Multivariate Multiscale Entropy Research Articles

Refined composite multivariate generalized multiscale fuzzy entropy: A tool for complexity analysis of multichannel signals

Abstract Multiscale entropy (MSE) is an appealing tool to characterize the complexity of time series over multiple temporal scales. Recent developments in the field have tried to extend the MSE technique in different ways. Building on these trends, we propose the so-called refined composite multivariate multiscale fuzzy entropy (RCmvMFE) whose coarse-graining step uses variance (RCmvMFE σ 2 ) or mean (RCmvMFE μ ). We investigate the behavior of these multivariate methods on multichannel white Gaussian and 1/ f noise signals, and two publicly available biomedical recordings. Our simulations demonstrate that RCmvMFE σ 2 and RCmvMFE μ lead to more stable results and are less sensitive to the signals’ length in comparison with the other existing multivariate multiscale entropy-based methods. The classification results also show that using both the variance and mean in the coarse-graining step offers complexity profiles with complementary information for biomedical signal analysis. We also made freely available all the Matlab codes used in this paper.

MEMD-enhanced multivariate fuzzy entropy for the evaluation of complexity in biomedical signals.

Multivariate multiscale entropy (mvMSE) has been proposed as a combination of the coarse-graining process and multivariate sample entropy (mvSE) to quantify the irregularity of multivariate signals. However, both the coarse-graining process and mvSE may not be reliable for short signals. Although the coarse-graining process can be replaced with multivariate empirical mode decomposition (MEMD), the relative instability of mvSE for short signals remains a problem. Here, we address this issue by proposing the multivariate fuzzy entropy (mvFE) with a new fuzzy membership function. The results using white Gaussian noise show that the mvFE leads to more reliable and stable results, especially for short signals, in comparison with mvSE. Accordingly, we propose MEMD-enhanced mvFE to quantify the complexity of signals. The characteristics of brain regions influenced by partial epilepsy are investigated by focal and non-focal electroencephalogram (EEG) time series. In this sense, the proposed MEMD-enhanced mvFE and mvSE are employed to discriminate focal EEG signals from non-focal ones. The results demonstrate the MEMD-enhanced mvFE values have a smaller coefficient of variation in comparison with those obtained by the MEMD-enhanced mvSE, even for long signals. The results also show that the MEMD-enhanced mvFE has better performance to quantify focal and non-focal signals compared with multivariate multiscale permutation entropy.

Multivariate multiscale sample entropy of traffic time series

Multivariate time series are common in the traffic system and are necessary for understanding the property of the traffic system. This paper introduces the multivariate multiscale sample entropy (MMSE) to evaluate the complexity in multiple data channels over different timescales. We illustrate the necessity and advantage of MMSE method by comparing MMSE results with the multiscale sample entropy results on original and shuffled traffic time series, respectively. MMSE is capable of revealing the long-range correlations and providing robust estimates for the complexity of traffic time series. Then, we utilize the MMSE to assess relative complexity of normalized multichannel temporal data in the traffic system and also reveal the weekday and weekend patterns containing in traffic signals by MMSE. MMSE can provide more accurate and helpful knowledge about the complexity of traffic time series for the dynamics and inner mechanism of traffic system from the view of multiple variables.

Multivariate refined composite multiscale entropy analysis

Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE.

Characterizing slug to churn flow transition by using multivariate pseudo Wigner distribution and multivariate multiscale entropy

Uncovering transitional behavior of slug flow under different flow conditions constitutes a challenging problem of significant importance. Based on the experimental multi-channel measurements, we first calculate multivariate pseudo Wigner distribution (MPWD) and extract time–frequency features to probe the transient behavior of slug flow and churn flow. Then we calculate the multivariate multiscale sample entropy (MMSE) for different flow conditions and find that the MMSE allows us to uncover the dynamic flow behavior governing the transition from slug flow to churn flow. Our results indicate combining the MPWD and MMSE enables to reveal the transient and multiscale flow behavior underlying the formation and transition of slug flow and churn flow.

Information theoretic multiscale truncated SVD for multilead electrocardiogram

Background and objectiveIn this paper an information theory based multiscale singular value decomposition (SVD) is proposed for multilead electrocardiogram (ECG) signal processing. The shrinkage of singular values for different multivariate multiscale matrices at wavelet scales is based on information content. It aims to capture and preserve the information of clinically important local waves like P-waves, Q-waves, T-waves and QRS-complexes. MethodsThe information is derived through clinically relevant multivariate multiscale entropy in SVD domain modifying Shannon's entropy. This optimizes the approximate ranks for matrices to capture the clinical components of ECG signals appearing at different scales. A newly introduced multivariate clinical distortion (MCD) metric is computed and compared with existing subjective and objective signal distortion measures. The proposed method is tested with records from CSE multilead measurement library and PTB diagnostic ECG database for various pathological cases. ResultsIt gives average percentage root mean square difference (PRD), average normalized root mean square error (NRMSE), average wavelet energy based diagnostic distortion measure (WEDD) values 5.8879%, 0.0059 and 1.0760% respectively for myocarditis pathology. The corresponding MCD value is 1.9429%. The highest average PRD and average WEDD values are 11.4053% and 5.5194% for cardiomyopathy with the corresponding MCD value 1.4003%. ConclusionsBased on WEDD values and mean opinion scores (MOS), the quality group of all processed signals fall under excellent category.

