The orthogonally constrained regression revisited

Chu, M.T. and Trendafilov, N.T. (2001). The orthogonally constrained regression revisited. Journal of Computational and Graphical Statistics, 10(4) pp. 746–771.




The Penrose regression problem, including the orthonormal Procrustes problem and rotation problemto a partially specified target, is an important class of data matching problems arising frequently in multivariate analysis, yet its optimality conditions have never been clearly understood.This work offers a way to calculate the projected gradient and the projectedHessian explicitly.One consequenceof this calculationis the complete characterization of the first order and the second order necessaryand sufficient optimality conditions for this problem. Another application is the natural formulation of a continuous steepest descent ow that can serve as a globally convergentnumerical method. Applications to the
orthonormal Procrustes problem and Penrose regression problem with partially specified target are demonstrated in this article. Finally, some numerical results are reported and commented.

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