Semi-invariant function of Jacobi algorithm in independent component analysis

Author

Matsuda, Yuuki ; Yamaguchi, Kazuhiro

Author_Institution

The University of Tokyo

Volume

3

fYear

2004

fDate

25-29 July 2004

Firstpage

2147

Abstract

It has been known that several Jacobi algorithms (e.g. JADE, MaxKurt, EML, and so on) are useful in independent component analysis (ICA). This work shows that the sum of 4th order (iijj-) cumulants over all the pairs of components is a "semi-invariant" function of such Jacobi algorithms. Then we prove that MaxKurt algorithm converges monotonically without loss to a local minimum of the semi-invariant function, which is consistent with the result obtained by the symmetrical maximization of kurtoses. In addition, a new algorithm combining EML and JADE is proposed. The EML-JADE algorithm not only uses both maximization and minimization of kurtoses suitably like EML but also utilizes JADE in the cases where super- and sub-gaussian sources are highly mixed.

Keywords

Gaussian distribution; Jacobian matrices; blind source separation; convergence; eigenvalues and eigenfunctions; independent component analysis; maximum likelihood estimation; optimisation; Jacobi algorithm; MaxKurt algorithm; blind separation; extended maximum likelihood algorithm; independent component analysis; joint approximate diagonalization of eigen matrices; kurtoses maximization; kurtoses minimisation; monotonic convergence; semi-invariant function; sub-Gaussian sources; super Gaussian sources; Art; Artificial neural networks; Convergence; Independent component analysis; Jacobian matrices; Laboratories; Minimization methods; Pain; Signal generators; Signal processing algorithms;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on

ISSN

1098-7576

Print_ISBN

0-7803-8359-1

Type

conf

DOI

10.1109/IJCNN.2004.1380949

Filename

1380949