Symbolic Analysis of High-Dimensional Time Series

In order to extract and to visualize qualitative information from a high-dimensional time series, we apply ideas from symbolic dynamics. Counting certain ordinal patterns in the given series, we obtain a series of matrices whose entries are symbol frequencies. This matrix series is explored by simple methods from nominal statistics and information theory. The method is applied to detect and visualize qualitative changes of EEG data related to epileptic activity.

[1]  Werner Ebeling,et al.  Word frequency and entropy of symbolic sequences: a dynamical perspective , 1992 .

[2]  I. Grosse,et al.  MEASURING CORRELATIONS IN SYMBOL SEQUENCES , 1995 .

[3]  Gilbert Saporta,et al.  L'analyse des données , 1981 .

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

[5]  R. Clarke,et al.  Theory and Applications of Correspondence Analysis , 1985 .

[6]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[7]  P. Agostino Accardo,et al.  Use of the fractal dimension for the analysis of electroencephalographic time series , 1997, Biological Cybernetics.

[8]  James Theiler,et al.  On the evidence for how-dimensional chaos in an epileptic electroencephalogram , 1995 .

[9]  Alfréd Rényi.  Wahrscheinlichkeitsrechnung : mit einem Anhang über Informationstheorie , 1979 .

[10]  G. Keller,et al.  Entropy of interval maps via permutations , 2002 .

[11]  Annette Witt,et al.  Analysis of solar spike events by means of symbolic dynamics methods , 1993 .

[12]  C. Finney,et al.  Symbol Statistics: A New Tool for Understanding Multiphase Flow Phenomena , 1998, Heat Transfer: Volume 5 — Numerical and Experimental Methods in Heat Transfer.

[13]  C. S. Daw,et al.  Symbolic Time-Series Analysis of Engine Combustion Measurements , 1998 .

[14]  A. Sahs,et al.  Atlas of pediatric electroencephalography , 1982 .

[15]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[16]  David E. Hapeman.  Statistical Analysis of Categorical Data , 2000, Technometrics.

[17]  Klaus Lehnertz,et al.  POSSIBLE CLINICAL AND RESEARCH APPLICATIONS OF NONLINEAR EEG ANALYSIS IN HUMANS , 2000 .

[18]  B. Hao,et al.  Applied Symbolic Dynamics and Chaos , 1998 .