@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",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
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",
}