exemplar-based accounts of “multiple system” phenomena in perceptual categorization r. m....

Exemplar-based accounts Exemplar-based accounts of “multiple system” of “multiple system”

phenomena in perceptual phenomena in perceptual categorizationcategorization

R. M. Nosofsky and M. K. JohansenR. M. Nosofsky and M. K. Johansen

Presented by Chris FaganPresented by Chris Fagan

BackgroundBackground

Most theorizing in perceptual classification Most theorizing in perceptual classification has lead to models involving multiple has lead to models involving multiple categorization systemscategorization systems

Typically, one system computes rules and Typically, one system computes rules and prototypes, and the second relies on prototypes, and the second relies on specific exemplars and complex decision specific exemplars and complex decision boundariesboundaries

So, what’s wrong with this?So, what’s wrong with this?


First, the models are flexible and loosely-First, the models are flexible and loosely-defined, so they may unduly resist defined, so they may unduly resist falsificationfalsification

Second, the principle of parsimony calls Second, the principle of parsimony calls for a single system with fewer free for a single system with fewer free parametersparameters

Occam >>


Exemplar models: categories are Exemplar models: categories are represented by storage of individual represented by storage of individual exemplars and objects are classified exemplars and objects are classified based on similarity to thesebased on similarity to theseSuccessful at explaining relations between Successful at explaining relations between categorization and other fundamental categorization and other fundamental cognitive processescognitive processes Object identification, old-new recognition Object identification, old-new recognition

memory, problem solvingmemory, problem solving

Model OverviewModel Overview

Generalized Context Generalized Context Model (GCM), Model (GCM), Ashby Ashby & Maddox, 1993; & Maddox, 1993; Nosofsky, 1984, Nosofsky, 1984, 1986, 19911986, 1991

Uses Uses multidimensional multidimensional scalingscaling


Exemplars presented in Exemplars presented in multidimensional multidimensional psychological spacepsychological space

Similarity between them Similarity between them is a decreasing function is a decreasing function of their distanceof their distance

Observers often learn to Observers often learn to distribute attention across distribute attention across dimensions so as to dimensions so as to optimize overall optimize overall performanceperformance


The probability that item The probability that item i i is classified into is classified into Category J is given by:Category J is given by:

SSijij denotes similarity of item denotes similarity of item i i to exemplar to exemplar jj and and

the index the index j j € J € J denotes that the sum is over all denotes that the sum is over all exemplarsexemplars j j belonging to category belonging to category J.J.


The probability that item The probability that item i i is classified into is classified into Category J is given by:Category J is given by:

A critical assumption is that similarity is a A critical assumption is that similarity is a context-dependent relation, rather than an context-dependent relation, rather than an invariant oneinvariant one


The distance between exemplars is The distance between exemplars is computed by the Minkowski power-model computed by the Minkowski power-model formula, where r defines the distance formula, where r defines the distance metric of the space, and the wmetric of the space, and the wmm

parameters model the degree of attention parameters model the degree of attention given to each dimensiongiven to each dimension


The distance between exemplars is The distance between exemplars is assumed to be a nonlinearly decreasing assumed to be a nonlinearly decreasing function of their distance, as given by…function of their distance, as given by…

……where where cc is an overall scaling or is an overall scaling or sensitivity parameter, and the value sensitivity parameter, and the value p p gives the form of the similarity gradient.gives the form of the similarity gradient.

Model overviewModel overview

Accounts of the PhenomenaAccounts of the Phenomena

Bias toward verbal rulesBias toward verbal rules

Study by Ashby et al. (1998)Study by Ashby et al. (1998)

COVIS model (competion between a COVIS model (competion between a verbal and implicit system) believed to verbal and implicit system) believed to predict results better than GCM predict results better than GCM (specifically referenced by the authors)(specifically referenced by the authors)

RULEX Classification ModelRULEX Classification Model

Nosofksy, Palmeri, and McKinley (1994)Nosofksy, Palmeri, and McKinley (1994)

Model states that people learn to classify objects by Model states that people learn to classify objects by forming simple logical rules along single dimensions, and forming simple logical rules along single dimensions, and storing the occasional exceptions to these rules.storing the occasional exceptions to these rules.

Example of model is given in the form of classic category Example of model is given in the form of classic category structure used by Medin and Shaffer (1978)structure used by Medin and Shaffer (1978)

RULEX ModelRULEX Model

Stimuli vary along 4 binary-valued dimensionsStimuli vary along 4 binary-valued dimensions

5 Category A exemplars, 4 Category B exemplars, 7 5 Category A exemplars, 4 Category B exemplars, 7 transfer stimulitransfer stimuli

Logical value 1 on each dimension indicates Category A, Logical value 1 on each dimension indicates Category A, and logical value 2 indicates Category B, with no and logical value 2 indicates Category B, with no necessary and jointly sufficient feature sets for eithernecessary and jointly sufficient feature sets for either


