Phase-Locked Matrix Factorization with Estimation of the Common Oscillation

  • Miguel Almeida
  • Ricardo Vigário
  • José Bioucas-Dias
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 30)

Abstract

Phase-Locked Matrix Factorization (PLMF) is an algorithm to perform separation of synchronous sources. Such a problem cannot be addressed by orthodox methods such as Independent Component Analysis, because synchronous sources are highly mutually dependent. PLMF separates available data into the mixing matrix and the sources; the sources are then decomposed into amplitude and phase components. Previously, PLMF was applicable only if the oscillatory component, common to all synchronized sources, was known, which is clearly a restrictive assumption. The main goal of this paper is to present a version of PLMF where this assumption is no longer needed—the oscillatory component can be estimated alongside all the other variables, thus making PLMF much more applicable to real-world data. Furthermore, the optimization procedures in the original PLMF are improved. Results on simulated data illustrate that this new approach successfully estimates the oscillatory component, together with the remaining variables, showing that the general problem of separation of synchronous sources can now be tackled.

Keywords

Matrix factorization Phase synchrony Phase-locking Independent component analysis Blind source separation Convex optimization 

Notes

Acknowledgements

This work was partially funded by the DECA-Bio project of the Institute of Telecommunications, and by the Academy of Finland through its Centres of Excellence Program 2006–2011.

References

  1. .
    Almeida, M., Schleimer, J.-H., Vigário, R. V., Dias, J.: “Source Separation and Clustering of Phase-Locked Subspaces”, IEEE Trans. on Neural networks, 22(9), pp. 1419–1434 (2011)CrossRefGoogle Scholar
  2. .
    Almeida, M., Schleimer, J.-H., Bioucas-Dias, J., Vigário, R.: Source separation and clustering of phase-locked subspaces. IEEE Trans. Neural Networks 22(9), 1419–1434 (2011)CrossRefGoogle Scholar
  3. Almeida, M., Vigário, R.V., Dias, J.: “Phase Locked Matrix Factorization”, Proc European Signal Processing Conf. - EUSIPCO, Barcelona, Spain, 0, 1728–1732, (2011)Google Scholar
  4. .
    Ben-Israel, A., Greville, T.: Generalized Inverses: Theory and Applications. Springer, Berlin (2003)MATHGoogle Scholar
  5. .
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)MATHGoogle Scholar
  6. .
    Gold, B., Oppenheim, A.V., Rader, C.M.: Theory and implementation of the discrete hilbert transform. In: Rabiner, L.R., Rader, C.M. (eds.) Discrete Signal Processing, John Wiley & Sons Inc; 1st edition, (1973)Google Scholar
  7. .
    Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001)CrossRefGoogle Scholar
  8. .
    Todd K. Leen, Thomas G. Dietterich, Volker Tresp In Advances in Neural Information Processing Systems 13, pp. 556–562 (2001)Google Scholar
  9. .
    Nunez, P.L., Srinivasan, R., Westdorp, A.F., Wijesinghe, R.S., Tucker, D.M., Silberstein, R.B., Cadusch, P.J.: EEG coherency I: statistics, reference electrode, volume conduction, laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalogr. Clin. Neurophysiol. 103, 499–515 (1997)CrossRefGoogle Scholar
  10. .
    Palva, J.M., Palva, S., Kaila, K.: Phase synchrony among neuronal oscillations in the human cortex. J. Neurosci. 25(15), 3962–3972 (2005)CrossRefGoogle Scholar
  11. .
    Pikovsky, A., Rosenblum, M., Kurths, J.: In: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge Nonlinear Science Series. Cambridge University Press, Cambridge (2001)MATHCrossRefGoogle Scholar
  12. .
    Schoffelen, J.-M., Oostenveld, R., Fries, P.: Imaging the human motor system’s beta-band synchronization during isometric contraction. NeuroImage 41, 437–447 (2008)CrossRefGoogle Scholar
  13. .
    Torrence, C., Compo, G.P.: A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79, 61–78 (1998)CrossRefGoogle Scholar
  14. .
    Uhlhaas, P.J., Singer, W.: Neural synchrony in brain disorders: Relevance for cognitive dysfunctions and pathophysiology. Neuron 52, 155–168 (2006)CrossRefGoogle Scholar
  15. .
    Vigário, R., Särelä, J., Jousmäki, V., Hämäläinen, M., Oja, E.: Independent component approach to the analysis of EEG and MEG recordings. IEEE Trans. Biom. Eng. 47(5), 589–593 (2000)CrossRefGoogle Scholar
  16. .
    Niklasson, L., Bodén, M., Ziemke, T.: Perspectives in Neural Computing, Proceedings of the 8th International Conference on Artificial Neural Networks, ICANN’98, Springer Verlag, 675–680 (1998)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Miguel Almeida
    • 1
    • 2
  • Ricardo Vigário
    • 2
  • José Bioucas-Dias
    • 1
  1. 1.Institute of Telecommunications, Instituto Superior TécnicoLisbonPortugal
  2. 2.Department of Information and Computer ScienceAalto UniversityHelsinkiFinland

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