Title :
Orthonormalization Learning Algorithms
Author :
Hasan, Mohammed A.
Author_Institution :
Univ. of Minnesota Duluth, Duluth
Abstract :
Orthonormalization is an essential stabilizing task in many signal processing algorithms and can be accomplished using the Gram-Schmidt process. In this paper, dynamical systems for orthonormalization are proposed. These systems converge to the desired limits without computing matrix square root. Stability and domain of attractions are established via Lyapunov stability theory. Applications of the proposed methods to principal sub space /component analysis are given.
Keywords :
Lyapunov methods; convergence; learning (artificial intelligence); matrix algebra; optimisation; principal component analysis; stability; Gram-Schmidt process; Lyapunov stability; convergence; dynamical system; matrix algebra; optimisation; orthonormalization learning algorithm; principal component analysis; principal subspace analysis; signal processing algorithm; Computer networks; Constraint optimization; Cost function; Equations; Least squares methods; Lyapunov method; Neural networks; Optimization methods; Signal processing algorithms; Stability;
Conference_Titel :
Neural Networks, 2007. IJCNN 2007. International Joint Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-4244-1379-9
Electronic_ISBN :
1098-7576
DOI :
10.1109/IJCNN.2007.4371247
