Independent Component Analysis (ICA)
ICA is a blind source separation method that decomposes multichannel data into a set of maximally statistically independent components by exploiting non-Gaussianity or higher-order statistics rather than mere decorrelation. It assumes the sensors observe a linear, instantaneous mixture of underlying sources, an assumption that is physically well matched to EEG because volume conduction spreads each source to the scalp essentially instantaneously and linearly. Popular estimators include Infomax, FastICA, and the more thorough AMICA.
In BCI it serves two roles: isolating and removing stereotyped artifacts (eye blinks, lateral eye movement, ECG, and muscle) by rejecting their components, and separating physiologically distinct cortical sources for cleaner feature extraction. Its intrinsic ambiguities are that component scale and sign are arbitrary and their ordering is not meaningful, so components are labelled by their scalp map, spectrum, and time course, increasingly with automated classifiers such as ICLabel.
Decomposing a 64-channel record often yields one component whose scalp map is a frontal dipole, whose time course spikes at every blink; zeroing that one component and back-projecting removes blinks while preserving posterior alpha.
Artifact removal by selective component rejection.
ICA breaks when the mixing is not instantaneous or is nonstationary, when sources outnumber sensors, or when the artifact and brain source are genuinely dependent; it does not certify that a component is purely brain or purely artifact.