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B,B
of biclusters for matrix
A
as
and match score between two sets
|S
i
∩S
i
|
|S
1
|B|
∑
(
S
i
,F
i
)
∈B
S
∗
(
B,B
)=
max
(
S
i
,
F
i
)
∈
B
|
,
∪S
i
i
which reflects the average of the maximum match scores for all biclusters in
B
with
B
.
In [44], Prelic et al. used this score to comparing the algorithms of Bimax, CC,
OPSM, SAMBA, xMotifs, and ISA with respect to the data set of a metabolic path-
way map. And in [12], Cho and Dhillon also use this score to compare several
biclustering algorithms on human cancer microarrays data sets.
respect to the biclusters in
6.4 Application of Biclustering in Computational Neuroscience
Epilepsy is one of the most common nervous system disorders. It affects about
1% of the world's population with the highest incidence among infants and the el-
derly [20, 21]. For many years there have been attempts to control epileptic seizures
by electrically stimulating the brain [25]. This alternate method of treatment is the
subject of much study since the approval of the chronic vagus nerve stimulation
(VNS) implant for treatment of intractable seizures [56, 24, 49]. The device con-
sists of an electric stimulator implanted subcutaneously in the chest and connected,
via subcutaneous electrical wires, to the left cervical vagus nerve. The VNS is pro-
grammed to deliver electrical stimulation at a set intensity, duration, pulse width,
and frequency. Optimal parameters are determined on a case-by-case basis, depend-
ing on clinical efficacy (seizure frequency) and tolerability.
Busygin et al. used supervised consistent biclustering [6] to develop a physio-
logic marker for optimal VNS parameters (e.g., output current, signal frequency)
using measures of scalp EEG signals.
The raw EEG data was obtained from two patients
A
and
B
at 512 Hz sam-
pling rate from 26 scalp EEG channels arranged in the standard international 10-20
system (see Fig. 6.1). Then the EEG was transformed into a sequence of short-
term largest Lyapunov exponents (STL
max
) values. A famous practical applica-
tion of STL
max
measure of EEG signal time series is to predict epileptic seizures,
see [29, 41, 42]. Thus, Lyapunov exponents are considered to be a perfect descriptor
of such extremely complex dynamic system as human brain.
STL
max
values were computed for each scalp EEG channel recorded from two
epileptic patients using the algorithm developed by Iasemidis et al. [29]. Then the
STL
max
values were used as features of the two data sets. The averaged samples
from stimulation periods were then separated from averaged samples from nonstim-
ulation periods by feature selection performed within the consistent biclustering
routine.
