Skip to main content
Log in

On robustifying some second order blind source separation methods for nonstationary time series

  • Regular Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Blind source separation (BSS) is an important analysis tool in various signal processing applications like image, speech or medical signal analysis. The most popular BSS solutions have been developed for independent component analysis (ICA) with identically and independently distributed (iid) observation vectors. In many BSS applications the assumption on iid observations is not realistic, however, as the data are often an observed time series with temporal correlation and even nonstationarity. In this paper, some BSS methods for time series with nonstationary variances are discussed. We also suggest ways to robustify these methods and illustrate their performance in a simulation study.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Belouchrani A, Abed-Meraim K, Cardoso JF, Moulines E (1997) A blind source separation technique using second-order statistics. IEEE Trans Signal Process 45: 434–444

    Article  Google Scholar 

  • Cardoso JF (1989) Sources separation using higher moments. In: Proceedings of the 2000 IEEE International conference on Acoustics, Speech and Signal Processing, pp 2109–2112

  • Cardoso JF, Souloumiac A (1993) Blind beamforming for non Gaussian signals. IEE Proc F 140: 362–370

    Google Scholar 

  • Choi S, Cichocki A (2000a) Blind separation of nonstationary sources in noisy mixtures. Electron Lett 36: 848–849

    Article  Google Scholar 

  • Choi S, Cichocki A (2000b) Blind separation of nonstationary and temporally correlated sources from noisy mixtures. In: Proceedings of the 2000 IEEE Signal Processing Society Workshop Neural Networks for Signal Processing X, vol 1, pp 405–414

  • Choi S, Cichocki A, Belouchrani A (2001) Blind separation of second-order nonstationary and temporally colored sources. In Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing, pp 444–447

  • Cichocki A, Amari S (2002) Adaptive blind signal and image processing: learning algorithms and applications. Wiley, Cichester

    Book  Google Scholar 

  • Jutten C (2010) Handbook of blind source separation. Independent component analysis and applications. Academic Press, Amsterdam

    Google Scholar 

  • Hettmansperger TP, Randles RH (2002) A practical affine equivariant multivariate median. Biometrika 89: 851–860

    Article  MATH  MathSciNet  Google Scholar 

  • Hyvärinen A, Karhunen J, Oja E (2001) Independent component analysis. Wiley, New York

    Book  Google Scholar 

  • Ilmonen P, Nordhausen K, Oja H, Ollila E (2010) A new performance index for ICA: properties, computation and asymptotic analysis. In: Vigneron V, Zarzoso V, Moreau E, Gribonval R, Vincent E (eds) Latent variable analysis and signal separation. Springer, Heidelberg, pp 229–236

    Chapter  Google Scholar 

  • Maronna RA, Martin RD, Yohai, VJ (2006) Robust statistics. Theorey and methods. Wiley, Cichester

  • Matsuoka K, Ohya M, Kawamoto M (1995) A neural net for blind separation of nonstationary signals. Neural Netw 8: 411–419

    Article  Google Scholar 

  • Miettinen J, Nordhausen K, Oja H, Taskinen S (2012a) Statistical properties of a blind source separation estimator for stationary time series. Stat Probab Lett 82: 1865–1873

    Article  MATH  MathSciNet  Google Scholar 

  • Miettinen J, Nordhausen K, Oja H, Taskinen S (2012b) Deflation-based separation of uncorrelated stationary time series (submitted)

  • Nordhausen K, Oja H, Tyler DE (2008) Tools for exploring multivariate data: the package ICS. J Stat Softw 28: 1–31

    Google Scholar 

  • Nordhausen K, Ollila E, Oja H (2011) On the performance indices of ICA and blind source separation. In: Proceedings of 2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2011), pp 486–490

  • Nordhausen K, Cardoso J-F, Miettinen J, Oja H, Ollila E, Taskinen, S (2012). JADE: JADE and other BSS methods as well as some BSS performance criteria. R package version 1.1-0

  • Nordhausen K, Sirkiä, Oja H, Tyler DE (2012) ICSNP: tools for multivariate nonparametrics. R package version 1.0-8.

  • Oja H, Sirkiä S, Eriksson J (2006) Scatter matrices and independent component analysis. Austrian J Stat 35: 175–189

    Google Scholar 

  • Pham D-T (2002) Exploiting source non stationary and coloration in blind source separation. In: Proceedings of 14th International Conference on Digital Signal Processing, pp 151–154

  • Pham D-T, Cardoso J-F (2001) Blind Separation of instantaneous mixtures of nonstationary sources. IEEE Trans Signal Process 49: 1837–1848

    Article  MathSciNet  Google Scholar 

  • R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria

  • Tanaka A, Imai H, Miyakoshi M (2006) Theoretical foundations of second-order-statistics-based blind surce separation for non-stationary sources. In: Proceedings of the 2006 IEEE International Conference on on Acoustics, Speech and Signal Processing. ICASSP 2006, pp 600–603

  • Theis FJ, Inouye Y (2006) On the use of joint diagonalization in blind signal processing. In: Proceedings of the 2006 IEEE International Symposium on Circuits and Systems, ISCAS 2006, pp 3586–3589

  • Theis FJ, Müller N, Plant C, Böhm C (2010) Robust second-order source separation identifies experimental responses in biomedical imaging. In: Vigneron V, Zarzoso V, Moreau E, Gribonval R, Vincent E (eds) Latent variable analysis and signal separation.. Springer, Heidelberg, pp 466–473

    Chapter  Google Scholar 

  • Tong L, Soon VC, Huang YF, Liu R (1990) AMUSE: a new blind identification algorithm. In: Proceedings of IEEE International Symposium on Circuits and Systems, pp 1784–1787

  • Würtz D, Chalabi Y with contribution from Miklovic M, Boudt C, Chausse P and others (2009) fGarch: Rmetrics-Autoregressive Conditional Heteroskedastic Modelling. R package version 2110.80

  • Yeredor A (2010) Second-order methods based on color. In: Comon P, Jutten C (eds) Handbook of blind source separation.. Independent component analysis and applications. Academic Press, Amsterdam, pp 227–279

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Klaus Nordhausen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nordhausen, K. On robustifying some second order blind source separation methods for nonstationary time series. Stat Papers 55, 141–156 (2014). https://doi.org/10.1007/s00362-012-0487-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-012-0487-5

Keywords

Mathematics Subject Classification (2000)

Navigation