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      Approximate entropy (ApEn) as a complexity measure.

      Chaos (Woodbury, N.Y.)

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          Abstract

          Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity, which appears to have potential application to a wide variety of relatively short (greater than 100 points) and noisy time-series data. The development of ApEn was motivated by data length constraints commonly encountered, e.g., in heart rate, EEG, and endocrine hormone secretion data sets. We describe ApEn implementation and interpretation, indicating its utility to distinguish correlated stochastic processes, and composite deterministic/ stochastic models. We discuss the key technical idea that motivates ApEn, that one need not fully reconstruct an attractor to discriminate in a statistically valid manner-marginal probability distributions often suffice for this purpose. Finally, we discuss why algorithms to compute, e.g., correlation dimension and the Kolmogorov-Sinai (KS) entropy, often work well for true dynamical systems, yet sometimes operationally confound for general models, with the aid of visual representations of reconstructed dynamics for two contrasting processes. (c) 1995 American Institute of Physics.

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          Most cited references 17

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          Ergodic theory of chaos and strange attractors

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            Approximate entropy as a measure of system complexity.

             S Pincus (1991)
            Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.
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              Measuring the strangeness of strange attractors

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                Author and article information

                Journal
                12780163
                10.1063/1.166092

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