Newton-like methods for nonparametric independent component analysis

Authors:
Hao Shen;Knut Hüper;Alexander J. Smola
Affiliations:
Systems Engineering and Complex Systems Research Program;Systems Engineering and Complex Systems Research Program;Statistical Machine Learning Research Program, National ICT Australia, Canberra, ACT, Australia
Venue:
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Year:
2006

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Abstract

The performance of ICA algorithms significantly depends on the choice of the contrast function and the optimisation algorithm used in obtaining the demixing matrix. In this paper we focus on the standard linear nonparametric ICA problem from an optimisation point of view. It is well known that after a pre-whitening process, the problem can be solved via an optimisation approach on a suitable manifold. We propose an approximate Newton's method on the unit sphere to solve the one-unit linear nonparametric ICA problem. The local convergence properties are discussed. The performance of the proposed algorithms is investigated by numerical experiments.