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

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

R. M. Nosofsky and M. K. Johansen

Presented by Chris Fagan


Background
Background in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

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

  • Uses multidimensional scaling


Model overview1
Model Overview in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization


Accounts of the phenomena
Accounts of the Phenomena in perceptual categorization


Bias toward verbal rules
Bias toward verbal rules in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization


Rulex model2
RULEX Model in perceptual categorization


Rulex model3
RULEX Model in perceptual categorization


Rulex model4
RULEX Model in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization


Atrium model3
ATRIUM Model in perceptual categorization

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


Prototype vs exception
Prototype vs. Exception in perceptual categorization

  • 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 in perceptual categorization


Prototype vs exception2
Prototype vs. Exception in perceptual categorization


Prototype vs exception3
Prototype vs. Exception in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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 in perceptual categorization

  • 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



Conclusion
Conclusion in perceptual categorization

  • 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