Multivariate EEG Synchronization Strength Measures



EEG synchronization is considered to be the important performance of the brain to inform, communicate, interact, and coordinate between various regions. There exist lots of bivariate methods to quantify the EEG synchronization between two EEG signals. However, multivariate data contain more information than those inferable from multiple bivariate examinations. Multivariate synchronization analysis aiming at the global information has been paid much more attention recently. It is a useful technique for studying the interactions in a group of multivariate channels for the understanding of overall dynamical properties in the brain. In this chapter, the multivariate synchronization methods including phase synchronization cluster analysis, S-estimator, correlation matrix analysis, omega complexity, partial directed coherence, directed transfer function, and complex network analysis and their applications in studying the relationship among neural signals are presented.


Synchronization EEG Correlation matrix analysis Complex networks 


  1. Abarbanel HDI, Rulkov NF, Sushchik MM. Generalized synchronization of chaos: the auxiliary system approach. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996;53(5):4528–35.PubMedGoogle Scholar
  2. Albo Z, Di Prisco GV, Chen Y, et al. Is partial coherence a viable technique for identifying generators of neural oscillations? Biol Cybern. 2004;90(5):318–26.PubMedCrossRefGoogle Scholar
  3. Allefeld C, Kurths J. An approach to multivariate phase synchronization analysis and its application to event-related potentials: synchronization cluster analysis. Int J Bifurcation Chaos. 2004;14:417–26.CrossRefGoogle Scholar
  4. Allefeld C, Müller M, Kurths J. Eigenvalue decomposition as a generalized synchronization cluster analysis. Int J Bifurcation Chaos. 2007;17(10):3493–7.CrossRefGoogle Scholar
  5. Arnhold J, Lehnertz K, Grassberger P, et al. A robust method for detecting interdependences: application to intracranially recorded EEG. Physica D Nonlinear Phenomena. 1999;134(4):419–30.CrossRefGoogle Scholar
  6. Astolfi L, Cincotti F, Mattia D, et al. Causality estimates among brain cortical areas by partial directed coherence: simulations and application to real data. Int J Bioelectromagnetism. 2005;7(1):1–4.Google Scholar
  7. Babiloni C, Ferri R, Binetti G, et al. Directionality of EEG synchronization in Alzheimer’s disease subjects. Neurobiol Aging. 2009;30(1):93–102.PubMedCrossRefGoogle Scholar
  8. Baccalá LA, Sameshima K. Overcoming the limitations of correlation analysis for many simultaneously processed neural structures. Prog Brain Res. 2001a;130(1):33–47.PubMedCrossRefGoogle Scholar
  9. Baccalá LA, Sameshima K. Partial directed coherence: a new concept in neural structure determination. Biol Cybern. 2001b;84(6):463–74.PubMedCrossRefGoogle Scholar
  10. Bendat JS, Piersol AG. Random data analysis and measurement procedures. Mea Sci Technol. 2000;11(12):1825–6.Google Scholar
  11. Bhattacharya J, Petsche H, Pereda E. Long-range synchrony in the gamma band: role in music perception. J Neurosci Off J Soc Neurosci. 2001;21(16):6329–37.Google Scholar
  12. Bialonski S, Lehnertz K. Identifying phase synchronization clusters in spatially extended dynamical systems. Phys Rev E Stat Nonlin Soft Matter Phys. 2006;74(5 Pt 1):051909.PubMedCrossRefGoogle Scholar
  13. Boccaletti S, Kurths J, Osipov G, et al. The synchronization of chaotic systems. Phys Rep. 2002;366:1–101.CrossRefGoogle Scholar
  14. Breakspear M, Terry JR. Topographic organization of nonlinear interdependence in multichannel human EEG. Neuroimage. 2002;16(3 Pt 1):822–35.PubMedCrossRefGoogle Scholar
  15. Brovelli A, Ding M, Ledberg A, et al. Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality. Proc Natl Acad Sci U S A. 2004;101(26):9849–54.PubMedPubMedCentralCrossRefGoogle Scholar
  16. Bruns A. Fourier-, Hilbert- and wavelet-based signal analysis: are they really different approaches? J Neurosci Methods. 2004;137:321–32.PubMedCrossRefGoogle Scholar
  17. Büchel C, Friston K. Assessing interactions among neuronal systems using functional neuroimaging. Neural Netw. 2000;13(8):871–82.PubMedCrossRefGoogle Scholar
  18. Buzsáki G. Large-scale recording of neuronal ensembles. Nat Neurosci. 2004;7(5):446–51.PubMedCrossRefGoogle Scholar
  19. Buzsáki G, Draguhn A. Neuronal oscillations in cortical networks. Science. 2004;304(1):1926–9.PubMedCrossRefGoogle Scholar
  20. Carmeli C, Knyazeva MG, Innocenti GM, et al. Assessment of EEG synchronization based on state-space analysis. Neuroimage. 2005;25(2):339–54.PubMedCrossRefGoogle Scholar
  21. Clifford Carte G. Coherence and time delay estimation. Proc IEEE. 1987;75(2):236–55.CrossRefGoogle Scholar
  22. Cohen MI, Yu Q, Huang WX. Preferential correlations of a medullary neuron’s activity to different sympathetic outflows as revealed by partial coherence analysis. J Neurophysiol. 1995;74(1):474–8.PubMedGoogle Scholar
  23. Cui D, Liu XZ, Wan Y, et al. Estimation of genuine and random synchronization in multivariate neural series. Neural Netw. 2010;23:698–704.PubMedCrossRefGoogle Scholar
  24. Cui D, Liu J, Bian Zh J, et al. Cortical source multivariate EEG synchronization analysis on amnestic mild cognitive impairment in type 2 diabetes. Scientific World Journal. 2014;523216:1–9.Google Scholar
  25. Darbellay GA, Vajda I. Estimation of the information by an adaptive partitioning of the observation space. IEEE Trans Inf Theory. 1999;45(4):1315–21.CrossRefGoogle Scholar
  26. David O, Cosmelli D, Lachaux JP, et al. A theoretical and experimental introduction to the non-invasive study of large-scale neural phase synchronization in human beings. Int J Comput Cogn. 2003;1(4):53–77.Google Scholar
  27. Ding M, Bressler SL, Yang W, et al. Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment. Biol Cybern. 2000;83:35–45.PubMedCrossRefGoogle Scholar
  28. Engel AK, Fries P, Singer W. Dynamic predictions: oscillations and synchrony in top-down processing. Nat Rev Neurosci. 2001;2(10):704–16.PubMedCrossRefGoogle Scholar
  29. Fanselow EE, Sameshima K, Baccala LA, et al. Thalamic bursting in rats during different awake behavioral states. Proc Natl Acad Sci. 2001;98(26):15330–5.PubMedPubMedCentralCrossRefGoogle Scholar
  30. Ferri R, Rundo F, Bruni O, et al. Small-world network organization of functional connectivity of EEG slow-wave activity during sleep. Clin Neurophysiol Off J Int Fed ClinNeurophysiol. 2007;118(2):449–56.CrossRefGoogle Scholar
  31. Fine AS, Nicholls DP, Mogul DJ. Assessing instantaneous synchrony of nonlinear nonstationary oscillators in the brain. J Neurosci Methods. 2010;186(1):42–51.PubMedCrossRefGoogle Scholar
  32. Friston KJ. The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans Royal Soc Lond. 2000;355(1394):215–36.CrossRefGoogle Scholar
