Modern Multidimensional Scaling

Theory and Applications

Ingwer Borg, P.J.F. Groenen - Collection Springer Series In Statistics

632 pages, parution le 30/11/2005 (2^eme édition)

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Résumé

The book provides a comprehensive treatment of multidimensional scaling (MDS), a family of statistical techniques for analyzing the structure of (dis)similarity data. Such data are widespread, including, for example, intercorrelations of survey items, direct ratings on the similarity on choice objects, or trade indices for a set of countries. MDS represents the data as distances among points in a geometric space of low dimensionality. This map can help to see patterns in the data that are not obvious from the data matrices. MDS is also used as a psychological model for judgments of similarity and preference.

This book may be used as an introduction to MDS for students in psychology, sociology, and marketing. The prerequisite is an elementary background in statistics. The book is also well suited for a variety of advanced courses on MDS topics. All the mathematics required for more advanced topics is developed systematically.

This second edition is not only a complete overhaul of its predecessor, but also adds some 140 pages of new material. Many chapters are revised or have sections reflecting new insights and developments in MDS. There are two new chapters, one on asymmetric models and the other on unfolding. There are also numerous exercises that help the reader to practice what he or she has learned, and to delve deeper into the models and its intricacies. These exercises make it easier to use this edition in a course. All data sets used in the book can be downloaded from the web. The appendix on computer programs has also been updated and enlarged to reflect the state of the art.

Written for: Researchers, graduate students

Sommaire

Fundamentals of MDS: The four purposes of multidimensional scaling
- Constructing MDS representations
- MDS models and measures of fit
- Three applications of MDS MDS and facet theory
- How to obtain proximities
MDS models and solving MDS problems
- Matrix algebra for MDS
- A majorization algorithm for solving MDS
- Metric and non-metric MDS
- Confirmatory MDS
- MDS fit measures, their relations, and some algorithms
- Classical scaling
- Special solutions, degeneracies, and local minima
Unfolding
- Unfolding
- Avoiding trivial solutions in unfolding
- Special unfolding models
MDS geometry as a substantive model
- MDS as a psychological model
- Scalar products and Euclidean distances
- Euclidean embeddings
MDS and related methods Procrustes procedures
- Three-way Procrustean models
- Three-way MDS models
- Modeling asymmetric data
- Methods related to MDS
Appendices

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Ingwer Borg, P.J.F. Groenen
Collection	Springer Series In Statistics
Parution	30/11/2005
Édition	2^eme édition
Nb. de pages	632
Format	16 x 24
Couverture	Relié
Poids	1015g
Intérieur	Noir et Blanc
EAN13	9780387251509
ISBN13	978-0-387-25150-9