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A Weighted Procrustes Criterion

Published online by Cambridge University Press:  01 January 2025

Martin A. Koschat  and
Deborah F. Swayne
Martin A. Koschat
Affiliation:
Yale School of Organization and Management
Deborah F. Swayne*
Affiliation:
Bellcore
*
Requests for reprints and code should be sent to Deborah F. Swayne, Bellcore, 445 South Street, Room 2L-331, Box 1910, Morristown, NJ, 07960-1910, or by electronic mail to dfs@bellcore.com (Internet) or ... !dfs!bellcore (uucp).
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Abstract

The Procrustes criterion is a common measure for the distance between two matrices X and Y, and can be interpreted as the sum of squares of the Euclidean distances between their respective column vectors. Often a weighted Procrustes criterion, using, for example, a weighted sum of the squared distances between the column vectors, is called for. This paper describes and analyzes the performance of an algorithm for rotating a matrix X such that the column-weighted Procrustes distance to Y is minimized. The problem of rotating X into Y such that an aggregate measure of Tucker's coefficient of congruence is maximized is also discussed.

Keywords

rotationmatchingProcrustes analysisTucker's coefficient of congruence
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 2 , June 1991 , pp. 229 - 239
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

We wish to thank Richard A. Harshman and C. F. Jeff Wu for valuable discussions in the early stages of this work. We would also like to thank Jos ten Berge, John Gower, and the Editor, Associate Editor, and referees whose comments and suggestions greatly improved this paper.

References

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