Multivariate Empirical Mode Decomposition Research Articles

Removal of muscle artefacts from few‐channel EEG recordings based on multivariate empirical mode decomposition and independent vector analysis

Electroencephalography (EEG) recordings are often contaminated by muscle artefacts. To address the problem, various methods have been proposed to suppress muscle artefacts from either multichannel or single-channel EEG recordings. However, there exist few studies for muscle artefact removal from few-channel EEG recordings. An effective solution for the few-channel situation by combining multivariate empirical mode decomposition (MEMD) with independent vector analysis (IVA), termed as MEMD-IVA, is proposed. The proposed method consists of two steps. MEMD is first utilised to decompose a few-channel EEG recording into intrinsic mode functions (IMFs) and then IVA is applied on the IMFs to separate sources related to muscle activity. The performance of the proposed method on simulated and real-life data is evaluated. The results demonstrated that MEMD-IVA outperforms other possible existing methods in a few-channel situation.

Synergistic recruitment of multi-scale myoelectric oscillations of upper limb during infant crawling.

It has been widely accepted that the central nervous system (CNS) modulates muscle synergies to simplify motion control. However, it is still unclear that if there is a synergistic recruitment strategy to organize oscillation components of surface electromyography (sEMG) signals for limb movement. The sEMG signals were recorded from bilateral biceps brachii (BB) and triceps brachii (TB) muscles during infant crawling. The multivariate empirical mode decomposition (MEMD) was applied to decompose multi-channel sEMG signals into multi-scale oscillations. Then, non-negative matrix factorization (NMF) method was employed to extract oscillation synergy patterns. The results indicated that there were three stable oscillation synergies in sEMG signals for crawling movement, and the recruitment coefficient curves reflected the role of muscle during crawling movement. Our preliminary work suggested that synergistic recruitment of multi-scale oscillation components maybe a new way to understand the organization of MU recruitment strategy by the CNS.

Using Interictal HFOs to Improve the Identification of Epileptogenic Zones in Preparation for Epilepsy Surgery.

For the more than 15 million patients who have drug-resistant epilepsy, surgical resection of the region where seizure arise is often the only alternative therapy. However, the identification of this epileptogenic zone (EZ) is often imprecise. Generally, insufficient EZ identification and resection may cause seizures to continue and too much resection may lead to unnecessary neurological deficits. In this paper, an automatic high frequency oscillations (HFOs) detection method based on noise-assisted multivariate EMD (NA-MEMD) is proposed to improve the localization of the EZ for epilepsy patients. In this method, different detected HFO types such as fast-ripple (FR), ripple (R), and fast-ripple concurrent with ripple (FRandR) are utilized to investigate their clinical relevance in identifying EZ. The proposed method may significantly improve the precision by which pathological brain tissue can be identified.

Frequency-Resolved Dynamic Functional Connectivity Reveals Scale-Stable Features of Connectivity-States.

Investigating temporal variability of functional connectivity is an emerging field in connectomics. Entering dynamic functional connectivity by applying sliding window techniques on resting-state fMRI (rs-fMRI) time courses emerged from this topic. We introduce frequency-resolved dynamic functional connectivity (frdFC) by means of multivariate empirical mode decomposition (MEMD) followed up by filter-bank investigations. In general, we find that MEMD is capable of generating time courses to perform frdFC and we discover that the structure of connectivity-states is robust over frequency scales and even becomes more evident with decreasing frequency. This scale-stability varies with the number of extracted clusters when applying k-means. We find a scale-stability drop-off from k = 4 to k = 5 extracted connectivity-states, which is corroborated by null-models, simulations, theoretical considerations, filter-banks, and scale-adjusted windows. Our filter-bank studies show that filter design is more delicate in the rs-fMRI than in the simulated case. Besides offering a baseline for further frdFC research, we suggest and demonstrate the use of scale-stability as a possible quality criterion for connectivity-state and model selection. We present first evidence showing that connectivity-states are both a multivariate, and a multiscale phenomenon. A data repository of our frequency-resolved time-series is provided.

