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Modern Multidimensional Scaling : Theory and Applications

Author: Ingwer Borg; Patrick Groenen
Publisher: New York, NY : Springer New York, 1997.
Series: Springer series in statistics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The book provides a comprehensive treatment of multidimensional scaling (MDS), a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space. Such data are widespread, for example, intercorrelations of attitude items, direct ratings of similarity on choice objects, or trade indices for a set of countries. MDS models such data as distances among points in a  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ingwer Borg; Patrick Groenen
ISBN: 9781475727111 1475727119
OCLC Number: 851820688
Description: 1 online resource (xvii, 472 pages).
Contents: I Fundamentals of MDS --
1 The Four Purposes of Multidimensional Scaling --
2 Constructing MDS Representations --
3 MDS Models and Measures of Fit --
4 Three Applications of MDS --
5 MDS and Facet Theory --
6 How to Obtain Proximities --
II MDS Models and Solving MDS Problems --
7 Matrix Algebra for MDS --
8 A Majorization Algorithm for Solving MDS --
9 Metric and Nonmetric MDS --
10 Confirmatory MDS --
11 MDS Fit Measures, Their Relations, and Some Algorithms --
12 Classical Scaling --
13 Special Solutions, Degeneracies, and Local Minima --
III Unfolding --
14 Unfolding --
15 Special Unfolding Models --
IV MDS Geometry as a Substantive Model --
16 MDS as a Psychological Model --
17 Scalar Products and Euclidean Distances --
18 Euclidean Embeddings --
V MDS and Related Methods --
19 Procrustes Procedures --
20 Three-Way Procrustean Models --
21 Three-Way MDS Models --
22 Methods Related to MDS --
VI Appendices --
A Computer Programs for MDS --
B Notation --
References --
Author Index.
Series Title: Springer series in statistics.
Responsibility: by Ingwer Borg, Patrick Groenen.

Abstract:

The book provides a comprehensive treatment of multidimensional scaling (MDS), a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space. Such data are widespread, for example, intercorrelations of attitude items, direct ratings of similarity on choice objects, or trade indices for a set of countries. MDS models such data as distances among points in a geometric space of low dimensionality. This makes complex data sets accessible to visual exploration and thus aids in seeing structure not obvious from the numbers. Other uses of MDS interpret the geometry and, in particular, the distance function as a psychological composition rule. The book may be used as an introduction to MDS for students in many areas including statistics, psychology, sociology, political sciences, and marketing. The prerequisite is a two-semester course in statistics for the social or managerial sciences. The book is also suited for several varieties of advanced courses on MDS, either with an emphasis on data analysis or with a focus on the psychology of similarity. All the mathematics required for more advanced topics is developed systematically.

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