The rigid orthogonal Procrustes rotation problem

JMF Ten Berge*

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    12 Citations (Scopus)

    Abstract

    The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has proposed a method for suppressing reflections in cases where that is necessary. This paper proves that Gower's solution does indeed give the best least squares fit over rigid rotation when the unconstrained solution is not rigid. Also, special cases that have multiple solutions are discussed.

    Original languageEnglish
    Pages (from-to)201-205
    Number of pages5
    JournalPsychometrika
    Volume71
    Issue number1
    DOIs
    Publication statusPublished - Mar-2006

    Keywords

    • orthogonal Procrustes rotation
    • rigid rotation
    • least squares rotation

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