Parameters Selection for Bivariate Multiscale Entropy Analysis of Postural Fluctuations in Fallers and Non-Fallers Older Adults.

Entropy measures are often used to quantify the regularity of postural sway time series. Recent methodological developments provided both multivariate and multiscale approaches allowing the extraction of complexity features from physiological signals; see "Dynamical complexity of human responses: A multivariate data-adaptive framework," in Bulletin of Polish Academy of Science and Technology, vol. 60, p. 433, 2012. The resulting entropy measures are good candidates for the analysis of bivariate postural sway signals exhibiting nonstationarity and multiscale properties. These methods are dependant on several input parameters such as embedding parameters. Using two data sets collected from institutionalized frail older adults, we numerically investigate the behavior of a recent multivariate and multiscale entropy estimator; see "Multivariate multiscale entropy: A tool for complexity analysis of multichannel data," Physics Review E, vol. 84, p. 061918, 2011. We propose criteria for the selection of the input parameters. Using these optimal parameters, we statistically compare the multivariate and multiscale entropy values of postural sway data of non-faller subjects to those of fallers. These two groups are discriminated by the resulting measures over multiple time scales. We also demonstrate that the typical parameter settings proposed in the literature lead to entropy measures that do not distinguish the two groups. This last result confirms the importance of the selection of appropriate input parameters.

Evaluation of resting-state magnetoencephalogram complexity in Alzheimer's disease with multivariate multiscale permutation and sample entropies.

Alzheimer's disease (AD) is one of the fastest growing neurological diseases in the world. We evaluate multivariate multiscale sample entropy (mvMSE) and multivariate multiscale permutation entropy (mvMPE) approaches to distinguish resting-state magnetoencephalogram (MEG) signals of 36 AD patients from those of 26 normal controls. We also discuss about choosing the appropriate embedding dimension value as an effective parameter for mvMPE and MPE for the first time. The results illustrate that both the mvMPE and mvMSE can be useful in the diagnosis of AD, although with different running times and abilities. In addition, our findings show that the MEG complexity analysis performed on deeper time scales by mvMPE and mvMSE may be a useful tool to characterize AD. In most scale factors, the average of the mvMPE and mvMSE values of AD patients are lower than those of controls.

Posture and Texting: Effect on Balance in Young Adults.

Using a mobile phone while doing another activity is a common dual-task activity in our daily lives. This study examined the effect of texting on the postural stability of young adults. Twenty college students were asked to perform static and dynamic postural stability tasks. Traditional COP and multivariate multiscale entropy (MMSE) were used to assess the static postural stability and the Star Excursion Balance Test (SEBT) was used to assess the dynamic postural stability. Results showed that (1) texting impaired postural stability, (2) the complexity index did not change much although the task conditions changed, and (3) performing texting is perceived to be more difficult.

Multi-scale complexity analysis of muscle coactivation during gait in children with cerebral palsy.

The objective of this study is to characterize complexity of lower-extremity muscle coactivation and coordination during gait in children with cerebral palsy (CP), children with typical development (TD) and healthy adults, by applying recently developed multivariate multi-scale entropy (MMSE) analysis to surface electromyographic (EMG) signals. Eleven CP children (CP group), eight TD children and seven healthy adults (considered as an entire control group) were asked to walk while surface EMG signals were collected from five thigh muscles and three lower leg muscles on each leg (16 EMG channels in total). The 16-channel surface EMG data, recorded during a series of consecutive gait cycles, were simultaneously processed by multivariate empirical mode decomposition (MEMD), to generate fully aligned data scales for subsequent MMSE analysis. In order to conduct extensive examination of muscle coactivation complexity using the MEMD-enhanced MMSE, 14 data analysis schemes were designed by varying partial muscle combinations and time durations of data segments. Both TD children and healthy adults showed almost consistent MMSE curves over multiple scales for all the 14 schemes, without any significant difference (p > 0.09). However, distinct diversity in MMSE curve was observed in the CP group when compared with the control group. There appears to be diverse neuropathological processes in CP that may affect dynamical complexity of muscle coactivation and coordination during gait. The abnormal complexity patterns emerging in the CP group can be attributed to different factors such as motor control impairments, loss of muscle couplings, and spasticity or paralysis in individual muscles. This study expands our knowledge of neuropathology of CP from a novel point of view of muscle co-activation complexity, which might be useful to derive a quantitative index for assessing muscle activation characteristics as well as motor function in CP.

