Biomedical Engineering Reference
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nonlinear. In current applications, ICA attempts only to “undo” the linear mixing
produced by volume conduction and linear summation of fields at the electrodes.
Assumption (3), of independence or near independence of the underlying source
signals, is compatible with physiological models that emphasize the role of anatomi-
cally dominant local, short-range intracortical and radial thalamocortical coupling in
the generation of local electrical synchronies in the EEG [41]. These facts suggest that
synchronous field fluctuations should arise within compact cortical source domains,
although they do not in themselves determine the spatial extent of these domains. If
we assume, therefore, that the complexity of EEG dynamics can be modeled, in sub-
stantial part at least, as summing activities of a number of very weakly linked and,
therefore, nearly statistically independent brain processes, EEG data should satisfy
assumption (3). However, in practice, it is important to consider which EEG pro-
cesses may express their independence in the EEG or ERP training data because the
assumption of temporal independence used by ICA cannot be satisfied when the
training dataset is too small. The number of time points required for training is pro-
portional to the number of variables in the unmixing matrix (the square of the num-
ber of channels). Decomposing a single 1-second ERP average (32 channels, 512 time
points) from one task condition, for example, is unlikely to obtain comprehensible
results. In this case, temporal independence might be achieved or approximated by
sufficiently and systematically varying the experimental stimulus and task conditions,
creating an ERP average for each stimulus/task condition, and then decomposing the
concatenated collection of resulting ERP averages. However, simply varying stimuli
and tasks does not always guarantee that all of the spatiotemporally overlapping EEG
processes contributing to the averaged responses will be independently activated in
the ensemble of input data. These issues imply that results of ICA decomposition of
averaged ERPs must be interpreted with caution. A better solution is likely to be
obtained by decomposing the concatenated data trials as a single dataset. Because the
definition of independence used by many ICA algorithms is based on instantaneous
relationships, discontinuities in the data are not an obstacle. Whatever the data ICA
decomposition is applied to, converging behavioral or other evidence must be
obtained before concluding that spatiotemporally overlapping ICA components mea-
sure neurophysiologically or functionally distinct activities.
Assumption (4), that
N
-channel EEG data mixes the activities of
N
or fewer
sources, is certainly questionable, since we do not know in advance the effective
number of statistically independent brain signals contributing to the EEG recorded
from the scalp. As demonstrated by simulations [42], when training data consist of
fewer large source components than channels, plus many more small source compo-
nents, as might be expected in actual EEG data, large source components are accu-
rately separated into separate output components, with the remaining output
components consisting of mixtures of smaller source components. In this sense, per-
formance of the ICA degrades gracefully as the number of smaller sources or the
amount of noise in the data increases.
2.4.2.2 Component Projections and Artifact Removal
Brain activities of interest accounted for by single or by multiple components can be
obtained by projecting selected ICA component(s)
k
back onto the scalp,
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