Multi-scale entropy analysis and Hurst exponent

Complexity of spontaneous BOLD activity in default mode network is correlated with cognitive function in normal male elderly: a multiscale entropy analysis

Cardiovascular systems essentially have multiscale control mechanisms. Multiscale entropy (MSE) analysis permits the dynamic characterization of the cardiovascular time series for both short-term and long-term processes, and thus can be more illuminating. The traditional MSE analysis for heart rate variability (HRV) is performed on the original RR interval time series (named as MSE_RR). In this study, we proposed an MSE analysis for the differential RR interval time series signal, named as MSE_dRR. The motivation of using the differential RR interval time series signal is that this signal has a direct link with the inherent non-linear property of electrical rhythm of the heart. The effectiveness of the MSE_RR and MSE_dRR were tested and compared on the long-term MIT-Boston’s Beth Israel Hospital (MIT-BIH) 54 normal sinus rhythm (NSR) and 29 congestive heart failure (CHF) RR interval recordings, aiming to explore which one is better for distinguishing the CHF patients from the NSR subjects. Four RR interval length for analysis were used ( N = 500 , N = 1000 , N = 2000 and N = 5000 ). The results showed that MSE_RR did not report significant differences between the NSR and CHF groups at several scales for each RR segment length type (Scales 7, 8 and 10 for N = 500 , Scales 3 and 10 for N = 1000 , Scales 2 and 3 for both N = 2000 and N = 5000 ). However, the new MSE_dRR gave significant separation for the two groups for all RR segment length types except N = 500 at Scales 9 and 10. The area under curve (AUC) values from the receiver operating characteristic (ROC) curve were used to further quantify the performances. The mean AUC of the new MSE_dRR from Scales 1–10 are 79.5%, 83.1%, 83.5% and 83.1% for N = 500 , N = 1000 , N = 2000 and N = 5000 , respectively, whereas the mean AUC of MSE_RR are only 68.6%, 69.8%, 69.6% and 67.1%, respectively. The five-fold cross validation support vector machine (SVM) classifier reports the classification Accuracy ( A c c ) of MSE_RR as 73.5%, 75.9% and 74.6% for N = 1000 , N = 2000 and N = 5000 , respectively, while for the new MSE_dRR analysis accuracy was 85.5%, 85.6% and 85.6%. Different biosignal editing methods (direct deletion and interpolation) did not change the analytical results. In summary, this study demonstrated that compared with MSE_RR, MSE_dRR reports better statistical stability and better discrimination ability for the NSR and CHF groups.

Characterization of Electromyogram (EMG) signals is important for identifying neuromuscular diseases. Although various techniques were implemented for classification, none of them were implemented in the complexity domain. In this study, characterization of EMG signals recorded from healthy, neuropathic and myopathic subjects has been performed in complexity domain based on Multiscale Entropy (MSE) method. To do this, the multiscale entropy method has been applied to an EMG database publicly available in PhysioNet. The complexity profile curves obtained with the MSE approach have shown promising classification among healthy subject, neuropathic and myopathic patients in terms of complexity. One way ANOVA test has shown statistically significant differences (p<0.01) among these three classes. Moreover, Support Vector Machine (SVM) has demonstrated a classification accuracy of 86.1% for characterizing EMG signals of neuromuscular disorders. Furthermore, myopathic and neuropathic patients have been recognized with 66.7% sensitivity at 95.8% specificity and 100% sensitivity at 100% specificity respectively.

Quantifying the complexity of physiologic time series has been of considerable interest. Several entropy-based measures have been proposed, although there is no straightforward correspondence between entropy and complexity. These traditional algorithms may generate misleading results because an increase in system entropy is not always associated with an increase in its complexity, and because the algorithms are based on single time scales. Recently, we introduced a new method, multiscale entropy (MSE) analysis, to calculate entropy over a wide range of scales. In this study, we sought to determine whether loss of complexity due to aging could be distinguished from that due to major cardiac pathology. We analyzed RR time series from young subjects (n = 26), elderly subjects (n = 46) and subjects with congestive heart failure (n = 43). The mean MSE measures of each of the three groups revealed characteristic curves, suggesting that they capture fundamental changes in the heart rate dynamics due to age and disease. We used Fisher's linear discriminant to evaluate the use of MSE features for classification. In discriminant tests on the training data, we found that MSE features could separate elderly, young and heart failure subjects with 92% accuracy and that older healthy subjects (mean age = 65.9) could be separated from subjects with heart failure (mean age = 55.5) with 94% accuracy. Also, we discriminated data from heart failure subjects and elderly healthy subjects with a positive predictivity of 76% and a specificity of 83% using only the MSE features. Larger databases will be needed to confirm if automatic classification results can match separation results. We conclude that MSE features capture differences in complexity due to aging and heart failure. These differences have implications for modeling neuroautonomic perturbations in health and disease.

