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Investigation on the skewness for independent component analysis

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Abstract

Skewness has received much less attention than kurtosis in the independent component analysis (ICA). In particular, the skewness seems to become a useless statistics after the kurtosis related one-bit-matching theorem was proven. However, as the non-Gaussianity of one signal comes mainly from skewness, it is intuitively understandable that its recovery should not rely on kurtosis. In this paper we discuss the skewness based ICA, and show that any probability density function (pdf) with non-zero skewness can be employed by ICA for the recovery of the source with non-zero skewness, without needing to consider the skewness sign. The observation together with the one-bit-matching theorem provides a basic guideline for the model pdf design in ICA algorithm.

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References

  1. Tong L, Inouye Y, Liu R. Waveform-preserving blind estimation of multiple independent sources. IEEE Trans Signal Process, 1993, 41: 2461–2470

    Article  MATH  Google Scholar 

  2. Comon P. Independent component analysis-a new concept? Signal Process, 1994, 36: 287–314

    Article  MATH  Google Scholar 

  3. Xu L, Cheung C C, Yang H H, et al. Independent component analysis by the information-theoretic approach with mixture of density. In: Proc of 1997 IEEE Intl Conf on Neural Networks (IEEE-INNS IJCNN97) III, Houston, TX, USA, 1997. 1821–1826

  4. Xu L, Cheung C C, Amari S I. Learned parametric mixture based ICA algorithm. Neurocomput, 1998, 22: 69–80

    Article  MATH  Google Scholar 

  5. Xu L, Cheung C C, Amari S I. Further results on nonlinearity and separation capability of a liner mixture ICA method and learned LPM. In: Fyfe C, ed. Proceedings of the I&ANN’98, La Laguna, Tenerife, Spain, 1998. 39–45

  6. Everson R, Roberts S. Independent component analysis: A flexible nonlinearity and decorrelating manifold approach. Neural Comput, 1999, 11: 1957–1983

    Article  Google Scholar 

  7. ELee T W, Girolami M, Sejnowski T J. Independent component analysis using an Extended Infomax algorithm for mixed sub-Gaussian and super-Gaussian sources. Neural Comput, 1999, 11: 417–441

    Article  Google Scholar 

  8. Welling M, Weber M. A constrained EM algorithm for independent component analysis. Neural Comput, 2001, 13: 677–689

    Article  MATH  Google Scholar 

  9. Hulle M M V. Constrained subspace ICA based on mutual information optimization directly. Neural Comput, 2007, 19: 546–569

    Article  MathSciNet  Google Scholar 

  10. Bell A, Sejnowski T. An information-maximization approach to blind separation and blind deconvolution. Neural Comput, 1995, 7: 1129–1159

    Article  Google Scholar 

  11. Amari S I, Cichocki A, Yang H. A new learning algorithm for blind separation of sources. Adv Neural Inf Process Syst, 1996, 8: 757–763

    Google Scholar 

  12. Cardoso J F. Infomax and maximum likelihood for source separation. IEEE Signal Process Lett, 1997, 4: 112–114

    Article  Google Scholar 

  13. Cheung C C, Xu L. Some global and local convergence analysis on the information-theoretic independent component analysis approach. Neurocomput, 2000, 30: 79–102

    Article  Google Scholar 

  14. Amari S I, Chen T P. Stability analysis of adaptive blind source separation. Neural Netw, 1997, 10: 1345–1351

    Article  Google Scholar 

  15. Xu L. One-bit-matching theorem for ICA, convex-concave programming on polyhedral set, and distribution approximation for combinations. Neural Comput, 2007, 19: 964–973

    Article  Google Scholar 

  16. Dyrholm M, Makeig S, Hansen L K. Model selection for convolutive ICA with an application to spatiotemporal analysis of EEG. Neural Comput, 2007, 19: 934–955

    Article  MATH  Google Scholar 

  17. Cha S M, Chan LW. Applying independent component analysis to factor model in finance. In: Proceedings of the Second International Conference on Intelligent Data Engineering and Automated Learning, Data Mining, Financial Engineering, and Intelligent Agents, Hong Kong, China, 2000. 538–544

  18. Liu Z Y, Chiu K C, Xu L. One-bit-matching conjecture for independent component analysis. Neural Comput, 2004, 16: 383–399

    Article  MATH  Google Scholar 

  19. Zarzoso V, Phlypo R, Comon P. A contrast for independent component analysis with priors on the source kurtosis signs. IEEE Signal Process Lett, 2008, 15: 501–504

    Article  Google Scholar 

  20. Hyvainen A. Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans Neural Netw, 1999, 10: 626–634

    Article  Google Scholar 

  21. Choi S J, Liu RW, Cichocki A. A spurious equilibria-free learning algorithm for the blind separation of non-zero skewness signals. Neural Process Lett, 1998, 7: 61–68

    Article  Google Scholar 

  22. Blaschke T, Wiskott L. Cubica: Independent component analysis by simultaneous third-and fourth-order cumulant diagonalization. IEEE Trans Signal Process, 2004, 52: 1250–1256

    Article  MathSciNet  Google Scholar 

  23. Stuart A, Ord J. Kendall’s Advanced Theory of Statistics, Volume 1: Distribution Theory. London: Edward Arnold, 1994

    Google Scholar 

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Authors and Affiliations

  1. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    ZhiYong Liu & Hong Qiao

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  1. ZhiYong Liu
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  2. Hong Qiao
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Correspondence to ZhiYong Liu.

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Liu, Z., Qiao, H. Investigation on the skewness for independent component analysis. Sci. China Inf. Sci. 54, 849–860 (2011). https://doi.org/10.1007/s11432-010-4160-0

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  • DOI: https://doi.org/10.1007/s11432-010-4160-0

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