Modern multidimensional scaling : theory and applications

✍ Scribed by Ingwer Borg, Patrick J.F. Groenen

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 612
• Series: Springer series in statistics
• Category: Library

✦ Synopsis

"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."--Jacket.  Read more...

Part I. 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.- Part II. 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; III. Unfolding. Unfolding. Avoiding trivial solutions in unfolding. Special unfolding models.- Part IV. MDS geometry as a substantive model. MDS as a psychological model. Scalar products and Euclidean distances. Euclidean embeddings.- Part V. MDS and related methods. Procrustes procedures. Three-way Procrustean models. Three-way MDS models. Modeling asymmetric data. Methods related to MDS.- Part VI. Appendices