Modified multiscale fuzzy entropy: A robust method for short-term physiologic signals

Abstract

The introduction of the multiscale entropy (MSE) method was a milestone in the field of complex physiological signal analysis. However, since MSE is inapplicable for short signals, several variants of MSE have been proposed. One of the most important variants of MSE is the modified multiscale entropy (MMSE), even though it can still produce biased estimates due to the hard similarity criteria of sample entropy. Taking the advantages of MMSE and the concept of fuzzy entropy, we propose the modified multiscale fuzzy entropy (MMFE). We evaluated the robustness of MMSE and MMFE using segmented stochastic noises and actual heart rate variability series and compared it with the classical MSE results obtained with the full signals. Results show that MMFE is much more robust than MMSE for short physiological time series, resembling MSE for series as shorter as 400 samples. We also show the existence of an exponential relationship between the MMFE fuzzy parameter and the signal size. We suggest the use of this relationship to choose the optimal MMFE parameter as part of the method.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants

“…4. Although a similar error plot can be found in a previous study [5], here we expanded the range of exponents evaluated to calculate the minimum MMFE error. Error curves are illustrated for the fuzzy exponents ranging from n = 0.8 to n = 1.5 (rats) and n = 0.85 to n = 0.92 (humans).…”

“…The average time consumed to process three randomly selected human HRV series is reported as a segment size function (from 400 to 12000 points). The fuzzy exponent n adopted in this experiment followed the equation previously found for the choice of the best exponent according to the segment size (x) [5]:…”

“…MMFE was recently proposed [5] and consists in the application of the same coarse-graining procedure as MMSE (Eq. 22) followed by the estimation of entropy using a delayed version of FuzzyEn, with a delay equal to τ for each scale.…”

“…Heart rate variability (HRV) series from rats and humans were obtained from previous studies [5,17]. [11].…”

“…Both CMFE and RCMFE were evaluated in the biomedical and non-biomedical contexts [23] [2]. In a recent study, we proposed and evaluated the modified multiscale fuzzy entropy (MMFE) for heart rate variability (HRV) analysis [5]. In a systematic comparison, we showed that MMFE is more robust for estimating original MSE than MMSE when the fuzzy parameter is optimized.…”