GCM exemplar models that allow for GCM exemplar models that allow for individual-subject variation in attention individual-subject variation in attention weighting can account for the dataweighting can account for the data

Variation in distribution-of-generalization Variation in distribution-of-generalization data reported in original study is poorer data reported in original study is poorer than originally believed as a diagnostic of than originally believed as a diagnostic of rule use and multiple categorization rule use and multiple categorization systemssystems

ATRIUM ModelATRIUM Model

Erickson and Kruschke (1998)Erickson and Kruschke (1998)

Hybrid connectionist model for Hybrid connectionist model for categorization; encorporates both rule- categorization; encorporates both rule- and exemplar-based representationsand exemplar-based representations

Consists of single-dimensional decision Consists of single-dimensional decision boundaries, exemplar module for boundaries, exemplar module for differentiating exemplars and categories, differentiating exemplars and categories, and a gating mechanism to link the twoand a gating mechanism to link the two


Predicts that exemplar module will Predicts that exemplar module will contribute to classification judgments contribute to classification judgments primarily for stimuli similar to learned primarily for stimuli similar to learned exceptionsexceptions

Rule module predicted to dominate in Rule module predicted to dominate in other casesother cases


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

Prototype vs. ExceptionPrototype vs. Exception

Smith, Murray, and Minda (1997; Smith Smith, Murray, and Minda (1997; Smith and Minda, 1998)and Minda, 1998)Mixed prototype-plus-exemplar model of Mixed prototype-plus-exemplar model of categorizationcategorizationPrototypes abstracted during early Prototypes abstracted during early category learning or with highly coherent category learning or with highly coherent categoriescategoriesExemplars used to supplement prototype Exemplars used to supplement prototype abstractionsabstractions

Prototype vs. ExceptionPrototype vs. Exception

Prototype vs. Prototype vs. ExceptionException

Prototype vs. ExceptionPrototype vs. ExceptionFor some subjects and stages of learning, the exemplar For some subjects and stages of learning, the exemplar model provides roughly the same fit as prototype modelmodel provides roughly the same fit as prototype model

Generally, however, the exemplar model provides a Generally, however, the exemplar model provides a better explanation for the databetter explanation for the data

Dissociations between Categorization and Dissociations between Categorization and Similarity JudgmentSimilarity Judgment

Rips (1989), Rips and Collins (1993)Rips (1989), Rips and Collins (1993)Participants imagined 3” object, decided if Participants imagined 3” object, decided if it was:it was: more more similarsimilar to a quarter or a pizza to a quarter or a pizza belonging to the belonging to the category category quarter or pizzaquarter or pizza

Similarity group judged it more similar to Similarity group judged it more similar to quarterquarterCategorization group placed it in pizza Categorization group placed it in pizza categorycategory


It is theorized that the 3” object is classified as a “pizza” It is theorized that the 3” object is classified as a “pizza” (B) because the size range in the category is highly (B) because the size range in the category is highly variable, whereas that of “quarter” is notvariable, whereas that of “quarter” is not


This poses a challenge to the single-system This poses a challenge to the single-system model, but this can be reconciled by allowing for model, but this can be reconciled by allowing for differing sensitivity parameters for similarity differing sensitivity parameters for similarity computations in the low- and high-variability computations in the low- and high-variability conditionsconditions

Variable sensitivity parameters allow observers Variable sensitivity parameters allow observers to optimize percentage of correct classificationsto optimize percentage of correct classifications


A follow-up study examined histogram classification of A follow-up study examined histogram classification of temperature measurements (Rips and Collins, 1993)temperature measurements (Rips and Collins, 1993)

A similar dissociation between similarity and A similar dissociation between similarity and categorization judgments was foundcategorization judgments was found

This can still be explained in terms of the single-system This can still be explained in terms of the single-system model, given the assumptions:model, given the assumptions:

Histogram frequency counts translate directly into stored copies Histogram frequency counts translate directly into stored copies of exemplarsof exemplars

Configuration of exemplars in psychological space corresponds Configuration of exemplars in psychological space corresponds directly to physical layout of figuredirectly to physical layout of figure

Category-likelihood judgment is monotonically related to Category-likelihood judgment is monotonically related to summed similarity of value to histogram exemplarsummed similarity of value to histogram exemplar

ConclusionConclusion

The single-system exemplar model can The single-system exemplar model can adequately predict results of studies originally adequately predict results of studies originally designed with more-complex multiple-system designed with more-complex multiple-system modelsmodelsThe single-system model is more parsimoniousThe single-system model is more parsimoniousThe single-system model is, however, not The single-system model is, however, not always better, and sometimes can fail to account always better, and sometimes can fail to account for certain patterns in datafor certain patterns in dataThe model has potential for application in study The model has potential for application in study higher-level cognitive tasks, such as inferencehigher-level cognitive tasks, such as inference

exemplar-based accounts of “multiple system” phenomena in perceptual categorization r. m....

Documents

model overview slide

model overview exemplars

dimension slide

model states

example of model

exemplars j

category j

multidimensional scaling