Abstract
This work focuses on the experimental data analysis of electroencephalography (EEG) data, in which multiple sensors are recording oscillatory voltage time series. The EEG data analyzed in this manuscript has been acquired using a low-cost commercial headset, the Emotiv EPOC+. Our goal is to compare different techniques for the optimal estimation of collective rhythms from EEG data. To this end, a traditional method such as the principal component analysis (PCA) is compared to more recent approaches to extract a collective rhythm from phase-synchronized data. Here, we extend the work by Schwabedal and Kantz (PRL 116, 104101 (2016)) evaluating the performance of the Kosambi-Hilbert torsion (KHT) method to extract a collective rhythm from multivariate oscillatory time series and compare it to results obtained from PCA. The KHT method takes advantage of the singular value decomposition algorithm and accounts 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 a common rhythm. We evaluate the performance of these methods for two particular sets of data: EEG data recorded with closed eyes and EEG data recorded while observing a screen flickering at 15 Hz. We found an improvement in the signal-to-noise ratio of the collective signal for the KHT over the PCA, particularly when random temporal shifts are added to the channels.