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 Typically, one system computes rules and prototypes, and the second relies on specific exemplars and complex decision boundaries So, what’s wrong with this?

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 >>

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 Object identification, old-new recognition memory, problem solving

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

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 Overview The probability that item i is classified into Category J is given by: S ij denotes 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 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 Overview The distance between exemplars is computed by the Minkowski power-model formula, where r defines the distance metric of the space, and the w m parameters model the degree of attention given to each dimension

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 overview

Accounts of the Phenomena

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 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 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 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 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 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 Model

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

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. 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 Rips (1989), Rips and Collins (1993) Participants imagined 3” object, decided if it was: more similar to a quarter or a pizza more similar to a quarter or a pizza belonging to the category quarter or 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 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 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 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 Histogram frequency counts translate directly into stored copies of exemplars Configuration of exemplars in psychological space corresponds directly to physical layout of figure 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 Category-likelihood judgment is monotonically related to summed similarity of value to histogram exemplar

Dissociations between Categorization and Similarity Judgment

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