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The multimode Procrustes problem

Trendafilov, Nickolay T. and Lippert, Ross A. (2002). The multimode Procrustes problem. Linear Algebra and its Applications, 349(1-3) pp. 245–264.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/S0024-3795(02)00253-7
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Abstract

In this paper, we consider a generalization of the well-known Procrustes problem relevant to principal component analysis of multidimensional data arrays. This multimode Procrustes problem is a complex constrained minimization problem which involves the simultaneous least-squares fitting of several matrices. We propose two solutions of the problem: the projected gradient approach which leads to solving ordinary differential equations on matrix manifolds, and differential-geometric approach for optimization on products of matrix manifolds. A numerical example concerning the three-mode Procrustes illustrates the developed algorithms.

Item Type: Journal Article
ISSN: 0024-3795
Keywords: Multidimensional data arrays; Principal components; Constrained optimization; Manifold of orthogonal and oblique matrices; Dynamical system on product manifold; Riemannian connection; Optimality conditions
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 4019
Depositing User: Nickolay Trendafilov
Date Deposited: 04 Jul 2006
Last Modified: 02 Dec 2010 19:50
URI: http://oro.open.ac.uk/id/eprint/4019
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