Title :
A Framework for Eigen and Singular Component Analysis
Author :
Hasan, Mohammed A.
Author_Institution :
Univ. of Minnesota Duluth, Duluth
Abstract :
A framework that involves an unconstrained optimization of a polynomial type cost function weighted with a diagonal matrix is utilized to develop learning rules for principal and minor component analyzers. With some modifications, this cost function is also used to derive generalized principal and minor component analyzers, and principal singular component analyzers. Global and asymptotic stability of the proposed systems are analyzed via Liapunov theory and the Lasalle invariance principle.
Keywords :
Lyapunov methods; asymptotic stability; learning (artificial intelligence); optimisation; principal component analysis; singular value decomposition; Lasalle invariance principle; Liapunov theory; diagonal matrix; eigen component analysis; polynomial type cost function; principal component analysis; singular component analysis; unconstrained optimization; Asymptotic stability; Cities and towns; Computer applications; Convergence; Cost function; Lagrangian functions; Matrix decomposition; Polynomials; Principal component analysis; Singular value decomposition; Dynamical system; Lasalle invariance principle; MCA; PCA; PSCA; PSSA; SVD; asymptotic stability; generalized PCA; global convergence; global stability; invariant set; principal singular flow; unconstrained optimization;
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2007.4282961
