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o
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l
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s
o
lu
t
i
o
n
[
1
3
]
.
E
a
ch
c
e
l
l
r
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p
r
e
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e
n
t
s
a
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a
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la
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e
d
a
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d
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s
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t
o
an
s
w
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r
q
u
er
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e
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.
T
h
e
ad
v
an
t
ag
e
o
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t
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a
p
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a
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-
d
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m
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s
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o
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a
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s
p
a
c
e
[
1
4
]
.
H
o
we
v
er
,
t
h
e
p
e
r
f
o
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m
a
n
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a
lg
o
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d
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r
i
d
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e,
w
h
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ch
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l
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we
r
t
h
a
n
th
e
d
a
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a
s
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s
i
z
e
.
Fo
r
h
i
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h
l
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ir
r
eg
u
l
ar
d
a
ta
d
i
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io
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s
,
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q
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ir
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t
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o
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th
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m
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an
d
d
a
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a
[
1
5
]
.
T
h
i
s
m
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h
o
d
c
h
ar
a
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d
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wh
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o
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p
ap
p
ea
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s
w
i
th
a
c
l
a
s
s
.
T
h
e
m
a
in
c
h
a
l
l
en
g
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i
n
m
o
d
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l
-
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c
lu
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ty
p
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le
m
,
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h
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a
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o
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in
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u
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b
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o
f
p
a
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a
m
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er
s
[
1
5
]
.
I
n
d
en
s
i
t
y
-
b
a
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d
c
l
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in
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,
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a
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if
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h
ig
h
-
a
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lo
w
-
d
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s
it
y
ar
e
a
s
[
1
6
]
.
T
h
e
a
l
g
o
r
i
t
h
m
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a
n
h
an
d
l
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o
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s
e,
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t
o
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er
s
,
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d
id
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if
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l
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in
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ap
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.
Ho
w
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v
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r
,
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f
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cu
l
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y
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d
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a
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ig
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.
T
h
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c
l
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in
g
a
s
s
i
g
n
m
en
t
[
1
6
]
,
[
1
7
]
.
H
i
er
a
r
c
h
i
ca
l
c
l
u
s
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t
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ag
g
lo
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t
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v
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o
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d
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v
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s
iv
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h
i
e
r
ar
c
h
ic
a
l
ap
p
r
o
a
ch
e
s
[
1
8
]
.
T
h
e
f
o
r
m
e
r
p
er
f
o
r
m
s
o
p
p
o
s
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t
e
l
y
,
t
h
a
t
i
s
,
c
lu
s
t
e
r
in
g
i
s
p
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r
f
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m
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d
b
y
c
o
m
p
u
t
in
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th
e
s
i
m
il
a
r
i
ty
b
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tw
e
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n
c
lu
s
t
e
r
s
an
d
t
h
en
jo
i
n
in
g
th
e
t
wo
m
o
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s
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m
i
l
ar
c
lu
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i
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g
l
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c
l
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s
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b
s
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v
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d
.
T
h
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l
a
t
t
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w
o
r
k
s
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r
ev
e
r
s
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m
an
n
er
,
t
h
at
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s
,
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tr
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cl
u
s
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.
T
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b
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it
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t
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b
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s
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ev
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w
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d
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ta
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s
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ie
r
a
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ch
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o
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q
u
a
l
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ty
c
lu
s
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e
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s
an
d
d
o
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s
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o
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r
eq
u
ir
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e
n
u
m
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er
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f
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l
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s
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r
s
,
wh
i
ch
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s
a
d
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a
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a
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k
o
f
p
ar
t
i
t
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n
a
l
a
l
g
o
r
i
t
h
m
[
1
9
]
.
H
i
e
r
ar
c
h
ic
a
l
c
l
u
s
t
e
r
in
g
p
e
r
f
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s
c
lu
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t
e
r
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n
g
b
a
s
ed
o
n
th
e
p
r
o
x
i
m
i
t
y
m
a
t
r
ix
,
w
h
i
ch
i
s
c
a
l
c
u
l
a
t
ed
u
s
in
g
th
e
d
i
s
t
an
c
e
b
e
t
w
e
en
e
a
ch
p
o
i
n
t
.
T
h
e
d
i
s
ta
n
c
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b
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w
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a
ch
p
o
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ca
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r
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s
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t
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m
e
t
h
o
d
s
,
n
am
e
l
y
,
s
i
n
g
l
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,
co
m
p
l
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t
e
,
a
n
d
a
v
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ag
e
l
i
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k
ag
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s
.
T
h
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s
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g
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in
k
ag
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n
h
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a
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ch
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c
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w
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s
.
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h
e
co
m
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k
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t
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w
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if
f
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c
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s
.
T
h
e
av
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a
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k
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a
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m
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t
in
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e
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e
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c
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.
I
n
an
y
c
l
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s
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i
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ap
p
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o
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ch
e
s
,
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h
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f
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b
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a
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m
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e
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e
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th
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d
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c
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n
in
g
f
u
l
l
y
c
l
u
s
te
r
e
d
o
r
n
o
t
[
2
0
]
.
H
i
e
r
a
r
ch
i
c
a
l
c
lu
s
t
e
r
in
g
i
s
m
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s
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ta
b
l
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in
i
n
d
u
c
in
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th
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c
l
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t
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in
g
t
en
d
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f
d
a
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th
a
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th
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p
a
r
t
i
t
io
n
a
l
o
n
e
[
2
1
]
.
T
h
e
h
i
e
r
ar
c
h
ic
a
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lu
s
t
e
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a
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a
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d
a
t
a
a
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a
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a
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s
.
A
s
m
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ed
,
t
h
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t
o
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g
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t
i
v
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d
d
iv
i
s
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v
e
m
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th
o
d
s
[
2
2
]
.
T
h
e
a
g
g
l
o
m
e
r
a
t
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v
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m
et
h
o
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s
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g
d
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c
t
c
l
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s
(
i
t
em
s
)
b
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.
T
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i
a
l
c
l
u
s
t
e
r
in
g
o
f
ap
p
l
i
c
a
t
io
n
s
w
i
t
h
n
o
i
s
e
(
D
B
S
C
A
N
)
a
l
g
o
r
i
t
h
m
.
I
t
u
t
i
l
i
z
e
s
th
e
k
-
m
ea
n
s
a
l
g
o
r
i
th
m
f
o
r
p
a
r
t
i
t
io
n
s
o
f
th
e
d
a
ta
s
e
t
a
s
t
h
e
f
i
r
s
t
s
t
a
g
e
a
n
d
th
en
em
p
lo
y
s
t
h
e
M
a
x
–
M
in
m
e
th
o
d
to
s
e
l
e
c
t
p
o
i
n
t
s
f
o
r
t
h
e
D
B
S
C
A
N
a
l
g
o
r
i
t
h
m
a
s
th
e
s
e
co
n
d
s
t
a
g
e.
T
h
e
r
e
s
u
l
t
s
o
f
th
e
p
r
o
p
o
s
ed
a
lg
o
r
i
t
h
m
o
u
t
p
e
r
f
o
r
m
e
d
th
e
o
r
ig
i
n
a
l
DB
S
C
A
N
.
T
h
e
q
u
a
l
i
t
y
o
f
r
e
s
u
l
t
i
s
s
e
n
s
i
t
i
v
e
b
e
c
au
s
e
i
t
i
s
b
a
s
ed
o
n
th
e
p
r
e
-
d
e
f
in
e
d
n
u
m
b
e
r
o
f
c
l
u
s
t
er
s
th
a
t
s
h
o
u
l
d
b
e
a
s
s
u
m
e
d
b
y
t
h
e
u
s
er
.
M
o
r
e
o
v
e
r
,
t
h
e
a
lg
o
r
i
th
m
i
s
s
e
n
s
i
t
iv
e
t
o
o
u
t
l
i
er
s
.
I
n
2
0
1
6
,
o
th
e
r
r
e
l
a
t
e
d
wo
r
k
p
r
o
p
o
s
ed
a
n
ag
g
lo
m
er
a
t
i
v
e
h
i
e
r
a
r
ch
i
c
a
l
c
lu
s
t
e
r
i
n
g
t
h
a
t
em
p
l
o
y
ed
a
n
e
w
c
l
u
s
t
er
i
n
g
v
a
l
i
d
i
ty
i
n
d
e
x
p
e
r
f
o
r
m
ed
o
n
t
h
e
b
a
s
i
s
o
f
tw
o
c
o
n
c
ep
t
s
,
i
n
c
lu
d
in
g
d
i
s
p
er
s
i
o
n
an
d
s
y
n
th
e
s
i
s
d
e
g
r
e
e
s
[
3
0
]
.
T
h
e
f
i
r
s
t
c
a
l
cu
la
t
i
o
n
d
if
f
er
e
n
t
ia
t
e
s
th
e
in
t
r
a
-
c
l
u
s
t
e
r
c
o
m
p
a
c
tn
e
s
s
an
d
i
n
te
r
-
c
l
u
s
t
e
r
s
e
p
a
r
a
t
io
n
,
w
h
e
r
e
a
s
th
e
s
y
n
th
e
s
i
s
d
eg
r
e
e
s
u
m
s
i
n
t
r
a
-
c
l
u
s
t
er
c
o
m
p
a
c
tn
es
s
w
i
t
h
i
n
t
e
r
-
c
lu
s
t
e
r
s
ep
a
r
a
t
io
n
.
T
h
e
r
a
t
io
o
f
th
e
c
l
u
s
t
e
r
in
g
d
i
s
p
er
s
i
o
n
d
eg
r
e
e
a
n
d
c
l
u
s
t
e
r
in
g
s
y
n
th
e
s
i
s
d
e
ter
m
i
n
e
s
th
e
q
u
a
l
i
ty
o
f
c
lu
s
t
e
r
a
c
c
o
r
d
in
g
to
th
e
l
e
v
e
l
o
f
p
a
r
t
i
t
io
n
i
n
a
g
g
l
o
m
e
r
a
t
i
v
e
h
i
er
a
r
ch
i
c
a
l
c
l
u
s
t
er
i
n
g
.
