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Statistics and Computing

, Volume 8, Issue 2, pp 125–133 | Cite as

On a differential equation approach to the weighted orthogonal Procrustes problem

  • MOODY T. CHU
  • NICKOLAY T. TRENDAFILOV
Article

Abstract

The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples.

constrained regression Procrustes rotation projected gradient optimality condition 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • MOODY T. CHU
    • 1
  • NICKOLAY T. TRENDAFILOV
    • 2
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Computer Stochastics Laboratory, Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria

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