Formal Approaches in Categorization

350 Pages·2011·2.139 MB·English

by  Emmanuel M. Pothos, Andy J. Wills

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Formal Approaches in Categorization

The process of constructing concepts underpins our capacity to encode
information in an efficient and competent manner and also, ultimately,
our ability to think in terms of abstract ideas such as justice, love, and
happiness. But what are the mechanisms which correspond to psy-
chological categorization processes? This book unites many promi-
nent approaches in modelling categorization. Each chapter focuses
on a particular formal approach to categorization, presented by the
proponent(s) or advocate(s) of that approach, and the authors consider
the relation of this approach to other models and the ultimate objectives
in their research programmes. The volume evaluates progress that has
been made in the field and where it goes from here. This is an essen-
tial companion to any scientist interested in the formal description of
categorization and, more generally, in formal approaches to cognition.
It will be the definitive guide to formal approaches in categorization
research for years to come.
Emmanuel M. Pothos is a reader in the Department of Psychology at
Swansea University.
Andy J. Wills is an associate professor in the School of Psychology at the
University of Exeter.

Formal Approaches in
Categorization
Emmanuel M. Pothos and Andy J. Wills
Editors
cambridge university press
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Cambridge University Press
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Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521140720
© Cambridge University Press 2011
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2011
Printed in the United Kingdom at the University Press, Cambridge
A catalogue record for this publication is available from the British Library.
Library of Congress Cataloguing in Publication data
Formal Approaches in Categorization / Emmanuel M. Pothos,
Andy J. Wills, Editors.
p. cm
Includes bibliographical references and index.
ISBN 978-0-521-19048-0 (hardback) – ISBN 978-0-521-14072-0 (paperback)
1. Categorization (Psychology) I. Pothos, Emmanuel M., 1973–
II. Wills, Andy J., 1972–
BF445.F66 2011
153.2–dc22
2010045712
ISBN 978-0-521-19048-0 Hardback
ISBN 978-0-521-14072-0 Paperback
Cambridge University Press has no responsibility for the persistence or
accuracy of URLs for external or third-party internet websites referred to in
this publication, and does not guarantee that any content on such websites is,
or will remain, accurate or appropriate.
Contents

List of figures page vii
List of tables x
List of contributors xi
1 Introduction 1
emmanuel m. pothos and andy j. wills
2 The generalized context model: an exemplar model
of classification 18
robert m. nosofsky
3 Prototype models of categorization: basic formulation,
predictions, and limitations 40
john paul minda and j. david smith
4 COVIS 65
f. gregory ashby, erick j. paul and
w. todd maddox
5 Semantics without categorization 88
timothy t. rogers and james l. mcclelland
6 Models of attentional learning 120
john k. kruschke
7 An elemental model of associative learning and memory 153
evan livesey and ian mclaren
8 Nonparametric Bayesian models of categorization 173
thomas l. griffiths, adam n. sanborn,
kevin r. canini, daniel j. navarro and
joshua b. tenenbaum
9 The simplicity model of unsupervised categorization 199
emmanuel m. pothos, nick chater and
peter hines
v
vi Contents
10 Adaptive clustering models of categorization 220
john v. mcdonnell and todd m. gureckis
11 Cobweb models of categorization and probabilistic
concept formation 253
wayne iba and pat langley
12 The knowledge and resonance (KRES) model of
category learning 274
harlan d. harris and bob rehder
13 The contribution (and drawbacks) of models to the
study of concepts 299
gregory l. murphy
14 Formal models of categorization: insights from
cognitive neuroscience 313
lukas strnad, stefano anzellotti and
alfonso caramazza
15 Comments on models and categorization theories:
the razor’s edge 325
douglas medin
Index 332
Figures

2.1 Schematic illustration of a category structure to explain
the workings of the GCM. page 20
2.2 Confusion matrices for an identification and classification
experiment. 25
2.3 Schematic illustration of four category structures which
have been used to test the GCM. 31
2.4 GCM predictions versus observed data. 33
3.1 Examples of the dot-pattern stimuli which have been
used in tests of the prototype model. 44
3.2 Categorization performance with the dot-pattern stimuli. 45
3.3 Simulated predictions of the prototype model,
assuming a categorization mode based on prototypes. 51
3.4 Further simulations with the prototype model. 52
3.5 Fitting the prototype model to hypothetical classification
data, which reflect either linearly separable or non-linearly
separable classifications. 55
3.6 Fitting the prototype model to two hypothetical sets of
classification data. 57
4.1 Schematic illustration of the architecture of the COVIS
procedural system. 72
4.2 COVIS simulations and corresponding empirical data. 79
5.1 An example of the neural network considered in this
chapter. 96
5.2 An example of the graphical interface of the PDPTool
Matlab application. 101
5.3 Progressive differentiation of concepts and preservation
of superordinate information in the PDP model. 104
5.4 Naming data using more or less general category terms
and corresponding semantic dementia patient data. 106
5.5 The similarity structure of the same objects in different
contexts. 109
vii
viii List of figures
5.6 Activation of an object property for different objects,
depending on context. 111
6.1 Category structures that illustrate the benefits of
selective attention. 121
6.2 General framework for models of attentional learning. 128
6.3 The RASHNL model. 130
6.4 The EXIT model. 133
6.5 The ATRIUM and POLE models. 137
6.6 Locally Bayesian learning. 141
7.1 A simple connectionist system. 154
7.2 Representation of a stimulus dimension in a
connectionist system. 157
7.3 A model architecture based on McLaren and
Mackintosh (2000, 2002). 158
7.4 Examples of ‘icon’ stimuli. 161
7.5 Data from Oakeshott (2002) and simulation. 163
7.6 Data and simulation. 165
8.1 Example stimuli. 178
8.2 Hierarchical Dirichlet process. 181
8.3 Local MAP, particle filtering, and Gibbs sampling
approximation algorithms. 186
8.4 Results of the approximation algorithms compared
to the exact posterior. 187
8.5 Data and simulation for Smith and Minda (1998,
Experiment 2). 192
9.1 Illustrating the kind of similarity employed by the
simplicity model. 206
9.2 Examining the predictions of the simplicity model. 207
10.1 Schematic illustration of SUSTAIN. 224
10.2 The stimulus encoding process and cluster representation. 228
10.3 Simulation of Y ounger and Cohen (1986, Experiment 2). 237
10.4 Gureckis and Goldstone’s (2008) experimental design
and results. 240
11.1 A concept hierarchy. 264
11.2 Multiple alternative updates to a concept hierarchy. 265
12.1 A KRES network. 277
12.2 Fitting a KRES model to data from Hoffman et al.
(2008). 284
12.3 Further fits of a KRES model to data from Hoffman
et al. (2008). 285
12.4 An alternative KRES network. 289