Skip to main content

ICA over Finite Fields

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6365)

Abstract

Independent Component Analysis is usually performed over the fields of reals or complex numbers and the only other field where some insight has been gained so far is GF(2), the finite field with two elements. We extend this to arbitrary finite fields, proving separability of the model if the sources are non-uniform and non-degenerate and present algorithms performing this task.

Keywords

  • Independent Component Analysis
  • Finite Field
  • Independent Component Analysis
  • Marginal Probability
  • LDPC Code

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-15995-4_80
  • Chapter length: 8 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-15995-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   149.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bingham, E., Hyvärinen, A.: A fast fixed-point algorithm for independent component analysis of complex valued signals. International Journal of Neural Systems 10(1), 1–8 (2000)

    Google Scholar 

  2. Delfosse, N., Loubaton, P.: Adaptive blind separation of independent sources: a deflation approach. Signal Processing 45(1), 59–83 (1995)

    MATH  CrossRef  Google Scholar 

  3. Eriksson, J., Koivunen, V.: Complex random vectors and ICA models: identifiability, uniqueness, and separability. IEEE Transactions on Information Theory 52(3), 1017–1029 (2006)

    CrossRef  MathSciNet  Google Scholar 

  4. Lang, S.: Algebra. Addison-Wesley, Reading (1965)

    MATH  Google Scholar 

  5. Nakamura, K., Kabashima, Y., Saad, D.: Statistical mechanics of low-density parity check error-correcting codes over galois fields. EPL (Europhysics Letters) 56(4), 610–616 (2001)

    CrossRef  Google Scholar 

  6. Stein, W., et al.: Sage Mathematics Software (Version 4.3.5). The Sage Development Team (2010), http://www.sagemath.org

  7. Yeredor, A.: ICA in boolean XOR mixtures. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 827–835. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gutch, H.W., Gruber, P., Theis, F.J. (2010). ICA over Finite Fields. In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2010. Lecture Notes in Computer Science, vol 6365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15995-4_80

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15995-4_80

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15994-7

  • Online ISBN: 978-3-642-15995-4

  • eBook Packages: Computer ScienceComputer Science (R0)