Detecting connectivity in EEG: A comparative study of data-driven effective connectivity measures

In this paper, we perform the first comparison of a large variety of effective connectivity measures in detecting causal effects among observed interacting systems based on their statistical significance. Well-known measures estimating direction and strength of interdependence between time series are compared: information theoretic measures, model-based multivariate measures in the time and frequency domains, and phase-based measures. The performance of measures is tested on simulated data from three systems: three coupled Hénon maps; a multivariate autoregressive (MVAR) model with and without EEG as an exogenous input; and simulated EEG. No measure was consistently superior. Measures that model the data as MVAR perform well when the data are drawn from that model. Frequency domain measures perform well when the data have a clearly defined band of interest. When neither of these is true, information theoretic measures perform well. Overall, the measure with the best performance in a variety of situations and with a low computational cost is conditional Granger causality. Partial Granger causality and multivariate Granger causality are also good measures, but their computational cost rises rapidly with the number of channels. Copula Granger causality can also be used reliably, but its computational cost rises rapidly with the number of data.

[1]  L. Faes,et al.  A framework for assessing frequency domain causality in physiological time series with instantaneous effects , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[2]  Karl J. Friston,et al.  A systematic framework for functional connectivity measures , 2014, Front. Neurosci..

[3]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[4]  N. Montano,et al.  Complexity and Nonlinearity in Short-Term Heart Period Variability: Comparison of Methods Based on Local Nonlinear Prediction , 2007, IEEE Transactions on Biomedical Engineering.

[5]  M. Kaminski,et al.  Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method , 2003, Journal of Neuroscience Methods.

[6]  Yan Liu,et al.  Sparse-GEV: Sparse Latent Space Model for Multivariate Extreme Value Time Serie Modeling , 2012, ICML.

[7]  Blas Echebarria,et al.  Characterization of the nonlinear content of the heart rate dynamics during myocardial ischemia. , 2009, Medical engineering & physics.

[8]  Jochen Kaiser,et al.  Transfer entropy in magnetoencephalographic data: quantifying information flow in cortical and cerebellar networks. , 2011, Progress in biophysics and molecular biology.

[9]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[10]  Andrzej Cichocki,et al.  A new nonlinear similarity measure for multichannel signals , 2008, Neural Networks.

[11]  Derek Greene,et al.  Normalized Mutual Information to evaluate overlapping community finding algorithms , 2011, ArXiv.

[12]  R. Burke,et al.  Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Dimitris Kugiumtzis,et al.  A Nonparametric Causality Test: Detection of Direct Causal Effects in Multivariate Systems Using Corrected Partial Transfer Entropy , 2014 .

[14]  Andrea Lancichinetti,et al.  Detecting the overlapping and hierarchical community structure in complex networks , 2008, 0802.1218.

[15]  Olivier J. J. Michel,et al.  On directed information theory and Granger causality graphs , 2010, Journal of Computational Neuroscience.

[16]  K. Hlavácková-Schindler,et al.  Causality detection based on information-theoretic approaches in time series analysis , 2007 .

[17]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[18]  M. Paluš,et al.  Information theoretic test for nonlinearity in time series , 1993 .

[19]  Joseph T. Lizier,et al.  JIDT: An Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems , 2014, Front. Robot. AI.

[20]  William A. Sethares,et al.  Conditional Granger causality and partitioned Granger causality: differences and similarities , 2015, Biological Cybernetics.

[21]  Joydeep Bhattacharya,et al.  Effective detection of coupling in short and noisy bivariate data , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Dimitris Kugiumtzis,et al.  Simulation Study of Direct Causality Measures in Multivariate Time Series , 2013, Entropy.

[23]  Dimitris Kugiumtzis,et al.  Non-uniform state space reconstruction and coupling detection , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M. Paluš,et al.  Inferring the directionality of coupling with conditional mutual information. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  S. Aviyente,et al.  Information Theoretic Measures for Quantifying the Integration of Neural Activity , 2007, 2007 Information Theory and Applications Workshop.

[26]  Daniele Marinazzo,et al.  Causal Information Approach to Partial Conditioning in Multivariate Data Sets , 2011, Comput. Math. Methods Medicine.

[27]  Kenneth J. Pope,et al.  Towards Detecting Connectivity in EEG: A Comparative Study of Parameters of Effective Connectivity Measures on Simulated Data , 2018, 2018 IEEE-EMBS Conference on Biomedical Engineering and Sciences (IECBES).

[28]  José Carlos Príncipe,et al.  Correntropy as a novel measure for nonlinearity tests , 2009, Signal Process..

[29]  C. Stam,et al.  Heritability of “small‐world” networks in the brain: A graph theoretical analysis of resting‐state EEG functional connectivity , 2008, Human brain mapping.

[30]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[31]  Michel Verleysen,et al.  Feature Scoring by Mutual Information for Classification of Mass Spectra , 2006 .

[32]  Joseph T. Lizier,et al.  Directed Information Measures in Neuroscience , 2014 .

[33]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[34]  Yan Liu,et al.  An Examination of Practical Granger Causality Inference , 2013, SDM.

[35]  S. Frenzel,et al.  Partial mutual information for coupling analysis of multivariate time series. , 2007, Physical review letters.

