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Title:Kernel-based nonlinear blind source separation
Authors: Stefan Harmeling ; Andreas Ziehe ; Motoaki Kawanabe ; Klaus-Robert Muller
Date: 2003
Publication Title:Neural Computation
Publisher:MIT Press
Publication Type:Journal Article Publication Status:Published
Volume No:15 Page Nos:1089-112
We propose kTDSEP, a kernel-based algorithm for nonlinear blind source separation (BSS). It combines complementary research fields: kernel feature spaces and BSS using temporal information. This yields an efficient algorithm for nonlinear BSS with invertible nonlinearity. Key assumptions are that the kernel feature space is chosen rich enough to approximate the nonlinearity and that signals of interest contain temporal information. Both assumptions are fulfilled for a wide set of real-world applications. The algorithm works as follows: First, the data are (implicitly) mapped to a high (possibly infinite)dimensional kernel feature space. In practice, however, the data form a smaller submanifold in feature space---even smaller than the number of training data points---a fact that has already been used by, for example, reduced set techniques for support vector machines. We propose to adapt to this effective dimension as a preprocessing step and to construct an orthonormal basis of this submanifold. The latter dimension-reduction step is essential for making the subsequent application of BSS methods computationally and numerically tractable. In the reduced space, we use a BSS algorithm that is based on second-order temporal decorrelation. Finally, we propose a selection procedure to obtain the original sources from the extracted nonlinear components automatically. Experiments demonstrate the excellent performance and efficiency of our kTDSEP algorithm for several problems of nonlinear BSS and for more than two sources.
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Bibtex format
author = { Stefan Harmeling and Andreas Ziehe and Motoaki Kawanabe and Klaus-Robert Muller },
title = {Kernel-based nonlinear blind source separation},
journal = {Neural Computation},
publisher = {MIT Press},
year = 2003,
volume = {15},
pages = {1089-112},
doi = {10.1162/089976603765202677},

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