Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals

Author: Airton Monte Serrat Borin Jr1, Anne Humeau-Heurtier2, Luiz Eduardo Virgílio Silva3, Luiz Otávio Murta Jr4
1 Federal Institute of Education, Science and Technology of Triangulo Mineiro, Uberaba 38064-790, Brazil.
2 LARIS-Laboratoire Angevin de Recherche en Ingénierie des Systèmes, University of Angers, 49035 Angers, France.
3 Department of Internal Medicine, Ribeirão Preto Medical School, University of São Paulo, Ribeirão Preto 14049-900, Brazil.
4 Department of Computing and Mathematics, School of Philosophy, Sciences and Languages of Ribeirão Preto, University of São Paulo, Ribeirão Preto 14040-901, Brazil.
Conference/Journal: Entropy (Basel)
Date published: 2021 Dec 1
Other: Volume ID: 23 , Issue ID: 12 , Pages: 1620 , Special Notes: doi: 10.3390/e23121620. , Word Count: 193

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.

Keywords: multiscale fuzzy entropy; time series.

PMID: 34945926 DOI: 10.3390/e23121620