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Cited by 320

The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.

Orthogonal Procrustes Rotation for Two or More Matrices

Ten Berge, Jos M. F.·1977·Psychometrika
DOI 10.1007/bf02294053
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Abstract

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem by Fischer and Roppert, which solves the case of two matrices, is given a more straightforward proof. A sufficient condition for a best least-squares fit for more than two matrices is formulated and shown to be not necessary. In addition, necessary conditions suggested by Kristof and Wingersky are shown to be not sufficient. A rotation procedure that is an alternative to the one by Kristof and Wingersky is presented. Upper bounds are derived for determining the extent to which the procedure falls short of attaining the best least-squares fit. The problem of scaling matrices to maximal agreement is discussed. Modifications of Gower’s method of generalized Procrustes analysis are suggested.

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Metadata

Authors
Ten Berge, J. M. F.
Venue
Psychometrika
Publisher
Cambridge University Press (CUP)
Published
1977-06
Volume
42
Issue
2
Pages
267-276
ISSN
  • 0033-3123 (ISSN-L)
  • 1860-0980
DOI
10.1007/bf02294053
OpenAlex
W2150657707
Cited by
320
References
8
FWCI
2.21
Type
journal article
Language
en
Open access
closed

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