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q
l
p
l
max_
disqp
=
max(
X
−
X
)
q
,
p
∈
1
..
N
(1)
Then the normalized variance of
X
i
l
(
i
∈
1..N
) denoted by
nvar
is defined as follow.
q
l
n
var
=
Var
(
X
)
/
max_
disqp
q
∈
1
..
N
(2)
Var
is the variance of X
q
l
. Now
var
is calculated according the
following equations.
q
where
(
X
)
l
0
n
var
<
v
⎧
1
⎪
⎨
var
=
1
v
≤
n
var
<
v
(3)
1
2
⎪
⎩
2
v
≤
n
var
2
where
v
1
and
v
2
are two user-specified thresholds. For calculating
dis
j
1
,
max_disp
is
first defined as following equation
.
p
max_
disp
=
max(
X
−
X
)
p
∈
1
..
N
(4)
g
l
Then the normalized distance between
X
j
l
and
X
g
denoted by
ndis
j
1
is defined as
follow.
j
j
ndis
=
(
X
−
X
)
/
max_
disp
(5)
1
g
l
Now
dis
j
1
is calculated according the following equations.
⎧
j
0
ndis
<
d
1
11
⎪
⎨
j
j
dis
=
1
d
≤
ndis
<
d
(6)
1
11
1
12
⎪
⎩
j
2
d
≤
ndis
12
1
where
d
11
and
d
12
are two user-specified thresholds. And finally for calculating
dis
j
2
,
max_disq
is first defined as following equation
.
p
max_
disq
=
max(
X
−
X
)
p
∈
1
..
N
(7)
Then the normalized distance between
X
j
l
and
x
j
denoted by
ndis
j
2
is defined as
following.
p
l
j
p
l
ndis
=
(
X
−
X
)
/
max_
disq
(8)
2
p
Now
dis
j
2
is calculated according the following equation.
⎧
j
0
ndis
<
d
2
21
⎪
⎨
j
j
dis
=
1
d
≤
ndis
<
d
(9)
2
21
2
22
⎪
⎩
j
2
d
≤
ndis
22
2
where
d
21
and
d
22
are two user-specified thresholds. Pseudo code of the proposed
algorithm is presented in the Fig. 1. In this code
r
1
and
r
2
are both 0.5. Also all
w
1
,
w
2
and
w
3
are 0.33.
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