Monotonic convergence of a nonnegative ICA algorithm on stiefel manifold

Authors:
Mao Ye;Xuqian Fan;Qihe Liu
Affiliations:
Computational Intelligence Lab, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China;Department of Mathematics, Jinan University, Guangzhou, P.R. China;Computational Intelligence Lab, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China
Venue:
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Year:
2006

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Abstract

When the independent sources are known to be nonnegative and well-grounded, which means that they have a non-zero pdf in the region of zero, a few nonnegative independent component analysis (ICA) algorithms have been proposed to separate these positive sources. In this paper, by using the property of skew-symmetry matrix, rigorous convergence proof of a nonnegative ICA algorithm on Stiefel manifold is given. And sufficient convergence conditions are presented. Simulations are employed to confirm our convergence theory. Our techniques may be useful to analyze general ICA algorithms on Stiefel manifold.