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A Solution to the Weighted Procrustes Problem in which the Transformation is in Agreement with the Loss Function

Published online by Cambridge University Press:  01 January 2025

Robert W. Lissitz ,
Peter H. Schönemann  and
James C. Lingoes
Robert W. Lissitz*
Affiliation:
University of Georgia
Peter H. Schönemann
Affiliation:
Purdue University
James C. Lingoes
Affiliation:
University of Michigan
*
Requests for reprints should be sent to Robert W. Lissitz, Department of Psychology, University of Georgia, Athens, Georgia 30602.
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Abstract

This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.

Keywords

rotationmatching
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 4 , December 1976 , pp. 547 - 550
Copyright
Copyright © 1976 The Psychometric Society

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References

Reference Notes

Schönemann, P. H. On the formal differentiation of traces and determinants, 1965, Chapel Hill: University of North Carolina Psychometric Laboratory.Google Scholar
Schönemann, P. H., Bock, R. D., and Tucker, L. R. Some notes on a theorem by Eckart and Young, 1965, Chapel Hill: University of North Carolina Psychometric Laboratory.Google Scholar

References

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