Trendafilov, Nickolay T. and Lippert, Ross A.
|DOI (Digital Object Identifier) Link:||http://doi.org/10.1016/S0024-3795(02)00253-7|
|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 Article|
|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:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Nickolay Trendafilov|
|Date Deposited:||04 Jul 2006|
|Last Modified:||04 Oct 2016 09:51|
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