Reference-Based Extraction of Phase Synchronous Components

  • Jan-Hendrik Schleimer
  • Ricardo Vigário
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4132)


Phase synchronisation is a phenomenon observed in measurements of dynamic systems, composed of several interacting oscillators. It can be quantified by the phase locking factor (plf), which requires knowledge of the instantaneous phase of an observed signal. Linear sources separation methods treat scenarios in which measurements do not represent direct observations of the dynamics, but rather superpositions of underlying latent processes. Such a mixing process can cause spuriously high plfs between the measurements, and camouflage the phase locking to a provided reference signal. The plf between a linear projection of the data and a reference can be maximised as an optimisation criterion revealing the most synchronous source component present in the data, with its corresponding amplitude. This is possible despite the amplitude distributions being Gaussian, or the signals being statistically dependent, common assumptions in blind sources separation techniques without a-priori knowledge, e.g. in form of a reference signal.


Reference Signal Independent Component Analysis Phase Synchronisation Volume Conduction Singular Spectrum Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization – A universal concept in nonlinear sciences. Cambridge Nonlinear Science Series, vol. 12. Cambridge University Press, UK (2001)MATHCrossRefGoogle Scholar
  2. 2.
    Kuramoto, Y.: Chemical Oscillations, Waves and Turbulences. Springer, Berlin (1984)Google Scholar
  3. 3.
    Strogatz, S.H.: From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators. Physica D 143, 1–20 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Hindmarsh, J.L., Rose, R.M.: A model of neuronal bursting using three coupled first–order differential equations. Proceedings of the Royal Society of London 221, 87–102 (1984)CrossRefGoogle Scholar
  5. 5.
    Frank, T.D., Daffertshofer, A., Pepper, C.E., Beek, P.J., Haken, H.: Towards a comprehensive theory of brain activity: Coupled oscillator systems under external forces. Physica D 144, 62–86 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. In: Adaptive and Learning Systems for Signal Processing, Communications, and Control, John Wiley & Sons, Inc., Chichester (2001)Google Scholar
  7. 7.
    Lachaux, J.P., Rodriguez, E., Martinerie, J., Varela, F.J.: Measuring phase synchrony in brain signals. Human Brain Mapping 8(4), 194–208 (1999)CrossRefGoogle Scholar
  8. 8.
    Ghil, M., Allen, M.R., Dettinger, M.D., Ide, K., Kondrashov, D., Mann, M.E., Robertson, A., Saunders, A., Tian, Y., Yiou, P.: Advanced Spectral Methods for Climatic Time Series. Reviews of Geophysics 40(1) (2001)Google Scholar
  9. 9.
    Vigário, R., Jensen, O.: Identifying Cortical Sources of Corticomuscle Coherence During Bimanual Muscle Contraction by Temporal Decorrelation. In: Proceedings of IEEE International Symposium on Signal Processing and Its Applications (2003)Google Scholar
  10. 10.
    Meinecke, F.C., Ziehe, A., Kurths, J., Müller, K.R.: Measuring Phase Synchronization of Superimposed Signals. Physical Review Letters 94(8) (2005)Google Scholar
  11. 11.
    Nolte, G., Bai, O., Wheaton, L., Mari, Z., Vorbach, S., Hallett, M.: Identifying true brain interaction from EEG data using the imaginary part of coherency. Clinical Neurphysiology 115, 2292–2307 (2004)Google Scholar
  12. 12.
    Hämäläinen, M., Hari, R., Ilmoniemi, R., Knuutila, J., Lounasmaa, O.V.: Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain. Reviews of Modern Physics 65(2), 413–497 (1993)CrossRefGoogle Scholar
  13. 13.
    Vigário, R., Särelä, J., Jousmäki, V., Hämäläinen, M., Oja, E.: Independent component approach to the analysis of EEG and MEG recordings. IEEE Transactions on Biomedical Engineering 47(5), 589–593 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jan-Hendrik Schleimer
    • 1
  • Ricardo Vigário
    • 1
  1. 1.Adaptive Informatics Research CentreHelsinki University of TechnologyEspooFinland

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