Independent Component Analysis

Independent Component Analysis (ICA) is a computational technique for separating a multivariate signal into additive subcomponents by assuming that the subcomponents are statistically independent rather than merely uncorrelated. Where PCA finds axes of maximum variance, ICA finds axes of maximum statistical independence—a stronger and more biologically plausible criterion. ICA was originally developed for the blind source separation problem: recovering individual voices from a cocktail-party recording without knowing the mixing process in advance.

The most widely used ICA algorithm, FastICA, iteratively finds directions in which the projected data has maximum non-Gaussianity, exploiting the central limit theorem's implication that mixtures of independent signals are more Gaussian than the sources themselves. ICA has become a foundational method in neuroimaging, where it is used to separate artifactual and neural signals in fMRI and EEG data. Unlike PCA components, which are ordered by variance, ICA components are unordered and must be interpreted by their statistical properties or domain relevance—a feature that makes ICA more flexible but also more cognitively demanding for the analyst.