Iterative Projection Approximation Algorithms for PCA

Author

Choi, Seungjin ; Ahn, Jong-Hoon ; Cichocki, Andrzej

Author_Institution

Dept. of Comput. Sci., POSTECH

Volume

5

fYear

2006

fDate

14-19 May 2006

Abstract

In this paper we introduce a new error measure, integrated reconstruction error (IRE), the minimization of which leads to principal eigenvectors (without rotational ambiguity) of the data covariance matrix. Then we present iterative algorithms for the IRE minimization, through the projection approximation. The proposed algorithm is referred to as constrained projection approximation (COPA) algorithm and its limiting case is called COPAL. We also discuss regularized algorithms, referred to as R-COPA and R-COPAL. Numerical experiments demonstrate that these algorithms successfully find exact principal eigenvectors of the data covariance matrix

Keywords

covariance matrices; eigenvalues and eigenfunctions; iterative methods; principal component analysis; IRE minimization; PCA; constrained projection approximation algorithm; data covariance matrix; error measure; integrated reconstruction error; iterative projection approximation algorithms; principal eigenvectors; Approximation algorithms; Biological neural networks; Computer errors; Computer science; Covariance matrix; Iterative algorithms; Machine learning algorithms; Principal component analysis; Signal processing algorithms; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on

Conference_Location

Toulouse

ISSN

1520-6149

Print_ISBN

1-4244-0469-X

Type

conf

DOI

10.1109/ICASSP.2006.1661408

Filename

1661408