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Epilepsy is a global disease with considerable incidence due to recurrent unprovoked seizures. These seizures can be noninvasively diagnosed using electroencephalogram (EEG), a measure of neuronal electrical activity in brain recorded along scalp. EEG is highly nonlinear, nonstationary and non-Gaussian in nature. Nonlinear adaptive models such as empirical mode decomposition (EMD) provide intuitive understanding of information present in these signals. In this study a novel methodology is proposed to automatically classify EEG of normal, inter-ictal and ictal subjects using EMD decomposition. EEG decomposition using EMD yields few intrinsic mode functions (IMF), which are amplitude and frequency modulated (AM and FM) waves. Hilbert transform of these IMF provides AM and FM frequencies. Features such as spectral peaks, spectral entropy and spectral energy in each IMF are extracted and fed to decision tree classifier for automated diagnosis. In this work, we have compared the performance of classification using two types of decision trees (i) classification and regression tree (CART) and (ii) C4.5. We have obtained the highest average accuracy of 95.33%, average sensitivity of 98%, and average specificity of 97% using C4.5 decision tree classifier. The developed methodology is ready for clinical validation on large databases and can be deployed for mass screening.

Dementia is one of the most common neurological disorders causing defection of cognitive functions, and seriously affects the quality of life. In this study, various methods have been proposed for the detection and follow-up of Alzheimer’s dementia (AD) with advanced signal processing methods by using electroencephalography (EEG) signals. Signal decomposition-based approaches such as empirical mode decomposition (EMD), ensemble EMD (EEMD), and discrete wavelet transform (DWT) are presented to classify EEG segments of control subjects (CSs) and AD patients. Intrinsic mode functions (IMFs) are obtained from the signals using the EMD and EEMD methods, and the IMFs showing the most significant differences between the two groups are selected by applying previously suggested selection procedures. Five-time-domain and 5-spectral-domain features are calculated using selected IMFs, and five detail and approximation coefficients of DWT. Signal decomposition processes are conducted for both 1 min and 5 s EEG segment durations. For the 1 min segment duration, all the proposed approaches yield prominent classification performances. While the highest classification accuracies are obtained using EMD (91.8%) and EEMD (94.1%) approaches from the temporal/right brain cluster, the highest classification accuracy for the DWT (95.2%) approach is obtained from the temporal/left brain cluster for 1 min segment duration.

This paper presents a new approach called the empirical mode decomposition — window fractal (EMDWF) algorithm in classification of fingerprint of medicinal herbs. In this way, we consider a glycyrrhiza fingerprint of medicinal herb as a signal sequence, and apply empirical mode decomposition (EMD) and Hiaguchis fractal dimension to construct a feature vector. By using EMD, the glycyrrhiza fingerprint of medicinal herb can be decomposed into some intrinsic mode functions (IMFs). As window fractal dimension (WFD) is applied to each IMF and original signal, the features of the glycyrrhiza fingerprint of medicinal herb can be obtained. Thereafter, SVM is applied as a classifier. The results of the experiments state clearly that the feature extracted by EMDWF is better than that of the existing methods including the pure EMD. With the increase of the number of training samples and the increase of the number of layers in EMD, the classification result achieves more stability.

Magnetoencephalography (MEG) is a powerful and non-invasive technique for measuring human brain activity with a high temporal resolution. The motivation for studying MEG data analysis is to extract the essential features from real-world measured data and represent them corresponding to the human brain functions. This usually depends on how to reduce a high level noise from the measurement. In this paper, a novel multistage MEG data analysis method based on the empirical mode decomposition (EMD) and independent component analysis (ICA) approaches is proposed for the feature extraction. Moreover, EMD and ICA algorithms are investigated for analyzing the MEG single-trial data which is recorded from the experiment of phantom. The analyzed results are presented to illustrate the effectiveness and high performance both in high level noise reduction by EMD associated with ICA approach and source localization by equivalent current dipole fitting method.

Recently, the automation of the age estimation technique is hoped for in various fields. Therefore, we propose an apparent-age estimation system using empirical mode decomposition (EMD). Conventional study reported that the time-frequency features are important for age estimation. However, these cannot necessarily extract the time-frequency feature in detail, because the classical technique that have a relationship of trade-off between the time resolution and the frequency resolution are used. On the other hand, the EMD is the novel time-frequency analysis technique that do not have the relationship of trade-off between the time resolution and the frequency resolution. The EMD gives a time-frequency analysis decomposing a signal into several intrinsic mode functions (IMFs). The IMF together with their Hilbert transforms are called the Hilbert–Huang spectrum, which leads to instantaneous frequency and amplitude. We use these features effectively for extracting human's age perception. We estimate the age by a neural network that learns pairs of face image and the Hilbert–Huang spectrum. Furthermore, we compress the data for neural network by using the simple principal component analysis (SPCA). In order to show the effectiveness of the proposed method, computer simulations are done by the actual human data.

The electrocardiogram (ECG) signal is widely used for diagnosis of heart disorders. However, ECG signal is a kind of weak signal to be interfered with heavy background interferences. Moreover, there are some overlaps between the interference frequency sub-bands and the ECG frequency sub-bands, so it is difficult to inhibit noise in the ECG signal. In this paper, the ECG signal in-band noise de-noising method based on empirical mode decomposition (EMD) is proposed. This method uses random permutation to process intrinsic mode functions (IMFs). It abstracts QRS complexes to separate them from noise so that the clean ECG signal is obtained. The method is validated through simulations on the MIT-BIH Arrhythmia Database and experiments on the measured test data. The results indicate that the proposed method can restrain noise, improve signal noise ratio (SNR) and reduce mean squared error (MSE) effectively.

Accurate short-term price forecasting is crucial for the power system and electricity market. This paper proposes a hybrid short-term electricity price forecasting model based on empirical mode decomposition (EMD) and deep neural network (DNN). Firstly, EMD is used to denoise the data set. Next, the reconstructed data are input into the DNN composed of a convolutional neural network (CNN) and long-short-term memory (LSTM) neural network to analyze the characteristics and output the prediction results. Finally, the superiority of this model is verified by comparing the electricity price data of the Australian electricity market with a single LSTM network, EMD-CNN model, and CNN-LSTM model.

This work describes the application of an important tool which can extract periodic information from the time-series of fluctuating traffic data. Compared to the traditional approach using FFT techniques, the nonlinear empirical mode decomposition (EMD) method has a number of advantages. This method is adaptive and therefore highly efficient at identifying embedded structures, even those with small amplitudes. Using this analysis, the traffic time series can be completely decomposed into five temporal modes including a 24-hour cycle, a 1-week cycle and a trend. Simultaneity, long-range correlations in traffic time series are investigated by detrended fluctuation analysis (DFA). In order to accurately capture the scaling exponents, EMD analysis is performed for DFA of the traffic records. The results of DFA for the data cleaned by subtracting the first intrinsic mode functions (IMF) are apparently improved, although the DFA curves are not entirely straight on the log-log plot.

The purpose of this paper is to forecast the daily closing prices of stock markets based on the past sequences. In this paper, keeping in mind the recent trends and the limitations of previous researches, we proposed a new technique, called empirical mode decomposition combined with k-nearest neighbors (EMD–KNN) method, in forecasting the stock index. EMD–KNN takes the advantages of the KNN and EMD. To demonstrate that our EMD–KNN method is robust, we used the new technique to forecast four stock index time series at a specific time. Detailed experiments are implemented for both of the proposed forecasting models, in which EMD–KNN, KNN method and ARIMA are compared. The results demonstrate that the proposed EMD–KNN model is more successful than KNN method and ARIMA in predicting the stock closing prices.

In this paper, we propose multiscale detrended cross-correlation analysis (MSDCCA) to detect the long-range power-law cross-correlation of considered signals in the presence of nonstationarity. For improving the performance and getting better robustness, we further introduce the empirical mode decomposition (EMD) to eliminate the noise effects and propose MSDCCA method combined with EMD, which is called MS-EDXA method, then systematically investigate the multiscale cross-correlation structure of the real traffic signals. We apply the MSDCCA and MS-EDXA methods to study the cross-correlations in three situations: velocity and volume on one lane, velocities on the present and the next moment and velocities on the adjacent lanes, and further compare their spectrums respectively. When the difference between the spectrums of MSDCCA and MS-EDXA becomes unobvious, there is a crossover which denotes the turning point of difference. The crossover results from the competition between the noise effects in the original signals and the intrinsic fluctuation of traffic signals and divides the plot of spectrums into two regions. In all the three case, MS-EDXA method makes the average of local scaling exponents increased and the standard deviation decreased and provides a relative stable persistent scaling cross-correlated behavior which gets the analysis more precise and more robust and improves the performance after noises being removed. Applying MS-EDXA method avoids the inaccurate characteristics of multiscale cross-correlation structure at the short scale including the spectrum minimum, the range for the spectrum fluctuation and general trend, which are caused by the noise in the original signals. We get the conclusions that the traffic velocity and volume are long-range cross-correlated, which is accordant to their actual evolution, while velocities on the present and the next moment and velocities on adjacent lanes reflect the strong cross-correlations both in temporal and spatial dimensions. We also reveal the similarity and uniqueness in the cross-correlation situations between velocities. Besides, signals on one lane show stronger long-range cross-correlation than that on adjacent lanes. Thus, the multiscale cross-correlation structure acquired by MS-EDXA is more close to the intrinsic mechanism of traffic system and reflects more accurate and more abundant traffic information.

There are some methods to decompose a signal into different components such as: Fourier decomposition and wavelet decomposition. But they have limitations in some aspects. Recently, there is a new signal decomposition algorithm called the Empirical Mode Decomposition (EMD) Algorithm which provides a powerful tool for adaptive multiscale analysis of nonstationary signals. Recent works have demonstrated that EMD has remarkable effect in time series decomposition, but EMD also has several problems such as scale mixture and convergence property. This paper proposes two key points to design Bandwidth EMD to improve on the empirical mode decomposition algorithm. By analyzing the simulated and actual signals, it is confirmed that the Intrinsic Mode Functions (IMFs) obtained by the bandwidth criterion can approach the real components and reflect the intrinsic information of the analyzed signal. In this paper, we use Bandwidth EMD to decompose electricity consumption data into cycles and trend which help us recognize the structure rule of the electricity consumption series.

Empirical mode decomposition (EMD) is an adaptive and data-driven approach for analyzing multicomponent nonlinear and non-stationary signals. The mode-mixing problem is one of the most important topics for the improvement of the EMD algorithm. In this paper, we study the reasons of the mode mixing phenomenon. And then, we propose a new method to resolve this problem relying on the assumption that each IMF should be locally orthogonal to the others. We experiment on several signals, including simulated and real-life signals, to demonstrate the efficacy of the proposed method to resolve the mode mixing problem.

This paper proposes the fractal features for glycyrrhiza fingerprint of medicinal herbs, to obtain the intrinsic mode functions (IMFs) from high to low frequency by using empirical mode decomposition (EMD). The EMD fractal features are extracted through computing the fractal dimensions of each IMF. The novel approach is applied to the recognition of the three types of glycyrrhiza fingerprints. Experiments show that EMD fractal features have better recognition rate than that of the traditional ones in the case of concentration-change, i.e. the number of peak and peak drift of sample which has slight changes. An existing method to extract the fractal features for fingerprint of medicinal herbs based on wavelet transform, which is called fractal-wavelet features, was presented. This method has anti-jamming property against the change of samples concentration. However, the recognition rate based on fractal-wavelet features is not satisfactory when fingerprint of medicinal herbs has some slight concentrations changes, the number of peak and peak drift of samples are processed in the special situation.

The Hilbert-Huang Transform (HHT) method for nonlinear and non-stationary time series analysis is applied to wave field data from the nearshore area. The frequency-time distribution of the energy, designated as a Hilbert spectrum is utilized for the examination of the sea waves and their group structure. The key feature of the HHT method is Empirical Mode Decomposition (EMD), which provides a unique basis for expansion of the data, derived from and based on the data. The necessary condition for the existence of wave grouping is determined based on the results of Empirical Mode Decomposition of the data. An attempt is made to investigate the transformation of the sea waves by examination of the decomposition components along the beach profile. The cross-shore variations of the group characteristics are studied. The Hilbert-Huang Transform method provides new insights on the wave and group cross-shore transformation.

A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturally without any a priori subjective criterion selection as in the intermittence test for the original EMD algorithm. This new approach utilizes the full advantage of the statistical characteristics of white noise to perturb the signal in its true solution neighborhood, and to cancel itself out after serving its purpose; therefore, it represents a substantial improvement over the original EMD and is a truly noise-assisted data analysis (NADA) method.

A multi-dimensional ensemble empirical mode decomposition (MEEMD) for multi-dimensional data (such as images or solid with variable density) is proposed here. The decomposition is based on the applications of ensemble empirical mode decomposition (EEMD) to slices of data in each and every dimension involved. The final reconstruction of the corresponding intrinsic mode function (IMF) is based on a comparable minimal scale combination principle.

For two-dimensional spatial data or images, f(x,y), we consider the data (or image) as a collection of one-dimensional series in both x-direction and y-direction. Each of the one-dimensional slices is decomposed through EEMD with the slice of the similar scale reconstructed in resulting two-dimensional pseudo-IMF-like components. This new two-dimensional data is further decomposed, but the data is considered as a collection of one-dimensional series in y-direction along locations in x-direction. In this way, we obtain a collection of two-dimensional components. These directly resulted components are further combined into a reduced set of final components based on a minimal-scale combination strategy.

The approach for two-dimensional spatial data can be extended to multi-dimensional data. EEMD is applied in the first dimension, then in the second direction, and then in the third direction, etc., using the almost identical procedure as for the two-dimensional spatial data. A similar comparable minimal-scale combination strategy can be applied to combine all the directly resulted components into a small set of multi-dimensional final components.

For multi-dimensional temporal-spatial data, EEMD is applied to time series of each spatial location to obtain IMF-like components of different time scales. All the ith IMF-like components of all the time series of all spatial locations are arranged to obtain ith temporal-spatial multi-dimensional IMF-like component. The same approach to the one used in temporal-spatial data decomposition is used to obtain the resulting two-dimensional IMF-like components. This approach could be extended to any higher dimensional temporal-spatial data.

This work presents a discussion on the probability density function of Intrinsic Mode Functions (IMFs) provided by the Empirical Mode Decomposition of Gaussian white noise, based on experimental simulations. The influence on the probability density functions of the data length and of the maximum allowed number of iterations is analyzed by means of kernel smoothing density estimations. The obtained results are confirmed by statistical normality tests indicating that the IMFs have non-Gaussian distributions. Our study also indicates that large data length and high number of iterations produce multimodal distributions in all modes.

Gravitational waves are a consequence of Einstein's theory of general relativity applied to the motion of very dense and massive objects such as black holes and neutron stars. Their detection will reveal a wealth of information about these mysterious objects that cannot be obtained with electromagnetic probes. Two projects are underway to attempt the detection of gravitational waves: LISA, a space based mission being designed to search for waves from supermassive black holes at the centers of galaxies, and LIGO, a ground based facility that is now searching for waves from supernovae, pulsars, and the coalescence of black hole and neutron star systems. Because general relativity is an inherently nonlinear theory, many of the predicted source waveforms show strong frequency modulation. In addition, the LIGO and LISA detectors are highly sensitive devices that produce a variety of nonlinear, transient noise features. Thus the unique capabilities of the HHT, the extraction of intrawave modulation and the characterization of nonlinear and nonstationary signals, have a natural application to both signal detection and experimental characterization of the detectors.

The empirical mode decomposition (EMD) was a method pioneered by (N. Huang et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear nonstationary time series analysis, Proc. Roy. Soc. Lond. A454 (1998) 903–995) as an alternative technique to the traditional Fourier and wavelet techniques for studying signals. It decomposes a signal into several components called intrinsic mode functions (IMFs), which have shown to admit better behaved instantaneous frequencies via Hilbert transforms. In this paper, we propose an alternative algorithm for EMD based on iterating certain filters, such as Toeplitz filters. This approach yields similar results as the more traditional sifting algorithm for EMD. In many cases the convergence can be rigorously proved.

As a reliable approach for human identification, iris recognition has received increasing attention in recent years. This paper proposes a new analysis method for iris recognition based on Hilbert–Huang transform (HHT). We first divide a normalized iris image into several subregions. Then the main frequency center information based on HHT of each subregion is employed to form the feature vector. The proposed iris recognition method has nice properties, such as translation invariance, scale invariance, rotation invariance, illumination invariance and robustness to high frequency noise. Moreover, the experimental results on the CASIA iris database which is the largest publicly available iris image data sets show that the performance of the proposed method is encouraging and comparable to the best iris recognition algorithm found in the current literature.