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

fYear

2010

fDate

May 30 2010-June 2 2010

Firstpage

3517

Lastpage

3520

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/ISCAS.2010.5537821

Filename

5537821