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demonstrate such obscure mixture in the raw EEGs (Figs. 4.2b, 4.3b, and 4.4b). In
our implementation, ICA was applied to the whole 5-min recording of each patient
and the selection of the interval of interest prior to ICA calculation was not needed.
4.3 Methods
4.3.1 Independent Component Analysis and Extraction
of CJD-Related Components
Independent component analysis is a statistical method that has been developed to
extract independent signals from a linear mixture of sources. Let
mxn
denote the
measured data with
m
and
n
being the number of channels and the number of data
samples, respectively. In the context of ICA, it is assumed to be linear combinations
of unknown independent components and can be expressed as
X
(4.3)
S
kxn
,
mxn
=
A
mxk
·
where
S
contains
k
independent sources with the same data length as
X
, and
A
is a constant mixing matrix with the
k
th column representing the spatial weights
corresponding to the
k
th component of
S
. Given the measurement
X
, ICA techniques
attempt to recover both the mixing matrix
A
and the independent sources
S
.Inthe
present study, all calculations were performed using the FastICA algorithm [11, 23].
The FastICA technique first removes means of the row vectors in the
X
matrix and
then uses a whitening procedure, implemented by principal components analysis [1],
to transform the covariance matrix of the zero-mean data into an identity matrix. In
the next step, FastICA searches for a rotation matrix to further separate the whitened
data into a set of components which are as mutually independent as possible. In
combination with previous whitening process, the matrix
X
is transformed into a
matrix
S
via an unmixing matrix
W
, i.e.,
S
kxn
=
W
kxm
X
mxn
,
(4.4)
so that rows of
S
are mutually independent. The fixed-point method for solving
W
T
in the FastICA, where
k
is the number of independent sources,
can be summarized as follows [11]:
For
i
=(
w
i
, ··· ,
w
k
)
=
1:
k
,
1. Randomly choose a weighting vector
w
i
2. Let
w
+
=
w
i
x
g
(
w
i
x
E
{
xg
(
)
}−
E
{
)
}
w
i
, where
g
(
u
)=
tanh
(
c u
)
,
1
≤
c
≤
2
w
i
4. Go back to step 2 if not converge.
w
i
/
3. Let
w
i
=