H
o
w
e
v
er
,
t
h
e
c
l
u
s
t
e
r
i
n
g
r
a
t
io
c
a
n
b
e
c
a
l
c
u
la
t
e
d
i
n
t
h
e
f
i
n
a
l
s
t
a
g
e
o
f
th
e
ag
g
l
o
m
e
r
a
t
iv
e
h
i
e
r
a
r
ch
i
c
a
l
c
l
u
s
t
e
r
i
n
g
r
e
s
u
l
t
s
.
T
h
e
h
y
b
r
id
a
l
g
o
r
i
t
h
m
co
n
t
a
in
s
d
i
v
i
s
i
v
e
a
n
d
a
g
g
l
o
m
e
r
a
t
iv
e
-
p
e
r
f
o
r
m
ed
t
ex
t
c
l
u
s
t
e
r
in
g
[
3
1
]
.
I
t
c
o
n
t
a
i
n
s
th
e
a
d
v
an
t
a
g
e
o
f
b
o
th
a
l
g
o
r
i
th
m
s
.
T
h
i
s
h
y
b
r
id
i
z
a
t
i
o
n
s
o
l
v
e
s
t
h
e
p
r
o
b
l
e
m
o
f
l
o
c
a
l
m
in
i
m
u
m
p
r
o
d
u
c
e
d
i
n
th
e
h
i
er
a
r
ch
i
c
a
l
c
lu
s
t
e
r
i
n
g
d
u
e
t
o
t
h
e
d
i
f
f
ic
u
l
ty
i
n
r
e
-
j
o
in
i
n
g
i
t
em
s
i
n
d
if
f
er
e
n
t
s
t
a
g
e
s
.
I
n
th
e
f
i
r
s
t
s
t
a
g
e
,
a
g
r
e
a
t
er
to
t
a
l
n
u
m
b
e
r
o
f
c
lu
s
t
e
r
s
th
a
n
t
h
e
a
c
tu
a
l
n
u
m
b
er
i
s
p
r
o
d
u
c
ed
.
Ob
t
a
i
n
ed
ce
n
tr
o
id
s
a
r
e
m
er
g
ed
t
o
f
o
r
m
a
c
tu
a
l
c
lu
s
t
e
r
s
th
a
t
ar
e
co
n
s
i
d
e
r
ed
t
h
e
s
e
co
n
d
s
t
a
g
e
o
f
h
y
b
r
id
a
lg
o
r
i
th
m
.
R
e
s
u
l
t
s
ar
e
s
en
s
i
t
i
v
e
t
o
th
e
in
i
t
i
a
l
n
u
m
b
er
o
f
c
l
u
s
t
e
r
s
,
o
u
t
l
i
e
r
s
,
a
n
d
n
o
i
s
e
.
R
e
s
e
a
r
ch
h
a
s
b
e
e
n
co
n
d
u
c
t
ed
t
o
d
e
t
e
r
m
i
n
e
t
h
e
o
p
t
im
a
l
n
u
m
b
er
o
f
c
lu
s
t
e
r
s
i
n
h
ier
a
r
ch
i
c
a
l
c
l
u
s
t
er
i
n
g
b
y
p
r
o
p
o
s
i
n
g
a
n
e
w
c
l
u
s
t
e
r
v
a
l
i
d
i
t
y
i
n
d
e
x
to
f
i
n
d
th
e
b
e
s
t
p
a
r
t
i
t
io
n
[
3
2
]
.
T
h
e
p
r
o
p
o
s
ed
m
e
t
h
o
d
e
x
t
en
d
s
t
h
e
s
e
a
r
c
h
s
p
a
ce
to
f
in
d
t
h
e
ex
te
n
d
ed
p
ar
t
i
t
i
o
n
.
T
h
u
s
,
i
t
i
s
a
n
e
w
cl
u
s
t
e
r
in
g
v
a
l
i
d
i
ty
i
n
d
e
x
c
a
l
l
ed
c
o
n
t
ex
t
-
i
n
d
ep
e
n
d
en
t
o
p
t
im
a
l
i
ty
t
h
a
t
ca
n
b
e
u
s
e
d
to
f
i
n
d
t
h
e
b
e
s
t
p
a
r
t
i
t
i
o
n
i
n
h
i
e
r
ar
c
h
ic
a
l
c
l
u
s
t
er
i
n
g
.
Ho
w
e
v
e
r
,
th
i
s
s
t
u
d
y
u
s
e
s
a
v
a
l
i
d
i
ty
i
n
d
e
x
t
h
a
t
c
a
lc
u
l
a
t
ed
t
h
e
s
i
m
i
l
ar
i
t
y
o
n
th
e
b
a
s
i
s
o
f
c
e
n
tr
o
id
-
b
a
s
e
d
a
p
p
r
o
a
ch
,
wh
i
c
h
i
s
s
e
n
s
i
t
i
v
e
t
o
o
u
t
l
i
e
r
an
d
n
o
i
s
e
d
a
t
a
.
T
h
e
p
ar
t
i
t
i
o
n
a
l
an
d
h
i
e
r
a
r
ch
i
c
a
l
a
p
p
r
o
a
c
h
e
s
h
a
v
e
b
e
e
n
h
y
b
r
id
i
z
ed
t
o
o
v
er
c
o
m
e
d
i
s
ad
v
an
t
ag
e
s
o
f
b
o
t
h
a
l
g
o
r
i
th
m
s
[
3
3
]
.
A
m
o
d
i
f
i
ed
k
_
m
o
d
e
a
lg
o
r
i
t
h
m
p
er
f
o
r
m
ed
p
ar
t
i
t
i
o
n
a
l
c
l
u
s
t
e
r
in
g
b
a
s
e
d
o
n
a
p
r
e
-
d
e
f
i
n
ed
n
u
m
b
er
o
f
c
lu
s
t
e
r
s
as
t
h
e
in
i
t
i
a
l
s
t
ag
e
.
M
e
a
n
wh
il
e
,
t
h
e
f
in
a
l
s
t
ag
e
p
e
r
f
o
r
m
e
d
ag
g
lo
m
er
a
t
iv
e
c
l
u
s
t
e
r
i
n
g
to
c
o
n
s
t
r
u
c
t
a
h
i
e
r
a
r
ch
y
t
r
ee
.
H
o
w
ev
e
r
,
t
h
e
p
r
o
p
o
s
e
d
h
y
b
r
id
a
l
g
o
r
i
th
m
p
r
o
d
u
c
e
d
u
n
s
t
a
b
l
e
r
e
s
u
l
t
s
.
S
im
i
l
a
r
l
y
,
a
h
y
b
r
i
d
m
e
th
o
d
b
e
tw
e
e
n
p
a
r
t
i
t
io
n
in
g
a
r
o
u
n
d
m
ed
o
i
d
s
(
P
A
M
)
a
n
d
d
i
v
i
s
i
v
e
h
i
e
r
ar
ch
i
c
a
l
c
l
u
s
t
er
i
n
g
,
i
n
w
h
ic
h
t
h
e
n
u
m
b
er
o
f
m
a
i
n
c
l
u
s
t
e
r
s
i
s
d
e
t
er
m
in
e
d
u
s
i
n
g
D
a
v
ie
s
B
o
u
l
d
in
i
n
d
ex
(
D
B
I
)
v
a
lu
e
w
i
t
h
a
n
o
p
t
i
m
a
l
n
u
m
b
e
r
o
f
c
l
u
s
t
e
r
s
i
f
th
e
r
e
s
u
l
t
s
m
in
i
m
i
z
e
th
e
D
B
I
v
a
lu
e
,
w
a
s
p
r
o
p
o
s
ed
[
1
8
]
.
B
a
s
e
d
o
n
th
e
o
b
t
a
in
e
d
n
u
m
b
e
r
o
f
c
l
u
s
t
e
r
s
,
P
A
M
p
e
r
f
o
r
m
s
p
ar
t
i
t
i
o
n
a
l
cl
u
s
t
e
r
i
n
g
f
o
l
l
o
w
ed
b
y
d
i
v
i
s
i
v
e
h
i
er
a
r
ch
i
c
a
l
c
l
u
s
t
e
r
in
g
to
c
o
n
d
u
c
t
th
e
f
in
a
l
r
e
s
u
lt
s
.
O
t
h
e
r
s
tu
d
i
e
s
p
r
o
p
o
s
e
d
a
h
y
b
r
i
d
h
i
er
a
r
ch
i
c
a
l
c
l
u
s
t
e
r
in
g
a
lg
o
r
i
t
h
m
t
o
i
m
p
r
o
v
e
th
e
t
i
m
e
c
o
m
p
l
ex
i
t
y
o
f
h
i
e
r
ar
c
h
ic
a
l
c
l
u
s
t
er
i
n
g
a
lg
o
r
it
h
m
.
T
h
e
p
r
o
p
o
s
ed
a
l
g
o
r
i
t
h
m
s
p
e
r
f
o
r
m
c
lu
s
t
e
r
i
n
g
a
s
t
h
e
f
ir
s
t
s
t
e
p
u
s
in
g
k
-
m
ea
n
s
a
l
g
o
r
i
t
h
m
[
3
4
]
.
S
u
b
s
e
q
u
en
t
l
y
,
o
b
j
ec
t
s
w
i
t
h
i
n
e
a
c
h
c
lu
s
t
e
r
a
r
e
c
l
u
s
t
er
e
d
h
i
er
a
r
c
h
i
ca
l
l
y
b
y
u
s
i
n
g
th
e
ex
a
c
t
a
g
g
lo
m
er
a
t
i
v
e
h
i
er
a
r
c
h
i
c
a
l
c
lu
s
t
e
r
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a
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h
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s
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A
l
t
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a
t
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ly
,
t
h
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a
l
g
o
r
i
th
m
m
a
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a
p
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p
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t
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c
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m
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t
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s
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b
l
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s
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ch
a
s
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g
o
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m
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o
d
s
to
r
e
m
o
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h
e
o
u
t
l
i
e
r
s
.
F
r
o
m
t
h
i
s
p
o
in
t
,
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h
e
p
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p
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d
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lg
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m
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s
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s
m
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id
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b
a
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c
l
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t
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r
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g
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wh
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ia
l
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f
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f
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o
w
ed
b
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a
g
g
l
o
m
e
r
a
ti
v
e
a
p
p
r
o
a
ch
,
w
h
ic
h
r
ep
r
e
s
en
t
s
t
h
e
d
a
t
a
o
f
e
a
ch
c
lu
s
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e
r
a
s
a
n
ag
g
lo
m
er
a
t
i
v
e
h
i
e
r
a
r
ch
ic
a
l
t
r
e
e
.