Plant-wide oscillation detection using multivariate empirical mode decomposition

Plant-wide oscillation detection is an important task in the maintenance of large-scale industrial control systems, owing to the fact that in an interactive multi-loop environment oscillation generated in one loop may propagate to the different parts of the plant. In such a scenario, it is required that different loops oscillating due to a common cause and hence similar frequency may be grouped together. In this paper an adaptive method for plant-wide oscillation detection based on multivariate empirical mode decomposition (MEMD) along with a grouping algorithm is proposed. The method can identify multiple oscillation groups among different variables as well as variables with random noise only. The proposed method is also applicable to both non-linear and non-stationary time series where the techniques based on the conventional Fourier analysis are prone to errors. Within each group that oscillate due to a common cause, the method can also indicate the location of the probable root cause of oscillations. The efficacy of the proposed method is established with the help of both simulation and industrial case studies.

Multivariate empirical mode decomposition and multiscale entropy analysis of EEG signals from SSVEP-based BCI system

The steady-state visual evoked potential (SSVEP)-based Brain-Computer Interface (BCI) has been employed in the brain-controlled wheelchair system for patients with severe dyskinesia disease. However, a long-time operation brings about users fatigue, leading to a decrease of performance of the BCI system in practical applications. The characterization of the fatigued mechanism and the improvement of the SSVEP classification accuracy remains a challenging problem of significant importance. In this letter, we first conduct SSVEP experiments to acquire the EEG signals during both normal and fatigued states. Then we develop a novel framework, which integrates the advantages of multivariate empirical mode decomposition (MEMD) and Support Vector Machine (SVM), for improving the SSVEP classification accuracy, especially during the fatigued state. The results suggest that the novel framework enables us to obtain a higher SSVEP classification accuracy compared with the method without MEMD. Furthermore, in order to reveal the fatigued behavior, we use the multivariate multiscale sample entropy (MMSE) to analyze the multi-channel EEG signals corresponding to normal and fatigued states. We interestingly find that the MMSE values in the fatigued state are lower than that in the normal state, which reflects the increase of regularity in SSVEP signals during the fatigued state. That is, a greater synchronization of neural assemblies is required to realize cognitive impairment when fatigue happens. The knowledge for the understanding of the brain fatigued behavior underlying SSVEP-based BCI experiments is gained by our analysis.

Developing hourly intensity duration frequency curves for urban areas in India using multivariate empirical mode decomposition and scaling theory

Development of rainfall intensity–duration–frequency (IDF) curves of short duration such as hourly or sub-daily are quite essential for planning and design of urban storm water drains. However, in developing countries like India, at many places the meteorological observatories do not have long records of hourly rainfall data, at large which may have access to data at daily or higher time scale only. Therefore, the scale invariance property of rainfall and/or the disaggregation process can be a useful mean for obtaining of shorter duration rainfall IDF curves from the daily scale rainfall data. This study proposes an alternative approach for deriving the hourly and sub-daily IDF relationships by using the scale invariance property of rainfall, empirical mode decomposition (EMD) method and extreme value (EV) model formulations. The multivariate EMD method is used for decomposing the rainfall intensity series of different durations simultaneously into a number of orthogonal modes. The logarithmic plot between probability weighted moments of the orthogonal modes and the duration gives the scaling exponent, which is further used for deriving IDF relationships based on EV formulations. To validate the correctness of the proposed method, first the method is applied for rainfall data of Mumbai and Bangalore cities in India, and the results are compared with that obtained by the classical frequency factor method. The results of IDF relationships derived by the two methods displayed good agreement in general, but noticed a larger deviation for the curves of higher return periods. Then the method is applied for the derivation of IDF relationships for hourly durations from the daily rainfall data of eight major cities in Kerala State in India. The results of the study demonstrated the effectiveness of the proposed approach for data-scarce regions in deriving the short duration IDF relationships from the daily rainfall data.

