@inproceedings{d27e18ad597c4704a15601fd931988a0,

title = "Joint computation of principal and minor components using gradient dynamical systems over stiefel manifolds",

abstract = "This paper presents several dynamical systems for simultaneous computation of principal and minor subspaces of a symmetric matrix. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Necessary optimality conditions are given in terms of a gradient of certain cost functions over a Stiefel manifold. Stability analysis of equilibrium points of six algorithms is established using Liapunov direct method.",

keywords = "Eigenvalue spread, Gradient dynamical systems, Joint PCA-MCA, Joint PSA-MSA, Oja's rule, Stiefel manifold",

author = "Hasan, {Mohammed A.}",

year = "2008",

doi = "10.1109/CDC.2008.4739097",

language = "English (US)",

isbn = "9781424431243",

series = "Proceedings of the IEEE Conference on Decision and Control",

pages = "3287--3292",

booktitle = "Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008",

note = "47th IEEE Conference on Decision and Control, CDC 2008 ; Conference date: 09-12-2008 Through 11-12-2008",

}