Title :
Dynamical Systems for Principal Singular Subspace Analysis
Author :
Hasan, Mohammed A.
Author_Institution :
Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN
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 :
Lyapunov methods; asymptotic stability; gradient methods; matrix algebra; optimisation; signal processing; LaSalle invariance principle; Liapunov theory; arbitrary matrix; asymptotic stability analysis; control applications; dynamical systems; optimization; principal singular subspace analysis; signal processing; weighted gradient flows; Application software; Asymptotic stability; Constraint optimization; Convergence; Data mining; Process control; Signal analysis; Signal processing; Signal processing algorithms; Singular value decomposition;
Conference_Titel :
Sensor Array and Multichannel Processing, 2006. Fourth IEEE Workshop on
Conference_Location :
Waltham, MA
Print_ISBN :
1-4244-0308-1
DOI :
10.1109/SAM.2006.1706109
