Generalizations of Oja's learning rule to non-symmetric matrices

Mohammed A. Hasan

doi:10.1109/iscas.2007.378017

Generalizations of Oja's learning rule to non-symmetric matrices

Mohammed A. Hasan

Electrical Engineering

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

New learning rules for computing eigenspaces and eigenvectors for symmetric and nonsymmetric matrices are proposed. By applying Liapunov stability theory, these systems are shown to be globally convergent. Properties of limiting solutions of the systems and weighted versions are also examined. The proposed systems may be viewed as generalizations of Oja's and Xu's principal subspace learning rules. Numerical examples showing the convergence behavior are also presented.

Original language	English (US)
Article number	4253004
Pages (from-to)	1779-1782
Number of pages	4
Journal	Proceedings - IEEE International Symposium on Circuits and Systems
DOIs	https://doi.org/10.1109/iscas.2007.378017
State	Published - 2007
Event	2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United States Duration: May 27 2007 → May 30 2007

Keywords

Global convergence
Liapunov stability
Minor components
Oja's learning rule
Principal components

Publisher link

10.1109/iscas.2007.378017

Find It

Find It at U of M Libraries

Cite this

@article{7954dac2803f44f7b68d1d2bbda731c4,

title = "Generalizations of Oja's learning rule to non-symmetric matrices",

abstract = "New learning rules for computing eigenspaces and eigenvectors for symmetric and nonsymmetric matrices are proposed. By applying Liapunov stability theory, these systems are shown to be globally convergent. Properties of limiting solutions of the systems and weighted versions are also examined. The proposed systems may be viewed as generalizations of Oja's and Xu's principal subspace learning rules. Numerical examples showing the convergence behavior are also presented.",

keywords = "Global convergence, Liapunov stability, Minor components, Oja's learning rule, Principal components",

author = "Hasan, {Mohammed A.}",

year = "2007",

doi = "10.1109/iscas.2007.378017",

language = "English (US)",

pages = "1779--1782",

journal = "Proceedings - IEEE International Symposium on Circuits and Systems",

issn = "0271-4310",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 ; Conference date: 27-05-2007 Through 30-05-2007",

}

TY - JOUR

T1 - Generalizations of Oja's learning rule to non-symmetric matrices

AU - Hasan, Mohammed A.

PY - 2007

Y1 - 2007

N2 - New learning rules for computing eigenspaces and eigenvectors for symmetric and nonsymmetric matrices are proposed. By applying Liapunov stability theory, these systems are shown to be globally convergent. Properties of limiting solutions of the systems and weighted versions are also examined. The proposed systems may be viewed as generalizations of Oja's and Xu's principal subspace learning rules. Numerical examples showing the convergence behavior are also presented.

AB - New learning rules for computing eigenspaces and eigenvectors for symmetric and nonsymmetric matrices are proposed. By applying Liapunov stability theory, these systems are shown to be globally convergent. Properties of limiting solutions of the systems and weighted versions are also examined. The proposed systems may be viewed as generalizations of Oja's and Xu's principal subspace learning rules. Numerical examples showing the convergence behavior are also presented.

KW - Global convergence

KW - Liapunov stability

KW - Minor components

KW - Oja's learning rule

KW - Principal components

UR - http://www.scopus.com/inward/record.url?scp=34548833923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548833923&partnerID=8YFLogxK

U2 - 10.1109/iscas.2007.378017

DO - 10.1109/iscas.2007.378017

M3 - Conference article

AN - SCOPUS:34548833923

SN - 0271-4310

SP - 1779

EP - 1782

JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

M1 - 4253004

T2 - 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007

Y2 - 27 May 2007 through 30 May 2007

ER -

Generalizations of Oja's learning rule to non-symmetric matrices

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this