Improved detection of collective rhythms in multi-channel electroencephalography signals

Abstract

[eng] This work focuses on the experimental data analysis of phase-synchronized oscillators and, more specifically, electroencephalography data, in which multiple sensors are recording oscillatory voltage time series. The electroencephalography data analyzed in this dissertation were recorded by us through a commercial headset. Our goal is to optimally estimate the phase of phase-synchronized oscillators from noisy, phase lagged multivariate time series, which may be non-stationary. In other words, we want to recover the dynamics encoded in the noisy data of a system that behaves as a ”common oscillator”, which we cannot measure directly. To this end, we review some concepts and methods of signal processing, linear algebra and statistics, which we found necessary for the subject to be discussed. Traditional methods like principal and independent component analysis are compared to more recent approaches to extract a collective rhythm from phase-synchronized data. Furthermore, we reproduce and extend the work by Schwabedal and Kantz (PRL 116, 104101 (2016)) evaluating the performance of the Kosambi-Hilbert torsion method to extract a collective rhythm from multivariate oscillatory time series and comparing it to results obtained from principal component analysis. Their method generalizes singular value decomposition to account for possible phase lags among different time series and allows to focus the analysis on a specific spectral band, optimally amplifying the signal-to-noise ratio of the common rhythm. We found an improvement in the signal-to-noise ratio with respect to principal component analysis when the Kosambi-Hilbert torsion is applied to both synthetic and experimental data, namely, that the phase estimation is also improved.