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The Structural Representation of Proximity Matrices with MATLAB The Structural Representation of Proximity Matrices with MATLAB

Lawrence Hubert, Phipps Arabie, and Jacqueline Meulman



ASA-SIAM Series on Applied Probability 19

"The Structural Representation of Proximity Matrices with MATLAB combines state of the art proximity matrix representation with a modern programming language, making previously inaccessible techniques accessible to the general user. The material is not just a recapitulation of well-known techniques, but an insightful book that could only have been written by experts in the field. In short, this book fills a major gap in the literature."
Douglas L. Steinley, Assistant Professor, University of Missouri.

The Structural Representation of Proximity Matrices with MATLAB presents and demonstrates the use of functions (by way of M-files) within a MATLAB computational environment to effect a variety of structural representations for the proximity information that is assumed to be available on a set of objects. The representations included in the book have been developed primarily in the behavioral sciences and applied statistical literature (e.g., in psychometrics and classification), although interest in these topics now extends more widely to such fields as bioinformatics and chemometrics.

Throughout the book, two kinds of proximity information are analyzed: one-mode and two-mode. One-mode proximity data are defined between the objects from a single set and are usually given in the form of a square symmetric matrix; two-mode proximity data are defined between the objects from two distinct sets and are given in the form of a rectangular matrix. In addition, there is typically the flexibility to allow the additive fitting of multiple structures to either the given one- or two-mode proximity information.

This book is divided into three main sections, each based on the general class of representations being discussed. Part I develops linear and circular unidimensional and multidimensional scaling using the city-block metric as the major representational device. Part II discusses characterizations based on various graph-theoretic tree structures, specifically those referred to as ultrametrics and additive trees. Part III uses representations defined solely by order properties, particularly emphasizing what are called (strongly) anti-Robinson forms.

Audience
This book is intended to provide an applied documentation source for a collection of M-files of use to applied statisticians and data analysts, as well as bioinformaticians, chemometricians, and psychometricians. Industrial engineers, quantitative psychologists, and behavioral and social scientists will also find the content of this book beneficial.

About the Authors
Lawrence Hubert is Professor of Psychology and Statistics at the University of Illinois Urbana-Champaign.
Phipps Arabie is Professor of Management and Psychology at Rutgers University.
Jacqueline Meulman is Professor of Applied Data Theory in the Faculty of Social and Behavioral Sciences of Leiden University, The Netherlands.

Contents
List of Figures; List of Tables; Preface; Part I: (Multi- and Unidimensional) City-Block Scaling. Chapter 1: Linear Unidimensional Scaling; Chapter 2: Linear Multidimensional Scaling; Chapter 3: Circular Scaling; Chapter 4: LUS for Two-Mode Proximity Data; Part II: The Representation of Proximity Matrices by Tree Structures. Chapter 5: Ultrametrics for Symmetric Proximity Data; Chapter 6: Additive Trees for Symmetric Proximity Data; Chapter 7: Fitting Multiple Tree Structures to a Symmetric Proximity Matrix; Chapter 8: Ultrametrics and Additive Trees for Two-Mode (Rectangular) Proximity Data; Part III: The Representation of Proximity Matrices by Structures Dependent on Order (Only). Chapter 9: Anti-Robinson Matrices for Symmetric Proximity Data; Chapter 10: Circular Anti-Robinson Matrices for Symmetric Proximity Data; Chapter 11: Anti-Robinson Matrices for Two-Mode Proximity Data; Appendix A: Header Comments for the M-Files Mentioned in the Text and Given in Alphabetical Order; Bibliography; Indices.

2006 / xvi + 214 pages / Softcover / ISBN-13: 978-0-898716-07-8 / ISBN-10: 0-89871-607-1 /
List Price $88.50 / ASA/SIAM Member Price $61.95 / Order Code SA19
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)