  33. Gandrzejak R, Kraskov A, Stögbauer H, et al. Bivariate surrogate techniques: necessity, strengths, and caveats. Phys Rev E Stat Nonlin Soft Matt Phys. 2003;68:1855–62.Google Scholar
  34. Gersch W, Goddard GV. Epileptic focus location: spectral analysis method. Science. 1970;169(3946):701–2.PubMedCrossRefGoogle Scholar
  35. Gevins AS, Schaffer RE. A critical review of electroencephalographic (EEG) correlates of higher cortical functions. Crit Rev Bioeng. 1980;4(2):112–64.Google Scholar
  36. Granger CWJ. Investigating causal relations by econometric models and cross-spectral methods. Econometrica. 1969;37:424–38.CrossRefGoogle Scholar
  37. Granger CWJ. Testing for causality: a personal viewpoint. J Econ Dyn Control. 1980;2(1):329–52.CrossRefGoogle Scholar
  38. Haig AR, Gordon E, Wright JJ, et al. Synchronous cortical gamma-band activity in task-relevant cognition. Neuroreport. 2000;11(4):669–75.PubMedCrossRefGoogle Scholar
  39. Haufe S, Nikulin VV, Müller KR, et al. A critical assessment of connectivity measures for EEG data: a simulation study. Neuroimage. 2013;64:120–33.PubMedCrossRefGoogle Scholar
  40. Jalili M, Lavoie S, Deppen P, et al. Disconnection topography in schizophrenia revealed with state-space analysis of EEG. PLoS One. 2007;2(10):e1059.PubMedPubMedCentralCrossRefGoogle Scholar
  41. Jamal W, Das S, Maharatna K, et al. Brain connectivity analysis from EEG signals using stable phase-synchronized states during face perception tasks. Physica A. 2015;434:273–95.CrossRefGoogle Scholar
  42. Kamiński MJ, Blinowska KJ. A new method of the description of the information flow in the brain structures. Biol Cybern. 1991;65(3):203–10.PubMedCrossRefGoogle Scholar
  43. Kim CS, Bae CS, Tcha HJ. A phase synchronization clustering algorithm for identifying interesting groups of genes from cell cycle expression data. BMC Bioinformatics. 2008;9(1):56.PubMedPubMedCentralCrossRefGoogle Scholar
  44. Kim DJ, Bolbecker AR, Howell J, et al. Disturbed resting state EEG synchronization in bipolar disorder: a graph-theoretic analysis. NeuroImage Clin. 2013;2:414–23.PubMedPubMedCentralCrossRefGoogle Scholar
  45. Knyazeva MG, Innocenti GM, Carmeli C, et al. Assessment of EEG synchronization based on state-space analysis. Neuroimage. 2005;25(2):339–54.PubMedCrossRefGoogle Scholar
  46. Kocsis B, Bragin A, Buzsáki G. Interdependence of multiple theta generators in the hippocampus: a partial coherence analysis. J Neurosci Off J Soc Neurosci. 1999;19(14):6200–12.Google Scholar
  47. Kramer MA, Edwards E, Soltani M, et al. Synchronization measures of bursting data: application to the electrocorticogram of an auditory event-related experiment. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70:127–50.CrossRefGoogle Scholar
  48. Kraskov A, Stőgbauer H, Grassberger P. Estimating mutual information. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;69:279–307.CrossRefGoogle Scholar
  49. Kus R, Kaminski M, Blinowska KJ. Determination of EEG activity propagation: pair-wise versus multichannel estimate. IEEE Trans Bio-Med Eng. 2004;51(9):1501–10.CrossRefGoogle Scholar
  50. Lachaux J, Rodriguez E, Martinerie J, et al. Measuring phase synchrony in brain signals. Hum Brain Mapp. 1999;8(4):194–208.PubMedCrossRefGoogle Scholar
  51. Lawrence W. Synchronous neural oscillations and cognitive processes. Trends Cogn Sci. 2003;7(12):553–9.CrossRefGoogle Scholar
  52. Le Van Quyen M. Disentangling the dynamic core: a research program for a neurodynamics at the large scale. Biol Res. 2003;36:61–82.Google Scholar
