Event detection, multimodality and non-stationarity: Ordinal patterns, a tool to rule them all?

In this work, we apply ordinal analysis of time series to the characterisation of neuronal activity. Automatic event detection is performed by means of the so-called permutation entropy, along with the quantification of the relative cardinality of forbidden patterns. In addition, multivariate time series are characterised using the joint permutation entropy. In order to illustrate the suitability of the ordinal analysis for characterising neurophysiological data, we have compared the measures based on ordinal patterns of time series to the tools typically used in the context of neurophysiology.

[1]  Yun Gao,et al.  Estimating the Entropy of Binary Time Series: Methodology, Some Theory and a Simulation Study , 2008, Entropy.

[2]  Donald L. Kreher,et al.  Combinatorial algorithms: generation, enumeration, and search , 1998, SIGA.

[3]  A. Selverston,et al.  Interacting biological and electronic neurons generate realistic oscillatory rhythms , 2000, Neuroreport.

[4]  José María Amigó,et al.  Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity , 2004, Neural Computation.

[5]  Asok Ray,et al.  Statistical Mechanics of Complex Systems for Pattern Identification , 2009 .

[6]  K. Keller,et al.  TIME SERIES FROM THE ORDINAL VIEWPOINT , 2007 .

[7]  Blas Echebarria,et al.  Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  R. D. Pinto,et al.  Reliable circuits from irregular neurons: A dynamical approach to understanding central pattern generators , 2000, Journal of Physiology-Paris.

[9]  Thomas Kreuz,et al.  Characterizing unidirectional couplings between point processes and flows , 2011 .

[10]  B. M. Fulk.  MATH , 1992 .

[11]  Maurizio Vichi,et al.  Studies in Classification Data Analysis and knowledge Organization , 2011 .

[12]  A. Selverston,et al.  The Crustacean stomatogastric system : a model for the study of central nervous systems , 1987 .

[13]  Klaus Lehnertz,et al.  Inferring directional interactions from transient signals with symbolic transfer entropy. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Jose S. Cánovas,et al.  Using permutations to detect dependence between time series , 2011 .

[15]  J. D. Saddy,et al.  Symbolic dynamics of event-related brain potentials. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Attila Szücs,et al.  Applications of the spike density function in analysis of neuronal firing patterns , 1998 .

[17]  E. Basar,et al.  Wavelet entropy: a new tool for analysis of short duration brain electrical signals , 2001, Journal of Neuroscience Methods.

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

[19]  K. Keller,et al.  Ordinal analysis of EEG time series , 2005 .

[20]  P. Walters.  Introduction to Ergodic Theory , 1977 .

[21]  Pablo Varona,et al.  Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis , 2001, Biological Cybernetics.

[22]  L M Hively,et al.  Detecting dynamical changes in time series using the permutation entropy. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Gaoxiang Ouyang,et al.  Ordinal pattern based similarity analysis for EEG recordings , 2010, Clinical Neurophysiology.

[25]  Karl J. Friston.  Transients, Metastability, and Neuronal Dynamics , 1997, NeuroImage.

[26]  Prashant G. Mehta,et al.  The Kullback–Leibler Rate Pseudo-Metric for Comparing Dynamical Systems , 2010, IEEE Transactions on Automatic Control.

[27]  A. Selverston,et al.  The Crustacean Stomatogastric System , 1987, Springer Berlin Heidelberg.

[28]  P. Caminal,et al.  Symbolic Dynamic Analysis of Relations Between Cardiac and Breathing Cycles in Patients on Weaning Trials , 2010, Annals of Biomedical Engineering.

[29]  Todd P. Coleman,et al.  A Computationally Efficient Method for Nonparametric Modeling of Neural Spiking Activity with Point Processes , 2010, Neural Computation.

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

[31]  José María Amigó,et al.  Estimation of the control parameter from symbolic sequences: unimodal maps with variable critical point. , 2009, Chaos.

[32]  Ary L Goldberger,et al.  Statistical physics approach to categorize biologic signals: from heart rate dynamics to DNA sequences. , 2007, Chaos.