Multi-Fault Diagnosis of Rolling Bearings via Adaptive Projection Intrinsically Transformed Multivariate Empirical Mode Decomposition and High Order Singular Value Decomposition.

Rolling bearings are important components in rotary machinery systems. In the field of multi-fault diagnosis of rolling bearings, the vibration signal collected from single channels tends to miss some fault characteristic information. Using multiple sensors to collect signals at different locations on the machine to obtain multivariate signal can remedy this problem. The adverse effect of a power imbalance between the various channels is inevitable, and unfavorable for multivariate signal processing. As a useful, multivariate signal processing method, Adaptive-projection has intrinsically transformed multivariate empirical mode decomposition (APIT-MEMD), and exhibits better performance than MEMD by adopting adaptive projection strategy in order to alleviate power imbalances. The filter bank properties of APIT-MEMD are also adopted to enable more accurate and stable intrinsic mode functions (IMFs), and to ease mode mixing problems in multi-fault frequency extractions. By aligning IMF sets into a third order tensor, high order singular value decomposition (HOSVD) can be employed to estimate the fault number. The fault correlation factor (FCF) analysis is used to conduct correlation analysis, in order to determine effective IMFs; the characteristic frequencies of multi-faults can then be extracted. Numerical simulations and the application of multi-fault situation can demonstrate that the proposed method is promising in multi-fault diagnoses of multivariate rolling bearing signal.

Automated classification of non-motor mental task in electroencephalogram based brain-computer interface using multivariate autoregressive model in the intrinsic mode function domain

Abstract Objective In this paper, we proposed a new feature extraction approach based on the multivariate auto regressive model (MVAR) model of the sensitive intrinsic mode function (IMF) groups in the multivariate empirical mode decomposition (MEMD) domain. Approach We computed eigen values from the coefficient matrix of the MVAR model for classifying three different non-motor cognitive task in EEG based brain computer interface (BCI) system. In the first stage, the application of MEMD to multichannel EEG data gave rise to adaptive i.e. data driven decomposition of the multivariate time series data into a large number of IMF groups. In the second stage, the sensitive IMF groups were selected according to their task correlation factor. MVAR model of order six was developed from the five sensitive IMF groups and finally the eigen values of the correlation matrix derived from the coefficient matrix was employed for forming the feature vectors. At the last stage, the extracted feature vectors were fed to a Least Squares Support Vector Machine (LS-SVM) classifier for automatic classification of mental task EEG signals. We tested our approach on the mental task EEG data sets of three subjects. Main result We achieved highest value of average classification accuracy of 94.43% for binary classification of the first pair of mental task i.e baseline and mental arithmetic task using polynomial kernel and 91.65% for the second pair i.e mental arithmetic and mental letter composing task using radial basis function (RBF) with ten fold cross validation. We achieved highest value of average classification accuracy of 77.77% for three class classification employing One Vs One scheme of multiclass SVM classifier. Significance The performance of the binary classifier was evaluated on various parameters such as accuracy, specificity and sensitivity. The encouraging results show the potential of the proposed approach for classifying any non linear and non-stationary signals.

Multisensor-based hybrid empirical mode decomposition method towards system identification of structures

Multivariate empirical mode decomposition (MEMD) method is explored in this paper to perform modal identification of structures using the multisensor vibration data. Due to inherent sifting operation of empirical mode decomposition (EMD), the traditional MEMD results in mode-mixing that causes significant inaccuracy in modal identification and condition assessment of structures. Independent component analysis, another powerful blind signal decomposition method, is integrated with the MEMD to alleviate mode-mixing in the resulting modal responses. The proposed technique is verified using a suite of numerical, experimental, and full-scale studies (a building tower in China and a long-span bridge in Canada) considering several practical applications such as low-energy frequencies, closely spaced modes, and measurement noise. The results confirm the improved performance of the proposed method and prove that it can be considered as a robust system identification tool for flexible structures.

