- Title Pages
- Dedication
- Preface
- Acknowledgements
- 1 Introduction
- 2 Initial transformations
- 3 Two-set Procrustes problems—generalities
- 4 Orthogonal Procrustes problems
- 5 Projection Procrustes problems
- 6 Oblique Procrustes problems
- 7 Other two-sets Procrustes problems
- 8 Weighting, scaling, and missing values
- 9 Generalised Procrustes problems
- 10 Analysis of variance framework
- 11 Incorporating information on variables
- 12 Accuracy and stability
- 13 Links with other methods
- 14 Some application areas, future, and conclusion
- Appendix A Configurations
- Appendix B Rotations and reflections
- Appendix C Orthogonal projections
- Appendix D Oblique axes
- Appendix E A minimisation problem
- Appendix F Symmetric matrix products
- References
- Index
Oblique Procrustes problems
Oblique Procrustes problems
- Chapter:
- (p.73) 6 Oblique Procrustes problems
- Source:
- Procrustes Problems
- Author(s):
J. C. Gower
G. B. Dijksterhuis
- Publisher:
- Oxford University Press
This chapter considers oblique Procrustes problems where T is, or is a function of, a direction cosine matrix C. There are four possibilities and a new unified approach is developed, which determines the optimal direction of one axis conditional on the directions of the other axes. For all four methods, one iterates over all axes until convergence. All the cases have clear geometrical interpretations.
Keywords: oblique Procrustes, axis, projection, iteration
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- Title Pages
- Dedication
- Preface
- Acknowledgements
- 1 Introduction
- 2 Initial transformations
- 3 Two-set Procrustes problems—generalities
- 4 Orthogonal Procrustes problems
- 5 Projection Procrustes problems
- 6 Oblique Procrustes problems
- 7 Other two-sets Procrustes problems
- 8 Weighting, scaling, and missing values
- 9 Generalised Procrustes problems
- 10 Analysis of variance framework
- 11 Incorporating information on variables
- 12 Accuracy and stability
- 13 Links with other methods
- 14 Some application areas, future, and conclusion
- Appendix A Configurations
- Appendix B Rotations and reflections
- Appendix C Orthogonal projections
- Appendix D Oblique axes
- Appendix E A minimisation problem
- Appendix F Symmetric matrix products
- References
- Index