[33]  R. Harris-Warrick,et al.  Amine modulation of the transient potassium current in identified cells of the lobster stomatogastric ganglion. , 2001, Journal of neurophysiology.

[34]  Ehud Kaplan,et al.  Estimating the Amount of Information Conveyed by a Population of Neurons , 2011, Front. Neurosci..

[35]  Pablo Varona,et al.  Generalization of the Dynamic Clamp Concept in Neurophysiology and Behavior , 2012, PloS one.

[36]  Wolfram Bunk,et al.  Transcripts: an algebraic approach to coupled time series. , 2012, Chaos.

[37]  Osvaldo A. Rosso,et al.  Wavelet entropy in event-related potentials: a new method shows ordering of EEG oscillations , 2001, Biological Cybernetics.

[38]  Steve M. Potter,et al.  Closed-Loop, Open-Source Electrophysiology , 2010, Front. Neurosci..

[39]  Scott T. Rickard,et al.  A formal study of the nonlinearity and consistency of the Empirical Mode Decomposition , 2012, Signal Process..

[40]  Robert Haslinger,et al.  The Computational Structure of Spike Trains , 2009, Neural Computation.

[41]  C. M. Place,et al.  An Introduction to Dynamical Systems , 1990 .

[42]  Eric A Sobie,et al.  An Introduction to Dynamical Systems , 2011, Science Signaling.

[43]  José M. Amigó,et al.  The equality of Kolmogorov–Sinai entropy and metric permutation entropy generalized , 2012 .

[44]  Francisco de A. T. de Carvalho,et al.  Selected Contributions in Data Analysis and Classification , 2007 .

[45]  Mathieu Sinn,et al.  Ordinal analysis of time series , 2005 .

[46]  E. Marder,et al.  Central pattern generators and the control of rhythmic movements , 2001, Current Biology.

[47]  Mathieu Sinn,et al.  Kolmogorov-Sinai entropy from the ordinal viewpoint , 2010 .

[48]  Tak-Chung Fu,et al.  A review on time series data mining , 2011, Eng. Appl. Artif. Intell..

[49]  L. G. Gamero,et al.  Wavelet analysis and nonlinear dynamics in a nonextensive setting , 1997 .

[50]  Pablo Varona,et al.  Robust Transient Dynamics and Brain Functions , 2011, Front. Comput. Neurosci..

[51]  Shaul Mukamel,et al.  Multidimensional measures of impulsively driven stochastic systems based on the Kullback-Leibler distance. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Garrett Stuck,et al.  Introduction to Dynamical Systems , 2003 .

[53]  H. Nyquist,et al.  Certain Topics in Telegraph Transmission Theory , 1928, Transactions of the American Institute of Electrical Engineers.

[54]  C. Piccardi.  On parameter estimation of chaotic systems via symbolic time-series analysis. , 2006, Chaos.

[55]  J. Rogers.  Chaos , 1876 .

[56]  Pablo Varona,et al.  Information flow dynamics in the brain. , 2012, Physics of life reviews.

[57]  D. P. Mandic,et al.  Multivariate empirical mode decomposition , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[58]  Niels Wessel,et al.  Classifying cardiac biosignals using ordinal pattern statistics and symbolic dynamics , 2012, Comput. Biol. Medicine.

[59]  Gonzalo Alvarez,et al.  Cryptanalysis of a family of self-synchronizing chaotic stream ciphers , 2009, 0903.2928.

[60]  Miguel A. F. Sanjuán,et al.  Combinatorial detection of determinism in noisy time series , 2008 .

[61]  M. Mirzakhani,et al.  Introduction to Ergodic theory , 2010 .

[62]  Asok Ray,et al.  Symbolic time series analysis via wavelet-based partitioning , 2006 .

[63]  A I Selverston,et al.  Nonlinear behavior of sinusoidally forced pyloric pacemaker neurons. , 2001, Journal of neurophysiology.

[64]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[65]  Karl J. Friston,et al.  Recognizing Sequences of Sequences , 2009, PLoS Comput. Biol..