The recognition of partial discharge mode is an important indicator of the insulation condition in transformers, based on which maintenance can be arranged. Discharge feature extraction is the key to recognize discharge mode. To solve the problem of poor stability and low recognition rate of partial discharge mode, this paper proposes a feature extraction method based on synchrosqueezed windowed Fourier transform and multi-scale dispersion entropy. First, the four partial discharge signals collected under laboratory conditions are decomposed by synchrosqueezed windowed Fourier transform, then a number of band-limited intrinsic mode type functions are obtained, and the original feature quantities of partial discharge signals are obtained by calculating the multi-scale dispersion entropies of each intrinsic mode type function. Based on that, original feature quantity is optimized by using the maximum relevance and minimum redundancy criteria. Finally, the classification is implemented by the support vector machine. Experimental results show that in the case of noise interference, the proposed synchrosqueezed windowed Fourier transform–multi-scale dispersion entropy method can still accurately describe the feature of different discharge signals and has a higher recognition rate than both the empirical mode decomposition–multi-scale dispersion entropy method and the direct multi-scale dispersion entropy method.

This paper presents a novel framework for the complexity analysis of rainfall, runoff, and runoff coefficient (RC) time series using multiscale entropy (MSE). The MSE analysis of RC time series was used to investigate changes in the complexity of rainfall-runoff processes due to human activities. Firstly, a coarse graining process was applied to a time series. The sample entropy was then computed for each coarse-grained time series, and plotted as a function of the scale factor. The proposed method was tested in a case study of daily rainfall and runoff data for the upstream Wu–Tu watershed. Results show that the entropy measures of rainfall time series are higher than those of runoff time series at all scale factors. The entropy measures of the RC time series are between the entropy measures of the rainfall and runoff time series at various scale factors. Results also show that the entropy values of rainfall, runoff, and RC time series increase as scale factors increase. The changes in the complexity of RC time series indicate the changes of rainfall-runoff relations due to human activities and provide a reference for the selection of rainfall-runoff models that are capable of dealing with great complexity and take into account of obvious self-similarity can be suggested to the modeling of rainfall-runoff processes. Moreover, the robustness of the MSE results were tested to confirm that MSE analysis is consistent and the same results when removing 25% data, making this approach suitable for the complexity analysis of rainfall, runoff, and RC time series.

In this paper, we propose a new cross-sample entropy, namely the composite multiscale partial cross-sample entropy (CMPCSE), for quantifying the intrinsic similarity of two time series affected by common external factors. First, in order to test the validity of CMPCSE, we apply it to three sets of artificial data. Experimental results show that CMPCSE can accurately measure the intrinsic cross-sample entropy of two simultaneously recorded time series by removing the effects from the third time series. Then CMPCSE is employed to investigate the partial cross-sample entropy of Shanghai securities composite index (SSEC) and Shenzhen Stock Exchange Component Index (SZSE) by eliminating the effect of Hang Seng Index (HSI). Compared with the composite multiscale cross-sample entropy, the results obtained by CMPCSE show that SSEC and SZSE have stronger similarity. We believe that CMPCSE is an effective tool to study intrinsic similarity of two time series.

The present study explored multi-scale entropy (MSE) analysis to investigate the entropy of resting state fMRI signals across multiple time scales. MSE analysis was developed to distinguish random noise from complex signals since the entropy of the former decreases with longer time scales while the latter signal maintains its entropy due to a "self-resemblance" across time scales. A long resting state BOLD fMRI (rs-fMRI) scan with 1000 data points was performed on five healthy young volunteers to investigate the spatial and temporal characteristics of entropy across multiple time scales. A shorter rs-fMRI scan with 240 data points was performed on a cohort of subjects consisting of healthy young (age 23 ± 2 years, n = 8) and aged volunteers (age 66 ± 3 years, n = 8) to investigate the effect of healthy aging on the entropy of rs-fMRI. The results showed that MSE of gray matter, rather than white matter, resembles closely that of f (-1) noise over multiple time scales. By filtering out high frequency random fluctuations, MSE analysis is able to reveal enhanced contrast in entropy between gray and white matter, as well as between age groups at longer time scales. Our data support the use of MSE analysis as a validation metric for quantifying the complexity of rs-fMRI signals.

