Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 149

dependent component analysis (ICA, see Sect. 3.6.2). Linear data decompositions,
such as PCA or ICA, separate multichannel data into a sum of activities of com-
ponents each comprised of a time course of its activity in every trial and a single
scalp map giving the strength of the volume conducted component activity at each
scalp electrode. Note that polarity seen in the ICA and PCA maps of topographical
component distribution has no real meaning. The actual potential distribution is the
product of the map and the value of the component in a given moment in time.
The goals of PCA and ICA are different. Let us consider for a k channel signal that
the k values of potential measured at a certain moment in time are coordinates of a
point in the k -dimensional space. The PCA extracts temporally orthogonal directions
(axes) in that space. 6 The components are the projections of the original data onto
these axes, with the first principal component representing the maximum variation
in the data; the second principal component is orthogonal to the first and represents
the maximum variation of the residual data. This process of component extraction
is repeated several times, and since the original variables are correlated only a small
number of principal components accounts for a large proportion of the variance in
the original data [Skrandies, 1989, Skrandies, 2005].
The goal of ICA, on the other hand, is to find components in the data whose ac-
tivities are statistically as distinct from one another as possible, meaning that their
signals have the least possible mutual information. Minimizing mutual information
implies not only decorrelating the component signals, but also eliminating or reduc-
ing their higher-order joint statistics. This stronger statistical independence allows
ICA to relax the orthogonality of the component scalp maps, which is physiolog-
ically more plausible, and to separate phase-uncoupled activities generated in spa-
tially fixed cortical domains (or non-brain artifact sources).
If the scalp maps associated with different activities are not orthogonal, PCA will
mix portions of them into one or more principal components, rather than separating
them into different components, as is the case in ICA. Thus, if the recorded data
are in fact the sum of (nearly) independent signals from spatially confined and dis-
tinguishable sources, PCA will lump, and ICA will split the source activities across
resultant signal components.
Data reduction by PCA may be efficient for compression, but the higher flexibility
of ICA decomposition, with spatially overlapping scalp maps allowed, may result
in components which are easier to interpret in the physiological context. ICA can
be applied to EEG epochs averaged in the time domain [Makeig et al., 1997] or to
non-averaged concatenated EEG epochs [Makeig et al., 2004]. In both cited studies
ICA allowed separating late cognitive ERPs into distinct, independent constituents.
Applying ICA one has to be aware that an obtained independent component (IC)
does not necessarily represent an anatomically defined source of activity. Indeed, an
IC is defined by its temporal independence relative to the other sources of activity.
If the activities within two distinct regions of the brain strongly covary, they will be
represented within a single component. In case of unconstrained ICA, the total num-
6 Corresponding to necessarily orthogonal scalp maps.