Title :
Low rank approximation of a set of matrices
Author :
Hasan, Mohammed A.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Minnesota Duluth, Duluth, MN, USA
fDate :
May 30 2010-June 2 2010
Abstract :
In this paper, we present dynamical systems for computing the low rank approximation of a single matrix and of a set of matrices. These dynamical systems arise from solving an optimization problem involving these matrices. The proposed methods are based on applying smooth optimization techniques on smooth manifolds. Many of these systems are then modified to obtain power-like methods for computing a few dominant singular triplets of large matrices simultaneously.
Keywords :
approximation theory; optimisation; singular value decomposition; dynamical system; matrix analysis; rank approximation; singular value decomposition; smooth optimization technique; Constraint optimization; Data mining; Eigenvalues and eigenfunctions; Matrix decomposition; Neural networks; Optimization methods; Power engineering computing; Principal component analysis; Singular value decomposition; Statistical analysis; Stiefel manifold; constrained optimization; low-rank matrix approximation of multiple matrices; principal singular flow; singular value decomposition;
Conference_Titel :
Circuits and Systems (ISCAS), Proceedings of 2010 IEEE International Symposium on
Conference_Location :
Paris
Print_ISBN :
978-1-4244-5308-5
Electronic_ISBN :
978-1-4244-5309-2
DOI :
10.1109/ISCAS.2010.5537821
