Amplitude- and Fluctuation-Based Dispersion Entropy

Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.

[2]  M. C. Bisi,et al.  Complexity of human gait pattern at different ages assessed using multiscale entropy: From development to decline. , 2016, Gait & posture.

[3]  J. Kurths,et al.  Quantitative analysis of heart rate variability. , 1995, Chaos.

[4]  K Lehnertz,et al.  Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  C. Peng,et al.  What is physiologic complexity and how does it change with aging and disease? , 2002, Neurobiology of Aging.

[6]  C. Peng,et al.  Analysis of complex time series using refined composite multiscale entropy , 2014 .

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

[8]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[9]  Robert H. Habib,et al.  Effect of salt intake on beat‐to‐beat blood pressure nonlinear dynamics and entropy in salt‐sensitive versus salt‐protected rats , 2016, Physiological reports.

[10]  Deo Prakash Vidyarthi,et al.  Admission control in cloud computing using game theory , 2015, The Journal of Supercomputing.

[11]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[12]  Roberto Hornero,et al.  Interpretation of the Lempel-Ziv Complexity Measure in the Context of Biomedical Signal Analysis , 2006, IEEE Transactions on Biomedical Engineering.

[13]  Hamed Azami,et al.  Dispersion Entropy: A Measure for Time-Series Analysis , 2016, IEEE Signal Processing Letters.

[14]  Stphane Tuffry,et al.  Data Mining and Statistics for Decision Making , 2011 .

[15]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[16]  M. S. Keshner.  1/f noise , 1982, Proceedings of the IEEE.

[17]  Einar Steingrimsson,et al.  Generalized permutation patterns - a short survey , 2008, 0801.2412.

[18]  Hamed Azami,et al.  Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation , 2016, Comput. Methods Programs Biomed..

[19]  Luca Faes,et al.  Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics , 2015, Entropy.

[20]  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.

[21]  Jeffrey M. Hausdorff,et al.  Physionet: Components of a New Research Resource for Complex Physiologic Signals". Circu-lation Vol , 2000 .

[22]  Dingchang Zheng,et al.  Assessing the complexity of short-term heartbeat interval series by distribution entropy , 2014, Medical & Biological Engineering & Computing.

[23]  S. Guzzetti,et al.  Physiological time-series analysis using approximate entropy and sample entropy , 2000 .

[24]  Wlodzislaw Duch,et al.  Uncertainty of data, fuzzy membership functions, and multilayer perceptrons , 2005, IEEE Transactions on Neural Networks.

[25]  Hamed Azami,et al.  Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals , 2016, IEEE Transactions on Biomedical Engineering.

[26]  Ying Jiang,et al.  A Fast Algorithm for Computing Sample Entropy , 2011, Adv. Data Sci. Adapt. Anal..

[27]  Massimiliano Zanin,et al.  Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review , 2012, Entropy.

[28]  Shuen-De Wu,et al.  Refined Composite Multiscale Permutation Entropy to Overcome Multiscale Permutation Entropy Length Dependence , 2015, IEEE Signal Processing Letters.

[29]  Gordon Morison,et al.  Classification of partial discharge EMI conditions using permutation entropy-based features , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[30]  Jeffrey Lam.  Preserving Useful Info While Reducing Noise of Physiological Signals by Using Wavelet Analysis , 2011 .

[31]  Qianli D. Y. Ma,et al.  Modified permutation-entropy analysis of heartbeat dynamics. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Sergio Cerutti,et al.  Comparison of entropy-based regularity estimators: application to the fetal heart rate signal for the identification of fetal distress , 2006, IEEE Transactions on Biomedical Engineering.

[33]  Doreen Meier,et al.  Chaotic Dynamics An Introduction , 2016 .

[34]  Zhaohua Wu,et al.  On the trend, detrending, and variability of nonlinear and nonstationary time series , 2007, Proceedings of the National Academy of Sciences.

[35]  Ervin Sejdic,et al.  Necessity of noise in physiology and medicine , 2013, Comput. Methods Programs Biomed..

[36]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Hamed Azami,et al.  Dispersion entropy for the analysis of resting-state MEG regularity in Alzheimer's disease , 2016, 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[38]  Osvaldo A. Rosso,et al.  Bandt–Pompe approach to the classical-quantum transition , 2007 .

[39]  B. Hao,et al.  Symbolic dynamics and characterization of complexity , 1991 .

[40]  Jeffrey M. Hausdorff,et al.  Maturation of gait dynamics: stride-to-stride variability and its temporal organization in children. , 1999, Journal of applied physiology.

[41]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[42]  David J. C. MacKay,et al.  Variational Gaussian process classifiers , 2000, IEEE Trans. Neural Networks Learn. Syst..

[43]  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.

[44]  A L Goldberger,et al.  Physiological time-series analysis: what does regularity quantify? , 1994, The American journal of physiology.

[45]  Pere Caminal,et al.  Changes of autonomic information flow due to idiopathic dilated cardiomyopathy , 2007, Physiological measurement.

[46]  Miguel A. F. Sanjuán,et al.  True and false forbidden patterns in deterministic and random dynamics , 2007 .

[47]  Shuen-De Wu,et al.  Refined scale-dependent permutation entropy to analyze systems complexity , 2016 .

[48]  Ricardo Neisse,et al.  Physical layer authentication of Internet of Things wireless devices through permutation and dispersion entropy , 2017, 2017 Global Internet of Things Summit (GIoTS).

[49]  Norman Biggs,et al.  The roots of combinatorics , 1979 .

[50]  Karl M Newell,et al.  Age-related complexity and coupling of children's sitting posture. , 2008, Developmental psychobiology.

[51]  C. Stam,et al.  Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field , 2005, Clinical Neurophysiology.

[52]  Viktor K. Jirsa,et al.  Brain Dynamics of Aging: Multiscale Variability of EEG Signals at Rest and during an Auditory Oddball Task1,2,3 , 2015, eNeuro.

[53]  R. Rosenthal.  Parametric measures of effect size. , 1994 .

[54]  Badong Chen,et al.  Weighted-permutation entropy: a complexity measure for time series incorporating amplitude information. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  Jos Amig.  Permutation Complexity in Dynamical Systems: Ordinal Patterns, Permutation Entropy and All That , 2010 .

[56]  Leon Cohen,et al.  The history of noise [on the 100th anniversary of its birth] , 2005, IEEE Signal Processing Magazine.

[57]  A Voss,et al.  Improved analysis of heart rate variability by methods of nonlinear dynamics. , 1995, Journal of electrocardiology.

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

[59]  Hamed Azami,et al.  Evaluation of resting-state magnetoencephalogram complexity in Alzheimer's disease with multivariate multiscale permutation and sample entropies , 2015, 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[60]  I. P. Mitov.  A method for assessment and processing of biomedical signals containing trend and periodic components. , 1998, Medical engineering & physics.

[61]  Karsten Keller,et al.  Ordinal Patterns, Entropy, and EEG , 2014, Entropy.

[62]  Roberto Hornero,et al.  Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis. Application to electroencephalogram recordings , 2009, Physiological measurement.

[63]  Dirk Hoyer,et al.  Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction. , 2002, Medical engineering & physics.

[64]  Hamed Azami,et al.  Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis , 2016, Medical & Biological Engineering & Computing.

[65]  Osvaldo A. Rosso,et al.  Missing ordinal patterns in correlated noises , 2010 .

[66]  Karsten Keller,et al.  Efficiently Measuring Complexity on the Basis of Real-World Data , 2013, Entropy.