scholarly journals Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Luca Faes ◽  
Alberto Porta ◽  
Michal Javorka ◽  
Giandomenico Nollo
Keyword(s):  
Time Series ◽  
State Space ◽  
Physiological Stress ◽  
Parametric Representation ◽  
Analytical Framework ◽  
Multiscale Entropy ◽  
Efficient Computation ◽  
Temporal Scales ◽  
Linear State ◽  
Short Time

The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE) and refined MSE (RMSE) measures. In spite of their popularity, MSE and RMSE lack an analytical framework allowing their calculation for known dynamic processes and cannot be reliably computed over short time series. To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state-space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the complexity of the process. The resulting linear MSE (LMSE) measure is first tested in simulations, both theoretically to relate the multiscale complexity of AR processes to their dynamical properties and over short process realizations to assess its computational reliability in comparison with RMSE. Then, it is applied to the time series of heart period, arterial pressure, and respiration measured for healthy subjects monitored in resting conditions and during physiological stress. This application to short-term cardiovascular variability documents that LMSE can describe better than RMSE the activity of physiological mechanisms producing biological oscillations at different temporal scales.

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

2021 ◽  
Author(s):  
Airton Monte Serrat Borin ◽  
Anne Humeau-Heurtier ◽  
Luiz Otavio Murta ◽  
Luiz Eduardo Virgilio Silva
Keyword(s):  
Time Series ◽  
Multiscale Entropy ◽  
Entropy Analysis ◽  
Short Term ◽  
Series Length ◽  
Short Time Series ◽  
Fuzzy Algorithms ◽  
Computing Performance ◽  
Similar Accuracy ◽  
Short Time

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.

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

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
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.

Physiological Time Series Processing via Empirical Wavelet Transform

2020 ◽  
Vol 12 (5) ◽  
pp. 582-587
Author(s):  
Omkar Singh
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Empirical Mode Decomposition ◽  
Multivariate Data ◽  
Multiscale Entropy ◽  
Entropy Analysis ◽  
Temporal Scales ◽  
Physiological Time ◽  
Mode Decomposition ◽  
Empirical Wavelet Transform

This paper presents the efficacy of empirical wavelet transform (EWT) for physiological time series processing. At first, EWT is applied to multivariate heterogeneous physiological time series. Secondly, EWT is used for the removal of fast temporal scales in multiscale entropy analysis. Empirical mode decomposition is an adaptive data analysis method in the sense that it does not require prior information about the signal statistics and tend to decompose a signal into various constituent modes. The utility of Standard EMD algorithm is however limited to single channel data as it suffers from the problems of mode alignment and mode mixing when applied channel wise for multivariate data. The standard EMD algorithm was extended to multivariate Empirical mode decomposition (MEMD) that can be used analyze a multivariate data. The MEMD can only be applied to multivariate data in which all the channels have equal data length. EWT is another adaptive technique for mode extraction in a signal using empirical scaling and wavelet functions. The multiscale entropy (MSE) algorithm is generally used to quantify the complexity of a time series. The original MSE approach utilizes a coarse-graining process for the removal of fast temporal scales in a time series which is equivalent to applying a finite impulse response (FIR) moving average filter. In Refined Multiscale entropy (RMSE), the FIR filter was replaced with a low pass Butterworth filter which exhibits a better frequency response than that of a FIR filter. In this paper we have presented a new approach for the removal of fast temporal scales based on empirical wavelet transform. The empirical wavelet transform is also used as an innovative filtering approach in multiscale entropy analysis.

scholarly journals Multiscale Complexity Analysis of Rainfall in Northeast Brazil

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3213
Author(s):  
Antonio Samuel Alves da Silva ◽  
Ikaro Daniel de Carvalho Barreto ◽  
Moacyr Cunha-Filho ◽  
Rômulo Simões Cezar Menezes ◽  
Borko Stosic ◽  
...  
Keyword(s):  
Complexity Analysis ◽  
Statistical Significance ◽  
Entropy Method ◽  
Multiscale Methods ◽  
Northeastern Brazil ◽  
Multiscale Entropy ◽  
Temporal Scales ◽  
Wide Range ◽  
One Year ◽  
Short Time

In this work, we analyze the complexity of monthly rainfall temporal series recorded from 1962 to 2012, at 133 gauge stations in the state of Pernambuco, northeastern Brazil. To this end, we employ the modified multiscale entropy method (MMSE), which is well suited for short time series, to analyze the rainfall regularity across a wide range of temporal scales, from one month to one year. We identify the temporal scales that distinguish rainfall regularity in the inland semiarid Sertão region, the transitional inland Agreste region, and the coastal, tropical humid Zona da Mata region, by comparing the results for stations across the study area and performing statistical significance tests. Our work contributes to the establishment of multiscale methods based on information theory in climatological studies.

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

Entropy ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document