  53. Lee SH, Park YM, Kim DW, et al. Global synchronization index as a biological correlate of cognitive decline in Alzheimer’s disease. Neurosci Res. 2010;66(4):333–9.PubMedCrossRefGoogle Scholar
  54. Li XL, Cui D, Jiruska P, et al. Synchronization measurement of multiple neuronal populations. Neurosci Lett. 2007;98(6):3341–8.Google Scholar
  55. Liberati D, Cursi M, Locatelli T, et al. Total and partial coherence analysis of spontaneous and evoked EEG by means of multi-variable autoregressive processing. Med Biol Eng Comput. 1997;35(35):124–30.PubMedCrossRefGoogle Scholar
  56. Lopes da Silva FH, Vos JE, Mooibroek J, et al. Relative contributions of intracortical and thalamo-cortical processes in the generation of alpha rhythms, revealed by partial coherence analysis. Electroencephalogr Clin Neurophysiol. 1980;50:449–56.PubMedCrossRefGoogle Scholar
  57. Lytton WW. Computer modelling of epilepsy. Nat Rev Neurosci. 2008;9(8):626–37.PubMedPubMedCentralCrossRefGoogle Scholar
  58. Mckenna TM, Mcmullen TA, Shlesinger MF. The brain as a dynamic physical system. Neuroscience. 1994;60(3):587–605.PubMedCrossRefGoogle Scholar
  59. Micheloyannis S, Pachou E, Stam CJ, et al. Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis. Neurosci Lett. 2006;402(3):273–7.PubMedCrossRefGoogle Scholar
  60. Min BC, Jin SH, Kang IH, et al. Analysis of mutual information content for EEG responses to odor stimulation for subjects classified by occupation. Chem Senses. 2003;28(9):741–9.PubMedCrossRefGoogle Scholar
  61. Mirski MA, Tsai YC, Rossell LA, et al. Anterior thalamic mediation of experimental seizures: selective EEG spectral coherence. Epilepsia. 2003;44(3):355–65.PubMedCrossRefGoogle Scholar
  62. Mormann F, Lehnertz K, David P, et al. Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Physica D Nonlinear Phenomena. 2000;144:358–69.CrossRefGoogle Scholar
  63. Müller M, Baier G. Detection and characterization of changes of the correlation structure in multivariate time series. Phys Rev E. 2005;71:046116.CrossRefGoogle Scholar
  64. Müller M, Lopez Y, Rummel C, et al. Localized short-range correlations in the spectrum of the equal-time correlation matrix. Phys Rev E Stat Nonlin Soft Matter Phys. 2006a;74:159–63.CrossRefGoogle Scholar
  65. Müller M, Wegner K, Kummer U, et al. Quantification of cross correlations in complex spatiotemporal systems. Phys Rev E Stat Nonlin Soft Matter Phys. 2006b;73:046106.PubMedCrossRefGoogle Scholar
  66. Osipov GV, Kurths J. Regular and chaotic phase synchronization of coupled circle maps. Phys Rev E. 2001;65:016216.CrossRefGoogle Scholar
  67. Osipov GV, Pikovsky AS, Rosenblum MG, et al. Phase synchronization effects in a lattice of nonidentical Rössler oscillators. Phys Rev E Stat Nonlin Soft Matter Phys. 1997;55(3):2353–61.CrossRefGoogle Scholar
  68. Palus M, Stefanovska A. Direction of coupling from phases of interacting oscillators: an information-theoretic approach. Phys Rev E Stat Nonlin Soft Matter Phys. 2003;67:055201.PubMedCrossRefGoogle Scholar
  69. Pereda E, Quiroga EQ, Bhattacharya J. Nonlinear multivariate analysis of neurophysiological signals. Prog Neurobiol. 2005;77:1–37.PubMedCrossRefGoogle Scholar
  70. Pikovsky AS, Rosenblum MG, Kurths J. Synchronization in a population of globally coupled chaotic oscillators. Epl. 1996;34(3):165–70.CrossRefGoogle Scholar
  71. Pikovsky A, Rosenblum M, Kurths J. Synchronization: a universal concept in nonlinear sciences. Am J Phys. 2001;70(6):655–5.Google Scholar