The Use of Multivariate EMD and CCA for Denoising Muscle Artifacts From Few-Channel EEG Recordings

Electroencephalography (EEG) recordings are often contaminated by muscle artifacts. In the literature, a number of methods have been proposed to deal with this problem. Yet most denoising muscle artifact methods are designed for either single-channel EEG or hospital-based, high-density multichannel recordings, not the few-channel scenario seen in most ambulatory EEG instruments. In this paper, we propose utilizing interchannel dependence information seen in the few-channel situation by combining multivariate empirical mode decomposition and canonical correlation analysis (MEMD-CCA). The proposed method, called MEMD-CCA, first utilizes MEMD to jointly decompose the few-channel EEG recordings into multivariate intrinsic mode functions (IMFs). Then, CCA is applied to further decompose the reorganized multivariate IMFs into the underlying sources. Reconstructing the data using only artifact-free sources leads to artifact-attenuated EEG. We evaluated the performance of the proposed method through simulated, semisimulated, and real data. The results demonstrate that the proposed method is a promising tool for muscle artifact removal in the few-channel setting.

Land use dependent variation of soil water infiltration characteristics and their scale-specific controls

Land use change has remarkable impact on hydrological processes. However, little is known on the land use dependent variation of soil water infiltration characteristics. This study aims to investigate the effects of land use type on the spatial variation of infiltration characteristics and to identify their scale-specific controls. A total of 132 in-situ infiltration measurements were conducted using a disc infiltrometer along four 96-m transects under different land use types (forestland, shrubland, cropland with tillage, and cropland without tillage) in a typical agricultural region in north China. Classical statistics and multivariate empirical mode decomposition (MEMD) were used to explore the features of the overall and scale-specific spatial variation of four infiltration characteristics, i.e., cumulative infiltration over 30 min (I30), sorptivity (S), unsaturated hydraulic conductivity (K0, h0 = –2 cm) and saturated hydraulic conductivity (Ks). Besides, the scale-specific correlations between the infiltration characteristics and selected environmental factors, i.e., bulk density (BD), soil organic matter (SOM), initial soil water content (IWC) and water temperature (T) were investigated. The results indicated that land use type significantly affected not only the values of the infiltration characteristics but also their overall and scale-specific spatial variability. Tillage was found to have great impact on these infiltration characteristics. Generally, cropland with tillage revealed significantly higher values and weaker overall spatial variation of I30 and S; while its K0 and Ks were significantly lower. Four major common spatial scales, i.e., 8–9 m, 13–16 m, 28–34 m and 47–94 m, were identified for the infiltration characteristics under different land use types using MEMD. The spatial variation of infiltration characteristics in forestland and shrubland were decomposed into larger common scales than that in croplands. Furthermore, the dominating factors of infiltration characteristics were scale-specific and also varied with land use type. Generally, SOM and BD were considered as important controls in smaller scales in croplands and the impacts of IWC and T were more effective in larger scales in forestland and shrubland.

Assessment of slow wave propagation in multichannel electrogastrography by using noise-assisted multivariate empirical mode decomposition and cross-covariance analysis

