- 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
Other two-sets Procrustes problems
Other two-sets Procrustes problems
- Chapter:
- (p.84) 7 Other two-sets Procrustes problems
- Source:
- Procrustes Problems
- Author(s):
J. C. Gower
G. B. Dijksterhuis
- Publisher:
- Oxford University Press
This chapter briefly reviews other choices of T, such as when T is of given rank or is a permutation, symmetric, or positive matrix. It discusses double Procrustes problems of the form: where S and T are orthogonal. It is shown that S and T may be restricted in other ways, but these appear to be of little interest and are not discussed here.
Keywords: two-sets Procrustes, permutations, reduced range regression
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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
