Multivariate multiscale entropy: a tool for complexity analysis of multichannel data.

This work generalizes the recently introduced univariate multiscale entropy (MSE) analysis to the multivariate case. This is achieved by introducing multivariate sample entropy (MSampEn) in a rigorous way, in order to account for both within- and cross-channel dependencies in multiple data channels, and by evaluating it over multiple temporal scales. The multivariate MSE (MMSE) method is shown to provide an assessment of the underlying dynamical richness of multichannel observations, and more degrees of freedom in the analysis than standard MSE. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate stochastic processes and on real-world multichannel physiological and environmental data.

[1]  J. Kurths,et al.  A Comparative Classification of Complexity Measures , 1994 .

[2]  Radhakrishnan Nagarajan,et al.  Evidence of crossover phenomena in wind-speed data , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Danilo P. Mandic,et al.  Complex Valued Nonlinear Adaptive Filters , 2009 .

[4]  Kai Wang,et al.  A Theoretical Analysis of Multiscale Entropy under the Inverse Gaussian Distribution , 2009, Int. J. Bifurc. Chaos.

[5]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[6]  Jeffrey M. Hausdorff,et al.  Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. , 1996, Journal of applied physiology.

[7]  Hualou Liang,et al.  Adaptive Multiscale Entropy Analysis of Multivariate Neural Data , 2012, IEEE Transactions on Biomedical Engineering.

[8]  Naftali Tishby,et al.  Predictability, Complexity, and Learning , 2000, Neural Computation.

[9]  A. N. Sharkovskiĭ.  Dynamic systems and turbulence , 1989 .

[10]  Peter Grassberger,et al.  How to measure self-generated complexity , 1986 .

[11]  C. Peng,et al.  Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. , 1996, The American journal of physiology.

[12]  Luciano Telesca,et al.  Analysis of time dynamics in wind records by means of multifractal detrended fluctuation analysis and Fisher-Shannon information plane , 2011 .

[13]  Madalena Costa,et al.  Complex dynamics of human red blood cell flickering: alterations with in vivo aging. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  T. Mizuno,et al.  Age-related variation in EEG complexity to photic stimulation: A multiscale entropy analysis , 2009, Clinical Neurophysiology.

[15]  Holger Kantz,et al.  Practical implementation of nonlinear time series methods: The TISEAN package. , 1998, Chaos.

[16]  D. Rand,et al.  Dynamical Systems and Turbulence, Warwick 1980 , 1981 .

[17]  Jeffrey M. Hausdorff,et al.  Multiscale entropy analysis of human gait dynamics. , 2003, Physica A.

[18]  A. Wear.  CIRCULATION , 1964, The Lancet.

[19]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[20]  David J. Hewson,et al.  Intrinsic Mode Entropy for Nonlinear Discriminant Analysis , 2007, IEEE Signal Processing Letters.

[21]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[22]  J. Rogers.  Chaos , 1876 .

[23]  Jeffrey M. Hausdorff,et al.  Quantifying Fractal Dynamics of Human Respiration: Age and Gender Effects , 2002, Annals of Biomedical Engineering.

[24]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[25]  K. J. Blinowska,et al.  Linear model of brain electrical activity—EEG as a superposition of damped oscillatory modes , 1985, Biological Cybernetics.

[26]  Roberto Hornero,et al.  Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer's disease , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[27]  Holger Kantz,et al.  Long-term correlations and multifractality in surface wind speed , 2004 .

[28]  N. Packard,et al.  Symbolic dynamics of noisy chaos , 1983 .

[29]  Jeffrey M. Hausdorff,et al.  Fractal dynamics in physiology: Alterations with disease and aging , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[30]  P. Grassberger.  Toward a quantitative theory of self-generated complexity , 1986 .

[31]  Madalena Costa,et al.  Multiscale entropy analysis of biological signals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  A. Mees,et al.  Dynamics from multivariate time series , 1998 .

[33]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[34]  Chi-Ying Tsui,et al.  IEEE Transactions on Circuits and Systems—I:Regular Papers information for authors , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  Danilo P Mandic,et al.  Indications of nonlinear structures in brain electrical activity. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[37]  Danilo P. Mandic,et al.  A differential entropy based method for determining the optimal embedding parameters of a signal , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[38]  J. A. Stewart,et al.  Nonlinear Time Series Analysis , 2015 .

[39]  Pere Caminal,et al.  Refined Multiscale Entropy: Application to 24-h Holter Recordings of Heart Period Variability in Healthy and Aortic Stenosis Subjects , 2009, IEEE Transactions on Biomedical Engineering.

[40]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Madalena Costa,et al.  Multiscale entropy analysis of complex physiologic time series. , 2002, Physical review letters.