Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis

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 10.7488/ds/1477.

Multivariate Generalized Multiscale Entropy Analysis

“…For scales lower than 40, the multivariate data with channels containing only white noise show higher multivariate sample entropy than multivariate data with channels containing only 1/ f noise. Others have reported similar findings for univariate data [19]. Therefore, the scale for which the multivariate data containing only 1/ f noise shows larger entropy values than those of multivariate data containing only white noise is larger than what was observed with MGMSE µ : for scales lower than 40, trivariate data containing channels with only 1/ f noise have a lower multivariate sample entropy than trivariate data containing channels with only white noise; for MGMSE µ , for scales larger than 2, trivariate data containing channels with only 1/ f noise have a larger multivariate sample entropy than trivariate data containing channels with only white noise (see Figures 2a,b).…”

“…In our work, the parameter r was kept constant, as done in other studies [6,19]. However, the coarse-graining procedure is similar to smoothing and decimation of the original sequences [34].…”

Multiscale Fluctuation-Based Dispersion Entropy and Its Applications to Neurological Diseases

“…In spite of its popularity, MSE is undefined or unreliable for very short signals and computationally complex for real-time applications as a result of using SampEn [10], [15]. To address these shortcomings, multiscale PerEn (MPE) was proposed [15].…”

Electroencephalogram Profiles for Emotion Identification over the Brain Regions Using Spectral, Entropy and Temporal Biomarkers

“…Moreover, entropy has been considered as the most prevalent methods to evaluate the presence or absence of long-range dependence on physiological signal analysis including approximate entropy (ApEn), sample entropy (SampEn) and permutation entropy (PerEn) which are relatively robust to noise and powerful enough to quantify the complexity of a time series [62]. Amplitude-aware permutation entropy (AAPE) has demonstrated efficiency in discriminating between calmness and distress [63][64][65]. Fuzzy entropy (FuzEn) was proposed for EEG analysis in [66,67].…”