Independent Component Analysis of EEG data: A Primer and Some Collected Resources
Independent component analysis is an artificial neural network algorithm that is very good at extracting statistically independent signals/features/sources from a variety of data inputs, and does this already very well when purely data driven, meaning: It is able to do so without guidance (‘blind source separation’) and is often explained using the cocktail-party effect. Among other things, it has already shown its merits in image processing and a slew of other applications (- “color based detection of the ripeness of tomatoes”). In neuroscience/neuropsychology it finds many possible uses, with in vivo brain signal recordings in particular, among which are fMRI, DTI and, of course, EEG. Human brains themselves appear particularly well equipped to perform blind source separation. Taking the cocktail party effect as an example, think of how we manage to discern voices from background noise or a collection of other voices, in even the most difficult circumstances. A major difference though, is that intuitively human hearing would still be able to make sense of a lot of signals even when using a single ear. The ICA algorithm can do little with a single source of data, but will continue to improve its performance with every new source added, in some cases giving it an advantage over human cognition.
The idea to apply the ICA algorithm to EEG data was introduced in 1996 by Jung, Makeig, Bell & Sejnowski and undoubtedly became very popular due to its inclusion in the EEGLab toolbox made freely available by Delorme & Makeig in 2004. Thanks to the successes of Moore’s law, in recent years application of ICA on recorded brain signals became available to any lab/researcher in possession of a moderately powerful computer, and the algorithm appears to still to be improved upon in various ways, with new implementations and ongoing optimizations appearing regularly.
On the mathematical side of things, ICA seeks patterns in (any) data that are statistically highly independent. This is done using more advanced math and logic than I care to explain here, but essentially it is an (type of) algorithm that seeks to find a set of rotations of N-dimensional data that has been twisted and warped in such a fashion that one maximizes statistical independence of the data in it. Among other things, this involves clever application of the central limit theorem and maximizing non-gaussianity, by pre-whitening the data before a search for the particular rotations starts. This page appears to explain it well for the mathematicians, this (particularly well illustrated) page for intermediates, and this page by the author of the EEGLab plugin may be more suitable for the novice.
ICA decomposition and subsequent reconstruction (back-projection) of the data leaving out certain parts of the signal is already broadly wielded as a method to ‘subtract’ ocular artifacts (blinks and saccades) from EEG data (Cohen, 2014; Luck, 2014). Steven Luck, who appears skeptical -or careful- regarding its use, gives a nice explanation of that particular application in this online chapter.