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subjected to following equality constraints:
¼
T
g
y
i
x
ð
x
i
Þþ
b
1
e
i
;
i
¼
1
2
3
;
...
;
N
ð
23
Þ
;
;
T
. The Lagrangian multiplier
where, e
¼
ð
e
1
;
e
2
;
...
;
e
N
Þ
a
i
can be de
ned for (
22
) as:
X
N
i¼1
a
i
f
y
i
½
x
T
g
ð
x
i
Þþ
b
1
þ
e
i
g
L
ðx
;
b
;
e
; aÞ
¼J
ðx
;
b
;
e
Þ
ð
24
Þ
On solving (
24
), the LS-SVM classi
er can be expressed as:
"
#
sign
X
N
i¼1
a
i
y
i
K
ð
x
;
x
i
Þþ
b
f
ð
x
Þ
¼
ð
25
Þ
where, K
is a kernel function. The following kernel functions are used in this
work, which have been de
ð
x
x
i
Þ
;
ned in Khandoker et al. (
2007
):
1. Linear kernel: The linear kernel can be de
ned as:
x
T
x
i
ð
x
i
Þ
¼
ð
Þ
K
x
;
26
2. Polynomial kernel: The polynomial kernel can be de
ned as:
d
x
T
x
i
þ
K
ð
x
x
i
Þ
¼
ð
1
Þ
ð
27
Þ
;
where d is the degree of polynomial.
3. Radial basis function (RBF) kernel: The RBF kernel can be de
ned as:
e
jj
x
x
i
jj
2
K
ð
x
x
i
Þ
¼
ð
28
Þ
;
2
2
r
where, width of RBF kernel can be controlled by varying scaling factor
r
. The
performance evaluation parameters of the LS-SVM classi
er depends on the
selection of the kernel parameters. In this work, we have used trial and error
method in order to determine the suitable kernel parameters for classi
cation of
normal and epilpetic seizure EEG signals.
2.4.1 Performance Evaluation Parameters
The classi
cation of normal
and epileptic seizure EEG signals can be evaluated by computing the sensitivity,
speci
cation performance of the LS-SVM classi
er for classi
city, and accuracy. Sensitivity measures the ability of test to identify pro-
portion of actual positives as such. Considering an example where percentage of
epileptic seizure signals from test set, correctly falls in the category of epileptic
seizure signals after classification. Specificity measures the ability of test to exclude
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