Ebook: Modern multidimensional scaling : theory and applications
Author: Ingwer Borg Patrick J.F. Groenen
- Series: Springer series in statistics
- Year: 2005
- Publisher: Springer
- City: New York
- Language: English
- pdf
"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 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