules

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)


Rulex classification model

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)


Rulex model

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


Rulex model1

RULEX Model


Rulex model2

RULEX Model


Rulex model3

RULEX Model


Rulex model4

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


Atrium model

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


Atrium model1

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


Atrium model2

ATRIUM Model


Atrium model3

ATRIUM Model

  • Replication supports hypothesis that single-system exemplar model can sufficiently account for data


Prototype vs exception

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


Prototype vs exception1

Prototype vs. Exception


Prototype vs exception2

Prototype vs. Exception


Prototype vs exception3

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


Dissociations between categorization and similarity judgment

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


Dissociations between categorization and similarity judgment1

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


Dissociations between categorization and similarity judgment2

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


Dissociations between categorization and similarity judgment3

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


Dissociations between categorization and similarity judgment4

Dissociations between Categorization and Similarity Judgment


Conclusion

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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