A class of learning algorithms for principal component analysis and minor component analysis

Author

Zhang, Qingfu ; Leung, Yiu-Wing

Author_Institution

Dept. of Electr. Eng. & Electron., Univ. of Manchester Inst. of Sci. & Technol., UK

Volume

11

Issue

1

fYear

2000

fDate

1/1/2000 12:00:00 AM

Firstpage

200

Lastpage

204

Abstract

In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of principal component analysis (PCA) and minor component analysis (MCA) learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error

Keywords

convergence of numerical methods; differential equations; eigenvalues and eigenfunctions; learning (artificial intelligence); pattern recognition; principal component analysis; convergence; differential equations; eigenvalues; eigenvectors; learning algorithms; minor component analysis; pattern recognition; principal component analysis; Algorithm design and analysis; Convergence; Differential equations; Eigenvalues and eigenfunctions; Pattern analysis; Pattern recognition; Principal component analysis; Robustness; Signal analysis; Signal processing algorithms;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.822522

Filename

822522