Dynamical systems for joint principal and minor component analysis

Author

Hasan, Mohammed A.

Author_Institution

Dept. of Electr. & Comput. Eng., Minnesota Univ., Duluth, MN

fYear

2006

fDate

14-16 June 2006

Abstract

Most known principal or a minor subspace (or component) analyzers compute either the principal or the minor subspaces of a given data matrix but not both. This paper presents several methods for simultaneous computation of principal and minor subspaces of a symmetric matrix. Weighted versions of these methods for joint computation of principal and minor components are also given. The proposed methods are derived from the optimization of certain objective functions over orthogonal constraints. Several features such as penalty terms are added to obtain reliable algorithms

Keywords

matrix algebra; optimisation; principal component analysis; Oja rule; Stiefel manifold; asymptotic stability; dynamical systems; global stability; minor component analysis; minor subspace analysis; optimization; principal component analysis; principal subspace analysis; symmetric matrix; Asymptotic stability; Constraint optimization; Data engineering; Eigenvalues and eigenfunctions; Lagrangian functions; Performance analysis; Principal component analysis; Signal processing algorithms; Stability analysis; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2006

Conference_Location

Minneapolis, MN

Print_ISBN

1-4244-0209-3

Electronic_ISBN

1-4244-0209-3

Type

conf

DOI

10.1109/ACC.2006.1656558

Filename

1656558