S
e
l
e
c
t
in
g
m
e
d
o
i
d
-
b
a
s
ed
a
p
p
r
o
a
ch
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s
i
s
b
e
t
t
e
r
th
an
o
p
t
i
n
g
f
o
r
ce
n
tr
o
id
-
b
a
s
e
d
o
n
e
s
b
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c
au
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e
o
f
t
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p
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s
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n
c
e
o
f
n
o
i
s
e
a
n
d
o
u
t
l
i
e
r
s
in
th
e
d
a
t
a.
T
h
e
s
e
a
r
c
h
s
p
a
c
e
o
f
m
e
d
o
i
d
-
b
a
s
ed
ap
p
r
o
a
ch
e
s
i
s
le
s
s
e
r
co
m
p
ar
e
d
w
i
t
h
th
a
t
o
f
t
h
e
s
e
a
r
c
h
s
p
a
c
e
o
f
t
h
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ce
n
tr
o
id
-
b
a
s
e
d
o
n
e
wh
e
r
e
i
t
i
s
l
i
m
i
t
ed
t
o
t
h
e
n
u
m
b
e
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o
f
in
s
t
a
n
c
e
s
in
t
h
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d
a
t
a
s
e
t
.
T
h
e
l
i
m
i
t
a
t
i
o
n
in
[
4
9
]
l
e
ad
s
to
t
h
e
u
s
e
o
f
G
W
O
a
l
g
o
r
i
th
m
t
o
g
r
o
u
p
a
s
e
t
o
f
d
o
c
u
m
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n
t
s
i
n
to
d
i
f
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t
n
u
m
b
e
r
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c
l
u
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t
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r
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b
a
s
ed
o
n
m
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o
id
s
-
b
a
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l
u
s
t
er
i
n
g
,
w
h
ic
h
i
s
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e
tt
e
r
t
h
an
w
h
a
t
wa
s
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d
b
y
[
4
9
]
in
d
e
a
l
i
n
g
w
i
t
h
o
u
t
l
i
er
d
o
c
u
m
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n
t
s
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d
n
o
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d
a
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a
.
M
ed
o
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c
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lc
u
l
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io
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s
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w
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l
im
i
t
a
t
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o
n
i
n
[
3
6
]
,
[
3
7
]
wh
e
r
e
in
t
h
e
p
r
o
p
o
s
e
d
a
lg
o
r
i
t
h
m
w
i
l
l
s
w
a
p
th
e
m
ed
o
id
s
b
e
t
w
e
e
n
th
e
wo
l
v
e
s
t
o
k
e
ep
th
e
b
e
s
t
m
e
d
o
i
d
s
d
u
r
i
n
g
t
h
e
a
l
g
o
r
i
t
h
m
r
u
n
an
d
f
in
d
m
o
r
e
r
e
g
io
n
s
w
i
th
b
e
t
t
er
d
o
c
u
m
e
n
t
c
l
u
s
t
er
i
n
g
a
s
s
i
g
n
m
en
t
s
,
h
a
s
b
e
e
n
ad
d
ed
in
t
h
e
r
e
s
e
a
r
ch
.
T
h
i
s
p
ap
er
h
a
s
b
e
en
o
r
g
a
n
ize
d
i
n
t
o
s
ev
e
r
a
l
s
e
c
t
i
o
n
s
.
S
e
ct
i
o
n
2
s
h
o
w
s
t
h
e
m
e
th
o
d
o
lo
g
y
o
f
t
h
e
s
t
u
d
y
.
s
e
c
t
io
n
3
r
ep
r
e
s
en
t
s
th
e
p
r
o
p
o
s
e
d
a
l
g
o
r
i
t
h
m
.
S
e
c
ti
o
n
s
4
s
h
o
w
s
th
e
s
t
ep
s
o
f
p
r
e
-
p
r
o
c
e
s
s
i
n
g
a
n
d
s
e
c
t
i
o
n
5
d
i
s
cu
s
s
t
h
e
an
a
l
y
s
is
o
f
t
h
e
e
x
p
e
r
i
en
t
i
a
l
r
e
s
u
l
t
s
.
S
e
c
t
i
o
n
6
i
s
t
h
e
c
o
n
c
l
u
s
i
o
n
a
n
d
f
u
tu
r
e
wo
r
k
,
r
e
s
p
e
c
t
iv
e
l
y
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
p
r
o
ce
s
s
o
f
h
ier
ar
ch
ical
c
lu
s
ter
in
g
tex
t
b
ased
o
n
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
tech
n
iq
u
e
b
eg
in
s
b
y
p
er
f
o
r
m
in
g
tex
t
clu
s
ter
in
g
b
ased
o
n
m
ed
o
id
-
b
ased
clu
s
ter
in
g
k
n
o
w
n
as
m
ed
o
id
g
r
ey
wo
lf
o
p
tim
izatio
n
alg
o
r
ith
m
(
M
-
GW
O)
.
Af
ter
f
in
is
h
in
g
th
e
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
in
d
o
cu
m
e
n
t
r
ep
r
esen
tatio
n
,
ea
ch
d
o
cu
m
en
t
is
r
ep
r
esen
ted
b
y
a
s
et
o
f
f
ea
tu
r
es
th
at
s
h
o
ws
th
e
weig
h
t
o
f
th
e
d
o
c
u
m
en
t
c
o
m
p
ar
e
d
with
o
th
er
d
o
c
u
m
en
ts
.
W
eig
h
t
is
u
s
ed
in
clu
s
ter
in
g
to
class
if
y
ea
ch
d
o
cu
m
en
t
t
o
ap
p
r
o
p
r
iate
clu
s
ter
ac
co
r
d
i
n
g
to
th
e
d
is
tan
ce
b
etwe
en
th
e
d
o
c
u
m
en
ts
an
d
t
h
e
ce
n
ter
(
m
e
d
o
id
)
o
f
ea
ch
cl
u
s
ter
.
T
h
is
clu
s
ter
in
g
ass
ig
n
m
en
t
en
s
u
r
es
t
h
at
th
e
o
u
tp
u
t
o
f
ea
ch
clu
s
ter
is
b
ette
r
th
an
wh
en
t
h
e
GW
O
alg
o
r
ith
m
u
s
es
ce
n
tr
o
id
-
b
ased
clu
s
ter
in
g
.
T
h
e
o
u
tp
u
t
o
f
M
-
GW
O
i
s
a
s
p
h
er
ical
clu
s
ter
in
g
ass
ig
n
m
en
t th
at
c
an
b
e
u
s
ed
to
id
en
tify
th
e
d
o
cu
m
en
t g
r
o
u
p
s
.
Ho
wev
er
,
it is
n
o
t
u
s
ef
u
l
as
t
h
e
h
ier
a
r
ch
ica
l
tr
ee
,
wh
ich
s
h
o
ws
ea
ch
d
o
cu
m
en
t
in
a
clu
s
ter
with
ea
c
h
clo
s
e
d
o
c
u
m
en
t,
th
er
eb
y
n
ee
d
in
g
an
ad
ap
tatio
n
al
s
tag
e
th
at
co
n
v
er
ts
ea
ch
s
i
n
g
le
clu
s
ter
to
a
s
in
g
le
tr
ee
.
T
h
e
n
ex
t
s
tag
e
is
to
ap
p
ly
ag
g
l
o
m
er
ativ
e
clu
s
ter
in
g
f
o
r
ea
ch
o
f
th
e
s
in
g
le
clu
s
ter
p
r
o
d
u
ce
d
b
y
th
e
M
-
GW
O
alg
o
r
ith
m
,
as sh
o
wn
in
Fig
u
r
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
5
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4
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I
n
d
o
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J
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&
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24
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3
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Dec
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er
2
0
2
1
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1
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4
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1
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1748
Fig
u
r
e
1
.
R
esear
ch
m
eth
o
d
o
f
M
-
GW
O
alg
o
r
ith
m
3.
P
RO
P
O
SE
D
M
-
G
WO
A
L
G
O
RIT
H
M
F
O
R
T
E
X
T
C
L
U
ST
E
RING
T
h
e
m
ajo
r
d
if
f
er
e
n
ce
s
b
etwe
en
th
e
o
r
ig
i
n
al
GW
O
alg
o
r
ith
m
an
d
th
e
M
-
GW
O
alg
o
r
ith
m
is
th
at
th
e
f
o
r
m
er
p
r
o
d
u
ce
s
th
e
clu
s
ter
in
g
r
esu
lts
b
ased
o
n
ce
n
tr
o
id
s
,
w
h
ich
r
e
q
u
ir
e
wid
e
s
ea
r
c
h
s
p
ac
e,
wh
er
ea
s
t
h
e
latter
is
b
ased
o
n
m
ed
o
id
s
th
at
r
eq
u
i
r
es
s
ea
r
ch
s
p
ac
e
th
at
is
eq
u
als
to
th
e
n
u
m
b
e
r
o
f
o
b
jects
(
d
o
c
u
m
en
ts
)
.
Ho
wev
er
,
f
ew
m
o
d
if
icatio
n
s
ar
e
r
e
q
u
ir
e
d
to
p
er
f
o
r
m
th
e
GW
O
alg
o
r
i
th
m
in
a
m
ed
o
i
d
alg
o
r
ith
m
.
T
h
ese
m
o
d
if
icatio
n
s
will
b
e
d
escr
ib
ed
an
d
s
u
p
p
o
r
t
ed
b
y
ex
a
m
p
les
an
d
ex
p
lan
ati
o
n
s
.
T
h
e
M
-
GW
O
s
tep
s
ar
e
d
escr
ib
ed
in
d
etail
in
M
-
GW
O
alg
o
r
ith
m
.
Her
e,
th
e
wo
lf
is
d
esig
n
ated
as
a
s
ea
r
ch
ag
en
t.
T
h
e
p
r
o
p
o
s
ed
M
-
GW
O
alg
o
r
ith
m
h
as
o
n
e
m
o
d
if
icatio
n
p
lace
d
in
th
e
u
p
d
ate
p
o
s
itio
n
p
r
o
ce
d
u
r
e,
wh
er
e
m
ed
o
id
s
o
f
o
m
e
g
a
wo
lf
ar
e
u
p
d
ated
ac
co
r
d
in
g
to
th
e
th
r
ee
b
est
wo
lv
es,
in
clu
d
in
g
alp
h
a
(
α
)
,
b
eta
(
β),
d
elta
(
δ)
.
