We introduce a new entropy metric, AAPE, that enables us to consider amplitude information in the formulation of PE. The AAPE algorithm can be used in almost every irregularity-based application in various signal and image processing fields. We also made freely available the Matlab code of the AAPE.
Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel-Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.
Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of biomedical time series. Recent developments in the field have tried to alleviate the problem of undefined MSE values for short signals. Moreover, there has been a recent interest in using other statistical moments than the mean, i.e., variance, in the coarse-graining step of the MSE. Building on these trends, here we introduce the so-called refined composite multiscale fuzzy entropy based on the standard deviation (RCMFEσ) and mean (RCMFEμ) to quantify the dynamical properties of spread and mean, respectively, over multiple time scales. We demonstrate the dependency of the RCMFEσ and RCMFEμ, in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. The results evidenced that the RCMFEσ and RCMFEμ values are more stable and reliable than the classical multiscale entropy ones. We also inspect the ability of using the standard deviation as well as the mean in the coarse-graining process using magnetoencephalograms in Alzheimer’s disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicated that when the RCMFEμ cannot distinguish different types of dynamics of a particular time series at some scale factors, the RCMFEσ may do so, and vice versa. The results showed that RCMFEσ-based features lead to higher classification accuracies in comparison with the RCMFEμ-based ones. We also made freely available all the Matlab codes used in this study at 10.7488/ds/1477.
Permutation entropy (PE) is a well-known and fast method extensively used in many physiological signal processing applications to measure the irregularity of time series. Multiscale PE (MPE) is based on assessing the PE for a number of coarse-grained sequences representing temporal scales. However, the stability of the conventional MPE may be compromised for short time series. Here, we propose an improved MPE (IMPE) to reduce the variability of entropy measures over long temporal scales, leading to more reliable and stable results. We gain insight into the dependency of MPE and IMPE on several straightforward signal processing concepts which appear in biomedical activity via a set of synthetic signals. We also apply these techniques to real biomedical signals via publicly available electroencephalogram (EEG) recordings acquired with eyes open and closed and to ictal and non-ictal intracranial EEGs. We conclude that IMPE improves the reliability of the entropy estimations in comparison with the traditional MPE and that it is a promising technique to characterize physiological changes affecting several temporal scales. We provide the source codes of IMPE and the synthetic data in the public domain.
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