Chapter 17. Nonlinear ICA

  1. Aapo Hyvärinen,
  2. Juha Karhunen and
  3. Erkki Oja

Published Online: 15 MAY 2002

DOI: 10.1002/0471221317.ch17

Independent Component Analysis

Independent Component Analysis

How to Cite

Hyvärinen, A., Karhunen, J. and Oja, E. (2002) Nonlinear ICA, in Independent Component Analysis, John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471221317.ch17

Author Information

  1. Neural Networks Research Center, Helsinki University of Technology, Finland

Publication History

  1. Published Online: 15 MAY 2002
  2. Published Print: 21 MAY 2001

ISBN Information

Print ISBN: 9780471405405

Online ISBN: 9780471221319



  • nonlinear independent component analysis (ICA);
  • nonlinear blind source separation (BSS);
  • post-nonlinear mixtures;
  • self-organizing maps;
  • generative topographic mapping (GTM) approach;
  • ensemble learning approach


This chapter deals with independent component analysis (ICA) for nonlinear mixing models. The authors also address the nonlinear blind source separation (BSS) problem. After considering these matters, some methods introduced for solving the nonlinear ICA or BSS problems are discussed in more detail. Special emphasis is given to a Bayesian approach that applies ensemble learning to a flexible multilayer perceptron model for finding the sources and nonlinear mixing mapping that have most probably given rise to the observed mixed data. The efficiency of this method is demonstrated using both artificial and real-world data. At the end of the chapter, other techniques proposed for solving the nonlinear ICA and BSS problems are reviewed.