Information Technology Reference
In-Depth Information
5. Decorrelation by Gram-Schmidt-like scheme, Let
w
i
=
j
−
1
j
1
w
i
w
j
w
j
6. Renormalize
w
i
,Let
w
i
=
w
i
−
∑
=
w
i
/
w
i
end
Since EEG can be considered as a linear combination of electric brain activities
[5], we employed ICA to extract the disease-related components from the EEG of
five patients. In this study, each preprocessed epoch was arranged across
m
channels
(
m
=
=
∗
300) into a matrix
X
.The
i
th row contains
the observed signal from the
i
th EEG channel, and the
j
th column vector contains
the observed samples at the
j
th time point across all channels. FastICA was applied
on each preprocessed epoch to resolve the
W
and
S
. After estimating the unmixing
matrix
W
, we can recover the temporal waveforms by applying the inverse matrix
of
W
on both sides of Equation (4.4) to yield
17) and
n
sampled points (
n
250
W
−
1
mxk
·
X
mxn
=
S
kxn
,
(4.5)
where
W
−
1
is the best estimation of the mixing matrix
A
in Equation (4.3). In the
cocktail-party problem, a popular example of ICA model, the
k
th row of
S
represents
the voice from the
k
th speaker, and the element of mixing matrix
A
in the
m
th
column and
k
th row, i.e., represents the weighting of the voice from the
k
th speaker
recorded in the
m
th microphone. In other words, the
k
th column of
A
represents
the weightings of the voice of
k
th speaker at each microphone. In this study,
S
represents the time sequences of activation sources, i.e., temporal waveforms of ICs
in Figs. 4.2, 4.3, 4.4, and 4.5, and
A
stands for the weighting of sources recorded
from electrodes. Since
W
is the estimated unmixing matrix, each column represents
a spatial map describing the weightings of the corresponding temporal component
at each EEG channel. These spatial maps will hereinafter be referred to as IC spatial
maps. The validation of applying ICA to decompose EEG data has been addressed
in the previous studies [10,13,14,15,16,18,17,22,23,26]. In this study, we have also
varied the data length, namely 1-, 2-, 3-, 4-, and 5-min epoch of data, to evaluate
the performance of ICA and applied PCA on the same data sets for comparing their
results on the feature extraction.
4.3.2 Bayesian Information Criterion
We have adopted the Bayesian information criterion (BIC) [2, 9, 19], which was
based on the estimation of posterior probability
P
given the number of
sources
k
and the observed data
X
to estimate the number of sources. The poste-
rior probability was the function of
A
given by
(
X
|
A
,
k
)
exp
1
|
T
1
1
2
S
k
,
t
(
Λ
−
1
)
t
,
t
S
k
,
t
)=
∏
k
t
,
t
P
(
X
|
A
,
k
·
−
,
(4.6)
k
det
(
A
)
|
|
2
πΛ
k
|
