Studying embedded human EEG dynamics using generative topographic mapping

Abstract

A method has recently been proposed [1] to extract multiple signal source information from single-channel electroencephalogram (EEG) recordings. A dynamical systems approach is used to analyze the resulting EEG time series, and its dynamics are captured by the transformation of the original data into an embedding matrix residing in a Euclidean embedding space. Measurements in [1] are taken to be of ongoing unbounded EEG recordings. Many experiments concerning the study of cognitive tasks, though, are developed in a multi-subject repetitive setting where time-boundaries are defined in relation to the onset time of certain stimuli. Each repetition of an experiment is known as a trial and, although the experimental setting might induce to expect little variability amongst responses, the reality usually yields high inter-trial and inter-subject variability. Pooling all responses may mislead their interpretation. In this paper we resort to the Generative Topographic Mapping (GTM, [2]), a neural-network inspired but statistically principled unsupervised model, to achieve the following goals: First, the definition of groups of trials with intra-group similarities and inter-group differences in order to improve the interpretability of the results in the aforementioned experimental settings; second, the visualization of embedded EEG dynamics in a 2-dimensional latent space; finally, the study of the trajectories of these EEG dynamics over the GTM latent space representation, showing that transitions and stationary states in these trajectories correspond to special features in the time-power and time-frequency representations of the EEG data.