Title :
Gradient dynamical systems for principal singular subspace analysis
Author :
Hasan, Mohammed A. ; Hasan, Jawad A K
Author_Institution :
Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN
Abstract :
Principal singular component analysis has recently been proposed and analyzed by the author. It is a generalization of the principal singular subspace analysis which has been investigated in the literature. In this paper an unconstrained weighted cost function is utilized to develop dynamical systems that converge to the actual principal singular vectors of a given matrix. Stability analysis that reveals the domains of attraction of these systems is also given.
Keywords :
gradient methods; principal component analysis; stability; time-varying systems; gradient dynamical systems; principal singular component analysis; principal singular subspace analysis; principal singular vectors; stability analysis; unconstrained weighted cost function; Asymptotic stability; Control systems; Convergence; Cost function; Differential equations; Lyapunov method; Newton method; Polynomials; Signal processing algorithms; Stability analysis; Halley method; Lasalle invariance principle; Lyapunov stability; Newton method; asymptotic stability; global convergence; global stability; invariant set; polynomial dynamical systems;
Conference_Titel :
American Control Conference, 2008
Conference_Location :
Seattle, WA
Print_ISBN :
978-1-4244-2078-0
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2008.4587231
