The Embedding Transform. A Novel Analysis of Non-Stationarity in the EEG

We introduce a novel technique to analyze nonstationarity in single-channel Electroencephalogram (EEG) traces: the Embedding Transform. The approach is based on Walter J. Freeman's studies concerning active and rest stages and deviations from Gaussianity. Specifically, we generalize his idea in order to include cases where the neuromodulations are sparse in time. Specifically, the transform maps the temporal sequences to a set of $\ell ^{2}$-norms where modulated patters are emphasized. In this way, the background, chaotic activity can be modeled as the main lobe of the distribution, while the relevant synchronizations (or desynchronizations) fall on the right (or left) tail of the density of such norms. We test the algorithm on two different datasets: alpha bursts on synthetic data simulated in the BESA software and low-gamma oscillations in the motor cortex from the Brain-Computer Interface (BCI) Competition 4 Dataset 4. The results are promising and place the Embedding Transform as a quick, single-parameter tool to effectively assess which channels (or regions) are actively engaged in particular behaviors and which are in a more silent type of stage.