Abstract
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 http://dx.doi.org/10.7488/ds/1477.
Highlights
An important challenge in signal processing is to quantify the dynamical irregularity of time series [1]
The results showed that RCMFEσ-based features lead to higher classification accuracies in comparison with the RCMFEμ-based ones
Using the Lorentz system, we find that RCMFEσ, RCMFEμ, MSEμ, and refined composite MSEμ (RCMSEμ) respectively shown in Fig. 7q–t can distinguish two different non-linear dynamics
Summary
An important challenge in signal processing is to quantify the dynamical irregularity of time series [1]. To this end, there are a number of approaches, such as entropies and fractal dimensions. One of the most popular entropy-based approaches is sample entropy (SampEn), which is relatively robust to noise [2]. Another widely used entropy method is fuzzy entropy (FuzEn) [3]. These two entropy approaches have attracted a great deal of attention recently [4,5,6,7]. SampEn is slightly faster than FuzEn, the latter is more consistent and less dependent on the data length [3, 7]
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