Coarse-grained entropy rates for characterization of complex time series

Milan Palus
Santa Fe Institute, 1399 Hyde Park Road
Santa Fe, NM 87501, USA; and
Institute of Computer Science, Academy of Sciences of the Czech Republic
Pod vodárenskou vezí 2, 182 07 Prague 8, Czech Republic
E-mail: mp@uivt.cas.cz, mp@santafe.edu

Abstract:

A method for classification of complex time series using coarse-grained entropy rates (CER's) is presented. The CER's, which are computed from information-theoretic functionals -- redundancies, are relative measures of regularity and predictability, and for data generated by dynamical systems they are related to Kolmogorov-Sinai entropy. A deterministic dynamical origin of the data under study, however, is not a necessary condition for the use of the CER's, since the entropy rates can be defined for stochastic processes as well. Sensitivity of the CER's to changes in data dynamics and their robustness with respect to noise are tested by using numerically generated time series resulted from both deterministic -- chaotic and stochastic processes. Potential application of the CER's in analysis of physiological signals or other complex time series is demonstrated by using examples from pharmaco-EEG and tremor classification.