ERIC Number: EJ922150
Record Type: Journal
Publication Date: 2006-Mar
Abstractor: As Provided
Reference Count: 6
The Rigid Orthogonal Procrustes Rotation Problem
ten Berge, Jos M. F.
Psychometrika, v71 n1 p201-205 Mar 2006
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.
Descriptors: Least Squares Statistics, Computation, Equations (Mathematics), Statistical Analysis, Factor Analysis
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Authoring Institution: N/A