Data-driven time-frequency analysis of multivariate data

Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition and time-frequency analysis of real world nonstationary signals. Its main advantages over other time-frequency methods are its locality, data-driven nature, multiresolution-based decomposition, higher time-frequency resolution and its ability to capture oscillation of any type (nonharmonic signals). These properties have made EMD a viable tool for real world nonstationary data analysis. Recent advances in sensor and data acquisition technologies have brought to light new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore, imperative to design multivariate extensions of the existing nonlinear and nonstationary analysis algorithms as they are expected to give more insight into the dynamics and the interdependence between multiple channels of such signals. To this end, this thesis presents multivariate extensions of the empirical mode de- composition algorithm and illustrates their advantages with regards to multivariate non- stationary data analysis. Some important properties of such extensions are also explored, including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple data channels. Owing to the generality of the proposed methods, an improved multi- variate EMD-based algorithm is introduced which solves some inherent problems in the original EMD algorithm. Finally, to demonstrate the potential of the proposed methods, simulations on the fusion of multiple real world signals (wind, images and inertial body motion data) support the analysis

Noise-Assisted Instantaneous Coherence Analysis of Brain Connectivity

Characterizing brain connectivity between neural signals is key to understanding brain function. Current measures such as coherence heavily rely on Fourier or wavelet transform, which inevitably assume the signal stationarity and place severe limits on its time-frequency resolution. Here we addressed these issues by introducing a noise-assisted instantaneous coherence (NAIC) measure based on multivariate mode empirical decomposition (MEMD) coupled with Hilbert transform to achieve high-resolution time frequency representation of neural coherence. In our method, fully data-driven MEMD, together with Hilbert transform, is first employed to provide time-frequency power spectra for neural data. Such power spectra are typically sparse and of high resolution, that is, there usually exist many zero values, which result in numerical problems for directly computing coherence. Hence, we propose to add random noise onto the spectra, making coherence calculation feasible. Furthermore, a statistical randomization procedure is designed to cancel out the effect of the added noise. Computer simulations are first performed to verify the effectiveness of NAIC. Local field potentials collected from visual cortex of macaque monkey while performing a generalized flash suppression task are then used to demonstrate the usefulness of our NAIC method to provide highresolution time-frequency coherence measure for connectivity analysis of neural data

A different view on the vector-valued empirical mode decomposition (VEMD)

The empirical mode decomposition (EMD) has achieved its reputation by providing a multi-scale time-frequency representation of nonlinear and/or nonstationary signals. To extend this method to vector-valued signals (VvS) in multidimensional (multi-D) space, a multivariate EMD (MEMD) has been designed recently, which employs an ensemble projection to extract local extremum locations (LELs) of the given VvS with respect to different projection directions. This idea successfully overcomes the problems of locally defining extrema of VvS. Different from the MEMD, where vector-valued envelopes (VvEs) are interpolated based on LELs extracted from the 1-D projected signal, the vector-valued EMD (VEMD) proposed in this paper employs a novel back projection method to interpolate the VvEs from 1-D envelopes in the projected space. Considering typical 4-D coordinates (3-D location and time), we show by numerical simulations that the VEMD outperforms state-of-art methods.Comment: 7th International Congress on Image and Signal Processing (CISP

Multivariate Signal Denoising Based on Generic Multivariate Detrended Fluctuation Analysis

We propose a generic multivariate extension of detrended fluctuation analysis (DFA) that incorporates interchannel dependencies within input multichannel data to perform its long-range correlation analysis. We next demonstrate the utility of the proposed method within multivariate signal denoising problem. Particularly, our denosing approach first obtains data driven multiscale signal representation via multivariate variational mode decomposition (MVMD) method. Then, proposed multivariate extension of DFA (MDFA) is used to reject the predominantly noisy modes based on their randomness scores. The denoised signal is reconstructed using the remaining multichannel modes albeit after removal of the noise traces using the principal component analysis (PCA). The utility of our denoising method is demonstrated on a wide range of synthetic and real life signals

EEG signal analysis via a cleaning procedure based on multivariate empirical mode decomposition

IJCCI 2012Artifacts are present in most of the electroencephalography (EEG) recordings, making it difficult to interpret or analyze the data. In this paper a cleaning procedure based on a multivariate extension of empirical mode decomposition is used to improve the quality of the data. This is achieved by applying the cleaning method to raw EEG data. Then, a synchrony measure is applied on the raw and the clean data in order to compare the improvement of the classification rate. Two classifiers are used, linear discriminant analysis and neural networks. For both cases, the classification rate is improved about 20%

Dynamically sampled multivariate empirical mode decomposition

A method for accurate multivariate local mean estimation in the multivariate empirical mode decomposition algorithm by using a statistical data-driven approach based on the Menger curvature measure and normal-to-anything variate-generation method is proposed. This is achieved by aligning the projection vectors in the direction of the maximum `activity' of the input signal by considering the local curvature of the signal in multidimensional spaces, resulting in accurate mean estimation even for a very small number of projection vectors

Turning Tangent Empirical Mode Decomposition: A Framework for Mono- and Multivariate Signals.

International audienceA novel Empirical Mode Decomposition (EMD) algorithm, called 2T-EMD, for both mono- and multivariate signals is proposed in this paper. It differs from the other approaches by its computational lightness and its algorithmic simplicity. The method is essentially based on a redefinition of the signal mean envelope, computed thanks to new characteristic points, which offers the possibility to decompose multivariate signals without any projection. The scope of application of the novel algorithm is specified, and a comparison of the 2T-EMD technique with classical methods is performed on various simulated mono- and multivariate signals. The monovariate behaviour of the proposed method on noisy signals is then validated by decomposing a fractional Gaussian noise and an application to real life EEG data is finally presented