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

Characterizing nonlinear dynamic behaviors in the 3D near-surface wind field is a challenging problem of significant importance. The study of pollutant transport, wind power evaluation, forest damage assessment, among others, would benefit from this research. In this paper, we first use a high-resolution 3D ultrasonic anemometer to simultaneously measure three wind components. Then the multiscale entropy (MSE) and multivariate multiscale entropy (MMSE) method are employed to quantitatively analyze complexity of the 3D wind speed/direction signals with different time lags respectively. Results suggest that the vertical wind speed time series is more complex than the two horizontal ones. Moreover, the results of MSE show that the complexity of one vertical wind direction signal is similar to that of the horizontal one, while the complexity of another vertical wind direction signal is very low compared with the horizontal one. Furthermore, the results of MMSE indicate that the two combined vertical wind direction signals and the horizontal one exhibit very similar complexity. These interesting findings suggest that the MSE and MMSE can potentially be useful tools for uncovering the complex dynamic behaviors underlying the 3D wind variation records.

A method based on compound multiscale permutation entropy, support vector machine, and particle swarm optimization for roller bearings fault diagnosis was presented in this study. Firstly, the roller bearings vibration signals under different conditions were decomposed into permutation entropy values by the multiscale permutation entropy and compound multiscale permutation entropy methods. The compound multiscale permutation entropy model combined the different graining sequence information under each scale factor. The average value of each scale factor was regarded as the final entropy value in the compound multiscale permutation entropy model. The compound multiscale permutation entropy model suppressed the shortcomings of poor stability caused by the length of the original signals in the multiscale permutation entropy model. Validity and accuracy are considered in the numerical experiments, and then compared with the computational efficiency of the multiscale permutation entropy method. Secondly, the entropy values of the multiscale permutation entropy/compound multiscale permutation entropy under different scales are regarded as the input of the particle swarm optimization–support vector machine models for fulfilling the fault identification, the classification accuracy is used to verify the effectiveness of the multiscale permutation entropy/compound multiscale permutation entropy with particle swarm optimization–support vector machine. Finally, the experimental results show that the classification accuracy of the compound multiscale permutation entropy model is higher than that of the multiscale permutation entropy.

The recently introduced multiscale entropy (MSE) method accounts for long range correlations over multiple time scales and can therefore reveal the complexity of biological signals. The existing MSE algorithm deals with scalar time series whereas multivariate time series are common in experimental and biological systems. To that cause, in this paper the MSE method is extended to the multivariate case. This allows us to gain a greater insight into the complexity of the underlying signal generating system, producing multifaceted and more robust estimates than standard single channel MSE. Simulations on both synthetic data and brain consciousness analysis support the approach.

Objective. This study explored the feasibility of detecting hidden muscle activity in surface electromyogram (EMG) baseline. Approach. Power spectral density (PSD) analysis and multi-scale entropy (MSE) analysis were used. Both analyses were applied to computer simulations of surface EMG baseline with the presence (representing activity data) or absence (representing reference data) of hidden muscle activity, as well as surface electrode array EMG baseline recordings of healthy control and amyotrophic lateral sclerosis (ALS) subjects. Main results. Although the simulated reference data and the activity data yielded no distinguishable difference in the time domain, they demonstrated a significant difference in the frequency and signal complexity domains with the PSD and MSE analyses. For a comparison using pooled data, such a difference was also observed when the PSD and MSE analyses were applied to surface electrode array EMG baseline recordings of healthy control and ALS subjects, which demonstrated no distinguishable difference in the time domain. Compared with the PSD analysis, the MSE analysis appeared to be more sensitive for detecting the difference in surface EMG baselines between the two groups. Significance. The findings implied the presence of a hidden muscle activity in surface EMG baseline recordings from the ALS subjects. To promote the presented analysis as a useful diagnostic or investigatory tool, future studies are necessary to assess the pathophysiological nature or origins of the hidden muscle activity, as well as the baseline difference at the individual subject level.

To solve the defects that the generalization ability of the traditional data-driven fault diagnosis model reduces or even fails in mechanical system diagnosis, a multi-scale transfer sample entropy is proposed based on the idea of transfer learning. First, the multi-scale transfer sample entropy method is proposed to extract fault features based on multi-scale sample entropy and feature transfer learning. Second, the parameters of the multiscale transfer sample entropy method are optimized to further improve the fault identification accuracy. Finally, the experiment results of rolling bearing show that the proposed multi-scale transfer sample entropy can effectively improve the generalization ability of the data-driven model and realize the accurate identification of different fault locations of the rolling bearing under a small number of samples.

Dynamic characteristics of absence EEG recordings with multiscale permutation entropy analysis