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Flexible Independent Component Analysis

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Abstract

This paper addresses an independent component analysis (ICA) learning algorithm with flexible nonlinearity, so named as flexible ICA, that is able to separate instantaneous mixtures of sub- and super-Gaussian source signals. In the framework of natural Riemannian gradient, we employ the parameterized generalized Gaussian density model for hypothesized source distributions. The nonlinear function in the flexible ICA algorithm is controlled by the Gaussian exponent according to the estimated kurtosis of demixing filter output. Computer simulation results and performance comparison with existing methods are presented.

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References

  1. J.-F. Cardoso and A. Souloumiac, “Blind Beamforming for Non Gaussian Signals,”IEE Proceedings-F, vol. 140, no.6, 1993, pp. 362–370.

    Google Scholar 

  2. S. Choi, “Adaptive Blind Signal Separation for Multiuser Communications: An information-Theoretic Approach,” Journal of Electrical Engineering and Information science,, vol. 4, no.2, April 1999, pp. 249–256.

    Google Scholar 

  3. A. Bell and T. Sejnowski, “Learning the Higher-Order Structure of a Natural Sound,” Network: Computation in Neural Systems, vol. 7, 1996, pp. 261–266.

    Article  MATH  Google Scholar 

  4. A. Bell and T. Sejnowski, “The Independent Components of Natural Scenes are Edge Filters,” Vision Research, vol. 37, no.23, 1997, pp. 3327–3338.

    Article  Google Scholar 

  5. S. Choi, A. Cichocki, and S. Amari, “Fetal Electrocardiogram Data Analysis Using Flexible Independent Component Analysis,” in The 4th Asia-Pacific Conference on Medical and Biological Engineering (APCMBE'99), Seoul, Korea, 1999.

  6. S. Makeig, A. Bell, T.-P. Jung, and T. Sejnowski, “Blind Separation of Auditory Event-Related Brain Responses into Independent Components,” in Proc. of National Academy of Sciences, vol. 94, 1997, pp. 10979–10984.

    Article  Google Scholar 

  7. T.-P. Jung, C. Humphries, T. Lee, S. Makeig, M. McKeown, V. Iragui, and T. Sejnowski, “Extended ICA Removes Artifacts from Electroencephalographic Recordings,” in Advances in Neural Information Processing Systems, vol. 10, 1998, pp. 894–900.

    Google Scholar 

  8. M. Girolami, “Hierarchic Dichotomizing of Polychotomous Data–An ICA Based Data Mining Tool,” in First International Workshop on Independent Component Analysis and Signal Separation, 1999, pp. 197–201.

  9. P. Comon, “Independent Component Analysis, A New Concept?,” Signal Processing, vol. 36, no.3, 1994, pp. 287–314.

    Article  MATH  Google Scholar 

  10. S. Amari and J.-F. Cardoso, “Blind Source Separation: Semiparametric Statistical Approach,” IEEE Trans. Signal Processing, vol. 45, 1997, pp. 2692–2700.

    Article  Google Scholar 

  11. C. Jutten and J. Herault, “Blind Separation of Sources, Part I: An Adaptive Algorithm Based on Neuromimetic Architecture,” Signal Processing, vol. 24, 1991, pp. 1–10.

    Article  MATH  Google Scholar 

  12. A. Cichocki, R. Unbehauen, and E. Rummert, “Robust Learning Algorithm for Blind Separation of Signals,” Electronics Letters, vol. 43, no.17, 1994, pp. 1386–1387.

    Article  Google Scholar 

  13. A. Cichocki and R. Unbehauen, “Robust Neural Networks with On-Line Learning for Blind Identification and Blind Separation of Sources,” IEEE Trans. Circuits and Systems-I: Fundamental Theory and Applications, vol. 43, 1996, pp. 894–906.

    Article  Google Scholar 

  14. A. Bell and T. Sejnowski, “An Information Maximisation Approach to Blind Separation and Blind Deconvolution,” Neural Computation, vol. 7, 1995, pp. 1129–1159.

    Article  Google Scholar 

  15. S. Amari, A. Cichocki, and H.H. Yang, “A New Learning Algorithm for Blind Signal Separation,” in Advances in Neural Information Processing Systems, D.S. Touretzky, M.C. Mozer, and M.E. Hasselmo (Eds.), MIT press, vol. 8, 1996, pp. 757–763.

  16. S. Amari and A. Cichocki, “Adaptive Blind Signal Processing– Neural Network Approaches,” in Proc. of IEEE, on Blind Identification and Estimation, Special Issue, vol. 86, no.10, Oct. 1998, pp. 2026–2048.

    Google Scholar 

  17. D.T. Pham, “Blind Separation of Instantaneous Mixtures of Sources Via an Independent Component Analysis,”IEEE Trans. Signal Processing, vol. 44, no.11, 1996, pp. 2768–2779.

    Article  Google Scholar 

  18. D.J.C. MacKay, “Maximum Likelihood and Covariant Algorithms for Independent Component Analysis,” Technical Report Draft 3.7, University of Cambridge, Cavendish Laboratory, 1996.

  19. B. Pearlmutter and L. Parra, “Maximum Likelihood Blind Source Separation:AContext-Sensitive Generalization of ICA,” in Advances in Neural Information Processing Systems, M.C. Mozer, M.I. Jordan, and T. Petsche (Eds.), vol. 9, 1997, pp. 613–619.

  20. J.-F. Cardoso, “Infomax and Maximum Likelihood for Source Separation,” IEEE Signal Processing Letters, vol. 4, no.4, Apr. 1997, pp. 112–114.

