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.
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References
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)
Delfosse, N., Loubaton, P.: Adaptive blind separation of independent sources: a deflation approach. Signal Processing 45(1), 59–83 (1995)
Eriksson, J., Koivunen, V.: Complex random vectors and ICA models: identifiability, uniqueness, and separability. IEEE Transactions on Information Theory 52(3), 1017–1029 (2006)
Lang, S.: Algebra. Addison-Wesley, Reading (1965)
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)
Stein, W., et al.: Sage Mathematics Software (Version 4.3.5). The Sage Development Team (2010), http://www.sagemath.org
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)
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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
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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
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