Alireza Ahrabian

Classification of Motor Imagery BCI Using Multivariate Empirical Mode Decomposition

Brain electrical activity recorded via electroencephalogram (EEG) is the most convenient means for brain-computer interface (BCI), and is notoriously noisy. The information of interest is located in well defined frequency bands, and a number of standard frequency estimation algorithms have been used for feature extraction. To deal with data nonstationarity, low signal-to-noise ratio, and closely spaced frequency bands of interest, we investigate the effectiveness of recently introduced multivariate extensions of empirical mode decomposition (MEMD) in motor imagery BCI. We show that direct multichannel processing via MEMD allows for enhanced localization of the frequency information in EEG, and, in particular, its noise-assisted mode of operation (NA-MEMD) provides a highly localized time-frequency representation. Comparative analysis with other state of the art methods on both synthetic benchmark examples and a well established BCI motor imagery dataset support the analysis.

Synchrosqueezing-based time-frequency analysis of multivariate data

The modulated oscillation model provides physically meaningful representations of time-varying harmonic processes, and has been instrumental in the development of modern time-frequency algorithms, such as the synchrosqueezing transform. We here extend this concept to multivariate signals, in order to identify oscillations common to multiple data channels. This is achieved by introducing a multivariate extension of the synchrosqueezing transform, and using the concept of joint instantaneous frequency multivariate data. For rigor, an error bound which assesses the accuracy of the multivariate instantaneous frequency estimate is also provided. Simulations on both synthetic and real world data illustrate the advantages of the proposed algorithm. HighlightsMultivariate time-frequency algorithm using synchrosqueezing transform.By frequency partitioning, thus identifying multivariate monocomponent signals.In conjunction with the joint instantaneous frequency estimator.So as to represent multivariate data with a single time-frequency representation.

Bivariate Empirical Mode Decomposition for Unbalanced Real-World Signals

The bivariate empirical mode decomposition (BEMD) algorithm employs uniform sampling on a circle to perform projections in multiple directions, in order to calculate the local mean of a bivariate signal. However, this approach is adequate only for equal powers in both the data channels within a bivariate signal, and results in suboptimal performance for data channels exhibiting power imbalance, a typical case in practice. To that end, we exploit second-order bivariate statistical properties to introduce a nonuniform sampling scheme for data adaptive selection of the projection directions. In this way, the resulting nonuniformly sampled BEMD (NS-BEMD) algorithm provides a more accurate time-frequency representation of bivariate data than standard BEMD, for the same number of projections. The advantages of the proposed approach are demonstrated in case studies on BEMD for correlated data channels, selection of optimal noise power in noise-assisted BEMD, and for speed estimation using Doppler radar.

A Class of Multivariate Denoising Algorithms Based on Synchrosqueezing

Univariate thresholding techniques based on high resolution time-frequency algorithms, such as the synchrosqueezing transform, have emerged as important tools in removing noise from real world data. Low cost multichannel sensor technology has highlighted the need for direct multivariate denoising, and to this end, we introduce a class of multivariate denoising techniques based on the synchrosqueezing transform. This is achieved by partitioning the time-frequency domain so as to identify a set of modulated oscillations common to the constituent data channels within multivariate data, and by employing a modified universal threshold in order to remove noise components, while retaining signal components of interest. This principle is used to introduce both the wavelet and Fourier based multivariate synchrosqueezing denoising algorithms. The performance of the proposed multivariate denoising algorithm is illustrated on both synthetic and real world data.

Algorithmic Trading Using Phase Synchronization

A novel trading algorithm which performs trading decisions by making use of phase synchronization between oscillatory components of asset pairs is proposed. This way the phase information ascertains a leading asset, which is then used to predict the lagging asset. The oscillatory components of asset pairs are identified using the Synchrosqueezed Transform (SST), which facilitates stable and online implementation. The performance of the proposed approach is compared with existing algorithms used extensively by traders, such as the moving average cross-over, and an extrapolation algorithm based upon the multichannel-least mean square (MLMS).

Nonuniformly sampled trivariate empirical mode decomposition

Multichannel data-driven time-frequency algorithms, such as the multivariate empirical mode decomposition (MEMD), have emerged as important tools in the analysis of inter-channel dependencies that arise in multivariate data. Such methods employ uniform projection schemes on hyperspheres in order to estimate the local mean, thus requiring dense but underutilised sampling when processing unbalanced data channels. To this end, we propose a nonuniform projection scheme that adapts to the second order statistics of trivariate data; this provides the estimation of the local mean in the case of power imbalances and correlations between the channels. The algorithm is particularly useful for generating a low number of direction vectors within MEMD. Its performance is illustrated on synthetic and real-world data.

Selective Time-Frequency Reassignment Based on Synchrosqueezing

Reassignment methods seek to sharpen the time-frequency representation of conventional time-frequency algorithms, such as the continuous wavelet transform (CWT). However, such methods aim to localize both noise components and signal components of interest, which makes the discrimination between such components for low SNR signals a difficult task. Inspired by the recovery of modes (RCM) algorithm, we propose a selective time-frequency reassignment procedure that attempts to identify and localize oscillatory components of interest for the continuous wavelet transform (CWT), where the reassignment is carried out for selective localization. The performance of the proposed method is illustrated on both synthetic and real world data.

Estimation of phase synchrony using the synchrosqueezing transform

Phase synchronization has emerged as an important concept in quantifying interactions between dynamical systems. In this work a robust estimate of the phase synchrony between bivariate signals is presented. This is achieved by extending the recently introduced synchrosqueezing transform (SST), a method that belongs to the class of reassignment techniques that generates highly localized time-frequency representations, so as to cater for bivariate data. The proposed method is shown to generate accurate estimates of phase synchrony on both synthetic and real world signals.