Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

NLDyn - An open source MATLAB toolbox for the univariate and multivariate nonlinear dynamical analysis of physiological data

BACKGROUND AND OBJECTIVE

We present NLDyn, an open-source MATLAB toolbox tailored for in-depth analysis of nonlinear dynamics in biomedical signals. Our objective is to offer a user-friendly yet comprehensive platform for researchers to explore the intricacies of time series data.

METHODS

NLDyn integrates approximately 80 distinct methods, encompassing both univariate and multivariate nonlinear dynamics, setting it apart from existing solutions. This toolbox combines state-of-the-art nonlinear dynamical techniques with advanced multivariate entropy methods, providing users with powerful analytical capabilities. NLDyn enables analyses with or without a sliding window, and users can easily access and customize default parameters.

RESULTS

NLDyn generates results that are both exportable and visually informative, facilitating seamless integration into research and presentations. Its ongoing development ensures it remains at the forefront of nonlinear dynamics analysis.

CONCLUSIONS

NLDyn is a valuable resource for researchers in the biomedical field, offering an intuitive interface and a wide array of nonlinear analysis tools. Its integration of advanced techniques empowers users to gain deeper insights from their data. As we continually refine and expand NLDyn's capabilities, we envision it becoming an indispensable tool for the exploration of complex dynamics in biomedical signals.

Decreased frontal lobe complexity in left-behind children during joint attention: a fNIRS study with multivariable and multiscale sample entropy analysis

Human brain development is shaped by experiences, especially during preschool, the critical period for cognitive and socioemotional development. This study employed the functional Near-Infrared Spectroscopy technique to explore the neural differences between left-behind children (LBC) and non-left-behind children (NLBC) on joint attention. Through collecting brain image data of 50 children (26 boys, aged 65.08 ± 6.28 months) and conducting multivariable and multiscale sample entropy (MMSE) analysis, the present study found that: (i) LBC showed lower brain complexity than NLBC in right prefrontal cortex; (ii) all participants demonstrated higher brain complexity in responding to joint attention conditions, compared to initiating joint attention ones; (iii) their brain complexity during joint attention was negatively associated with their emotional abilities. The findings advance our understanding of early brain development in LBC by providing evidence for the neural process characteristics of joint attention. Implications for early intervention to promote their brain development are also addressed.

Variable-Step Multiscale Fuzzy Dispersion Entropy: A Novel Metric for Signal Analysis

Fuzzy dispersion entropy (FuzDE) is a newly proposed entropy metric, which combines the superior characteristics of fuzzy entropy (FE) and dispersion entropy (DE) in signal analysis. However, FuzDE only reflects the feature from the original signal, which ignores the hidden information on the time scale. To address this problem, we introduce variable-step multiscale processing in FuzDE and propose variable-step multiscale FuzDE (VSMFuzDE), which realizes the characterization of abundant scale information, and is not limited by the signal length like the traditional multiscale processing. The experimental results for both simulated signals show that VSMFuzDE is more robust, more sensitive to dynamic changes in the chirp signal, and has more separability for noise signals; in addition, the proposed VSMFuzDE displays the best classification performance in both real-world signal experiments compared to the other four entropy metrics, the highest recognition rates of the five gear signals and four ship-radiated noises reached 99.2% and 100%, respectively, which achieves the accurate identification of two different categories of signals.

Quantifying the predictability of renewable energy data for improving power systems decision-making

Decision-making in the power systems domain often relies on predictions of renewable generation. While sophisticated forecasting methods have been developed to improve the accuracy of such predictions, their accuracy is limited by the inherent predictability of the data used. However, the predictability of time series data cannot be measured by existing prediction techniques. This important measure has been overlooked by researchers and practitioners in the power systems domain. In this paper, we systematically assess the suitability of various predictability measures for renewable generation time series data, revealing the best method and providing instructions for tuning it. Using real-world examples, we then illustrate how predictability could save end users and investors millions of dollars in the electricity sector.

