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p
05). Accordingly, the concurrent existence of multiple features presented in
the early EEG of CJD patients can be used as an assistive tool for the early diagnosis
of CJD.
The order of same CJD-related components may vary from patient to patient
since both the mixing matrix A and source matrix S are unknown, which allows the
change of the order of rows in S. To see this, we can substitute a permutation matrix
P and its inverse into the model,
X
<
0
.
AP
−
1
. The matrix
AP
−
1
is a new unknown mixing matrix to be solved by the FastICA algorithm [11]
and the rows of
PS
are original sources but in different order because each row or
column in
P
consists of only one nonzero element with value 1. It is much easier
to detect the CJD-related patterns from the unmixed signals rather than from the
obscured mixing signals as illustrated in Figs. 4.2, 4.3, and 4.4, although the same
CJD-related sources would occur at different channels among patients. In addition,
we found that the ICs consisting of larger spikes, such as irregular waveforms and
bursts, tended to be decomposed earlier from the mixing signals in the calculation of
FastICA. All the CJD-related features, i.e., sharp waves or epileptiform, have been
recognized from ICs lower than IC8.
It is noted that the matrix
S
has lower amplitude in comparison with the matrix
X
.
Such an amplitude difference comes from the nature of the linear mixing model and
the algorithm of FastICA. Based on the vector form of the model
x
j
=
AS
,togive
X
=(
)(
PS
)
=
a
j
s
1
+
···
+
a
ji
α
−
1
a
ij
s
i
+
···
, it can be rewritten into the form
x
j
=
a
j
1
s
1
+
···
+(
)(
α
s
i
)+
···
,
where
is any arbitrarily nonzero scalar. In other words, the solutions of mixing
A
and source matrix
S
are not unique since any source can be multiplied by a nonzero
scalar which can always be canceled by dividing the corresponding column of
A
by
the same scalar. In order to fix the magnitude of the independent components, each
source is restricted to have unit variance in the FastICA calculation [11]. As a result,
the resolved matrix
S
has lower amplitude than the matrix
X
.
α
4.6 Conclusions
We have employed ICA to detect the co-occurrence of multiple CJD-related
patterns from the EEG recording for aiding to the early diagnosis. Results demon-
strate that ICA is an effective tool for simultaneously recovering the FIRDA,
PLEDs, and triphasic waves (early PSWCs) that can be hardly discerned by vi-
sual inspection from the contaminated EEG recordings. The concurrent appear-
ance of FIRDA and PLEDs or triphasic waves from the same EEG data suggests
that the heterogeneity of EEG in the early diagnosis of CJD should be taken into
account.
Acknowledgments
The study was funded by the Taipei Veterans General Hospital (V96 ER1-
005) and National Science Council (NSC 96-2221-E-010-003-MY3, NSC 97-2752-B-075-001-
PAE, NSC 97-2752-B-010-003-PAE).