Electrogastrography (EGG) is a noninvasive technique for recording the myoelectrical activity of the stomach. An electrogastrographic signal recorded by using a four-channel system with electrodes placed on the surface of the skin is a mixture of a low-frequency gastric pacesetter potential known as a slow wave, electrical activity from other organs, and random noise. The aim of this work was to investigate the possibility of detecting the propagation of the gastric slow wave from multichannel EGG data. Noise-assisted multivariate empirical mode decomposition (NA-MEMD) and cross-covariance analysis (CCA) are proposed as new detection tools. NA-MEMD was applied to attenuate the noise and extract the EGG signal from four channels, while CCA was performed to assess the time shift between the EGG signal channels. Validation of the method was performed using synthetic EGG signals and the methodology was tested on four young, healthy adults. After validation, the proposed method was applied for two kinds of human EGG data: 10-min (short) EGG data from the preprandial phase and 90–120-min (long) EGG data from the preprandial phase as well as the postprandial phase. The results obtained for both synthetic and human EGG data confirm that the proposed method could be a useful tool for assessing the propagation of slow waves. The time shift calculation from the preprandial phase of the EGG examination yielded more consistent results than the postprandial phase. The mean value of the slow wave time lag between neighbouring channels for synthetic data was found to be 4.99±0.47 s. In addition, it was confirmed that the proposed method, that is, NA-MEMD and CCA together, are robust to noise.

Fast Multivariate Empirical Mode Decomposition

The multivariate empirical mode decomposition (MEMD) has been pioneered recently for adaptively processing of multichannel data. Despite its high efficiency on time-frequency analysis of nonlinear and nonstationary signals, high computational load and over-decomposition have restricted wider applications of MEMD. To address these challenges, a fast MEMD (FMEMD) algorithm is proposed and featured by the following contributions: 1) A novel concept, pseudo direction-independent multivariate intrinsic mode function (IMIMF) which allows the interchange of sifting and projection operations, is defined for the purpose of developing FMEMD; 2) FMEMD is computationally efficient. Compared with MEMD, the number of time-consuming sifting operations reduces from $K \cdot p$ to $K$ for each iteration, where $K$ and $p$ denote the number of projection directions and signal dimension, respectively; 3) FMEMD is consistent with EMD in terms of the dyadic filter bank property; and 4) FMEMD is more effective in working at low sampling rate. Validity of the raised approach is demonstrated on a wide variety of real world applications.

Exploring Scale‐Specific Controls on Soil Water Content across a 500‐Kilometer Transect Using Multivariate Empirical Mode Decomposition

Core Ideas We used MEMD to explore scale‐specific controls of SWC at a 500‐km transect. The largest mean scale of SWC and environmental factors along the transect was 121 km. Precipitation and temperature were large‐scale factors controlling SWC. Elevation and sand were moderate‐scale factors controlling SWC. Clay content was the dominant factor controlling SWC at all scales. Soil water content (SWC) varies both spatially and temporally and is highly controlled by various factors operating at different intensities and scales. In this study, we investigated the scale‐specific controls of SWC along a 500‐km transect using multivariate empirical mode decomposition (MEMD) at 42 sites. Soil water content and six environmental factors were divided into different intrinsic mode functions (IMFs) and residuals to represent different scales. Different values of IMFs for SWC and environmental factors were obtained throughout the whole profile and within five soil layers (0–1, 1–2, 2–3, 3–4, and 4–5 m). The largest scales (i.e., the scales that explain largest portion of variances) of SWC and environmental factors depended on the soil layer from which SWC was involved in MEMD analysis, and they were 272, 126, 134, 126, 117, and 121 km for soil layers from 0 to 1, 1 to 2, 2 to 3, 3 to 4, 4 to 5, and 0 to 5 m, respectively. The residuals accounted for a majority (33–78.1%) of the variance of the original data. At large scales (>250 km), precipitation and temperature were the controlling factors on SWC, whereas at moderate scales (65 km), elevation and sand were the factors determining SWC. In contrast, at all scales, clay content affected SWC distribution. The scale‐specific prediction of SWC on the basis of IMFs and residuals contained more information on environmental factors than the results obtained at the measurement scale. Overall, SWC prediction from IMFs and their residuals were superior to those based on the original data. Using information obtained from MEMD could improve our understanding of the scale‐specific characteristics of soil water and environmental factors across a long transect scale.

Fetal heart rate extraction from abdominal electrocardiograms through multivariate empirical mode decomposition

Assessment of fetal heart rate (FHR) and fetal heart rate variability (fHRV) reveals important information about fetal well-being, specifically in high risk pregnancies. Abdominal electrocardiogram (abdECG) recording is a non-invasive method to capture fetal electrocardiograms. In this paper, we propose a methodology to extract FHR (fetal RR time series) from the abdECG recordings using the recently introduced multivariate empirical mode decomposition (MEMD) technique. MEMD breaks a signal into a finite set of intrinsic mode functions (IMFs). First, elimination of the noisier abdECG channels, based on comparison of similar indexed IMFs that were obtained through the MEMD technique, is conducted. Thereafter, denoising of the remaining abdECG channels is performed by eliminating certain similar indexed IMFs. The unwanted mother QRS complexes are removed from these noise-free abdECG channels, and the candidate fetal R-peaks are detected through a wavelet based approach. The proposed methodology is validated using an open source real-life clinical database. The proposed technique resulted in a high value (0.983) of cross correlation between the detected and true FHR signals.

Weighted Window Sliding Multivariate Empirical Mode Decomposition for Online Multichannel Filtering

Affected by nonlinear and non-stationary problems, classical linear analysis approaches may fail in analyzing real-world signals, such as the biomedical data. As a fully data-driven and unsupervised signal analysis algorithm, the empirical mode decomposition (EMD) has been developed and applied widely in various fields, especially for de-noising filtering. Due to the increasing need of high speed continuous sampling for multichannel signals, it is necessitated for the more efficient real-time filtering approach to deal with the large-scale time series data. Unfortunately, although the multivariate empirical mode decomposition (MEMD) performs better for multichannel analysis, it is extremely time-consuming to realize the signal time-frequency decomposition. Therefore, in this paper, a novel online multidimensional filtering algorithm combined with MEMD is proposed. With weighted sliding window, it not only improves the real time property for multichannel de-noising, but also realizes the continuous smooth filtering. Moreover, a novel statistic-based algorithm is also proposed to determine the optimal window size quantitatively. Finally, the proposed novel multichannel filtering approach is validated and analyzed by utilizing the real measured electrooculography data and wind power generation system operation data.

Wii Balanced Board-Based Utilization for the Human Body Center of Pressure for the Falling Detection via Multivariate Empirical Mode Decomposition and Multivariate Multi-scale Entropy

Wii Balanced Board-Based Utilization for the Human Body Center of Pressure for the Falling Detection via Multivariate Empirical Mode Decomposition and Multivariate Multi-scale Entropy

Motor imagery classification from human EEG signatures

Brain-computer interface (BCI) systems translate the imagination in the human brain to an action in real world by means of machines. These systems can prove to be a blessing for severely impaired patients in terms of BCI prosthetics. This paper proposes a motor imagery classification system based upon Wavelet Packet Decomposition (WPD) and Support Vector Machine (SVM). The wavelet packet transform is used for both selection of sensory motor frequency band and feature extraction. The publically available BCI competition-IV data set-I has been used to evaluate the performance of the proposed scheme. The obtained classification results outperform the previously reported results of the technique Noise Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) for subjects 'a' and 'b', where 'a' and 'b' refers to two subjects from BCI competition data set-IV.

Extraction of Plant-wide Oscillations using Fast Multivariate Empirical Mode Decomposition

This paper proposes a novel time-frequency method for plant-wide oscillation analysis based on the multivariate extension of standard empirical mode decomposition (EMD). The raised fast multivariate empirical mode decomposition (FMEMD) is generalized from EMD by solving an overdetermined system of linear equations. Due to its capability to analyze multiple channels data, FMEMD is especially suitable for characterizing plant-wide control loop oscillations. Unlike traditional methods, both the regularity of oscillations (in frequency domain) and evolution of local characteristics (in time scale) can be well captured via FMEMD. Validity of the raised approach is demonstrated on simulations as well as an industrial case.