Brain–Computer Interfaces - Index of

Digital Signal Processing and Machine Learning 311
2.1.5 Independent Component Analysis (ICA)
ICA can also be used to extract or separate useful components from noise in brain
signals. ICA is a common approach for solving the blind source separation problem
that can be explained with the classical “cocktail party effect”, whereby many
people talk simultaneously in a room but a person has to pay attention to only
one of the discussions. Humans can easily separate these mixed audio signals, but
this task is very challenging for machines. However, under some quite strict limitations,
this problem can be solved by ICA. Brain signals are similar to the “cocktail
party effect”, because the signal measured at a particular electrode originates from
many neurons. The signals from these neurons are mixed and then aggregated at
the particular electrode. Hence the actual brain sources and the mixing procedure is
unknown.
Mathematically, assuming there are n mutually independent but unknown sources
s1(t), ··· , sn(t) in the brain signals denoted as s(t) = [s1(t), ··· , sn(t)] T with zero
mean, and assuming there are n electrodes such that the sources are instantaneously
linearly mixed to produce the n observable mixtures x(t) = [x1(t), ··· , xn(t)] T ,
x1(t),··· , xn(t)[13, 14], then
x(t) = As(t), (6)
where A is an n×n time-invariant matrix whose elements need to be estimated from
observed data. A is called the mixing matrix, which is often assumed to be full rank
with n linearly independent columns.
The ICA method also assumes that the components si are statistically independent,
which means that the source signals si generated by different neurons are
independent to each other. The ICA method then computes a demixing matrix W
using the observed signal x to obtain n independent components as follows,
y(t) = Wx(t), (7)
where the estimated independent components are y1, ··· , yn, denoted as y(t) =
[y1(t), ··· , yn(t)] T .
After decomposing the brain signal using ICA, the relevant components can then
be selected or equivalently irrelevant components can be removed and then projected
back into the signal space using
˜x(t) = W −1 y(t). (8)
The reconstructed signal ˜x represents a cleaner signal than x [15].
There are many ICA algorithms such as the information maximization approach
[13] and the second order or high order statistics based approaches [16]. Several of
them are freely available on the net. There is another source separation technique
called sparse component analysis (SCA) which assumes that the number of source