Modern Multidimensional Scaling

Theory and Applications

  • Ingwer Borg
  • Patrick Groenen

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Fundamentals of MDS

    1. Front Matter
      Pages 1-1
    2. Ingwer Borg, Patrick Groenen
      Pages 3-14
    3. Ingwer Borg, Patrick Groenen
      Pages 15-28
    4. Ingwer Borg, Patrick Groenen
      Pages 29-48
    5. Ingwer Borg, Patrick Groenen
      Pages 49-69
    6. Ingwer Borg, Patrick Groenen
      Pages 71-89
    7. Ingwer Borg, Patrick Groenen
      Pages 91-106
  3. MDS Models and Solving MDS Problems

    1. Front Matter
      Pages 107-107
    2. Ingwer Borg, Patrick Groenen
      Pages 109-134
    3. Ingwer Borg, Patrick Groenen
      Pages 135-157
    4. Ingwer Borg, Patrick Groenen
      Pages 159-180
    5. Ingwer Borg, Patrick Groenen
      Pages 181-197
    6. Ingwer Borg, Patrick Groenen
      Pages 199-205
    7. Ingwer Borg, Patrick Groenen
      Pages 207-212
    8. Ingwer Borg, Patrick Groenen
      Pages 213-228
  4. Unfolding

    1. Front Matter
      Pages 229-229
    2. Ingwer Borg, Patrick Groenen
      Pages 231-252
    3. Ingwer Borg, Patrick Groenen
      Pages 253-269
  5. MDS Geometry as a Substantive Model

    1. Front Matter
      Pages 271-271

About this book

Introduction

Multidimensional scaling (MDS) is a technique for the analysis of similarity or dissimilarity data on a set of objects. Such data may be intercorrelations of test items, ratings of similarity on political candidates, or trade indices for a set of countries. MDS attempts to model such data as distances among points in a geometric space. The main reason for doing this is that one wants a graphical display of the structure of the data, one that is much easier to understand than an array of numbers and, moreover, one that displays the essential information in the data, smoothing out noise. There are numerous varieties of MDS. Some facets for distinguishing among them are the particular type of geometry into which one wants to map the data, the mapping function, the algorithms used to find an optimal data representation, the treatment of statistical error in the models, or the possibility to represent not just one but several similarity matrices at the same time. Other facets relate to the different purposes for which MDS has been used, to various ways of looking at or "interpreting" an MDS representation, or to differences in the data required for the particular models. In this book, we give a fairly comprehensive presentation of MDS. For the reader with applied interests only, the first six chapters of Part I should be sufficient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.

Keywords

algorithms best fit correlation data analysis multidimensional scaling sociology statistics

Authors and affiliations

  • Ingwer Borg
    • 1
  • Patrick Groenen
    • 2
  1. 1.Zentrum für Umfragen, Methoden und AnalysenMannheimGermany
  2. 2.Department of Data TheoryLeiden UniversityLeidenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2711-1
  • Copyright Information Springer-Verlag New York 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2713-5
  • Online ISBN 978-1-4757-2711-1
  • Series Print ISSN 0172-7397
  • About this book