A General Solution of the Weighted Orthonormal Procrustes Problem
- 1 December 1990
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 55 (4) , 657-663
- https://doi.org/10.1007/bf02294614
Abstract
A general solution for weighted orthonormal Procrustes problem is offered in terms of the least squares criterion. For the two-demensional case. this solution always gives the global minimum; for the general case, an algorithm is proposed that must converge, although not necessarily to the global minimum. In general, the algorithm yields a solution for the problem of how to fit one matrix to another under the condition that the dimensions of the latter matrix first are allowed to be transformed orthonormally and then weighted differentially, which is the task encountered in fitting analogues of the IDIOSCAL and INDSCAL models to a set of configurations.Keywords
This publication has 13 references indexed in Scilit:
- Multidimensional Rotation and Scaling of Configurations to Optimal AgreementPsychometrika, 1988
- Orthogonal Rotations to Maximal Agreement for Two or More Matrices of Different Column OrdersPsychometrika, 1984
- Anwendungsorientierte Multidimensionale SkalierungPublished by Springer Nature ,1981
- A Direct Approach to Individual differences Scaling using Increasingly Complex TransformationsPsychometrika, 1978
- Orthogonal Procrustes Rotation for Two or More MatricesPsychometrika, 1977
- A Solution to the Weighted Procrustes Problem in which the Transformation is in Agreement with the Loss FunctionPsychometrika, 1976
- On Browne's Solution for Oblique Procrustes RotationPsychometrika, 1974
- A Generalized Solution of the Orthogonal Procrustes ProblemPsychometrika, 1966
- On the Stationary Values of a Second-Degree Polynomial on the Unit SphereJournal of the Society for Industrial and Applied Mathematics, 1965
- Determining a Simple Structure When Loadings for Certain Tests are KnownPsychometrika, 1939