    Article  Google Scholar 

  21. J.-F. Cardoso and B.H. Laheld, “Equivariant Adaptive Source Separation,” IEEE Signal Processing Letters, vol. 44, no.12, Dec. 1996, pp. 3017–3030.

    Article  Google Scholar 

  22. J. Karhunen, “Neural Approaches to Independent Component Analysis, in European Symposium on Artificial Neural Networks, 1996, pp. 249–266.

  23. E. Oja, “The Nonlinear PCA Learning Rule and Signal Separation–Mathematical Analysis,” Technical Report A26, Helsinki University of Technology, Laboratory of Computer and Information Science, 1995.

  24. A. Hyvärinen and E. Oja, “A Fast Fixed-Point Algorithm for Independent Component Analysis,” Neural Computation, vol. 9, 1997, pp. 1483–1492.

    Article  Google Scholar 

  25. N. Delfosse and P. Loubaton, “Adaptive Blind Separation of Independent Sources: A Deflation Approach,” Signal Processing, vol. 45, 1995, pp. 59–83.

    Article  MATH  Google Scholar 

  26. A. Cichocki, R. Thawonmas, and S. Amari, “Sequential Blind Signal Extraction in Order Specifed by Stochastic Properties,” Electronics Letters, vol. 33, no.1, 1997, pp. 64–65.

    Article  Google Scholar 

  27. S. Choi, R. Liu, and A. Cichocki, “A Spurious Equlibria-Free Learning Algorithm for the Blind Separation of Non-Zero Skewness Signals,” Neural Processing Letters, vol. 7, 1998, pp. 61–68.

    Article  Google Scholar 

  28. J.-P. Nadal and N. Parga, “Redundancy Reduction and Independent Component Analysis:Conditions on Cumulants and Adaptive Approaches,” Neural Computation, vol. 9, 1997, pp. 1421–1456.

    Article  Google Scholar 

  29. S. Choi and A. Cichocki, “A Linear Feedforward Neural Network with Lateral Feedback Connections for Blind Source Separation,” in IEEE Signal Processing Workshop on Higherorder Statistics, Banff, Canada, 1997, pp. 349–353.

  30. M. Girolami and C. Fyfe, “Generalized Independent Component Analysis through Unsupervised Learning with Emergent Bussgang Properties,” in Proc. ICNN, 1997, pp. 1788–1791.

  31. S.C. Douglas, A. Cichocki, and S. Amari, “Multichannel Blind Separation and Deconvolution of Sources with Arbitrary Distributions,” in Neural Networks for Signal Processing VII, J. Principe, L. Gile, N. Morgan, and E. Wilson (Eds.), 1997, pp. 436–445.

  32. A. Cichocki, I. Sabala, S. Choi, B. Orsier, and R. Szupiluk, “Self-adaptive Independent Component Analysis for Sub-Gaussian and Super-Gaussian Mixtures with Unknown Number of Source Signals,” in International Symposium on Nonlinear Theory and Applications, 1997, pp. 731–734.

  33. M. Girolami, “An Alternative Perspective on Adaptive Independent Component Analysis Algorithms,” Neural Computation, vol. 10, no.8, 1998, pp. 2103–2114.

    Article  MathSciNet  Google Scholar 

  34. T.-W. Lee, M. Girolami, and T. Sejnowski, “Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources,” Neural Computation, vol. 11, no.2, 1999, pp. 609–633.

    Article  Google Scholar 

  35. S. Choi, A. Cichocki, and S. Amari, “Flexible Independent Component Analysis,” in Neural Networks for Signal Processing VIII, T. Constantinides, S.-Y. Kung, M. Niranjan, and E. Wilson (Eds.), 1998, pp. 83–92.

  36. S. Amari, “Natural Gradient Works Efficiently in Learning,” Neural Computation, vol. 10, no.2, Feb. 1998, pp. 251–276.

    Article  MathSciNet  Google Scholar 

  37. S. Amari, “Natural Gradient for Over-and Under-Complete Bases in ICA,” Neural Computation, vol. 11, no.8, Nov. 1999, pp. 1875–1883.

    Article  MathSciNet  Google Scholar 

  38. A. Cichocki, I. Sabala, and S. Amari, “Intelligent Neural Networks for Blind Signal Separation with Unknown Number of Sources,” in Int. Symp. Engineering of Intelligent Systems, Tenerife, Spain, 1998, pp. 148–154.

  39. I.S. Gradshteyn, I.M. Ryzhik, and A. Jeffrey, Table of Integrals, Series, and Products, Academic Press, 1994.

  40. S. Amari, T.-P. Chen, and A. Cichocki, “Stability Analysis of Learning Algorithms for Blind Source Separation,” Neural Networks, vol. 10, no.8, 1997, pp. 1345–1351.

    Article  Google Scholar 

  41. J.-F. Cardoso, “On the Stability of Source Separation Algorithms,” in Neural Networks for Signal Processing VIII, T. Constantinides, S.-Y. Kung, M. Niranjan, and E. Wilson (Eds.), 1998, pp. 13–22.

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Authors and Affiliations

  1. Department of Electrical Engineering, Chungbuk National University, South Korea

    Seungjin Choi

  2. Brain-Style Information Systems Research Group, Brain Science Institute, Riken, Japan

    Andrzej Cichocki & Shun-Ichi Amari

  3. Warsaw University of Technology, Poland

    Andrzej Cichocki

Authors
  1. Seungjin Choi
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  2. Andrzej Cichocki
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  3. Shun-Ichi Amari
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Choi, S., Cichocki, A. & Amari, SI. Flexible Independent Component Analysis. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 26, 25–38 (2000). https://doi.org/10.1023/A:1008135131269

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