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A Continuous-Time Approach to the Oblique Procrustes Problem

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Abstract

In the paper proposed we will make use of the gradient flow approach to consider a generalization of the well-known oblique Procrustes rotation problem, involving oblique simple structure rotation of both the core and component matrices resulting from three-mode factor analysis. The standard oblique Procrustes rotations to specified factor-structure and factor-pattern follw as special cases. The approach adopted leads to globally convergent algorithm and includes solving of initial value problem for certain matrix ordinary differential equation. Necessary conditions are established for the solution of the problem. The same approach is extended easily to the weighted oblique Procrustes rotation. Finally, some simulated numerical results are given and commented.

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Authors and Affiliations

  1. Computer Stochastics Laboratory, Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, Sofia, 1090, Bulgaria

    Nickolay T. Trendafilov

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  1. Nickolay T. Trendafilov
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Additional information

This research was performed while visiting ESAT/SISTA, Katholieke Universiteit Leuven and was supported by DWTC, Flemish Goverment, BELGIUM.

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Trendafilov, N.T. A Continuous-Time Approach to the Oblique Procrustes Problem. Behaviormetrika 26, 167–181 (1999). https://doi.org/10.2333/bhmk.26.167

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  • DOI: https://doi.org/10.2333/bhmk.26.167

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