Decomposing the EEG in time, space and frequency: a formal model, existing methods, and new proposals

Abstract

In order to discuss and extend the different EEG analysis methods, we propose a general model of the EEG that views brain electric data as composed of a set of waveshapes (the so-called dictionary) and a set of topographies. Dictionary and topographies are related through a weighting matrix (the so-called coefficients). Many existing methods, such as waveshape analysis, power maps, FFT approximation, microstates, principal component analysis, and the recently proposed topographic time-frequency decomposition can be seen as special cases of this framework that make specific, a priori assumptions about the dictionary and the maps, and the coefficients are then treated as dependent variables. The current article briefly discusses the validity and implications of these assumptions, which allows deducing the validity and properties of the corresponding methods. From this discussion, it becomes obvious that there is a shift from older methods that are a priori unique because they use orthogonal elements to newer methods that require additional, physiological constraints because they use non-orthogonal elements. The advantage of these new methods is that while they are objective, quantifiable, and mathematically well-defined procedures, they produce a data-driven phenomenology that is in close correspondence with the actual physiological events.