[36]  L.A. Baccald,et al.  Generalized Partial Directed Coherence , 2007, 2007 15th International Conference on Digital Signal Processing.

[37]  J. Geweke,et al.  Measures of Conditional Linear Dependence and Feedback between Time Series , 1984 .

[38]  Jens Timmer,et al.  Handbook of time series analysis : recent theoretical developments and applications , 2006 .

[39]  Luca Faes,et al.  MuTE: A MATLAB Toolbox to Compare Established and Novel Estimators of the Multivariate Transfer Entropy , 2014, PloS one.

[40]  Luiz A. Baccalá,et al.  Studying the Interaction Between Brain Structures via Directed Coherence and Granger Causality , 1998 .

[41]  Lee M. Miller,et al.  Measuring interregional functional connectivity using coherence and partial coherence analyses of fMRI data , 2004, NeuroImage.

[42]  Patrick L Purdon,et al.  A study of problems encountered in Granger causality analysis from a neuroscience perspective , 2017, Proceedings of the National Academy of Sciences.

[43]  Dimitris Kugiumtzis,et al.  Partial transfer entropy on rank vectors , 2013, ArXiv.

[44]  James Theiler,et al.  Constrained-realization Monte-carlo Method for Hypothesis Testing , 1996 .

[45]  Hualou Liang,et al.  Causal influence: advances in neurosignal analysis. , 2005, Critical reviews in biomedical engineering.

[46]  Luca Faes,et al.  Testing Frequency-Domain Causality in Multivariate Time Series , 2010, IEEE Transactions on Biomedical Engineering.

[47]  Régine Le Bouquin-Jeannès,et al.  Linear and nonlinear causality between signals: methods, examples and neurophysiological applications , 2006, Biological Cybernetics.

[48]  Joseph T. Lizier,et al.  Measuring the Dynamics of Information Processing on a Local Scale in Time and Space , 2014 .

[49]  Jürgen Kurths,et al.  Estimation of the direction of the coupling by conditional probabilities of recurrence. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  R. Quiroga,et al.  Learning driver-response relationships from synchronization patterns. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[51]  Matthäus Staniek,et al.  Symbolic transfer entropy. , 2008, Physical review letters.

[52]  Kenneth J. Pope,et al.  Detecting synchrony in EEG: A comparative study of functional connectivity measures , 2019, Comput. Biol. Medicine.

[53]  Chunfeng Yang.  Contribution à l'analyse de la connectivité effective en épilepsie , 2012 .

[54]  J. Kurths,et al.  Phase synchronization: from theory to data analysis , 2003 .

[55]  Ana L. N. Fred,et al.  Robust data clustering , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[56]  Laura Astolfi,et al.  Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data , 2006, IEEE Transactions on Biomedical Engineering.

[57]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[58]  Kenneth J. Pope,et al.  Improved artefact removal from EEG using Canonical Correlation Analysis and spectral slope , 2018, Journal of Neuroscience Methods.

[59]  Dimitris Kugiumtzis,et al.  Detection of Direct Causal Effects and Application to epileptic Electroencephalogram Analysis , 2012, Int. J. Bifurc. Chaos.

[60]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[61]  G. Wilson.  The Factorization of Matricial Spectral Densities , 1972 .

[62]  Jukka Kortelainen,et al.  Experimental comparison of connectivity measures with simulated EEG signals , 2012, Medical & Biological Engineering & Computing.

[63]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[64]  Michael Eichler,et al.  Abstract Journal of Neuroscience Methods xxx (2005) xxx–xxx Testing for directed influences among neural signals using partial directed coherence , 2005 .

[65]  Heinz Georg Schuster,et al.  Reviews of nonlinear dynamics and complexity , 2008 .

[66]  N. Kamel,et al.  Review of EEG, ERP, and Brain Connectivity Estimators as Predictive Biomarkers of Social Anxiety Disorder , 2020, Frontiers in Psychology.

[67]  R Quian Quiroga,et al.  Performance of different synchronization measures in real data: a case study on electroencephalographic signals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[68]  George Zouridakis,et al.  A comparison of multivariate causality based measures of effective connectivity , 2011, Comput. Biol. Medicine.

[69]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[70]  Andrzej Cichocki,et al.  A comparative study of synchrony measures for the early diagnosis of Alzheimer's disease based on EEG , 2010, NeuroImage.

[71]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[72]  Anil K. Seth,et al.  The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference , 2014, Journal of Neuroscience Methods.

[73]  Giandomenico Nollo,et al.  Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series , 2011 .

[74]  K. Kendrick,et al.  Partial Granger causality—Eliminating exogenous inputs and latent variables , 2008, Journal of Neuroscience Methods.

[75]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[76]  L. Baccalá,et al.  Overcoming the limitations of correlation analysis for many simultaneously processed neural structures. , 2001, Progress in brain research.

[77]  Gordon Pipa,et al.  Transfer entropy—a model-free measure of effective connectivity for the neurosciences , 2010, Journal of Computational Neuroscience.

[78]  Luca Faes,et al.  Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions , 2010, Biological Cybernetics.

[79]  F. Mormann,et al.  Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients , 2000 .

[80]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[81]  Raul Vicente,et al.  Efficient Estimation of Information Transfer , 2014 .