# Independent Component Analysis (ICA)

An excellent introduction to ICA analysis and it's application to the analysis of event-related brain potentials can be found on the EEGLAB website.

# Blind Source Separation (BSS)

Blind Source Separation, refer to methods which allow the separation of a set of signals from a set of mixed signals, without the aid of information about the nature of the signals. Blind Source Separation algorithms rely on the following assumption: the source signals are mutually statistically independent. BSS thus separates a set of signals into a set of other signals, such that the statistical independence is maximized.

In the Cocktail-Party-Problem, you are attending a party with several simultaneous conversations. Several microphones, located at different places in the room, are simultaneously recording the conversations. Each microphone recording can be considered as a linear mixture of each 'independent' conversation.

Each microphone signal can be modeled as linear superpositions of the recorded source signals (linear mixture by unknown matrix A).

The objective of BSS is to find a matrix (W) allowing to recover the original source signals.

The cocktail party problem applies to EEG recordings. Indeed, at each electrode location, the signal recorded can be considered as a linear mixture of underlying neural generators.

# Independent Component Analysis (ICA)

ICA determines what spatially fixed and temporally independent component activations compose an observed time-varying response. Spatially-stable and sparsely-active independent components are hypothesized to sum to the observed multichannel recordings.

(adapted from Makeig et al. (1999)

To apply ICA to EEG recordings, one must assume that the mixing medium is linear, that propagation delays are negligible, and that the spatial location of the artifactual source is fixed across time (see also Jung et al. 2000).

# Spatio-temporal decomposition of event-related potentials using ICA

Decompose one or more ERPs into a linear sum of activations of independent sources with spatially fixed scalp distributions with maximally independent time-courses.

Applying ICA to separate ERP peaks into 'independent sources' requires the following assumptions: (1) the summation at scalp electrodes of potentials arising from different brain areas is linear, (2) that ERPs are largely the sum of relatively brief activations in a restricted set of spatially stable brain areas, and (3) that the activation time-courses of different sources are largely temporally independent.

ICA decomposition was applied to the average waveform of laser-evoked brain potentials (128-channel recording). The six first independent components (ICs) are displayed, in order of their projected variance.