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Refined composite multiscale fluctuation-based dispersion Lempel-Ziv complexity for signal analysis

Dispersion Lempel-Ziv complexity (DLZC) and multiscale DLZC (MDLZC) are very recently introduced complexity indicators to quantify the dynamic change of time series in acoustics signals. They introduce the mapping steps of dispersion entropy (DE), which can effectively identify time series with different characteristics, but ignore the fluctuation information and have poor stability. In order to overcome these shortcomings, this paper firstly adds fluctuation information to DLZC and proposes fluctuation-based DLZC (FDLZC) as an alternative to the classical time series complexity index, followed by introducing an improved coarse-graining operation to propose the refined composite multiscale FDLZC (RCMFDLZC), which increases the number of features and also ensures the stability of FDLZC, and finally select the subsequence containing the most information by the minimum redundancy maximum relevance (mRMR) feature selection algorithm for subsequent experiments. The experimental results show that the extracted RCMFDLZC features have the strongest separability and better clustering effect in both bearing fault signals and ship radiated noise signals, and the RCMFDLZC-based signal analysis method also has higher recognition rate compared with other methods in bearing fault diagnosis and ship signal classification.

Assessment and Comparison of Nonlinear Measures in Resting-State Magnetoencephalograms in Alzheimer's Disease and Mild Cognitive Impairment

BACKGROUND

Nonlinear dynamical measures, such as fractal dimension (FD), entropy, and Lempel-Ziv complexity (LZC), have been extensively investigated individually for detecting information content in magnetoencephalograms (MEGs) from patients with Alzheimer's disease (AD).

OBJECTIVE

To compare systematically the performance of twenty conventional and recently introduced nonlinear dynamical measures in studying AD versus mild cognitive impairment (MCI) and healthy control (HC) subjects using MEG.

METHODS

We compared twenty nonlinear measures to distinguish MEG recordings from 36 AD (mean age = 74.06±6.95 years), 18 MCI (mean age = 74.89±5.57 years), and 26 HC subjects (mean age = 71.77±6.38 years) in different brain regions and also evaluated the effect of the length of MEG epochs on their performance. We also studied the correlation between these measures and cognitive performance based on the Mini-Mental State Examination (MMSE).

RESULTS

The results obtained by LZC, zero-crossing rate (ZCR), FD, and dispersion entropy (DispEn) measures showed significant differences among the three groups. There was no significant difference between HC and MCI. The highest Hedge's g effect sizes for HC versus AD and MCI versus AD were respectively obtained by Higuchi's FD (HFD) and fuzzy DispEn (FuzDispEn) in the whole brain and was most prominent in left lateral. The results obtained by HFD and FuzDispEn had a significant correlation with the MMSE scores. DispEn-based techniques, LZC, and ZCR, compared with HFD, were less sensitive to epoch length in distinguishing HC form AD.

CONCLUSIONS

FuzDispEn was the most consistent technique to distinguish MEG dynamical patterns in AD compared with HC and MCI.

A new hybrid prediction model of air quality index based on secondary decomposition and improved kernel extreme learning machine

Air quality index (AQI) prediction is important to control air pollution. To improve its accuracy, a new hybrid prediction model of AQI based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), multivariate multiscale dispersion entropy (mvMDE), variational mode decomposition optimized by bald eagle search (BES) algorithm (BVMD) and kernel extreme learning machine optimized by rat swarm optimizer (RSO) algorithm (RSO-KELM), named CEEMDAN-mvMDE-BVMD-RSO-KELM, is proposed. Firstly, AQI series is decomposed by CEEMDAN to obtain multiple intrinsic mode function (IMF) components, and each IMF component's complexity is calculated by mvMDE. Secondly, VMD optimized by BES algorithm, named BVMD, is proposed to solve the problem of choosing the decomposition level K and penalty factor α of VMD, and BVMD is used to perform the secondary decomposition of high complexity components. Thirdly, the penalty coefficient and kernel parameter of KELM optimized by RSO algorithm, named RSO-KELM, is proposed, and all IMF components are predicted by RSO-KELM. Finally, the final prediction results are obtained by reconstructing the prediction results of all IMF components. The objective of this study is to propose a new hybrid prediction model of AQI based on secondary decomposition and improved KELM. Taking Shanghai, Beijing and Xi'an as examples, the results show that compared with the comparison models, the proposed model has the highest prediction accuracy.

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

Multivariate entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems, certain channels may overshadow the patterns of others, resulting in information loss. Here, we introduce the framework of Stratified Entropy to prioritize each channels' dynamics based on their allocation to respective strata, leading to a richer description of the multi-channel time-series. As an implementation of the framework, three algorithmic variations of the Stratified Multivariate Multiscale Dispersion Entropy are introduced. These variations and the original algorithm are applied to synthetic time-series, waveform physiological time-series, and derivative physiological data. Based on the synthetic time-series experiments, the variations successfully prioritize channels following their strata allocation while maintaining the low computation time of the original algorithm. In experiments on waveform physiological time-series and derivative physiological data, increased discrimination capacity was noted for multiple strata allocations in the variations when benchmarked to the original algorithm. This suggests improved physiological state monitoring by the variations. Furthermore, our variations can be modified to utilize a priori knowledge for the stratification of channels. Thus, our research provides a novel approach for the extraction of previously inaccessible information from multi-channel time series acquired from heterogeneous systems.