T
h
e
alg
o
r
ith
m
b
eg
i
n
s
its
tex
t
clu
s
ter
in
g
b
y
s
ettin
g
u
p
all
th
e
r
eq
u
ir
ed
p
a
r
am
eter
s
,
s
u
ch
as
th
e
n
u
m
b
er
o
f
wo
lv
es
,
th
e
n
u
m
b
e
r
o
f
it
er
atio
n
s
,
an
d
th
e
n
u
m
b
er
o
f
clu
s
ter
s
k
,
wh
ich
a
r
e
s
et
b
y
th
e
u
s
er
,
as
s
h
o
w
n
i
n
Step
1
.
Step
2
in
v
o
lv
es
th
e
in
itializatio
n
o
f
th
e
p
o
p
u
latio
n
wh
er
e
ea
ch
a
g
en
t
ass
ig
n
ed
a
d
o
cu
m
e
n
t
clu
s
ter
in
g
s
o
lu
tio
n
b
ased
o
n
t
h
e
m
ed
o
id
s
o
f
th
e
s
am
e
ag
en
t,
wh
ich
ar
e
r
an
d
o
m
ly
g
en
er
ated
.
T
h
is
s
tep
is
ex
p
lain
ed
in
Sectio
n
4
.
1
,
wh
i
ch
in
clu
d
es
ag
en
t
r
ep
r
esen
tatio
n
an
d
p
o
p
u
la
tio
n
in
itializatio
n
.
I
n
Step
3
,
ea
c
h
ag
en
t
ca
lcu
lates
its
f
itn
ess
f
u
n
ctio
n
to
f
in
d
th
e
t
h
r
e
e
b
e
s
t
w
o
l
v
e
s
,
w
h
i
c
h
i
n
c
l
u
d
e
s
,
,
a
n
d
i
n
a
s
ce
n
d
i
n
g
o
r
d
e
r
,
a
s
d
e
s
c
r
i
b
e
d
i
n
S
ec
t
i
o
n
4
.
2
.
I
n
S
t
e
p
s
4
a
n
d
5
,
th
e
alg
o
r
ith
m
b
e
g
in
s
its
iter
at
io
n
f
o
llo
wed
b
y
Step
6
an
d
7
,
wh
er
ein
th
e
p
o
s
itio
n
o
f
ea
c
h
ag
e
n
t
is
u
p
d
ated
ac
co
r
d
in
g
th
e
th
r
ee
b
est
wo
lv
es,
n
am
ely
,
,
,
an
d
.
T
h
e
o
p
er
atio
n
aim
s
to
m
o
v
e
th
e
p
o
s
itio
n
o
f
th
e
ag
e
n
t
in
to
a
b
etter
p
o
s
itio
n
n
ea
r
th
e
th
r
ee
b
est
wo
lv
es.
Step
7
is
d
escr
ib
ed
in
d
etail
in
Sectio
n
4
.
3
,
wh
ich
co
n
tain
s
th
e
co
n
tr
ib
u
ti
o
n
o
f
th
is
r
esear
ch
.
I
n
Step
s
9
,
1
0
,
an
d
1
1
,
th
e
a
lg
o
r
ith
m
co
m
p
u
tes
th
e
f
itn
ess
o
f
all
wo
lv
es
af
ter
u
p
d
atin
g
th
e
p
o
s
itio
n
an
d
id
e
n
tify
in
g
th
e
th
r
ee
b
est
wo
lv
es
,
,
an
d
b
ased
o
n
th
e
f
itn
ess
o
f
ea
ch
ag
en
t,
as
s
h
o
wn
in
Step
1
0
.
T
h
is
s
tep
i
s
f
o
llo
wed
b
y
in
cr
ea
s
in
g
th
e
lo
o
p
to
s
tar
t
im
p
r
o
v
in
g
th
e
f
itn
ess
f
u
n
ctio
n
o
f
ea
ch
ag
en
t
ag
ain
.
T
h
e
f
in
al
s
o
lu
tio
n
in
Step
1
3
ap
p
lies
ag
g
lo
m
er
ativ
e
clu
s
ter
in
g
to
p
r
o
d
u
ce
th
e
h
ier
ar
ch
ical
clu
s
ter
in
g
t
r
ee
o
f
ea
ch
s
in
g
le
clu
s
ter
.
M
-
GW
O
a
lg
o
r
ith
m
1:
Se
tu
p
th
e
pa
ra
me
te
rs
:
nu
mb
er
of
wo
lv
es
,
N,
and
maximum
number
of
iterations
_
and number of clusters
k
2:
Generate
initial
wolf
po
pu
la
ti
on
,
N
,
wh
er
e
ea
ch
wo
lf
,
,
=
{
1
,
2
,
3
,
…
,
}
an
d
ea
ch
has
own clustering assignment and own medoids randomly generated.
3:
Calculate
fitness,
f
(
X
i
)
,
fo
r
ea
ch
wo
l
f,
X
i
an
d
id
en
ti
fy
th
re
e
be
st
wo
lv
es
in
th
e
population
ba
se
d
on
fi
tn
es
s
of
ea
ch
on
e
an
d
so
rt
th
em
in
as
ce
nd
in
g
or
de
r
as
X
α
,
X
β
,
and X
δ
4:
Set
=
0
5:
while
(
<
_
)
do
6:
for
each
= 1
to
N
do
7:
Update position of agents
8:
end
-
for
9:
Compute fitness of all wolves
10:
Update value of
,
, and
based on fitness
11:
=
+
1
12:
end
-
while
13
Print
to
ur
so
lu
ti
on
wi
t
h
it
s
fi
tn
es
s
an
d
ap
pl
y
th
e
ag
gl
om
er
at
iv
e
cl
us
te
r
in
g
on
tour solution
end
-
algorithm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Grey
w
o
lf
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
h
iera
r
ch
ica
l d
o
cu
me
n
t
clu
s
teri
n
g
(
A
ya
d
Mo
h
a
mme
d
Ja
b
b
a
r
)
1749
3
.
1
.
Ag
ent
re
presenta
t
io
n a
nd
po
pu
la
t
io
n initia
liza
t
io
n
T
h
e
M
-
GW
O
alg
o
r
ith
m
b
eg
i
n
s
with
th
e
in
itial
clu
s
ter
in
g
s
o
lu
tio
n
,
wh
er
e
ea
c
h
d
o
cu
m
en
t r
ep
r
esen
ted
b
y
u
n
i
q
u
e
m
ed
o
id
n
u
m
b
er
.
As
s
h
o
wn
in
Fig
u
r
e
2
,
a
clu
s
te
r
in
g
s
o
lu
tio
n
c
o
n
s
is
ts
o
f
n
in
e
d
o
cu
m
e
n
ts
wh
er
e
ea
ch
d
o
cu
m
e
n
t
is
ass
ig
n
ed
to
a
clo
s
et
m
ed
o
id
,
s
u
ch
as
f
ir
s
t
o
n
e
to
m
ed
o
id
1
,
s
ec
o
n
d
d
o
c
u
m
en
t
to
m
ed
o
id
3
,
an
d
s
o
o
n
.
T
h
e
m
e
d
o
id
s
o
f
ea
ch
clu
s
ter
in
g
s
o
lu
tio
n
ca
n
b
e
r
e
p
r
esen
ted
as
th
r
ee
m
ed
o
id
s
f
o
r
th
is
s
in
g
le
s
o
lu
tio
n
,
as
s
h
o
w
n
as
e
x
am
p
l
e
in
Fig
u
r
e
2
.
I
n
Fig
u
r
e
3
,
a
n
ex
am
p
le
o
f
ag
e
n
t
h
as
th
r
ee
m
ed
o
id
s
,
th
e
th
r
ee
m
ed
o
id
s
(
th
r
ee
d
o
cu
m
en
ts
)
a
r
e
p
r
esen
ted
to
p
er
f
o
r
m
clu
s
ter
in
g
s
o
lu
tio
n
as
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
f
ir
s
t,
s
ec
o
n
d
,
an
d
th
ir
d
m
e
d
o
id
s
h
a
v
e
two
attr
ib
u
tes
ea
ch
(
0
.
9
9
,
0
.
8
7
)
,
(
0
.
3
4
,
0
.
5
4
)
,
an
d
(
0
.
6
8
,
0
.
9
8
)
,
r
esp
ec
tiv
ely
.
Me
d
o
id
s
ar
e
u
n
iq
u
e,
w
h
ich
m
ea
n
s
n
o
m
ed
o
i
d
s
h
av
e
d
u
p
licat
ed
attr
ib
u
tes.
Fig
u
r
e
2
.
So
lu
tio
n
r
ep
r
esen
tatio
n
Fig
u
r
e
3.
Me
d
o
id
r
e
p
r
esen
tatio
n
E
ac
h
ag
en
t
in
th
e
in
itial
s
o
lu
tio
n
p
h
ase
is
r
ep
r
esen
ted
b
y
s
in
g
le
s
o
lu
tio
n
(
Fig
u
r
e
2
)
,
an
d
th
e
m
ed
o
id
s
ar
e
s
et
o
n
th
e
b
asis
o
f
th
e
m
a
x
im
u
m
o
f
n
u
m
b
er
o
f
clu
s
ter
s
k
n
o
wn
as
k
s
et,
as
s
h
o
wn
in
Fig
u
r
e
3
.
I
n
th
e
in
itial
p
h
ase,
th
e
m
ed
o
id
s
ar
e
s
elec
ted
r
an
d
o
m
l
y
.
Su
b
s
eq
u
e
n
tly
,
d
u
r
in
g
th
e
alg
o
r
ith
m
r
u
n
,
th
e
m
ed
o
id
s
ar
e
s
to
ch
asti
ca
lly
im
p
r
o
v
ed
to
f
in
d
th
e
b
est s
et
o
f
m
e
d
o
id
s
th
at
p
r
o
d
u
ce
m
in
im
u
m
er
r
o
r
am
o
n
g
th
e
clu
s
ter
s
.
