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Kernel feature spaces and nonlinear blind source separation

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83954

Harmeling,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84096

Müller,  K-R
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Harmeling, S., Ziehe A, Kawanabe, M., & Müller, K.-R. (2002). Kernel feature spaces and nonlinear blind source separation. Advances in Neural Information Processing Systems 14: Proceedings of the NIPS 2001 Conference, 761-768.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-DF0D-3
Abstract
In kernel based learning the data is mapped to a kernel feature space of a dimension that corresponds to the number of training data points. In practice, however, the data forms a smaller submanifold in feature space, a fact that has been used e.g. by reduced set techniques for SVMs. We propose a new mathematical construction that permits to adapt to the intrinsic dimension and to find an orthonormal basis of this submanifold. In doing so, computations get much simpler and more important our theoretical framework allows to derive elegant kernelized blind source separation (BSS) algorithms for arbitrary invertible nonlinear mixings. Experiments demonstrate the good performance and high computational efficiency of our kTDSEP algorithm for the problem of nonlinear BSS.