PV System Failures Diagnosis Based on Multiscale Dispersion Entropy

Photovoltaic (PV) system diagnosis is a growing research domain likewise solar energy's ongoing significant expansion. Indeed, efficient Fault Detection and Diagnosis (FDD) tools are crucial to guarantee reliability, avoid premature aging and improve the profitability of PV plants. In this paper, an on-line diagnosis method using the PV plant electrical output is presented. This entirely signal-based method combines variational mode decomposition (VMD) and multiscale dispersion entropy (MDE) for the purpose of detecting and isolating faults in a real grid-connected PV plant. The present method seeks a low-cost design, an ease of implementation and a low computation cost. Taking into account the innovation of applying these techniques to PV FDD, the VMD and MDE procedures as well as parameters identification are carefully detailed. The proposed FFD approach performance is assessed on a real rooftop PV plant with experimentally induced faults, and the first results reveal the MDE approach has good suitability for PV plants diagnosis.

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Gait Stability Measurement by Using Average Entropy

Gait stability has been measured by using many entropy-based methods. However, the relation between the entropy values and gait stability is worth further investigation. A research reported that average entropy (AE), a measure of disorder, could measure the static standing postural stability better than multiscale entropy and entropy of entropy (EoE), two measures of complexity. This study tested the validity of AE in gait stability measurement from the viewpoint of the disorder. For comparison, another five disorders, the EoE, and two traditional metrics methods were, respectively, used to measure the degrees of disorder and complexity of 10 step interval (SPI) and 79 stride interval (SI) time series, individually. As a result, every one of the 10 participants exhibited a relatively high AE value of the SPI when walking with eyes closed and a relatively low AE value when walking with eyes open. Most of the AE values of the SI of the 53 diseased subjects were greater than those of the 26 healthy subjects. A maximal overall accuracy of AE in differentiating the healthy from the diseased was 91.1%. Similar features also exists on those 5 disorder measurements but do not exist on the EoE values. Nevertheless, the EoE versus AE plot of the SI also exhibits an inverted U relation, consistent with the hypothesis for physiologic signals.

Assessment of Outliers and Detection of Artifactual Network Segments Using Univariate and Multivariate Dispersion Entropy on Physiological Signals

Network physiology has emerged as a promising paradigm for the extraction of clinically relevant information from physiological signals by moving from univariate to multivariate analysis, allowing for the inspection of interdependencies between organ systems. However, for its successful implementation, the disruptive effects of artifactual outliers, which are a common occurrence in physiological recordings, have to be studied, quantified, and addressed. Within the scope of this study, we utilize Dispersion Entropy (DisEn) to initially quantify the capacity of outlier samples to disrupt the values of univariate and multivariate features extracted with DisEn from physiological network segments consisting of synchronised, electroencephalogram, nasal respiratory, blood pressure, and electrocardiogram signals. The DisEn algorithm is selected due to its efficient computation and good performance in the detection of changes in signals for both univariate and multivariate time-series. The extracted features are then utilised for the training and testing of a logistic regression classifier in univariate and multivariate configurations in an effort to partially automate the detection of artifactual network segments. Our results indicate that outlier samples cause significant disruption in the values of extracted features with multivariate features displaying a certain level of robustness based on the number of signals formulating the network segments from which they are extracted. Furthermore, the deployed classifiers achieve noteworthy performance, where the percentage of correct network segment classification surpasses 95% in a number of experimental setups, with the effectiveness of each configuration being affected by the signal in which outliers are located. Finally, due to the increase in the number of features extracted within the framework of network physiology and the observed impact of artifactual samples in the accuracy of their values, the implementation of algorithmic steps capable of effective feature selection is highlighted as an important area for future research.

