Blind Source Separation for Non-Stationary Mixing

  • Richard Everson
  • Stephen Roberts
Article

Abstract

Blind source separation attempts to recover independent sources which have been linearly mixed to produce observations. We consider blind source separation with non-stationary mixing, but stationary sources. The linear mixing of the independent sources is modelled as evolving according to a Markov process, and a method for tracking the mixing and simultaneously inferring the sources is presented. Observational noise is included in the model. The technique may be used for online filtering or retrospective smoothing. The tracking of mixtures of temporally correlated is examined and sampling from within a sliding window is shown to be effective for destroying temporal correlations. The method is illustrated with numerical examples.

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References

  1. 1.
    T-W. Lee, M. Girolami, A.J. Bell, and T.J. Sejnowski, “A Unifying Information-theoretic Framework for Independent Component Analysis,” International Journal on Mathematical and Computer Models, vol. 39, no.11, 2000, pp. 1–21. Available from http://www.cnl.salk.edu/~tewon/Public/mcm.ps.gz.MathSciNetMATHGoogle Scholar
  2. 2.
    A.J. Bell and T.J. Sejnowski, “An Information Maximization Approach to Blind Separation and Blind Deconvolution,” Neural Computation, vol. 7, no.6, 1995, pp. 1129–1159.CrossRefGoogle Scholar
  3. 3.
    D.J.C. MacKay, “Maximum Likelihood and Covariant Algorithms for Independent Component Analysis,” Technical report, University of Cambridge, December 1996. Available from http://wol.ra.phy.cam.ac.uk/mackay/.Google Scholar
  4. 4.
    J-F. Cardoso, “Infomax and Maximum Likelihood for Blind Separation,” IEEE Sig. Proc. Letters, vol. 4, no.4, 1997, pp. 112–114.CrossRefGoogle Scholar
  5. 5.
    B. Pearlmutter and L. Parra, “A Context-Sensitive Generalization of ICA,” in International Conference on Neural Information Processing, 1996.Google Scholar
  6. 6.
    S. Amari, A. Cichocki, and H. Yang, “A New Learning Algorithm For Blind Signal Separation,” in Advances in Neural Information Processing Systems, vol. 8, D. Touretzky, M. Mozer, and M. Hasselmo, (Eds.), Cambridge MA: MIT Press, 1996, pp. 757–763.Google Scholar
  7. 7.
    R.M. Everson and S.J. Roberts, ICA:Aflexible non-linearity and decorrelating manifold approach. Neural Computation, vol. 11, no.8, 1999, pp. 1957–1983. Available from http://www.dcs.ex.ac.uk/academics/reverson.CrossRefGoogle Scholar
  8. 8.
    J-F. Cardoso, “On the Stability of Source Separation Algorithms,” in Neural Networks for Signal processing VIII, T. Constantinides, S.-Y. Kung, M. Nifanjan, and E. Wilson, (Eds.), IEEE Signal Processing Society, IEEE, 1998, pp. 13–22.Google Scholar
  9. 9.
    H. Attias, “Independent Factor Analysis,” Neural Computation, vol. 11, no.5, 1999, pp. 803–852.CrossRefGoogle Scholar
  10. 10.
    T-W. Lee, M. Girolami, and T.J. Sejnowski, Independent Component Analysis using an Extended Infomax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources. Neural Computation, vol. 11, 1999, pp. 417–441.CrossRefGoogle Scholar
  11. 11.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. Numerical Recipes in C. 2 edition, Cambridge: Cambridge University Press, 1992.MATHGoogle Scholar
  12. 12.
    N. Gordon, D. Salmond, and A.F.M. Smith, Novel approach to nonlinear/non-Gaussian bayesian states estimation. IEE Proceedings-F, vol. 140, 1993, pp. 107–113.Google Scholar
  13. 13.
    M. Isard and A. Blake, “Contour Tracking by Stochastic Density Propagation of Conditional Density,” in Proc. European Conf. Computer Vision, Cambridge, UK, 1996, pp. 343–356.Google Scholar
  14. 14.
    R.M. Everson and S.J. Roberts, “Particle Filters for Non-Stationary Independent Components Analysis,” Technical Report TR99-6, Imperial College, 1999. Available from http://www.dcs.ex.ac.uk/academics/reversion.Google Scholar
  15. 15.
    Z. Ghahramani, “Learning Dynamic bayesian Networks,” in Adaptive Processing of Temporal Information, C.L. Giles and M. Gori, (eds.), Springer-Verlag, 1999, Lecture Notes in Artificial Intelligence.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Richard Everson
    • 1
  • Stephen Roberts
    • 2
  1. 1.Department of Computer ScienceUniversity of ExeterExeterUK
  2. 2.Department of Engineering ScienceUniversity of OxfordOxfordUK

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