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

Andreas Ziehe, Motoaki Kawanabe, Stefan Harmeling, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1319-1338
Number of pages20
JournalJournal of Machine Learning Research
Issue number7-8
Publication statusPublished - 2004 Oct 1


  • Blind Source Separation
  • Gaussianization
  • Maximal Correlation
  • Post-nonlinear Mixture
  • Temporal Decorrelation

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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