Multiscale entropy analysis of biological signals: a fundamental bi-scaling law.

Since introduced in early 2000, multiscale entropy (MSE) has found many applications in biosignal analysis, and been extended to multivariate MSE. So far, however, no analytic results for MSE or multivariate MSE have been reported. This has severely limited our basic understanding of MSE. For example, it has not been studied whether MSE estimated using default parameter values and short data set is meaningful or not. Nor is it known whether MSE has any relation with other complexity measures, such as the Hurst parameter, which characterizes the correlation structure of the data. To overcome this limitation, and more importantly, to guide more fruitful applications of MSE in various areas of life sciences, we derive a fundamental bi-scaling law for fractal time series, one for the scale in phase space, the other for the block size used for smoothing. We illustrate the usefulness of the approach by examining two types of physiological data. One is heart rate variability (HRV) data, for the purpose of distinguishing healthy subjects from patients with congestive heart failure, a life-threatening condition. The other is electroencephalogram (EEG) data, for the purpose of distinguishing epileptic seizure EEG from normal healthy EEG.

Identification of Human Emotions via Univariate and Multivarite Multiscale Entropy

This work analyzes the emotions of human in terms of complexity. This analysis is achieved by applying both univariate and multivariate multiscale entropy methods on a multimodal dataset. Most of the contemporary human-computer interaction systems are unable to identify human affective states. So, the benefit of analyzing human emotions is to fill this gap by detecting human affective states. The univariate and multivariate multiscale entropy analysis curves obtained using multimodal dataset show differences in terms of complexity among different affective states, which can be used for emotion detection and classification for machine vision applications.

Dynamic multivariate multiscale entropy based analysis on brain death diagnosis

The recently introduced multivariate multiscale sample entropy (MMSE) well evaluates the long correlations in multiple channels, so that it can reveal the complexity of multivariate biological signals. The existing MMSE algorithm deals with short time series statically whereas long time series are common for real-time computation in practical use. As a solution, we novelly proposed our dynamic MMSE (DMMSE) as an extension of MMSE. This helps us gain greater insight into the complexity of each section of time series, producing multifaceted and more robust estimates than the standard MMSE. The simulation results illustrated the feasibility and well performance in the brain death diagnosis.

Simple tai chi exercise for improving elderly postural stability via complexity index analysis

The main purpose of this study is to investigate twice a day simple 9-step tai chi effects of the center of pressure (COP) and physiological signals of elderly people. Data are collected from the COP signals, electromyography (EMG), and pulse oximetry for 1 min for the period of 12 weeks. The COP signals are analyzed using multivariate empirical mode decomposition and multivariate multiscale entropy to work out and compare the complexity index (CI). Subjects in this experiment are over 65 years old who are divided into 11 men and 7 women; the average age is 74 ± 8.18 years. In conclusion, it is found that tai chi exercise can improve human body balance by just walking some simple steps in our experiment. However, we cannot find any effect or improvement in the pulse oximetry and EMG signals analysis.

Application in Feature Extraction of AE Signal for Rolling Bearing in EEMD and Cloud Similarity Measurement

Due to the powerful ability of EEMD algorithm in noising, it is usually applied to feature extraction of fault signal of rolling bearing. But the selective correctness of sensitive IMF after decomposition can directly influence the correctness of feature extraction of fault signal. In order to solve the problem, the paper firstly proposes a new method on selecting sensitive IMF based on Cloud Similarity Measurement. By comparing this method in simulation experiment with the traditional mutual information method, it is obvious that the proposed method has overcome the misjudgment in the traditional method and it has higher accuracy, by factually collecting the normal, damage, and fracture fault AE signal of the inner ring of rolling bearing as samples, which will be decomposed by EEMD algorithm in the experiments. It uses Cloud Similarity Measurement to select sensitive IMF which can reflect the fault features. Finally, it sets the Multivariate Multiscale Entropy (MME) of sensitive IMF as the eigenvalue of original signal; then it is classified by the SVM to determine the fault types exactly. The results of the experiments show that the selected sensitive IMF based on Cloud Similarity Measurement is effective; it can help to improve the accuracy of the fault diagnosis and feature extraction.