  72. Ponten SC, Bartolomei F, Stam CJ. Small-world networks and epilepsy: graph theoretical analysis of intracerebrally recorded medial temporal lobe seizures. Clin Neurophysiol. 2007;118(4):918–27.PubMedCrossRefGoogle Scholar
  73. Quian Quiroga R, Arnhold J, Grassberger P. Learning driver-response relationships from synchronization patterns. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000;61:5142–8.Google Scholar
  74. Quian Quiroga R, Kraskov A, Kreuz T, et al. Performance of different synchronization measures in real data: a case study on electroencephalographic signals. Phys Rev E. 2002;65:041903.CrossRefGoogle Scholar
  75. Rodriguez E, George N, Lachaux JP, et al. Perception’s shadow: long-distance synchronization of human brain activity. Nature. 1999;397(6718):430–3.PubMedCrossRefGoogle Scholar
  76. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett. 1996;1(11):1804–7.CrossRefGoogle Scholar
  77. Rosenblum M, Pikovsky A, Kurths J. Phase synchronization: from theory to data analysis. Handb Biol Phys. 2001;4:93–4.Google Scholar
  78. Rosso OA, Blanco S, Yordanova J, et al. Wavelet entropy: a new tool for analysis of short duration brain electrical signals. J Neurosci Methods. 2001;105(1):65–75.PubMedCrossRefGoogle Scholar
  79. Rulkov NF, Sushchik MM, Tsimring LS, et al. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1995;51(2):980–94.PubMedGoogle Scholar
  80. Sameshima K, Baccalá LA. Using partial directed coherence to describe neuronal ensemble interactions. J Neurosci Methods. 1999;94(1):93–103.PubMedCrossRefGoogle Scholar
  81. Schelter B, Winterhalder M, Eichler M, et al. Testing for directed influences among neural signals using partial directed coherence. J Neurosci Methods. 2005;152:210–9.PubMedCrossRefGoogle Scholar
  82. Schelter B, Winterhalder M, Hellwig B, et al. Direct or indirect? Graphical models for neural oscillators. J Physiol Paris. 2006;99(1):37–46.PubMedCrossRefGoogle Scholar
  83. Schiff SJ, So P, Chang T, et al. Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996;54(6):6708–24.PubMedGoogle Scholar
  84. Schmitz A. Measuring statistical dependence and coupling of subsystems. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000;62:7508–11.PubMedGoogle Scholar
  85. Schreiber T, Schmitz A. Improved surrogate data for nonlinearity tests. Phys Rev Lett. 1996;77(4):635–8.PubMedCrossRefGoogle Scholar
  86. Seba P. Random matrix analysis of human EEG data. Phys Rev Lett. 2003;91(19):198104.PubMedCrossRefGoogle Scholar
  87. Shabunin A, Demidov V, Astakhov V, et al. Information theoretic approach to quantify complete and phase synchronization of chaos. Phys Rev E. 2002;65:634–4.Google Scholar
  88. Shannon CE. A mathematical theory of communication. Bell Syst Technic J. 1948;27(3):379–423.CrossRefGoogle Scholar
  89. Stam CJ, Reijneveld JC. Graph theoretical analysis of complex networks in the brain. Nonlinear Biomed Phys. 2007;1(1):3.PubMedPubMedCentralCrossRefGoogle Scholar
  90. Stam CJ, van Dijk BW. Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets. Physica D Nonlinear Phenomena. 2002;163:236–51.CrossRefGoogle Scholar
  91. Stam CJ, Jones BF, Nolte G, et al. Small-world networks and functional connectivity in Alzheimer’s disease. Cereb Cortex. 2007;17(1):92–9.PubMedCrossRefGoogle Scholar
  92. Steuer R, Kurths J, Daub CO, et al. The mutual information: Detecting and evaluating dependencies between variables. Bioinformatics. 2002;18:231–40.CrossRefGoogle Scholar
