Kernel feature spaces and nonlinear blind source separation

Harmeling, S; Ziehe, A; Kawanabe, M; Müller, K-R

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Kernel feature spaces and nonlinear blind source separation

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https://papers.nips.cc/paper/2094-kernel-feature-spaces-and-nonlinear-blind-souce-separation.pdf
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Harmeling, S., Ziehe, A., Kawanabe, M., & Müller, K.-R. (2002). Kernel feature spaces and nonlinear blind source separation. In T. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in Neural Information Processing Systems 14 (pp. 761-768). Cambridge, MA, USA: MIT Press.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-DF16-D

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.