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A General Solution of the Weighted Orthonormal Procrustes Problem

Published online by Cambridge University Press:  01 January 2025

Ab Mooijaart  and
Jacques J. F. Commandeur
Ab Mooijaart*
Affiliation:
Leiden University
Jacques J. F. Commandeur
Affiliation:
Leiden University
*
Requests for reprints should be sent to Ab Mooijaart, Department of Psychology, Leiden University, Wassenaarseweg 52, 2333AK, Leiden, THE NETHERLANDS.
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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

weighted orthonormal ProcrustesalgorithmIDIOSCALINDSCAL
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 657 - 663
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

The authors are grateful to the Editor and the anonymous reviewers for their helpful comments on an earlier draft of this paper.

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