Modern Multidimensional Scaling
Theory and Applications
(Sprache: Englisch)
The first edition was released in 1996 and has sold close to 2200 copies.
Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space.
The...
Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space.
The...
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Produktdetails
Produktinformationen zu „Modern Multidimensional Scaling “
The first edition was released in 1996 and has sold close to 2200 copies.
Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space.
The authors have added three chapters and exercise sets. The text is being moved from SSS to SSPP.
The book is suitable for courses in statistics for the social or managerial sciences as well as for advanced courses on MDS.
All the mathematics required for more advanced topics is developed systematically in the text.
Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space.
The authors have added three chapters and exercise sets. The text is being moved from SSS to SSPP.
The book is suitable for courses in statistics for the social or managerial sciences as well as for advanced courses on MDS.
All the mathematics required for more advanced topics is developed systematically in the text.
Klappentext zu „Modern Multidimensional Scaling “
Multidimensionalscaling(MDS)isatechniquefortheanalysisofsimilarity 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 forasetofcountries.MDSattemptstomodelsuchdataasdistancesamong pointsinageometricspace.Themainreasonfordoingthisisthatonewants 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 mapthedata,themappingfunction,thealgorithmsusedto?ndanoptimal 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 di?erent purposes for which MDS has been used, to various ways of looking at or "interpreting" an MDS representation, or to di?erences in the data required for the particular models. Inthisbook,wegiveafairlycomprehensivepresentationofMDS.Forthe reader with applied interests only, the ?rst six chapters of Part I should be su?cient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.
Inhaltsverzeichnis zu „Modern Multidimensional Scaling “
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 Nonmetric 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.
Bibliographische Angaben
- Autoren: I. Borg , P. J. F. Groenen
- 2010, 2. Aufl., XXII, 614 Seiten, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441920463
- ISBN-13: 9781441920461
Sprache:
Englisch
Pressezitat
From the reviews of the second edition: "[Modern Multidimensional Scaling: Theory and Applications] is without a doubt the most comprehensive and most rigorous book on MDS...The second edition is considerably (140 pages) longer than the first, mostly because of much more material on MDS of rectangluar matrices (also known as unfolding) and MDS of asymmetric matrices is included...this is currently by far the best available book on MDS, and it is quite likely to stay in that position for a long time." Journal of Statistical Software, August 2005
"This is an updated and expanded version of the first edition ... . the exercises at the end of each chapter are an attractive feature. I can recommend the book enthusiastically." (W.J. Krzanowski, Short Book Reviews, Vol. 26 (1), 2006)
"The authors provide a comprehensive treatment of multidimensional scaling (MDS), a family of statistical techniques for analyzing similarity or dissimilarity data on a set of objects. ... This book may be used as an introduction to MDS for students in psychology, sociology and marketing ... . It is also well suited for a variety of advanced courses on MDS topics." (Ivan Krivý, Zentralblatt MATH, Vol. 1085, 2006)
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