@inproceedings{5130da5eb33b44738aa045c3cd9bbd4f,
title = "Dynamical systems for principal singular subspace analysis",
abstract = "The computation of the principal subspaces is an essential task in many signal processing and control applications. In this paper novel dynamical systems for finding the principal singular subspace and/or components of arbitrary matrix are developed. The proposed dynamical systems are gradient flows or weighted gradient flows derived from the optimization of certain objective functions over orthogonal constraints. Global asymptotic stability analysis and domains of attractions of these systems are examined via Liapunov theory and LaSalle invariance principle. Weighted versions of these methods for computing principal singular components are also given. Qualitative properties of the proposed systems are analyzed in detail.",
keywords = "Asymptotic stability, Constrained optimization, Global convergence, Gradient flow, Invariant set, Lasalle invariance principle, Principal singular flow, SVD, Stiefel manifold",
author = "Hasan, {Mohammed A.}",
year = "2006",
doi = "10.1109/SAM.2006.1677175",
language = "English (US)",
isbn = "1424403081",
series = "2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006",
pages = "142--146",
booktitle = "2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006",
note = "4th IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006 ; Conference date: 12-07-2006 Through 14-07-2006",
}