A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery

In the fault monitoring of rotating machinery, the vibration signal of the bearing and gear in a complex operating environment has poor stationarity and high noise. How to accurately and efficiently identify various fault categories is a major challenge in rotary fault diagnosis. Most of the existing methods only analyze the single channel vibration signal and do not comprehensively consider the multi-channel vibration signal. Therefore, this paper presents Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE), a method which extracts the recognition information of multi-channel signals with different scale factors, and the refined composite analysis ensures the recognition stability. The simulation results show that this method has the characteristics of low sensitivity to signal length and strong anti-noise ability. At the same time, combined with Joint Mutual Information Maximisation (JMIM) and support vector machine (SVM), RCMMFDE-JMIM-SVM fault diagnosis method has been proposed. This method uses RCMMFDE to extract the state characteristics of the multiple vibration signals of the rotary machine, and then uses the JMIM method to extract the sensitive characteristics. Finally, different states of the rotary machine are classified by SVM. The validity of the method is verified by the composite gear fault data set and bearing fault data set. The diagnostic accuracy of the method is 99.25% and 100.00%. The experimental results show that RCMMFDE-JMIM-SVM can effectively recognize multiple signals.

A New dispersion entropy and fuzzy logic system methodology for automated classification of dementia stages using electroencephalograms

A new EEG-based methodology is presented for differential diagnosis of the Alzheimer's disease (AD), Mild Cognitive Impairment (MCI), and healthy subjects employing the discrete wavelet transform (DWT), dispersion entropy index (DEI), a recently-proposed nonlinear measurement, and a fuzzy logic-based classification algorithm. The effectiveness and usefulness of the proposed methodology are evaluated by employing a database of measured EEG data acquired from 135 subjects, 45 MCI, 45 AD and 45 healthy subjects. The proposed methodology differentiates MCI and AD patients from HC subjects with an accuracy of 82.6-86.9%, sensitivity of 91 %, and specificity of 87 %.

Complexity of heart rate variability during moral judgement of actions and omissions

Recent research strongly supports the idea that cardiac activity is involved in the organisation of behaviour, including social behaviour and social cognition. The aim of this work was to explore the complexity of heart rate variability, as measured by permutation entropy, while individuals were making moral judgements about harmful actions and omissions. Participants (N = 58, 50% women, age 21-52 years old) were presented with a set of moral dilemmas describing situations when sacrificing one person resulted in saving five other people. In line with previous studies, our participants consistently judged harmful actions as less permissible than equivalently harmful omissions (phenomenon known as the "omission bias"). Importantly, the response times were significantly longer and permutation entropy of the heart rate was higher when participants were evaluating harmful omissions, as compared to harmful actions. These results may be viewed as a psychophysiological manifestation of differences in causal attribution between actions and omissions. We discuss the obtained results from the positions of the system-evolutionary theory and propose that heart rate variability reflects complexity of the dynamics of neurovisceral activity within the organism-environment interactions, including their social aspects. This complexity can be described in terms of entropy and our work demonstrates the potential of permutation entropy as a tool of analyzing heart rate variability in relation to current behaviour and observed cognitive processes.

Identification of Denatured Biological Tissues Based on Compressed Sensing and Improved Multiscale Dispersion Entropy during HIFU Treatment

Identification of denatured biological tissue is crucial to high-intensity focused ultrasound (HIFU) treatment, which can monitor HIFU treatment and improve treatment efficiency. In this paper, a novel method based on compressed sensing (CS) and improved multiscale dispersion entropy (IMDE) is proposed to evaluate the complexity of ultrasonic scattered echo signals during HIFU treatment. In the analysis of CS, the method of orthogonal matching pursuit (OMP) is employed to reconstruct the denoised signal. CS-OMP can denoise the ultrasonic scattered echo signal effectively. Comparing with traditional multiscale dispersion entropy (MDE), IMDE improves the coarse-grained process in the multiscale analysis, which improves the stability of MDE. In the analysis of simulated signals, the entropy value of the IMDE method has less fluctuation compared with MDE, indicating that the IMDE method has better stability. In addition, MDE and IMDE are applied to the 300 cases of ultrasonic scattered echo signals after denoising (including 150 cases of normal tissues and 150 cases of denatured tissues). The experimental results show that the MDE and IMDE values of denatured tissues are higher than normal tissues. Both the MDE and IMDE method can be used to identify whether biological tissue is denatured. However, the multiscale entropy curve of IMDE is smoother and more stable than MDE. The interclass distance of IMDE is greater than MDE, and the intraclass distance of IMDE is less than MDE at different scale factors. This indicates that IMDE can better distinguish normal tissues and denatured tissues to obtain more accurate clinical diagnosis during HIFU treatment.

Multiscale Entropy Approaches and Their Applications

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