10/2/2023 0 Comments Entropy is a measure of![]() These measures have been applied with great success to numerous research fields, including heart rate variability, cardiovascular control, cerebrovascular dynamics, cardiac arrhythmias, financial time series analysis, gait and posture, climatology, earth sciences, cellular automata, electromyography, electroencephalography, magnetoencephalography, functional neuroimaging, and others. In fact, the popularity of entropy measures stems from their applicability to short and noisy processes with important stochastic components such as those describing the dynamical activity of real-world systems. These measures have emerged as a less ambitious but more practical alternative to classical techniques for the analysis of nonlinear dynamical systems, like correlation dimension, Lyapunov exponents, and nonlinear prediction methods. ![]() A variety of measures rooted in the concept of entropy and implemented according to several estimation approaches have been proposed, including approximate entropy, sample entropy, corrected conditional entropy, fuzzy entropy, compression entropy, permutation entropy, distribution entropy, multiscale entropy, self entropy and information storage. In this context, the utilization of tools taken from information theory has become extremely popular for the assessment of the degree of complexity of physical, biological, physiological, social, and econometric systems. ![]() The growing awareness that many real-world systems exhibit complex dynamics that are challenging to quantify has initiated extensive interest in developing measures and approaches for time series analysis to characterize these systems. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). ![]() However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields.
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