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 (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions—as a function of time series length—present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

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