Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation

Authors:
Andreas Ziehe;Motoaki Kawanabe;Stefan Harmeling;Klaus-Robert Müller
Affiliations:
Fraunhofer FIRST.IDA, Kekuléstr. 7, 12489 Berlin, Germany;Fraunhofer FIRST.IDA, Kekuléstr. 7, 12489 Berlin, Germany;Fraunhofer FIRST.IDA, Kekuléstr. 7, 12489 Berlin, Germany;Fraunhofer FIRST.IDA, Kekuléstr. 7, 12489 Berlin, Germany and Department of Computer Science, University of Potsdam, August-Bebel-Strasse 89, 14482 Potsdam, Germany
Venue:
The Journal of Machine Learning Research
Year:
2003

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Abstract

We propose two methods that reduce the post-nonlinear blind sourceseparation problem (PNL-BSS) to a linear BSS problem. The firstmethod is based on the concept of maximal correlation: weapply the alternating conditional expectation (ACE) algorithm---apowerful technique from non-parametric statistics---toapproximately invert the componentwise non-linear functions.Thesecond method is a Gaussianizing transformation, which is motivatedby the fact that linearly mixed signals before nonlineartransformation are approximately Gaussian distributed. Thisheuristic, but simple and efficient procedure works as good as theACE method.Using the framework provided by ACE, convergence can beproven. The optimal transformations obtained by ACE coincide withthe sought-after inverse functions of the nonlinearities. Afterequalizing the nonlinearities, temporal decorrelation separation(TDSEP) allows us to recover the source signals. Numericalsimulations testing "ACE-TD" and "Gauss-TD" on realistic examplesare performed with excellent results.