Local stability analysis of maximum nongaussianity estimation in independent component analysis

Authors:
Gang Wang;Xin Xu;Dewen Hu
Affiliations:
Telecommunication Engineering Institute, Air Force Engineering University, Xi’an, Shanxi, P.R.C.;College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan, P.R.C.;College of Mechatronics and Automation, National University of Defense Technology, Changsha, Hunan, P.R.C.
Venue:
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Year:
2006

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Abstract

The local stability analysis of maximum nongaussianity estimation (MNE) is investigated for nonquadratic functions in independent component analysis (ICA). Using trigonometric function, we first derive the local stability condition of MNE for nonquadratic functions without any approximation as has been made in previous literatures. The research shows that the condition is essentially the generalization of Xu’s one-bit-matching ICA theorem in MNE. Secondly, based on the generalized Gaussian model (GGM), the availability of local stability condition and robustness to outliers are addressed for three typical nonquadratic functions for various distributed independent components.