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

2003

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We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply the alternating conditional expectation (ACE) algorithm--a powerful technique from non-parametric statistics--to approximately invert the componentwise nonlinear functions. The second method is a Gaussianizing transformation, which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately Gaussian distributed. This heuristic, but simple and efficient procedure works as good as the ACE method. Using the framework provided by ACE, convergence can be proven. The optimal transformations obtained by ACE coincide with the sought-after inverse functions of the nonlinearities. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations testing "ACE-TD" and "Gauss-TD" on realistic examples are performed with excellent results.

Author(s): Ziehe, A. and Kawanabe, M. and Harmeling, S. and Müller, K-R.
Journal: Journal of Machine Learning Research
Volume: 4
Number (issue): 7-8
Pages: 1319-1338
Year: 2003
Month: November
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1162/jmlr.2003.4.7-8.1319
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@article{6361,
  title = {Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation},
  author = {Ziehe, A. and Kawanabe, M. and Harmeling, S. and M{\"u}ller, K-R.},
  journal = {Journal of Machine Learning Research},
  volume = {4},
  number = {7-8},
  pages = {1319-1338},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = nov,
  year = {2003},
  month_numeric = {11}
}