Procrustes Problems

Hardcover | March 1, 2004

byJohn C Gower, Garmt B Dijksterhuis

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Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. The name derives from the Greek myth where Procrustes invited passers-by in for a pleasant meal and a night's rest on a magical bed that would exactly fit any guest. He theneither stretched the guest on the rack or cut off their legs to make them fit perfectly into the bed. Theseus turned the tables on Procrustes, fatally adjusting him to fit his own bed.This text, the first monograph on Procrustes methods, unifies several strands in the literature and contains much new material. It focuses on matching two or more configurations by using orthogonal, projection and oblique axes transformations. Group-average summaries play an important part and linkswith other group-average methods are discussed. This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specificallyoriginal. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user'sperspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort andSylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction 29. Christopher G. Small and Jinfang Wang: Numerical Methods for Nonlinear Estimating Equations

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Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. The name derives from the Greek myth where Procrustes invited passers-by in for a pleasant meal and a night's rest on a magical bed that would exactly fit any guest. He theneither stretched the guest on the rack or cut off...

John C Gower is on the Editorial board of Journal of Classification and of The Mathematical Scientist. He is a past President of the International Federation of Classification Societies, a past President of the British Region of the International Biometric society, and a past Honorary Secretary of the Royal Statistical Society. Garm...

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Format:HardcoverDimensions:248 pages, 9.21 × 6.14 × 0.7 inPublished:March 1, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198510586

ISBN - 13:9780198510581

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Table of Contents

PrefaceContents1. Introduction2. Initial transformations3. Two-set Procrustes problems: generalities4. Orthogonal Procrustes problems5. Projection Procrustes problems6. Oblique Procrustes problems7. Other two-sets Procrustes problems8. Weighting, scaling and missing values9. Generalised Procrustes problems10. Analysis of variance framework11. Incorporating information on variables12. Accuracy and stability13. Links with other methods14. Some application areas, future and conclusionA1. ConfigurationsA2. Rotations and reflectionsA3. Orthogonal projectionsA4. Oblique axesA5. A minimisation problemA6. Symmetric matrix productsReferences