  93. Sun FT, Miller LM, D’Esposito M. Measuring interregional functional connectivity using coherence and partial coherence analyses of fMRI data. Neuroimage. 2004;21(2):647–58.PubMedCrossRefGoogle Scholar
  94. Tass P, Rosenblum MG, Weule J, et al. Detection of n: m phase locking from noisy data: application to magnetoencephalography. Phys Rev Lett. 1998;81:3291–4.CrossRefGoogle Scholar
  95. Thuraisingham RA. A new method using coherence to obtain the model order in the evaluation of partial directed coherence. Comput Biol Med. 2007;37(9):1361–5.PubMedCrossRefGoogle Scholar
  96. Traub RD, Spruston N, Soltesz I, et al. Gamma-frequency oscillations: a neuronal population phenomenon, regulated by synaptic and intrinsic cellular processes, and inducing synaptic plasticity. Prog Neurobiol. 1998;55(6):563–75.PubMedCrossRefGoogle Scholar
  97. Tucker DM, Roth DL, Bair TB. Functional connections among cortical regions: topography of EEG coherence. Electroencephalogr Clin Neurophysiol. 1986;63(3):242–50.PubMedCrossRefGoogle Scholar
  98. Van Albada SJ, Robinson PA. Mean-field modeling of the basal ganglia-thalamocortical system. I: firing rates in healthy and parkinsonian states. J Theor Biol. 2009;257(4):642–63.PubMedCrossRefGoogle Scholar
  99. Van Albada SJ, Gray RT, Drysdale PM, et al. Mean-field modeling of the basal ganglia-thalamocortical system. II: dynamics of parkinsonian oscillations. J Theor Biol. 2009;257(4):664–88.PubMedCrossRefGoogle Scholar
  100. Van Putten MJAM. Proposed link rates in the human brain. J Neurosci Methods. 2003;127(1):1–10.PubMedCrossRefGoogle Scholar
  101. Varela F, Lachaux JP, Rodriguez E, et al. The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci. 2001;2(4):229–39.PubMedCrossRefGoogle Scholar
  102. Winterhalder M, Schelter B, Hesse W, et al. Comparison of time series analysis techniques to detect direct and time-varying interrelations in multivariate, neural systems. Signal Process. 2005;85:2137–60.CrossRefGoogle Scholar
  103. Winterhalder M, Schelter B, Hesse W, et al. Detection of directed information flow in biosignals. Biomed Tech. 2006;51(5-6):281–7.CrossRefGoogle Scholar
  104. Womelsdorf T, Schoffelen JM, Oostenveld R. Modulation of neuronal interactions through neuronal synchronization. Science. 2007;316(5831):1609–12.PubMedCrossRefGoogle Scholar
  105. Wu MH, Frye RE, Zouridakis G. A comparison of multivariate causality based measures of effective connectivity. Comput Biol Med. 2011;41:1132–41.PubMedCrossRefGoogle Scholar
  106. Xu JW, Bakardjian H, Cichocki A, et al. A new nonlinear similarity measure for multichannel signals. Neural Netw Off J Int Neural Netw Soc. 2008;21:222–31.CrossRefGoogle Scholar
  107. Yoshimura M, Isotani T, Yagyu T, et al. Global approach to multichannel electroencephalogram analysis for diagnosis and clinical evaluation in mild Alzheimer’s disease. Neuropsychobiology. 2004;49(3):163–6.PubMedCrossRefGoogle Scholar

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© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.School of Information Science and EngineeringYanshan UniversityQinhuangdaoPeople’s Republic of China
  2. 2.State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain ResearchBeijing Normal UniversityBeijingPeople’s Republic of China
  3. 3.Center for Collaboration and Innovation in Brain and Learning SciencesBeijing Normal UniversityBeijingPeople’s Republic of China

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