Skip to main content

ICA over Finite Fields

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((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.

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

Buying options

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

Learn about institutional subscriptions

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)

    Article  MATH  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)

    Article  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)

    Article  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)

    Chapter  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)

Publish with us

Policies and ethics