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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.