Skip to main content

Source Separation in Post-nonlinear Mixtures by Means of Monotonic Networks

  • Conference paper
  • First Online:
Latent Variable Analysis and Signal Separation (LVA/ICA 2015)

Abstract

In this work, we investigate the use of monotonic neural networks as compensating functions in the context of source separation of post-nonlinear (PNL) mixtures. We first provide a numerical example that illustrates the importance of having bijective nonlinear compensating functions in PNL models. Then, we propose a separation framework in which a monotonic neural network is considered in the first stage of the PNL separating system. Finally, numerical experiments are performed to assess the proposed framework.

The authors would like to thank FAPESP and CNPq for funding this research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We here keep the index i, which is related to the mixtures, and also the sample index n.

References

  1. Comon, P., Jutten, C. (eds.): Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press, New York (2010)

    Google Scholar 

  2. Deville, Y., Duarte, L.T.: An overview of blind source separation methods for linear-quadratic and post-nonlinear mixtures. In: Submitted to the 12th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA) (2015)

    Google Scholar 

  3. Romano, J.M.T., Attux, R.R.F., Cavalcante, C.C., Suyama, R.: Unsupervised Signal Processing: Channel Equalization and Source Separation. CRC Press, Boca Raton (2011)

    Google Scholar 

  4. Taleb, A., Jutten, C.: Source separation in post-nonlinear mixtures. IEEE Trans. Signal Process. 47(10), 2807–2820 (1999)

    Article  Google Scholar 

  5. Duarte, L.T., Jutten, C., Moussaoui, S.: A Bayesian nonlinear source separation method for smart ion-selective electrode arrays. IEEE Sens. J. 9(12), 1763–1771 (2009)

    Article  Google Scholar 

  6. Gründler, P.: Chemical Sensors: An Introduction for Scientists and Engineers. Springer, Heidelberg (2007)

    Google Scholar 

  7. Achard, S., Jutten, C.: Identifiability of post-nonlinear mixtures. IEEE Signal Process. Lett. 12(5), 423–426 (2005)

    Article  Google Scholar 

  8. Comon, P.: Independent component analysis, a new concept? Sig. Process. 36, 287–314 (1994)

    Article  MATH  Google Scholar 

  9. Duarte, L.T., Suyama, R., de Faissol Attux, R.R., Von Zuben, F.J., Romano, J.M.T.: Blind source separation of post-nonlinear mixtures using evolutionary computation and order statistics. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 66–73. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Pham, D.T.: Flexible parametrization of postnonlinear mixtures model in blind sources separation. IEEE Signal Process. Lett. 11(6), 533–536 (2004)

    Article  Google Scholar 

  11. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice-Hall, New York (1998)

    Google Scholar 

  12. Sill, J.: Monotonic networks. In: Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS) (1998)

    Google Scholar 

  13. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Leonardo Tomazeli Duarte .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Duarte, L.T., de Oliveira Pereira, F., Attux, R., Suyama, R., Romano, J.M.T. (2015). Source Separation in Post-nonlinear Mixtures by Means of Monotonic Networks. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22482-4_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22481-7

  • Online ISBN: 978-3-319-22482-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics