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The Structural Representation of Proximity Matrices with MATLAB

The Structural Representation of Proximity Matrices with MATLAB

Part of ASA-SIAM Series on Statistics and Applied Probability

  • Date Published: March 2006
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716078


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About the Authors
  • The Structural Representation of Proximity Matrices with MATLAB presents and demonstrates the use of functions within a MATLAB computational environment, affecting various 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, although interest in these topics now extends more widely to such fields as bioinformatics and chemometrics. 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.

    • 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
    • Two kinds of proximity information are analyzed throughout the book: one-mode and two-mode
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: March 2006
    • format: Paperback
    • isbn: 9780898716078
    • length: 184 pages
    • dimensions: 255 x 177 x 12 mm
    • weight: 0.407kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Part I. (Multi- and Unidimensional) City-Block Scaling:
    1. Linear unidimensional scaling
    2. Linear multidimensional scaling
    3. Circular scaling
    4. LUS for two-mode proximity data
    Part II. The Representation of Proximity Matrices by Tree Structures:
    5. Ultrametrics for symmetric proximity data
    6. Additive trees for symmetric proximity data
    7. Fitting multiple tree structures to a symmetric sroximity matrix
    8. Ultrametrics and additive trees for two-mode (rectangular) proximity data
    Part III. The Representation of Proximity Matrices by Structures Dependent on Order (Only):
    9. Anti-Robinson matrices for symmetric proximity data
    10. Circular anti-Robinson matrices for symmetric proximity data
    11. Anti-Robinson matrices for two-mode proximity data

  • Authors

    Lawrence Hubert, University of Illinois, Urbana-Champaign

    Phipps Arabie, Rutgers University, New Jersey

    Jacqueline Meulman, Universiteit Leiden

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