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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08 Sep 2020
TL;DR: Results indicate that EEG signals discriminate SZ patients from healthy control (HC) subjects efficiently and have the potential to become a tool for the psychiatrist to support the positive diagnosis of SZ.
Abstract: Diagnosis of schizophrenia (SZ) is traditionally performed through patient’s interviews by a skilled psychiatrist. This process is time-consuming, burdensome, subject to error and bias. Hence the aim of this study is to develop an automatic SZ identification scheme using electroencephalogram (EEG) signals that can eradicate the aforementioned problems and support clinicians and researchers. This study introduces a methodology design involving empirical mode decomposition (EMD) technique for diagnosis of SZ from EEG signals to perfectly handle the behavior of non-stationary and nonlinear EEG signals. In this study, each EEG signal is decomposed into intrinsic mode functions (IMFs) by the EMD algorithm and then twenty-two statistical characteristics/features are calculated from these IMFs. Among them, five features are selected as significant feature applying Kruskal Wallis test. The performance of the obtained feature set is tested through several renowned classifierson a SZ EEG dataset. Among the considered classifiers, theensemble bagged tree performed as the best classifier producing 93.21% correct classification rate for SZ, with an overall accuracy of 89.59% for IMF 2. These results indicate that EEG signals discriminate SZ patients from healthy control (HC) subjects efficiently and have the potential to become a tool for the psychiatrist to support the positive diagnosis of SZ.
103 citations
Cites background or methods from "The empirical mode decomposition an..."
...The detail description of this method is available in [21], [25], [29], [34]–[36]....
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...as [21], [25], [29], [34], [35]: x (t) = ∑k m=1 I M Fm (t) + rk(t) (1)...
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...the instantaneous frequency (IF) of the intrinsic modes [21]....
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...Each IMF in the equation (1) presents a redolent local frequency, and different IMFs do not show the same frequency at the same time [21], [25], [29]....
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TL;DR: Confidence is shown that DPCCA is an useful method in addressing complex systems after physically explainable results on the winter-time Pacific Decadal Oscillation and Nino3 Sea Surface Temperature Anomaly.
Abstract: In this paper, a new method, detrended partial-cross-correlation analysis (DPCCA), is proposed. Based on detrended cross-correlation analysis (DCCA), this method is improved by including partial-correlation technique, which can be applied to quantify the relations of two non-stationary signals (with influences of other signals removed) on different time scales. We illustrate the advantages of this method by performing two numerical tests. Test I shows the advantages of DPCCA in handling non-stationary signals, while Test II reveals the “intrinsic” relations between two considered time series with potential influences of other unconsidered signals removed. To further show the utility of DPCCA in natural complex systems, we provide new evidence on the winter-time Pacific Decadal Oscillation (PDO) and the winter-time Nino3 Sea Surface Temperature Anomaly (Nino3-SSTA) affecting the Summer Rainfall over the middle-lower reaches of the Yangtze River (SRYR). By applying DPCCA, better significant correlations between SRYR and Nino3-SSTA on time scales of 6 ~ 8 years are found over the period 1951 ~ 2012, while significant correlations between SRYR and PDO on time scales of 35 years arise. With these physically explainable results, we have confidence that DPCCA is an useful method in addressing complex systems.
102 citations
TL;DR: The proposed algorithm can effectively extract the phase synchrony changes prior to the seizure onset and contribute to the application of the seizure prediction.
102 citations
Cites methods from "The empirical mode decomposition an..."
...The empirical mode decomposition (EMD) method can adaptively decompose a multi-component signal into a series of signal oscillators termed as intrinsic mode functions (IMFs) (Huang et al., 1998)....
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TL;DR: In this article, the authors examined the possibility of detecting climatic changes in ocean circulation from sea level data and showed that changes in the AMOC transport from the RAPID project since 2004 are consistent with the flow between Bermuda and the U.S. coast derived from the Oleander measurements and from the sea level difference (SLDIF).
102 citations
TL;DR: A novel method for an automated diagnosis of glaucoma using digital fundus images using Variational mode decomposition (VMD) method, which achieved classification accuracies of 95.19% and 94.79% using three-fold and ten-fold cross-validation strategies, respectively is presented.
102 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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