Skip to main content

Zero-Entropy Minimization for Blind Extraction of Bounded Sources (BEBS)

  • Conference paper
Book cover Independent Component Analysis and Blind Signal Separation (ICA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3889))

Abstract

Renyi’s entropy can be used as a cost function for blind source separation (BSS). Previous works have emphasized the advantage of setting Renyi’s exponent to a value different from one in the context of BSS. In this paper, we focus on zero-order Renyi’s entropy minimization for the blind extraction of bounded sources (BEBS). We point out the advantage of choosing the extended zero-order Renyi’s entropy as a cost function in the context of BEBS, when the sources have non-convex supports.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Principe, J.C., Xu, D., Fisher III, J.W.: Information-Theoretic Learning. In: Haykin, S. (ed.) Unsup. Adapt. Filtering, vol. I, pp. 265–319. Wiley, New York (2000)

    Google Scholar 

  2. Erdogmus, D., Hild, K.E., Principe, J.C.: Blind Source Separation Using Renyi’s α-marginal Entropies. Neurocomputing 49, 25–38 (2002)

    Article  MATH  Google Scholar 

  3. Guleryuz, O.G., Lutwak, E., Yang, D., Zhang, G.: Information-Theoretic Inequalities for Contoured Probability Distributions. IEEE Trans. Info. Theory 48(8), 2377–2383 (2000)

    Article  MathSciNet  Google Scholar 

  4. Cruces, S., Duran, I.: The Minimum Support Criterion for Blind Source Extraction: a Limiting Case of the Strengthened Young’s Inequality. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 57–64. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Vrins, F., Jutten, C., Verleysen, M.: SWM: a Class of Convex Contrasts for Source Separation. In: Proc. ICASSP, IEEE Int. Conf. on Acoustics, Speech and Sig. Process., Philadelphia (USA), pp. V.161–V.164 (2005)

    Google Scholar 

  6. Vrins, F., Verleysen, M.: On the Entropy Minimization of a Linear Mixture of Variables for Source Separation. Sig. Process. 85(5), 1029–1044 (2005)

    Article  MATH  Google Scholar 

  7. Learned-Miller, E.G., Fisher III, J.W.: ICA Using Spacings Estimates of Entropy. Journal of Machine Learning Research 4, 1271–1295 (2003)

    Article  MathSciNet  Google Scholar 

  8. Pham, D.T., Vrins, F.: Local Minima of Information-Theoretic Criteria in Blind Source Separation. IEEE Sig. Process. Lett. 12(11), 788–791 (2005)

    Article  Google Scholar 

  9. Cardoso, J.-C.: Entropic Contrast for Source Separation: Geometry & Stability. In: Haykin, S. (ed.) Unsup. Adapt. Filtering I, pp. 265–319. Wiley, New York (2000)

    Google Scholar 

  10. Cover, T., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)

    Book  MATH  Google Scholar 

  11. Gardner, R.J.: The Brunn-Minkowski Inequality. Bull. of Am. Math. Soc. 39(3), 355–405 (2002)

    Article  MATH  Google Scholar 

  12. Costa, M., Cover, T.: On the Similarity of the Entropy Power Inequality and the Brunn-Minkowski Inequality. IEEE Trans. Info. Theory 30(6), 837–839 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lutwak, E., Yang, D., Zhang, G.: Cramér-Rao and Moment-Entropy Inequalities for Renyi Entropy and Generalized Fisher Information. IEEE Trans. Info. Theory 51(2), 473–478 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vrins, F., Erdogmus, D., Jutten, C., Verleysen, M. (2006). Zero-Entropy Minimization for Blind Extraction of Bounded Sources (BEBS). In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_93

Download citation

  • DOI: https://doi.org/10.1007/11679363_93

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32630-4

  • Online ISBN: 978-3-540-32631-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics