Empirical Mode Decomposition Combined with Local Linear Quantile Regression for Automatic Boundary Correction

Biomedical signals are in general non-linear and non-stationary which renders them difficult to analyze with classical time series analysis techniques. Empirical Mode Decomposition (EMD) in conjunction with a Hilbert spectral transform, together called Hilbert-Huang Transform, is ideally suited to extract informative components which are characteristic of underlying biological or physiological processes. The method is fully adaptive and generates a complete set of orthogonal basis functions, called Intrinsic Mode Functions (IMFs), in a purely data-driven manner. Amplitude and frequency of IMFs may vary over time which renders them different from conventional basis systems and ideally suited to study non-linear and non-stationary time series. However, biomedical time series are often recorded over long time periods. This generates the need for efficient EMD algorithms which can analyze the data in real time. No such algorithms yet exist which are robust, efficient and easy to implement. The contribution shortly reviews the technique of EMD and related algorithms and develops an on-line variant, called slidingEMD, which is shown to perform well on large scale biomedical time series recorded during neuromonitoring.

A robust time series prediction method based on empirical mode decomposition and high-order fuzzy cognitive maps

In the marine environment, the recorded time series are often nonlinear and nonstationary and interact with each other. Their analysis faces new challenges and thus requires the implementation of adequate and specific methods. We use the Hilbert-Huang Transform (HHT) for the spectral analysis of high frequency sampled time series in near shore waters of Cambridge Bay, located in the Canadian Arctic. We focus particularly on automatic measurements of temperature records, salinity, turbidity and chlorophyll data sets from deployments on an Ocean Networks Canada cabled platform. We look at the contribution of different Intrinsic Mode Functions (IMFs) obtained by the Empirical Mode Decomposition (EMD). The inertial wave and several low-frequency tidal waves are identified by the application of EMD. Furthermore, the correlation between two nonstationary time series is investigated. By Time Dependent Intrinsic Correlation (TDIC) analysis, it was concluded that the high-frequency modes have small correlation; whereas the trends are perfectly correlated. The methodologies presented in this paper are general. They can be applied for identification of main properties of other time series from the environmental and oceanic sciences, where the records are complex with fluctuations over a large range of different spatial and temporal scales.

The electric power load is inherently nonlinear and nonstationary time series, which has periodicity and randomicity. It is difficult to accurately forecast with a single method. So a hybrid method based on empirical mode decomposition (EMD) and support vector machines (SVMs) was presented in this paper. First, load time series was adaptively decomposed into a series of smooth intrinsic mode functions (IMFs) with different scales via EMD; second, tendency of each IMF was forecasted with different SVM respectively according to its change and weather factors were taken account in forecasting; finally, final results were obtained by summing up these forecasting results of each IMF together. The simulation results show that the hybrid method has higher precision and greater generalization ability.

The Fourier transform of a nonstationary time series has the difficulty of providing a proper physical interpretation of the signal as the physical attributes and dynamics associated with the time series may consist of several transients that are different in their nature. The time series analysis method developed by NASA [N. Huang et al., ‘‘The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis’’ (to be published)] has a unique approach to adaptively break down the nonstationary time series into the sum of several simple mode functions. Each single mode function can then be expressed in terms of an analytical signal whose amplitude and phase can both be varied with time. Those time variations can be related to the abrupt changes associated with dynamic systems. Such a time variation characteristic can be used to observe the occurrence of a transient event even in a nonstationary process. Applications of this technique to observe various types of acoustic signals in noisy environments are discussed.

This paper presents an Empirical mode decomposition (EMD) approach for achieving high-speed frequency-tagged steady state visual evoked potential (SSVEP) brain computer interface (BCI) system. Empirical mode decomposition (EMD) has been demonstrated as a local and fully data-driven technique for the data processing of nonlinear and non-stationary time-series. It allows the frequency and amplitude of a time-series to be evaluated with excellent time resolution. The proposed system utilized flickering sources with high flickering rate acting as cursor system for the purpose of alternatively communication system. Induced EEG signal were decomposed into different scale of oscillation components namely intrinsic mode functions. In order to find out the SSVEP-related IMFs, instantaneous frequency were computed by generalized zero crossing (GZC). After identification of the frequency power by quadrature detection, the result shows the proposed system achieved 51.46 bits/min of average ITR. Compare with FFT approaches, EMD method provide better temporal and frequency sensitivity in detection of cognitive state of neuron activities.KeywordsBrain computer interface (BCI)Empirical mode decomposition (EMD)Steady-state visual evoked potential (SSVEP)

Biomedical signals are in general non-linear and non-stationary. Empirical Mode Decomposition in conjunction with Hilbert-Huang Transform provides a fully adaptive and data-driven technique to extract Intrinsic Mode Functions (IMFs). The latter represent a complete set of locally orthogonal basis functions to represent non-linear and non-stationary time series. Large scale biomedical time series necessitate an online analysis which is presented in this contribution. It shortly reviews the technique of EMD and related algorithms, discusses the newly proposed SEMD algorithm and presents some applications to biomedical time series recorded during neuromonitoring.

Semi-parametric regression model prediction method based on empirical mode decomposition was studied in this paper. Firstly, basic idea of the empirical mode decomposition was introduced, and the improved algorithm was proposed to mitigate the end effect in the iterative shift process. Secondly, least squares method was employed to estimate the parameter β based on the trend component of empirical mode decomposition, and the non-parametric g(·) was estimated through building the AR models of the intrinsic mode functions. The vector matrix was computed by Yule-Walker method. Finally, time series prediction of two nonlinear systems was analyzed based on the semi-parametric regression model. The results show that the proposed model predictive method is fit for nonlinear and non-stationary time series estimate.

Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity and nonstationarity. When a subset of the series exhibits nonlinear characteristics, frequency domain clustering methods based on higher-order spectral properties, such as the bispectra or trispectra are useful. While these methods address nonlinearity, they rely on the assumption of series stationarity. We propose the Bispectral Smooth Localized Complex EXponential (BSLEX) approach for clustering nonlinear and nonstationary time series. BSLEX is an extension of the SLEX approach for linear, nonstationary series, and overcomes the challenges of both nonlinearity and nonstationarity through smooth partitions of the nonstationary time series into stationary subsets in a dyadic fashion. The performance of the BSLEX approach is illustrated via simulation where several nonstationary or nonlinear time series are clustered, as well as via accurate clustering of the records of 16 seismic events, eight of which are earthquakes and eight are explosions. We illustrate the utility of the approach by clustering S&P 100 financial returns.

Most often, climate change signals are slow moving (in human terms), low amplitude changes embedded in high amplitude, noisy data. There are many techniques for extracting such signals. This paper introduces a technique which in contrast with empirical methods produces a decomposition of a time series into a set of equations plus a This is referred to as stepwise symbolic secomposition (SSD). The extraction of symbolic equations in lieu of empirical functions assists with characterization of time series. This paper takes two examples of climate data, and applies two different techniques for characterising the low amplitude, slow change embedded therein. The record of CO2 levels at Mauna-Loa since March 1958, is used to demonstrate and contrast empirical mode decomposition (EMD), and SSD. The mean monthly tidal gauge records from the small number of gauges which have more than 120 years of data are analysed in more detail by SSD, then three techniques are used to characterize the residual. The techniques are (a) LOESS smoothing, (b) EMD, and (c) high order polynomial regression. SSD uses a genetic programming system called Eureqa from Cornell Creative Machines Lab guided by an information metric, to extract the most compact informative function it can at each step; the process is repeated on the residuals until no sufficiently informative function is found. EMD and SSD are in stark contrast in the order in which signals are decomposed. EMD extracts high frequency components first. SSD extracts components based on a mixture of parsimonious representation and variance explained. EMD leaves a low frequency filtrate of the signal in its residue, SSD tends to operate as a broad band filter, leaving high frequency noise plus a possible low frequency signal. EMD, LOESS and polynomial fitting all serve to extract low frequency components of the signal from this SSD residual. For the set of tidal gauge data, in the absence of a change in global sea level rise, the SSD procedure should randomize all segments of residual signals equally - the residual should be whitened with respect to the initial signal. It is shown however that late 20th century portions of the residuals show behaviour that is consistent with accelerating sea level rise in keeping with the bulk of the literature.

Empirical Mode Decomposition (EMD) has proved to be an effective and powerful analytical tool for non-stationary time series and starts to exhibit its modeling potential for 3D geometry analysis. Yet, existing EMD-based geometry processing algorithms only concentrate on multi-scale data decomposition by way of computing intrinsic mode functions. More in-depth analytical properties, such as Hilbert spectra, are hard to study for 3D surface signals due to the lack of theoretical and algorithmic tools. This has hindered much more broader penetration of EMD-centric algorithms into various new applications on 3D surface. To tackle this challenge, in this paper we propose a novel and efficient EMD and Hilbert spectra computational scheme for 3D geometry processing and analysis. At the core of our scheme is the strategy of dimensionality reduction via space-filling curve. This strategy transforms the problem of 3D geometry analysis to 1D time series processing, leading to two major advantages. First, the envelope computation is carried out for 1D signal by cubic spline interpolation, which is much faster than existing envelope computation directly over 3D surface. Second, it enables us to calculate Hilbert spectra directly on 3D surface. We could take advantages of Hilbert spectra that contain a wealth of unexploited properties and utilize them as a viable indicator to guide our EMD-based 3D surface processing. Furthermore, to preserve sharp features, we develop a divide-and-conquer scheme of EMD by explicitly separating the feature signals from non-feature signals. Extensive experiments have been carried out to demonstrate that our new EMD and Hilbert spectra based method is both fast and powerful for 3D surface processing and analysis.

Financial time series forecasting has been a challenge for time series analysts and researchers because it is noisy, nonstationary and chaotic. To overcome this limitation, this study uses empirical mode decomposition (EMD) and phase space reconstruction (PSR) to assist in the task of financial time series forecasting. In addition, we propose an approach that combines these two data preprocessing methods with extreme learning machine (ELM). The approach contains four steps as follows. (1) EMD is used to decompose the dynamics of the exchange rate time series into several components of intrinsic mode function (IMF) and one residual component. (2) The IMF and residual time series phase space is reconstructed to reveal its unseen dynamics according to the optimum time delay $$\tau $$ź and embedding dimension m. (3) The reconstructed time series datasets are divided into two datasets: training and testing, in which the training datasets are used to build ELM models. (4) A regression forecast model is set up for each IMF as well as the residual component by using ELM. The final prediction results are obtained by compositing the prediction values. To verify the effectiveness of the proposed approach, four exchange rates are chosen as the forecasting targets. Compared with some existing state-of-the-art models, the proposed approach yields superior results. Academically, we demonstrated the validity and superiority of the proposed approach that integrates EMD, PSR, and ELM. Corporations or individuals can apply the results of this study to acquire accurate exchange rate information and reduce exchange rate expenses.

The importance of understanding the underlying characteristics of private placement Announcement Effect attracts much attention from academic researchers and financial practitioners. Due to the overwhelming complexity of the financial market, many traditional methods such as intervention method and event study fail to produce consistently good analysis results. Empirical Mode Decomposition (EMD), proposed by Huang et al., appears to be a promising data analysis method for nonlinear and non-stationary time series. In this paper, innovative EMD-based multi-scale event analysis method is proposed to estimate the impact of Announcement Date Effect on stock price volatility, and then take illustrative FangDa Group (000055 in Shenzhen Stock Market) to verify the effectiveness of the proposed method. The case study results show that this approach is a promising method from the multi-scale point of view to analyze the impact of Announcement Date Effect in stock market.

The condition of locomotive bearings, which are essential components in trains, is crucial to train safety. The morphologic analysis of the locomotive bearing vibration signal, which are always contaminated by certain types of noise, is very important standard for mechanical condition diagnosis of the locomotive bearing and mechanical failure phenomenon. In this paper a novel vibration signal enhancement method based on empirical mode decomposition (EMD) and adaptive filtering is proposed to filter out Gaussian noise contained in raw vibration signal. The reference signal of the adaptive filter is produced by selective reconstruction of the decomposition results of EMD. Real vibration signals from the locomotive bearing are used to validate the performance of the proposed method. Conventional EMD and adaptive EMD are tested to compare the filtering performance. The results of simulation show that the vibration signal can be significantly enhanced by using the proposed method. Besides, the proposed method is used to analyze real acoustic signals of locomotive bearing with inner race and outer race faults, respectively. The results confirm that the periods between the transients, which represent locomotive bearing fault characteristics, can be detected successfully.

A filtering method based on empirical mode decomposition (EMD) for coulostatically-induced transients (CITs) was presented. The effect of EMD filtering was evaluated from different simulation systems. To boost the applicable solution for EMD filtering and reduce the subjectivity of filtering, discussions of the simulating noises were mainly focused on white noise, high frequency noise, 50 Hz noise from commercial power and blend of above-mentioned noises. To illustrate the most importance of EMD filtering for the goodness of fit of CIS, one real corrosion system involving multi-time constant was simultaneously investigated by electrochemical impedance spectrum (EIS) and coulostatically-induced spectrum (CIS). The results reported here demonstrate that EMD de-noising is applicable for CITs. The proposed method shows good performance of de-noising and is an alternative de-noising method for the CITs analysis. CIS with EMD filtering are in good agreement with EIS. For practical application of EMD, removal of the first two items of intrinsic mode function (IMF) and 50 Hz element in forth IMF will be generally satisfactory for CIS analysis.