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

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

Entropy ◽

10.3390/e23121620 ◽

2021 ◽

Vol 23 (12) ◽

pp. 1620

Author(s):

Airton Borin ◽

Anne Humeau-Heurtier ◽

Luiz Virgílio Silva ◽

Luiz Murta

Keyword(s):

Time Series ◽

Multiscale Entropy ◽

Short Term ◽

Series Length ◽

Short Time Series ◽

Fuzzy Algorithms ◽

Computing Performance ◽

Similar Accuracy ◽

Short Time

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.

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Maximum entropy analysis of short time‐series biomedical rhythms

Journal of Interdisiplinary Cycle Research ◽

10.1080/09291017909359665 ◽

1979 ◽

Vol 10 (2) ◽

pp. 145-163 ◽

Cited By ~ 5

Author(s):

D. A. Linkens

Keyword(s):

Time Series ◽

Maximum Entropy ◽

Entropy Analysis ◽

Short Time Series ◽

Short Time

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Improved Multiscale Entropy Technique with Nearest-Neighbor Moving-Average Kernel for Nonlinear and Nonstationary Short-Time Biomedical Signal Analysis

Journal of Healthcare Engineering ◽

10.1155/2018/8632436 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

S. P. Arunachalam ◽

S. Kapa ◽

S. K. Mulpuru ◽

P. A. Friedman ◽

E. G. Tolkacheva

Keyword(s):

Time Series ◽

Nearest Neighbor ◽

Ex Vivo ◽

Moving Average ◽

Multiscale Entropy ◽

Series Data ◽

Physiological Data ◽

Short Time Series ◽

Biomedical Signals ◽

Short Time

Analysis of biomedical signals can yield invaluable information for prognosis, diagnosis, therapy evaluation, risk assessment, and disease prevention which is often recorded as short time series data that challenges existing complexity classification algorithms such as Shannon entropy (SE) and other techniques. The purpose of this study was to improve previously developed multiscale entropy (MSE) technique by incorporating nearest-neighbor moving-average kernel, which can be used for analysis of nonlinear and non-stationary short time series physiological data. The approach was tested for robustness with respect to noise analysis using simulated sinusoidal and ECG waveforms. Feasibility of MSE to discriminate between normal sinus rhythm (NSR) and atrial fibrillation (AF) was tested on a single-lead ECG. In addition, the MSE algorithm was applied to identify pivot points of rotors that were induced in ex vivo isolated rabbit hearts. The improved MSE technique robustly estimated the complexity of the signal compared to that of SE with various noises, discriminated NSR and AF on single-lead ECG, and precisely identified the pivot points of ex vivo rotors by providing better contrast between the rotor core and the peripheral region. The improved MSE technique can provide efficient complexity analysis of variety of nonlinear and nonstationary short-time biomedical signals.

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Multiscale Entropy Analysis of Page Views: A Case Study of Wikipedia

Entropy ◽

10.3390/e21030229 ◽

2019 ◽

Vol 21 (3) ◽

pp. 229 ◽

Cited By ~ 2

Author(s):

Chao Xu ◽

Chen Xu ◽

Wenjing Tian ◽

Anqing Hu ◽

Rui Jiang

Keyword(s):

Temporal Variations ◽

Multiscale Entropy ◽

Rank Test ◽

Entropy Analysis ◽

Short Time Series ◽

The Past ◽

Signed Rank ◽

Signed Rank Test ◽

Short Time

In this study, the Wikipedia page views for four selected topics, namely, education, the economy/finance, medicine, and nature/environment from 2016–2018 are collected and the sample entropies of the three years’ page views are estimated and investigated using a short-time series multiscale entropy (sMSE) algorithm for a comprehensible understanding of the complexity of human website searching activities. The sample entropies of the selected topics are found to exhibit different temporal variations. In the past three years, the temporal characteristics of the sample entropies are vividly revealed, and the sample entropies of the selected topics follow the same tendencies and can be quantitatively ranked. By taking the 95% confidence interval into account, the temporal variations of sample entropies are further validated by statistical analysis (non-parametric), including the Wilcoxon signed-rank test and the Mann-Whitney U-test. The results suggest that the sample entropies estimated by the sMSE algorithm are feasible for analyzing the temporal variations of complexity for certain topics, whereas the regular variations of estimated sample entropies of different selected topics can’t simply be accepted as is. Potential explanations and paths in forthcoming studies are also described and discussed.

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A strategy for meta-analysis of short time series microarray datasets

Frontiers in Bioscience ◽

10.2741/3512 ◽

2009 ◽

Vol Volume (14) ◽

pp. 4058 ◽

Cited By ~ 2

Author(s):

Ruping Sun

Keyword(s):

Time Series ◽

Meta Analysis ◽

Short Time Series ◽

Microarray Datasets ◽

Short Time ◽

Time Series Microarray

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Identifying bidirectional total and non-linear information flow in functional corticomuscular coupling during a dorsiflexion task: a pilot study

Journal of NeuroEngineering and Rehabilitation ◽

10.1186/s12984-021-00872-w ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Tie Liang ◽

Qingyu Zhang ◽

Xiaoguang Liu ◽

Bin Dong ◽

Xiuling Liu ◽

...

Keyword(s):

Time Series ◽

Information Flow ◽

Gamma Band ◽

Motor Dysfunction ◽

Beta Band ◽

Short Time Series ◽

Information Interaction ◽

Stroke Group ◽

Short Time ◽

Maximal Information Coefficient

Abstract Background The key challenge to constructing functional corticomuscular coupling (FCMC) is to accurately identify the direction and strength of the information flow between scalp electroencephalography (EEG) and surface electromyography (SEMG). Traditional TE and TDMI methods have difficulty in identifying the information interaction for short time series as they tend to rely on long and stable data, so we propose a time-delayed maximal information coefficient (TDMIC) method. With this method, we aim to investigate the directional specificity of bidirectional total and nonlinear information flow on FCMC, and to explore the neural mechanisms underlying motor dysfunction in stroke patients. Methods We introduced a time-delayed parameter in the maximal information coefficient to capture the direction of information interaction between two time series. We employed the linear and non-linear system model based on short data to verify the validity of our algorithm. We then used the TDMIC method to study the characteristics of total and nonlinear information flow in FCMC during a dorsiflexion task for healthy controls and stroke patients. Results The simulation results showed that the TDMIC method can better detect the direction of information interaction compared with TE and TDMI methods. For healthy controls, the beta band (14–30 Hz) had higher information flow in FCMC than the gamma band (31–45 Hz). Furthermore, the beta-band total and nonlinear information flow in the descending direction (EEG to EMG) was significantly higher than that in the ascending direction (EMG to EEG), whereas in the gamma band the ascending direction had significantly higher information flow than the descending direction. Additionally, we found that the strong bidirectional information flow mainly acted on Cz, C3, CP3, P3 and CPz. Compared to controls, both the beta-and gamma-band bidirectional total and nonlinear information flows of the stroke group were significantly weaker. There is no significant difference in the direction of beta- and gamma-band information flow in stroke group. Conclusions The proposed method could effectively identify the information interaction between short time series. According to our experiment, the beta band mainly passes downward motor control information while the gamma band features upward sensory feedback information delivery. Our observation demonstrate that the center and contralateral sensorimotor cortex play a major role in lower limb motor control. The study further demonstrates that brain damage caused by stroke disrupts the bidirectional information interaction between cortex and effector muscles in the sensorimotor system, leading to motor dysfunction.

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