Procrustes Procedures

I. Borg and J. Lingoes
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I. Borg: Justus-Liebig-Universität, Department of Psychology
J. Lingoes: University of Michigan, Computing Center

Chapter 19 in Multidimensional Similarity Structure Analysis, 1987, pp 309-328 from Springer

Abstract: Abstract The Procrustes problem is concerned with fitting one configuration, Y, to another, X, as closely as possible. In the simplest case, X and Y have the same dimensionality and the same number of points which can be brought into a 1–1 correspondence by substantive considerations. Under orthogonal transformations, Y can only be rotated and reflected in order to approximate X. More general transformations consist of rigid motions and dilations of Y. In the oblique case, Y can also be distorted linearly. Further generalizations include an incompletely specified target configuration X, different dimensionalities of X and Y, and different numbers of points in X and Y.

Keywords: orthogonal Procrustes problem; target matrix; scale factor; differentiation of a matrix trace with respect to a matrix; cyclic permutation; rigid motion; minimization of a function with side constraints; level curves; Lagrangean multiplier; Eckart-Young decomposition; singular-value decomposition; confirmatory Procrustes problem; partial target matrix; oblique rotation; congruence coefficient (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4768-5_19

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