Procrustes problems /
Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This text is a systematic overview of Procrustean methods, presenting a unifying Analysis of Variance framework for different matching methods and the development of statistical tests.
| Main Authors: | , |
|---|---|
| Format: | eBook |
| Language: | English |
| Language Notes: | English. |
| Published: |
Oxford ; New York :
Oxford University Press,
2004.
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| Series: | Oxford statistical science series ;
30. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Preface; Acknowledgements; 1 Introduction; 1.1 Historical review; 1.2 Current trends; 1.3 Overview of the topics in the book; 1.4 Closed form and algorithmic solutions; 1.5 Notation; 2 Initial transformations; 2.1 Data-scaling of variables; 2.1.1 Canonical analysis as a form of data-scaling; 2.1.2 Prior multivariate analyses; 2.1.3 Distance matrices; 2.2 Configuration-scaling; 2.2.1 Differing numbers of variables; 2.2.2 Isotropic and anisotropic scaling; 2.3 Types of data sets; 3 Two-set Procrustes problems-generalities; 3.1 Introduction; 3.1.1 Least-Squares criteria.
- 3.1.2 Correlational and inner-product criteria3.1.3 Robust criteria; 3.1.4 Quantifications; 3.1.5 Matching of rows and columns; 3.2 Translation; 3.2.1 Simple translation; 3.3 Isotropic scaling; 3.4 The general linear transformation; 3.5 A note on algorithms; 3.6 A K-sets problem with two-sets solutions; 4 Orthogonal Procrustes problems; 4.1 Solution of the orthogonal Procrustes problem; 4.2 Necessary and sufficient conditions for optimality; 4.3 Scaling; 4.4 Example of an orthogonal rotation of two sets, including a scaling factor; 4.5 Different dimensionalities in X[sub(1)] and X[sub(2)]
- 5.3.3 Green's problem5.4 Projection Procrustes by least squares; 5.4.1 The Kochat and Swayne approach; 5.4.2 The wind model; 5.5 Two-sided projection Procrustes by least-squares; 5.6 Maximising the projected average configuration; 5.6.1 Method 1; 5.6.2 Method 2; 5.7 Rotation into higher dimensions; 5.8 Some geometrical considerations; 6 Oblique Procrustes problems; 6.1 The projection method; 6.2 The parallel axes or vector-sums method; 6.3 The cases T = C[sup( -1)] and T = (C')[sup( -1)]; 6.4 Summary of results; 7 Other two-sets Procrustes problems; 7.1 Permutations; 7.2 Reduced rank regression.
- 7.3 Miscellaneous choices of T7.4 On simple structure rotations etc; 7.5 Double Procrustes problems; 7.5.1 Double Procrustes for symmetric matrices (orthogonal case); 7.5.2 Double Procrustes for rectangular matrices (orthogonal case); 8 Weighting, scaling, and missing values; 8.1 Weighting; 8.1.1 Translation with weighting; 8.1.2 General forms of weighting; 8.2 Missing values; 8.3 Anisotropic scaling; 8.3.1 Pre-scaling R; 8.3.2 Post-scaling S; 8.3.3 Estimation of T with post-scaling S; 8.3.4 Simultaneous estimation of R, S, and T; 8.3.5 Scaling with two-sided problems; 8.3.6 Row scaling.