3
.
2
.
F
i
t
nes
s
f
un
ct
io
n c
o
m
pu
t
a
t
io
n
T
h
e
f
itn
ess
f
u
n
ctio
n
,
as
s
h
o
wn
in
(
1
)
,
is
th
e
co
s
in
e
s
im
ilar
ity
m
ea
s
u
r
em
en
t
b
etwe
en
th
e
m
ed
o
id
s
an
d
th
e
d
o
cu
m
en
ts
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
wh
er
e
,
⃗
⃗
⃗
⃗
is
th
e
f
ir
s
t
m
ed
o
id
an
d
⃗
⃗
⃗
is
a
d
o
cu
m
en
t.
No
tab
ly
,
th
is
f
itn
ess
f
u
n
ctio
n
is
u
s
e
d
as
th
e
m
ain
o
b
jectiv
e
f
u
n
ctio
n
in
t
h
e
clu
s
ter
in
g
ass
ig
n
m
en
t
th
at
id
en
tifie
s
th
e
d
is
tan
ce
b
e
twee
n
th
e
m
e
d
o
id
s
an
d
th
e
d
o
c
u
m
en
ts
an
d
later
u
s
ed
as
a
f
itn
ess
f
u
n
ctio
n
to
ca
lcu
late
th
e
to
tal
d
is
tan
ce
b
e
twee
n
ea
ch
clu
s
ter
m
ed
o
id
a
n
d
th
e
r
em
ain
in
g
d
o
c
u
m
en
ts
in
th
e
s
am
e
clu
s
ter
.
(
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
)
=
∗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
√
∑
2
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
=
1
∗
√
∑
2
⃗
⃗
⃗
⃗
⃗
⃗
⃗
=
1
(
1
)
An
ag
en
t
h
as
th
r
ee
m
e
d
o
id
s
,
a
s
s
h
o
wn
in
Fig
u
r
e
3
,
an
d
a
d
o
cu
m
en
t
is
r
eq
u
ir
e
d
to
b
e
ass
ig
n
ed
to
o
n
e
o
f
th
e
m
ed
o
i
d
s
,
s
u
ch
as
m
ed
o
id
1
,
m
ed
o
i
d
2
o
r
m
e
d
o
id
3
.
I
f
th
e
d
o
cu
m
e
n
t
h
as
two
attr
ib
u
tes
(
ter
m
s
)
,
s
u
ch
as (
0
.
4
3
,
0
.
9
8
)
,
th
e
n
th
e
ass
ig
n
m
en
t w
ill b
e
p
er
f
o
r
m
ed
as f
o
ll
o
ws:
(
1
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
d
⃗
)
=
0
.
9
0
6
(
2
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
d
⃗
)
=
0
.
9
8
9
(
3
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
d
⃗
)
=
0
.
9
8
1
T
h
e
co
s
in
e
s
im
ilar
ity
m
ea
s
u
r
e
m
en
t
in
d
icate
s
th
at
th
e
s
im
ilar
ity
b
etwe
en
m
e
d
o
id
2
an
d
th
e
d
o
cu
m
e
n
t
is
h
ig
h
e
r
th
an
th
o
s
e
o
f
th
e
o
t
h
er
m
e
d
o
id
s
,
th
u
s
th
e
d
o
c
u
m
en
t
will
b
e
ass
ig
n
ed
to
th
e
clo
s
e
m
e
d
o
id
3
.
No
tab
l
y
,
th
e
d
etails o
f
ca
lcu
latio
n
ar
e
d
escr
ib
ed
in
th
e
p
r
e
-
p
r
o
ce
s
s
in
g
s
ec
tio
n
.
3.
3
.
P
o
s
it
io
n u
pd
a
t
ing
Me
d
o
id
g
r
ey
wo
lf
o
p
tim
izati
o
n
(
M
-
GW
O)
f
o
llo
wed
th
e
s
am
e
p
r
o
ce
d
u
r
e
o
f
GW
O
in
it
s
h
ier
ar
ch
y
lead
er
s
h
ip
s
,
wh
er
e
f
o
u
r
m
ain
wo
lv
es
in
cl
u
d
e
,
,
,
an
d
th
e
r
em
ain
in
g
m
em
b
er
s
ar
e
o
m
eg
a
(
)
,
a
r
e
av
ailab
le.
T
h
e
wo
lv
es
u
p
d
ate
th
eir
p
o
s
itio
n
o
n
th
e
s
ea
r
c
h
s
p
ac
e
a
cc
o
r
d
in
g
t
h
e
b
est
p
o
s
itio
n
s
r
ep
r
esen
ted
b
y
,
,
an
d
.
I
n
M
-
GW
O,
th
e
c
o
n
tr
ib
u
tio
n
o
f
th
is
r
esear
ch
is
th
at
th
e
p
o
s
itio
n
o
f
wo
lv
es
(
m
ed
o
id
s
)
ar
e
o
n
ly
u
p
d
ated
ac
co
r
d
i
n
g
to
th
e
t
h
r
ee
m
ain
wo
lv
es,
w
h
ich
ar
e
,
,
an
d
.
T
h
e
p
r
o
ce
s
s
o
f
u
p
d
ate
p
o
s
i
tio
n
b
eg
i
n
s
b
y
s
elec
tin
g
o
n
e
m
ed
o
id
f
r
o
m
th
e
wo
lf
in
r
a
n
d
o
m
ly
m
a
n
n
er
.
T
h
e
tar
g
et
o
f
th
is
s
elec
tio
n
is
to
p
e
r
f
o
r
m
s
wap
o
p
er
atio
n
b
e
twee
n
wo
lf
an
d
,
,
an
d
,
as
s
h
o
wn
in
Fig
u
r
e
4
.
As
s
h
o
wn
in
Fig
u
r
e
4
,
t
h
e
s
wap
o
p
er
atio
n
will
b
e
p
er
f
o
r
m
ed
b
etwe
en
a
n
d
th
e
th
r
ee
m
ain
wo
lv
es.
Nu
m
b
er
is
r
an
d
o
m
ly
g
en
er
ated
wh
er
e
<
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
7
4
4
-
1
7
5
8
1750
Su
b
s
eq
u
en
tly
,
b
ased
o
n
v
alu
e
,
th
e
alg
o
r
ith
m
s
elec
ts
o
n
e
o
f
m
ed
o
id
s
as
an
ac
tiv
e
m
ed
o
i
d
to
b
e
s
wap
p
ed
with
o
n
e
o
f
,
,
an
d
m
ed
o
id
s
.
Ho
wev
er
,
th
e
s
wap
o
p
er
atio
n
h
er
e
is
co
n
d
itio
n
al
if
an
d
o
n
l
y
if
th
e
f
itn
ess
o
f
a
n
ew
s
et
o
f
m
ed
o
id
s
is
b
etter
th
an
th
e
o
ld
er
o
n
e.
T
h
e
o
t
h
er
co
n
d
itio
n
is
th
at
th
e
s
wap
o
p
e
r
a
tio
n
alwa
y
s
lo
o
k
s
f
o
r
t
h
e
f
ir
s
t
im
p
r
o
v
em
en
t,
wh
ich
m
ea
n
s
s
wap
p
in
g
is
s
to
p
p
ed
af
ter
th
e
f
ir
s
t
im
p
r
o
v
e
m
en
t
is
ac
h
iev
ed
.
Su
c
h
co
n
d
itio
n
allo
ws
th
e
alg
o
r
ith
m
to
co
n
v
er
g
e
to
th
e
o
p
tim
al
s
o
lu
tio
n
s
lo
wly
an
d
av
o
id
s
tac
k
at
th
e
lo
ca
l
o
p
tim
a
b
ec
au
s
e
if
we
ac
ce
p
ted
h
ig
h
-
q
u
ality
s
o
lu
tio
n
s
in
th
e
b
eg
i
n
n
in
g
o
f
th
e
r
u
n
,
th
e
alg
o
r
ith
m
will
ig
n
o
r
e
th
e
ex
p
lo
r
atio
n
o
f
th
e
wid
e
r
eg
io
n
s
o
f
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
s
wap
o
p
er
atio
n
th
at
r
ep
r
esen
ted
in
Fig
u
r
e
4
is
th
e
m
ain
o
p
e
r
atio
n
u
s
ed
in
PAM
k
n
o
wn
as
th
e
m
e
d
o
id
ca
lc
u
latio
n
p
r
o
ce
s
s
,
wh
ich
allo
ws
th
e
d
is
co
v
er
y
o
f
o
th
er
o
p
tim
al
clu
s
ter
in
g
ass
ig
n
m
en
ts
in
th
e
s
ea
r
ch
s
p
ac
e.
An
ad
v
an
ta
g
e
o
f
th
e
o
p
er
ati
o
n
in
clu
d
es
r
e
d
u
ce
d
ca
lcu
latio
n
s
p
r
o
ce
s
s
wh
en
o
n
ly
th
e
wo
lf
an
d
th
e
th
r
ee
b
es
t
wo
lv
es
ar
e
ca
lcu
lated
.
T
h
is
o
p
er
atio
n
is
also
b
etter
th
an
PAM
alg
o
r
ith
m
,
wh
ich
r
eq
u
i
r
es
m
o
r
e
ca
lc
u
latio
n
b
etwe
en
t
h
e
m
ed
o
id
th
at
n
ee
d
to
b
e
ch
a
n
g
e
d
with
all
o
th
er
ca
n
d
id
ate
m
ed
o
id
s
in
th
e
s
ea
r
ch
s
p
ac
e.
No
t
e
th
at
M
in
Fig
u
r
e
4
co
r
r
esp
o
n
d
s
to
th
e
cu
r
r
en
t
m
ed
o
id
,
a
n
d
T
r
ef
er
s
to
th
e
ter
m
.
Fig
u
r
e
4
.
Me
d
o
id
s
’
p
o
s
itio
n
u
p
d
ate
r
ep
r
esen
tatio
n
As
s
h
o
wn
in
Fig
u
r
e
5
,
th
e
s
wap
o
p
er
ati
o
n
is
p
e
r
f
o
r
m
ed
b
etwe
en
th
e
wo
lf
a
n
d
th
e
th
r
ee
m
ain
wo
lv
es.
T
h
e
f
ir
s
t
co
n
d
itio
n
is
to
en
s
u
r
e
th
at
t
h
e
s
wap
o
p
er
at
io
n
is
ac
tiv
e.
Activ
e
m
ea
n
s
th
at
th
e
m
ed
o
i
d
th
at
n
ee
d
s
to
b
e
c
h
an
g
e
d
is
n
o
t
d
u
p
licated
with
o
n
e
o
f
th
e
m
ed
o
id
s
.
T
h
is
co
n
d
itio
n
is
r
eq
u
ir
ed
b
ec
au
s
e
d
u
p
licated
m
ed
o
id
s
p
r
o
d
u
ce
wr
o
n
g
ass
ig
n
m
en
ts
b
y
g
e
n
er
a
tin
g
a
s
m
aller
n
u
m
b
er
o
f
clu
s
ter
s
th
an
wh
at
was
d
ec
id
ed
b
y
t
h
e
u
s
er
.
Ho
wev
e
r
,
th
e
s
wap
o
p
er
atio
n
wo
r
k
s
in
s
eq
u
en
ce
,
th
at
is
,
all
m
ed
o
id
s
o
f
th
r
ee
m
ai
n
wo
lv
es
will
b
e
ex
am
in
e
d
.
On
ce
im
p
r
o
v
em
en
t
is
o
b
s
er
v
ed
,
t
h
e
o
p
e
r
atio
n
s
to
p
s
f
in
d
in
g
th
e
f
ir
s
t
im
p
r
o
v
em
en
t,
o
th
er
wis
e,
th
e
o
p
er
atio
n
co
n
tin
u
es
in
th
e
cu
r
r
en
t
m
ed
o
id
s
.
T
h
e
f
u
ll
s
tep
s
s
h
o
w
in
p
r
o
ce
d
u
r
e
m
ed
o
id
s
p
o
s
itio
n
up
d
ate
.
Fig
u
r
e
5
.
Me
d
o
id
s
p
o
s
itio
n
s
w
ap
o
p
er
atio
n
Pro
ce
d
u
r
e
m
ed
o
id
s
p
o
s
itio
n
u
p
d
ate
1:
Initialize a new memory called
% The Memory keeps only alpha, beta and
delta medoids, Initialize
,
,
where
short memory keeps one medoid from
omega medoids,
is amemory keeps not selected medoids from omega medoids,
is
temporary medoid mem
ory keeps one medoids selected from
,
2:
Memory
←
alpha, beta and delta medoids % Copy the medoids into the memory
3:
Generate
random number (1
-
k
) % generate random number, minimum
equals 1 and maximum equals
k
4:
Swapping operation starts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Grey
w
o
lf
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
h
iera
r
ch
ica
l d
o
cu
me
n
t
clu
s
teri
n
g
(
A
ya
d
Mo
h
a
mme
d
Ja
b
b
a
r
)
1751
5:
Select one of omega medoids based on
value and calculate the fitness function
of
the current assignment
6:
←
omega (
) % Copy
the selected medoid into the omega memory medoid
7:
←
omega (Medoid! =
) % Copy the not selected medoid into the not selected
medoid memory
8:
Status= false
9:
Count=0
10:
While
(Count < Memory length)
do
11:
←
Select single medoid from Memory based on count value % Copy the
single medoid into the temporary medoid memory
12:
if
(
!=
)
then
% to ensure no duplicated medoids occurs
13:
Status= true
14:
e
lse
15:
Status= false
Count=Count +1
16:
end
-
if
17:
if
(Status= true)
then
18:
Perform swap operation and calculate the new fitness function
∗
of the new
soaution
19:
end
-
if
20:
if
(
∗
<
)
then
21:
Accept the swap operation and break the while loop
22:
else
23:
Count=Count +1
24:
end
-
if
25:
end
-
while
end
-
procedure
T
h
e
p
r
o
d
u
ce
r
b
eg
in
s
b
y
in
itializin
g
all
s
h
o
r
t
m
e
m
o
r
ies,
i
n
clu
d
in
g
,
,
,
an
d
.
u
s
ed
to
co
p
y
an
d
k
ee
p
all
alp
h
a,
b
eta,
an
d
d
elta
m
ed
o
id
s
,
wh
ich
ar
e
u
s
ed
later
in
th
e
s
wap
o
p
er
atio
n
b
etwe
en
th
e
m
ed
o
i
d
s
in
t
h
e
m
em
o
r
y
an
d
o
m
e
g
a
m
e
d
o
id
s
.
I
n
Step
2
,
m
e
d
o
id
s
f
r
o
m
alp
h
a
,
b
eta,
a
n
d
d
elta
ar
e
co
p
ied
in
to
th
e
m
em
o
r
y
f
o
llo
wed
b
y
Step
3
,
wh
ich
g
en
e
r
ates
a
r
an
d
o
m
n
u
m
b
er
b
etwe
en
1
an
d
t
h
e
m
ax
im
i
n
v
alu
e
k.
Step
4
in
d
icate
s
th
e
s
tar
t
o
f
s
wap
p
in
g
o
p
er
atio
n
b
etwe
en
th
e
o
m
eg
a
m
ed
o
id
s
a
n
d
th
e
,
wh
ich
k
ee
p
s
th
e
alp
h
a,
b
eta,
an
d
d
elta
m
ed
o
id
s
.
I
n
Step
s
5
an
d
6
,
th
e
o
m
eg
a
m
ed
o
id
th
at
is
r
eq
u
ir
e
d
to
b
e
ch
an
g
ed
b
ased
o
n
th
e
r
an
d
o
m
n
u
m
b
e
r
p
r
o
d
u
ce
d
in
p
r
e
v
io
u
s
s
tep
is
s
elec
ted
an
d
k
e
p
t
in
m
em
o
r
y
,
wh
ich
is
a
s
h
o
r
t
m
em
o
r
y
u
s
ed
to
k
ee
p
o
n
e
m
ed
o
id
.
Step
7
co
p
i
es
an
d
k
ee
p
s
all
r
em
ain
in
g
m
ed
o
id
s
th
at
ar
e
n
o
t
s
elec
ted
in
a
s
h
o
r
t
m
em
o
r
y
ca
lled
.
T
h
e
ta
r
g
et
o
f
th
is
m
em
o
r
y
is
to
en
s
u
r
e
n
o
m
ed
o
id
s
ar
e
d
u
p
licated
in
th
e
s
elec
ted
m
ed
o
id
s
f
r
o
m
th
e
.
I
n
Step
s
8
an
d
9
,
th
e
S
tatu
s
an
d
co
u
n
t
v
ar
ia
b
les
ar
e
in
itialized
in
to
f
alse
v
al
u
e
a
n
d
0
,
r
esp
e
ctiv
ely
.
T
h
e
Statu
s
v
ar
iab
le
i
s
u
s
ed
to
ch
ec
k
wh
eth
er
d
u
p
l
icate
d
m
ed
o
i
d
s
ar
e
av
ailab
le
o
r
n
o
t.
Me
a
n
wh
ile,
t
h
e
co
u
n
t
v
a
r
iab
le
is
u
s
ed
in
th
e
lo
o
p
to
c
h
ec
k
all
m
ed
o
id
s
in
th
e
.
I
n
Step
1
0
,
th
e
p
r
o
ce
d
u
r
e
s
tar
ts
its
m
ain
lo
o
p
b
y
co
p
y
in
g
o
n
e
m
ed
o
id
f
r
o
m
t
h
e
in
to
th
e
s
h
o
r
t
m
em
o
r
y
as
s
h
o
wn
in
s
tep
1
1
.
C
h
ec
k
if
th
er
e
is
n
o
d
u
p
licated
m
e
d
o
id
s
b
etwe
en
th
e
o
m
eg
a
m
e
d
o
id
s
an
d
th
e
m
ed
o
id
s
av
ed
in
.
T
h
e
r
e
s
u
lt
is
tr
u
e
if
n
o
d
u
p
licatio
n
o
c
cu
r
s
,
o
th
er
wis
e,
th
e
r
esu
lt
is
f
alse,
as
s
h
o
wn
in
Step
s
1
2
–
1
5
.
I
f
th
e
c
o
n
d
iti
o
n
is
tr
u
e
,
th
en
th
e
s
wap
o
p
e
r
atio
n
is
p
er
f
o
r
m
e
d
an
d
ac
ce
p
t
ed
o
n
l
y
if
th
e
n
ew
f
itn
ess
∗
is
b
etter
th
an
th
e
o
ld
f
itn
ess
,
as
s
h
o
wn
in
Step
s
1
7
–
2
4
.
T
h
e
o
u
tp
u
t
o
f
th
is
p
r
o
ce
d
u
r
e
is
a
s
et
o
f
m
ed
o
id
s
u
s
ed
in
t
h
e
n
e
x
t iter
atio
n
to
co
n
s
tr
u
ct
a
n
ew
ass
ig
n
m
en
t.
4.
P
RE
-
P
RO
CE
S
SI
NG
T
E
X
T
F
O
R
CL
US
T
E
R
I
NG
T
h
e
tex
t
clu
s
ter
in
g
b
eg
i
n
s
with
a
d
ata
in
s
p
ec
tio
n
p
h
ase,
wh
ich
is
co
n
s
id
er
ed
a
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
wh
er
ein
th
e
d
ata
s
h
o
u
ld
b
e
p
r
ep
ar
ed
.
Data
in
s
p
ec
tio
n
co
n
s
id
er
s
th
e
p
r
ep
ar
atio
n
o
f
d
ata,
wh
ich
in
clu
d
es
d
ata
co
llectio
n
,
d
ata
clea
n
in
g
,
an
d
d
ata
r
ep
r
esen
tatio
n
.
Data
co
lle
ctio
n
r
ef
er
s
t
o
th
e
task
o
f
c
o
llectin
g
th
e
d
ata
th
at
w
i
l
l
b
e
u
s
e
d
a
n
d
e
v
a
l
u
a
te
d
i
n
th
i
s
r
es
e
a
r
c
h
.
T
h
e
b
e
n
c
h
m
a
r
k
d
a
t
a
s
et
s
t
h
a
t
w
i
ll
b
e
u
s
e
d
a
r
e
t
h
o
s
e
f
r
o
m
UC
I
[
5
0
]
.
B
ef
o
r
e
p
er
f
o
r
m
in
g
tex
t
clu
s
te
r
in
g
,
a
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
is
r
eq
u
ir
ed
to
c
o
n
v
e
r
t
th
e
u
n
s
tr
u
ctu
r
ed
tex
t
in
to
a
s
tr
u
ctu
r
ed
f
o
r
m
at
th
at
is
r
ea
d
ab
le
in
clu
s
ter
in
g
alg
o
r
ith
m
s
.
T
h
e
p
r
e
-
p
r
o
ce
s
s
in
g
in
cl
u
d
es
to
k
en
izatio
n
,
s
tem
m
in
g
o
f
d
o
c
u
m
en
t
w
o
r
d
s
,
an
d
s
to
p
wo
r
d
r
em
o
v
al
[
5
1
]
,
[
5
2
]
.
T
o
k
en
izatio
n
co
r
r
es
p
o
n
d
s
to
a
g
en
er
al
p
r
o
ce
s
s
th
at
is
u
s
ed
to
b
r
ea
k
a
tex
t
co
r
p
u
s
in
to
i
n
d
iv
id
u
al
elem
en
ts
.
Stem
m
in
g
is
d
ef
in
e
d
as
th
e
p
r
o
ce
s
s
o
f
co
n
v
er
tin
g
o
r
tr
a
n
s
f
o
r
m
in
g
a
wo
r
d
in
to
a
b
ase
wo
r
d
,
th
at
is
,
a
wo
r
d
is
co
n
v
er
ted
in
to
its
o
r
ig
in
al
r
o
o
t
f
o
r
m
.
T
h
e
n
ex
t
s
tep
is
to
r
em
o
v
e
s
to
p
p
in
g
w
o
r
d
s
th
at
ar
e
co
m
m
o
n
an
d
u
n
i
n
f
o
r
m
ativ
e
in
a
tex
t
c
o
r
p
u
s
,
s
u
ch
as
s
o
,
an
d
,
o
r
,
an
d
th
e.
T
h
ese
s
to
p
p
in
g
wo
r
d
s
,
wh
ich
ar
e
n
o
t
im
p
o
r
tan
t
in
in
f
o
r
m
atio
n
r
etr
iev
al,
ar
e
av
ailab
le
in
ev
er
y
d
o
cu
m
en
t
b
ec
a
u
s
e
th
ey
d
o
n
o
t
ca
r
r
y
an
y
in
f
o
r
m
atio
n
r
elate
d
to
th
eir
d
o
c
u
m
en
ts
.
I
n
tex
t
clu
s
ter
in
g
,
d
o
cu
m
e
n
ts
ar
e
n
o
t
s
u
itab
l
e
in
th
eir
o
r
ig
in
al
f
o
r
m
at
u
n
less
r
e
p
r
esen
ted
in
a
s
u
itab
le
f
o
r
m
.
VSM
is
an
ef
f
ec
tiv
e
r
ep
r
esen
tatio
n
m
o
d
el
th
at
tr
ea
ts
d
o
cu
m
en
ts
as
a
b
a
g
-
of
-
wo
r
d
s
an
d
u
s
es
wo
r
d
s
as
a
m
ea
s
u
r
e
to
d
is
co
v
er
t
h
e
s
im
ilar
ity
am
o
n
g
d
o
c
u
m
en
ts
[
5
3
]
.
L
et
=
{
1
,
2
,
3
…
…
…
}
d
en
o
te
a
co
llectio
n
o
f
d
o
cu
m
en
ts
,
an
d
is
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
7
4
4
-
1
7
5
8
1752
n
u
m
b
er
o
f
d
o
cu
m
e
n
ts
in
th
at
co
llectio
n
.
E
ac
h
d
o
cu
m
e
n
t
r
ep
r
esen
ts
a
v
ec
to
r
o
f
ter
m
s
,
w
h
ich
is
d
en
o
ted
as
=
{
1
,
2
,
3
…
…
…
}
,
wh
er
e
ter
m
r
ep
r
esen
ts
a
w
o
r
d
,
an
d
is
th
e
n
u
m
b
er
o
f
ter
m
s
.
T
h
e
d
o
cu
m
en
t
h
as
a
r
elatio
n
with
ter
m
,
wh
ich
is
d
en
o
ted
as
ter
m
f
r
eq
u
e
n
cy
(
T
F);
T
F
ca
n
b
e
r
ep
r
esen
ted
b
y
a
f
ix
ed
v
alu
e
th
at
r
ef
lects
th
e
d
eg
r
ee
o
f
ter
m
f
r
e
q
u
en
cy
in
th
at
d
o
c
u
m
en
t
[
5
4
]
.
Ho
wev
er
,
b
ased
o
n
th
e
d
ef
i
n
itio
n
o
f
VSM,
i
t
r
ep
r
esen
ts
all
th
e
co
llectio
n
o
f
d
o
cu
m
e
n
t
f
o
r
m
s
as
a
m
atr
ix
wh
er
e
th
e
r
o
ws
ar
e
d
o
c
u
m
en
ts
an
d
co
lu
m
n
s
ar
e
wo
r
d
s
,
an
d
ea
ch
ce
ll
co
n
tain
s
th
e
T
F
v
alu
e
o
f
th
e
w
o
r
d
with
in
th
e
d
o
cu
m
e
n
t.
Fig
u
r
e
6
s
h
o
ws
th
e
ter
m
f
r
eq
u
e
n
cy
m
atr
ix
.
Fig
u
r
e
6
.
T
e
r
m
f
r
e
q
u
en
c
y
m
at
r
ix
T
o
clar
if
y
th
e
i
d
ea
,
let
u
s
s
u
p
p
o
s
e
th
at
th
r
ee
d
o
cu
m
e
n
t
s
co
n
tain
f
o
u
r
ter
m
s
,
in
clu
d
in
g
class
,
u
n
iv
er
s
ity
,
b
o
o
k
,
an
d
lectu
r
e,
as
d
escr
ib
ed
an
d
s
h
o
wn
in
T
a
b
le
1
.
E
ac
h
d
o
c
u
m
en
t
is
r
elate
d
to
its
ter
m
co
u
n
t,
wh
ich
is
th
e
s
im
p
lest
ch
o
i
ce
o
f
T
F.
H
o
wev
er
,
o
th
er
p
o
s
s
ib
le
T
F
v
ar
ian
ts
in
th
e
s
ch
em
e,
s
u
ch
as
lo
g
ar
ith
m
ically
s
ca
led
f
r
e
q
u
en
cy
,
wh
ich
is
u
s
ed
in
t
h
is
r
esear
ch
,
ca
n
b
e
u
s
ed
,
as
s
h
o
wn
in
(
2
)
an
d
ap
p
lied
in
T
ab
le
2
.
(
,
)
=
1
+
l
og
(
,
)
(
2
)
T
ab
le
1
.
T
er
m
f
r
e
q
u
en
cies (
co
u
n
ts
)
Te
r
ms
D
o
c
1
D
o
c
2
D
o
c
3
c
l
a
ss
1
1
5
58
0
u
n
i
v
e
r
si
t
y
10
7
0
b
o
o
k
2
0
6
l
e
c
t
u
r
e
0
0
38
T
ab
le
2
.
L
o
g
f
r
eq
u
e
n
cy
weig
h
tin
g
Te
r
ms
D
o
c
1
D
o
c
2
D
o
c
3
C
l
a
s
s
3
.
0
6
2
.
7
6
0
U
n
i
v
e
r
si
t
y
2
.
0
0
1
.
8
5
0
B
o
o
k
1
.
3
0
0
1
.
7
8
Le
c
t
u
r
e
0
0
2
.
5
8
T
h
e
n
ex
t
s
tep
in
v
o
lv
es
in
v
er
s
e
d
o
cu
m
e
n
t
f
r
e
q
u
en
c
y
(
I
DF)
,
wh
ich
r
ef
er
s
to
t
h
e
weig
h
t
o
f
ea
ch
ter
m
with
r
eg
ar
d
to
th
e
to
tal
n
u
m
b
e
r
o
f
d
o
c
u
m
en
ts
(
)
an
d
th
e
n
u
m
b
er
o
f
d
o
c
u
m
en
ts
th
at
co
n
tain
t
h
at
ter
m
i
n
th
e
co
llectio
n
(
)
as a
s
co
r
e.
I
DF c
an
b
e
ca
lcu
lat
ed
u
s
in
g
(
3
)
an
d
a
p
p
lied
in
T
ab
le
3
.
=
l
og
(
)
(
3
)
T
ab
le
3
.
L
o
g
I
DF w
eig
h
tin
g
Te
r
ms
I
D
F
C
l
a
s
s
lo
g
(
3
2
)
=
0
.
176
U
n
i
v
e
r
si
t
y
lo
g
(
3
2
)
=
0
.
176
B
o
o
k
lo
g
(
3
2
)
=
0
.
176
Le
c
t
u
r
e
lo
g
(
3
1
)
=
0
.
477
T
h
e
n
ex
t step
is
to
o
b
tain
th
e
weig
h
t o
f
ter
m
s
,
wh
ic
h
is
ca
lcu
lated
u
s
in
g
(
4
)
an
d
ap
p
lied
in
T
ab
le
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Grey
w
o
lf
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
fo
r
h
iera
r
ch
ica
l d
o
cu
me
n
t
clu
s
teri
n
g
(
A
ya
d
Mo
h
a
mme
d
Ja
b
b
a
r
)
1753
,
=
,
∗
(
4
)
T
h
e
n
ex
t
s
tep
is
to
p
er
f
o
r
m
n
o
r
m
aliza
tio
n
f
o
r
th
e
len
g
th
o
f
ea
ch
ter
m
b
etwe
en
(
0
,
1
)
.
I
n
(
5
)
s
h
o
ws
th
e
n
o
r
m
aliza
tio
n
f
o
r
th
e
len
g
th
a
n
d
ap
p
lie
d
in
T
ab
le
5
.
,
√
∑
,
2
1
(
5
)
Fin
ally
,
we
ca
lcu
late
th
e
s
im
ilar
ity
am
o
n
g
d
o
cu
m
e
n
ts
u
s
i
n
g
a
co
s
in
e
s
im
ilar
ity
s
co
r
e,
as
s
h
o
wn
in
(
1
)
p
r
e
v
io
u
s
ly
wh
e
r
e
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
ar
e
th
e
d
o
cu
m
en
t
v
ec
t
o
r
s
,
th
er
e
b
y
p
r
o
d
u
cin
g
a
c
o
s
in
e
s
im
ilar
ity
ta
b
le
am
o
n
g
all
d
o
cu
m
e
n
ts
,
as
s
h
o
wn
in
T
a
b
le
6
,
an
d
an
ex
am
p
le
o
f
th
e
ca
lc
u
latio
n
o
f
c
o
s
in
e
s
im
ilar
ly
b
et
wee
n
d
o
c
u
m
en
ts
1
an
d
2
is
p
r
o
v
id
e
d
,
as sh
o
wn
b
ef
o
r
e
T
ab
le
6
.
(
1
,
2
)
=
0
.
94
2
0
4
1
5
5
99999
998
0
.
9998
8
8
90
4
4
3
2
2
6
0
3
=
0
.
942146228
2701233
T
ab
le
4
.
W
eig
h
t o
f
th
e
ter
m
Te
r
ms
D
o
c
1
D
o
c
2
D
o
c
3
C
l
a
s
s
0
.
5
3
8
5
0
.
4
8
5
7
0
U
n
i
v
e
r
si
t
y
0
.
3
5
2
0
.
3
2
5
6
0
B
o
o
k
0
.
2
2
8
8
0
0
.
3
1
3
2
Le
c
t
u
r
e
0
0
1
.
2
3
0
6
T
ab
le
5
.
L
e
n
g
th
n
o
r
m
aliza
tio
n
Te
r
ms
D
o
c
1
D
o
c
2
D
o
c
3
C
l
a
s
s
0
.
7
8
8
6
0
.
8
3
0
6
0
U
n
i
v
e
r
si
t
y
0
.
5
1
5
5
0
.
5
5
6
8
0
B
o
o
k
0
.
3
3
5
0
0
0
.
2
4
6
6
Le
c
t
u
r
e
0
0
0
.
9
6
9
1
T
ab
le.
6
C
o
s
in
e
s
im
ilar
ity
tab
l
e
f
o
r
Do
c1
,
Do
c2
,
an
d
D
o
c3
D
o
c
1
D
o
c
2
D
o
c
3
D
o
c
1
1
0
.
9
4
0
.
0
8
D
o
c
2
0
.
9
4
1
0
D
o
c
3
0
.
0
8
0
1
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
E
v
alu
atio
n
p
e
r
f
o
r
m
an
ce
is
a
n
im
p
o
r
ta
n
t
s
tep
in
d
ata
clu
s
ter
in
g
to
in
d
icate
th
e
ac
cu
r
ac
y
o
f
th
e
p
r
o
v
id
e
d
s
o
lu
tio
n
s
.
T
h
r
e
e
b
est
k
n
o
wn
b
e
n
ch
m
ar
k
s
u
s
ed
in
class
if
icatio
n
an
d
clu
s
ter
in
g
f
ield
ar
e
u
s
ed
in
th
e
ev
alu
atio
n
p
r
o
ce
s
s
.
T
h
e
f
ir
s
t
b
en
ch
m
ar
k
,
d
en
o
te
d
as
2
0
Ne
wsGro
u
p
,
was
also
o
b
tain
ed
f
r
o
m
th
e
UC
I
.
T
h
e
2
0
New
s
g
r
o
u
p
u
s
ed
in
th
is
r
esear
ch
co
n
tain
s
2
0
0
0
d
o
c
u
m
en
ts
d
is
tr
ib
u
ted
in
to
2
0
class
es
wh
er
e
1
0
0
d
o
cu
m
e
n
ts
in
ea
ch
class
.
T
h
is
r
esear
ch
h
as
s
elec
ted
th
r
ee
cl
ass
es:
h
ar
d
war
e,
b
aseb
all,
an
d
elec
tr
o
n
ic
with
a
to
tal
n
u
m
b
er
o
f
3
0
0
d
o
cu
m
e
n
ts
.
T
h
e
n
u
m
b
er
o
f
ter
m
s
co
llected
af
ter
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
is
2
2
,
wh
ich
in
clu
d
es th
e
m
o
s
t im
p
o
r
tin
g
ter
m
s
am
o
n
g
th
e
s
elec
ted
th
r
ee
class
es.
T
h
e
s
ec
o
n
d
b
en
ch
m
ar
k
,
wh
ich
is
d
en
o
te
d
as
R
eu
ter
s
-
2
1
5
7
8
,
was
o
b
tain
ed
f
r
o
m
UC
I
.
T
h
is
b
en
ch
m
a
r
k
in
clu
d
e
s
f
iv
e
ca
teg
o
r
ies,
in
clu
d
in
g
ex
c
h
an
g
es,
p
eo
p
le,
to
p
ics,
o
r
g
an
izatio
n
s
,
an
d
p
lace
s
.
E
ac
h
o
f
th
e
ca
teg
o
r
ies
is
d
iv
id
ed
in
to
s
u
b
ca
teg
o
r
ies.
Fo
u
r
s
u
b
ca
teg
o
r
ies
u
s
ed
in
th
e
ev
al
u
atio
n
in
cl
u
d
e
t
h
r
ee
class
es
with
a
to
tal
n
u
m
b
er
o
f
1
9
0
7
d
o
cu
m
en
ts
,
in
wh
ich
1
6
5
0
d
o
cu
m
e
n
ts
b
elo
n
g
to
ac
q
class
,
3
7
d
o
cu
m
en
ts
b
elo
n
g
to
g
as
clas
s
,
9
4
d
o
cu
m
en
ts
b
elo
n
g
to
g
o
ld
class
,
an
d
1
2
6
d
o
cu
m
e
n
ts
b
elo
n
g
to
s
u
g
ar
.
T
h
ese
s
u
b
ca
teg
o
r
ies
ar
e
s
elec
ted
b
ec
au
s
e
th
e
n
u
m
b
er
o
f
d
o
cu
m
e
n
ts
in
ea
ch
class
d
if
f
er
s
f
r
o
m
th
e
o
th
er
g
r
o
u
p
.
T
h
u
s
,
t
h
e
p
r
o
b
le
m
o
f
f
i
n
d
in
g
th
e
b
est
co
n
f
ig
u
r
atio
n
is
d
if
f
ic
u
lt,
esp
ec
ially
if
th
e
b
en
ch
m
a
r
k
c
o
n
tain
s
d
if
f
e
r
en
t
d
e
n
s
ities
.
T
h
e
n
u
m
b
er
o
f
ter
m
s
c
o
llected
a
f
ter
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
is
1
0
,
wh
ich
in
clu
d
es th
e
m
o
s
t im
p
o
r
tan
t te
r
m
s
am
o
n
g
t
h
e
d
o
cu
m
e
n
ts
o
f
all
clas
s
es.
T
h
e
th
i
r
d
b
en
ch
m
ar
k
in
clu
d
es
web
p
ag
es
p
lu
s
th
e
r
atin
g
s
o
f
a
s
in
g
le
S
y
s
k
ill
an
d
W
eb
er
t
web
p
ag
e
r
atin
g
s
,
w
h
ich
ar
e
d
e
n
o
ted
as
Sy
s
k
illW
eb
er
t
b
en
ch
m
ar
k
also
o
b
tain
ed
UC
I
with
f
o
u
r
d
if
f
er
en
t
k
in
d
s
o
f
d
o
cu
m
e
n
ts
,
in
clu
d
in
g
B
an
d
s
,
B
io
Me
d
ial,
Go
ats,
an
d
Sh
ee
p
.
T
h
e
last
b
en
c
h
m
ar
k
u
s
ed
in
t
h
is
r
esear
ch
is
s
en
ten
ce
class
if
icatio
n
b
en
c
h
m
ar
k
,
wh
ich
is
k
n
o
wn
as
th
e
Sen
te
n
ce
C
o
r
p
u
s
.
I
t
r
ep
r
esen
ts
t
h
e
ab
s
tr
ac
t
o
f
ar
ticles
c
o
llected
in
d
if
f
er
en
t
p
u
b
lis
h
er
s
.
I
n
th
is
s
tu
d
y
,
th
e
two
p
u
b
lis
h
er
s
u
s
ed
ar
e
th
e
J
am
an
d
Plo
s
,
wh
er
e
t
h
e
m
a
x
im
u
m
n
u
m
b
e
r
o
f
d
o
c
u
m
en
ts
ar
e
6
0
0
.
T
h
e
n
u
m
b
er
o
f
ter
m
s
co
llected
af
ter
th
e
p
r
e
-
p
r
o
ce
s
s
in
g
s
tep
is
8
0
ter
m
s
wi
th
tw
o
class
es.
T
ab
le
7
d
escr
ib
es a
ll b
en
ch
m
ar
k
s
u
s
ed
in
th
is
r
esear
ch
,
wh
ich
in
clu
d
es 1
3
d
if
f
er
en
t k
in
d
s
o
f
class
.
T
ab
le
7
.
C
h
ar
ac
ter
is
tics
o
f
b
en
ch
m
ar
k
s
B
e
n
c
h
mar
k
R
e
s
o
u
r
c
e
s
N
u
mb
e
r
o
f
d
o
c
u
m
e
n
t
s
To
t
a
l
n
u
m
b
e
r
o
f
d
o
c
u
me
n
t
s
N
u
mb
e
r
o
f
t
e
r
ms
N
u
mb
e
r
o
f
c
l
a
sse
s
2
0
n
e
w
sg
r
o
u
p
s
B
a
se
b
a
l
l
1
0
0
3
0
0
22
3
El
e
c
t
r
o
n
i
c
s
1
0
0
H
a
r
d
w
a
r
e
1
0
0
R
e
u
t
e
r
s
-
2
1
5
7
8
A
c
q
1
6
5
0
1
9
0
7
10
4
G
a
s
37
G
o
l
d
94
S
u
g
a
r
1
2
6
S
y
sk
i
l
l
W
e
b
e
r
t
B
a
n
d
s
61
2
9
0
5
4
B
i
o
M
e
d
i
a
l
1
2
4
G
o
a
t
s
57
S
h
e
e
p
48
S
e
n
t
e
n
c
e
C
o
r
p
u
s
Jd
m
3
0
0
6
0
0
80
2
P
l
o
s
3
0
0
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