On the convergence of SIPEX: a simultaneous principal components extraction algorithm

Author

Erdogmus, Deniz ; Rao, Yadunandana ; Ozturk, M. Can ; Vielva, Luis ; Principe, Jose C.

Author_Institution

Dept. of Electr. & Comput. Eng., Florida Univ., Gainesville, FL, USA

Volume

2

fYear

2003

fDate

6-10 April 2003

Abstract

We have previously proposed SIPEX as a fast-converging and accurate principal components algorithm (Erdogmus, D. et al., Proc. ICASSP´02, vol.1, p.1069-72, 2002; Proc. EUSIPCO´02, vol.2, p.335-8, 2002). Its superiority in terms of data efficiency and solution accuracy was demonstrated through Monte Carlo simulations. We focus on the convergence properties of the original gradient-based algorithm as well as two modified versions of SIPEX based on approximations to the Hessian matrix of the cost function. We provide practical bounds on the step sizes of these algorithms and compare their convergence properties.

Keywords

Hessian matrices; approximation theory; convergence of numerical methods; gradient methods; numerical stability; principal component analysis; signal processing; Hessian matrix; Monte Carlo simulations; PCA; SIPEX convergence; cost function; data efficiency; gradient-based algorithm; signal processing applications; simultaneous principal components extraction algorithm; stability conditions; Convergence; Cost function; Covariance matrix; DICOM; Direction of arrival estimation; Least squares approximation; Principal component analysis; Signal processing algorithms; Stability; Wiener filter;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on

ISSN

1520-6149

Print_ISBN

0-7803-7663-3

Type

conf

DOI

10.1109/ICASSP.2003.1202462

Filename

1202462