The Open UniversitySkip to content

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:
Google Scholar: Look up in Google Scholar


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 Item
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/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 4019
Depositing User: Nickolay Trendafilov
Date Deposited: 04 Jul 2006
Last Modified: 07 Dec 2018 08:55
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU