The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
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TL;DR: This work proposes a model that predicts epileptic seizures' sufficient time before the onset of seizure starts and provides a better true positive rate, and applies empirical mode decomposition (EMD) for preprocessing and extracted time and frequency domain features for training a prediction model.
Abstract: Epileptic seizures occur due to disorder in brain functionality which can affect patient's health. Prediction of epileptic seizures before the beginning of the onset is quite useful for preventing the seizure by medication. Machine learning techniques and computational methods are used for predicting epileptic seizures from Electroencephalograms (EEG) signals. However, preprocessing of EEG signals for noise removal and features extraction are two major issues that have an adverse effect on both anticipation time and true positive prediction rate. Therefore, we propose a model that provides reliable methods of both preprocessing and feature extraction. Our model predicts epileptic seizures' sufficient time before the onset of seizure starts and provides a better true positive rate. We have applied empirical mode decomposition (EMD) for preprocessing and have extracted time and frequency domain features for training a prediction model. The proposed model detects the start of the preictal state, which is the state that starts few minutes before the onset of the seizure, with a higher true positive rate compared to traditional methods, 92.23%, and maximum anticipation time of 33 minutes and average prediction time of 23.6 minutes on scalp EEG CHB-MIT dataset of 22 subjects.
140 citations
Cites methods from "The empirical mode decomposition an..."
...We have performed the empirical mode decomposition (EMD) after converting into the surrogate channel to increase the signal-to-noise ratio....
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...In empirical mode decomposition (EMD) [27], a time domain signal is broken into a number of oscillatory functions known as Intrinsic Mode Functions (IMFs)....
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...We have applied empirical mode decomposition (EMD) for preprocessing and have extracted time and frequency domain features for training a prediction model....
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...We have applied EMD on surrogate channels of each session for all subjects in MATLAB....
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...In the next step, empirical mode decomposition (EMD) is applied on the surrogate channel EEG signal for further increasing SNR. Statistical features in time domain and spectral features in frequency domain have been extracted....
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TL;DR: Spectral Proper Orthogonal Decomposition (SPOD) as discussed by the authors is based on classical POD and it can be applied to spatially and temporally resolved data, and it allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter.
Abstract: The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods fail when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these "rigid" approaches, we propose a new method termed Spectral Proper Orthogonal Decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical system theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap, and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range.
140 citations
Cites methods from "The empirical mode decomposition an..."
...The principal approach is comparable to the empirical mode decomposition (Huang et al. 1998), but the SPOD can also handle multiple sensors....
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01 May 2009
TL;DR: It is found that attention to a stimulus in their joint receptive field leads to enhanced oscillatory coupling between the two areas, particularly at gamma frequencies, which may optimize the postsynaptic impact of spikes from one area upon the other, improving cross-area communication with attention.
Abstract: Electrical recordings in humans and monkeys show attentional enhancement of evoked responses and gamma synchrony in ventral stream cortical areas. Does this synchrony result from intrinsic activity in visual cortex or from inputs from other structures? Using paired recordings in the frontal eye field (FEF) and area V4, we found that attention to a stimulus in their joint receptive field leads to enhanced oscillatory coupling between the two areas, particularly at gamma frequencies. This coupling appeared to be initiated by FEF and was time-shifted by about 8 to 13 milliseconds across a range of frequencies. Considering the expected conduction and synaptic delays between the areas, this time-shifted coupling at gamma frequencies may optimize the postsynaptic impact of spikes from one area upon the other, improving cross-area communication with attention.
140 citations
TL;DR: The proposed method for automated classification of sleep stages based on iterative filtering of EEG signals has provided better tenfold cross- validation classification accuracy than other existing methods.
Abstract: Computer-aided sleep monitoring system can effectively reduce the burden of experts in analyzing the large volume of electroencephalogram (EEG) recordings corresponding to sleep stages. In this paper, a new technique for automated classification of sleep stages based on iterative filtering of EEG signals is presented. In order to perform sleep stages classification, the EEG signals are decomposed using iterative filtering method. The modes obtained from iterative filtering of EEG signal can be considered as amplitude-modulated and frequency-modulated (AM-FM) components. The discrete energy separation algorithm (DESA) is applied to the modes to determine amplitude envelope and instantaneous frequency functions. The extracted amplitude envelope and instantaneous frequency functions have been used to compute Poincare plot descriptors and statistical measures. The Poincare plot descriptors and statistical measures are applied as input features for different classifiers in order to classify sleep stages. The classifiers namely, naive Bayes, k-nearest neighbor, multilayer perceptron, C4.5 decision tree, and random forest are applied in order to classify the EEG epochs corresponding to various sleep stages. The experimental study has been performed on online available Sleep-EDF database for two-class to six-class classification of sleep stages based on EEG signals. The two-class to six-class classification problems are formulated by taking different combinations of EEG signals corresponding to various sleep stages. The comparison of the results is presented for different multi-class classification problems with the other recently proposed methods. The results show that the proposed method has provided better tenfold cross-validation classification accuracy than other existing methods.
140 citations
Cites methods from "The empirical mode decomposition an..."
...Iterative filtering [15, 44] is an alternative algorithm for the empirical mode decomposition (EMD) method [26], and it can better handle the issues related to the sifting process and cubic spline algorithm....
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TL;DR: In this article, support vector regression machines are used to predict the signals before the signal is decomposed by EMD method, thus the end effects could be restrained effectively and the IMFs with certain physical sense could be obtained.
140 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
"The empirical mode decomposition an..." refers background in this paper
...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.
8,808 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
6,693 citations
"The empirical mode decomposition an..." refers background in this paper
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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01 Jan 1946
5,910 citations
"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
5,806 citations
"The empirical mode decomposition an..." refers background in this paper
...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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