On a differential equation approach to the weighted orthogonal Procrustes problem

Trendafilov, Nickolay T. and Chu, Moody T. (1998). On a differential equation approach to the weighted orthogonal Procrustes problem. Statistics and Computing, 8(2) pp. 125–133.

DOI: https://doi.org/10.1023/A:1008934100736

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.

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About

• Item ORO ID
• 28348
• Item Type
• Journal Item
• ISSN
• 0960-3174
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	National Science Foundation [DMS-9422280]

• Keywords
• constrained regression; Procrustes rotation; projected gradient; optimality condition
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 1998 Chapman & Hall
• Depositing User
• Sarah Frain