Gas–water two-phase flow characterization with Electrical Resistance Tomography and Multivariate Multiscale Entropy analysis

Flow behavior characterization is important to understand gas-liquid two-phase flow mechanics and further establish its description model. An Electrical Resistance Tomography (ERT) provides information regarding flow conditions at different directions where the sensing electrodes implemented. We extracted the multivariate sample entropy (MSampEn) by treating ERT data as a multivariate time series. The dynamic experimental results indicate that the MSampEn is sensitive to complexity change of flow patterns including bubbly flow, stratified flow, plug flow and slug flow. MSampEn can characterize the flow behavior at different direction of two-phase flow, and reveal the transition between flow patterns when flow velocity changes. The proposed method is effective to analyze two-phase flow pattern transition by incorporating information of different scales and different spatial directions.

A new way of quantifying diagnostic information from multilead electrocardiogram for cardiac disease classification.

A new measure for quantifying diagnostic information from a multilead electrocardiogram (MECG) is proposed. This diagnostic measure is based on principal component (PC) multivariate multiscale sample entropy (PMMSE). The PC analysis is used to reduce the dimension of the MECG data matrix. The multivariate multiscale sample entropy is evaluated over the PC matrix. The PMMSE values along each scale are used as a diagnostic feature vector. The performance of the proposed measure is evaluated using a least square support vector machine classifier for detection and classification of normal (healthy control) and different cardiovascular diseases such as cardiomyopathy, cardiac dysrhythmia, hypertrophy and myocardial infarction. The results show that the cardiac diseases are successfully detected and classified with an average accuracy of 90.34%. Comparison with some of the recently published methods shows improved performance of the proposed measure of cardiac disease classification.

Multivariate multiscale entropy analysis of horizontal oil–water two-phase flow

Characterizing flow behavior underlying horizontal oil–water flows from experimental measurements is a challenging problem in the fields of time series analysis and fluid mechanics. We systematically conduct a horizontal oil–water two-phase flow experiment and use our designed distributed conductance sensor to measure multivariate signals from five different flow patterns. Taking two coupled Lorenz systems as examples, we first demonstrate that the multivariate multiscale entropy (MMSE) enables to uncover the one-way/both-way coupling structure of dynamic systems. Then we use MMSE method to analyze the experimental measurements and extract the slopes and mean values from low scales of MMSE to quantitatively characterize the flow behavior. The results suggest that the MMSE enables to quantitatively distinguish different horizontal oil–water flow patterns and further allows deeply uncovering dynamic flow behavior in the transitions of different flow patterns.

Physiological sensor signals classification for healthcare using sensor data fusion and case-based reasoning.

Today, clinicians often do diagnosis and classification of diseases based on information collected from several physiological sensor signals. However, sensor signal could easily be vulnerable to uncertain noises or interferences and due to large individual variations sensitivity to different physiological sensors could also vary. Therefore, multiple sensor signal fusion is valuable to provide more robust and reliable decision. This paper demonstrates a physiological sensor signal classification approach using sensor signal fusion and case-based reasoning. The proposed approach has been evaluated to classify Stressed or Relaxed individuals using sensor data fusion. Physiological sensor signals i.e., Heart Rate (HR), Finger Temperature (FT), Respiration Rate (RR), Carbon dioxide (CO2) and Oxygen Saturation (SpO2) are collected during the data collection phase. Here, sensor fusion has been done in two different ways: (i) decision-level fusion using features extracted through traditional approaches; and (ii) data-level fusion using features extracted by means of Multivariate Multiscale Entropy (MMSE). Case-Based Reasoning (CBR) is applied for the classification of the signals. The experimental result shows that the proposed system could classify Stressed or Relaxed individual 87.5% accurately compare to an expert in the domain. So, it shows promising result in the psychophysiological domain and could be possible to adapt this approach to other relevant healthcare systems.

Resistance training exercise program for intervention to enhance gait function in elderly chronically ill patients: multivariate multiscale entropy for center of pressure signal analysis.

Falls are unpredictable accidents, and the resulting injuries can be serious in the elderly, particularly those with chronic diseases. Regular exercise is recommended to prevent and treat hypertension and other chronic diseases by reducing clinical blood pressure. The “complexity index” (CI), based on multiscale entropy (MSE) algorithm, has been applied in recent studies to show a person's adaptability to intrinsic and external perturbations and widely used measure of postural sway or stability. The multivariate multiscale entropy (MMSE) was advanced algorithm used to calculate the complexity index (CI) values of the center of pressure (COP) data. In this study, we applied the MSE & MMSE to analyze gait function of 24 elderly, chronically ill patients (44% female; 56% male; mean age, 67.56 ± 10.70 years) with either cardiovascular disease, diabetes mellitus, or osteoporosis. After a 12-week training program, postural stability measurements showed significant improvements. Our results showed beneficial effects of resistance training, which can be used to improve postural stability in the elderly and indicated that MMSE algorithms to calculate CI of the COP data were superior to the multiscale entropy (MSE) algorithm to identify the sense of balance in the elderly.