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-
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,
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e
2016
,
p
p
.
6
4
~
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I
SS
N:
2252
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8938
64
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Scie
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1.
I
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RO
D
UCT
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O
N
C
lu
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ter
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ter
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a
n
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n
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v
is
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NP
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m
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ar
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s
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m
eth
o
d
s
o
f
clu
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ter
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av
ailab
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in
liter
at
u
r
e.
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h
e
p
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f
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m
a
n
ce
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al
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s
is
o
f
s
ta
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o
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els h
a
s
b
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p
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p
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ed
b
y
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et
al
[
1
]
w
h
er
e
as c
lu
s
ter
in
g
an
d
it
s
u
n
d
er
l
y
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alg
eb
r
a
is
co
v
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ed
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v
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it
t
et
al
[
2
]
.
Gr
ap
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is
a
r
ep
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esen
tatio
n
w
h
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ch
m
o
d
els
t
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ip
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w
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es.
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d
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R
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[
3
]
.
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ap
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ased
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[
4
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w
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ased
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[
5
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ased
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Sch
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f
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[
6
]
.
T
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p
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ip
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ased
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.
T
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p
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it
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f
th
e
s
a
m
p
le
p
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ts
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
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N:
2252
-
8938
A
n
S
V
D
b
a
s
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R
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Ge
n
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A
lg
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(
P
a
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jit R
o
y
)
65
ca
lcu
lated
b
ased
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n
t
h
eir
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i
m
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lar
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to
w
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t
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ip
ar
tite
g
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h
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A
g
o
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d
liter
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r
e
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a
v
ai
lab
le
o
n
g
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ap
h
a
n
d
th
e
b
ip
ar
tit
e
d
u
e
to
B
o
llo
b
´
as [
7
]
.
Sin
g
u
lar
v
alu
e
d
ec
o
m
p
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s
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n
(
SVD)
is
a
f
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to
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o
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)
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w
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r
r
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ai
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VD
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ased
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ab
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d
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g
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[
8
]
.
SVD
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ased
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ter
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h
as
b
ee
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s
id
er
ed
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y
Dh
illo
n
[
9
]
.
So
m
e
ea
r
lier
w
o
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k
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s
i
n
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lar
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ased
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o
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b
y
Dr
in
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s
et
al[
1
0
]
.
Gen
etic
A
l
g
o
r
ith
m
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s
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m
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h
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w
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s
th
e
m
to
g
e
n
er
ate
o
f
f
s
p
r
in
g
s
o
lu
t
io
n
s
b
y
m
ati
n
g
.
T
h
e
o
f
f
s
p
r
in
g
o
f
g
o
o
d
s
o
lu
tio
n
s
ar
e
lik
el
y
to
b
e
b
etter
.
T
h
is
ass
u
m
p
t
io
n
i
s
t
h
e
f
u
n
d
a
m
en
tal
o
f
g
e
n
etic
al
g
o
r
ith
m
.
T
h
e
tar
g
e
t o
f
t
h
e
g
e
n
etic
al
g
o
r
ith
m
is
to
o
p
ti
m
ize
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
to
r
ea
ch
to
a
b
etter
s
o
lu
tio
n
.
A
n
o
v
e
l
eliti
s
t
G
A
m
o
d
el
is
p
r
o
p
o
s
ed
b
y
Deb
et
al
[
1
1
]
.
T
h
e
g
en
et
ic
alg
o
r
it
h
m
b
ased
clu
s
t
er
in
g
tec
h
n
iq
u
e
ar
e
d
is
c
u
s
s
ed
b
y
Ma
u
li
k
et
al
[
1
2
]
b
u
t
w
o
r
k
d
o
es
n
o
t
co
n
s
id
er
g
r
ap
h
b
ased
clu
s
ter
in
g
;
r
at
h
e
r
it
co
n
s
id
er
s
f
u
zz
y
clu
s
ter
i
n
g
o
n
i
m
a
g
e
d
ata.
So
m
e
m
o
r
e
g
en
et
ic
alg
o
r
it
h
m
b
ased
clu
s
ter
i
n
g
is
p
r
o
p
o
s
ed
b
y
C
h
e
[
1
3
]
w
h
er
ea
s
s
o
m
e
ap
p
licatio
n
o
f
cl
u
s
ter
i
n
g
in
g
e
n
eti
c
alg
o
r
ith
m
is
d
u
e
to
Kala
et
a
l
[
1
4
]
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
s
in
g
u
lar
v
al
u
e
d
ec
o
m
p
o
s
i
tio
n
b
a
s
e
d
g
e
n
etic
al
g
o
r
ith
m
m
o
d
el
f
o
r
clu
s
ter
i
n
g
b
ip
ar
tite g
r
ap
h
.
T
h
e
p
ap
er
is
o
r
ien
ted
as
f
o
llo
w
s
.
Sectio
n
2
.
d
is
c
u
s
s
es
t
h
e
n
ec
ess
ar
y
m
at
h
e
m
atics
u
s
ed
in
th
e
m
o
d
el.
Sectio
n
3
.
p
r
o
p
o
s
es
t
h
e
m
o
d
el.
T
h
e
ex
p
er
i
m
e
n
tal
s
et
u
p
h
a
s
b
ee
n
co
v
er
ed
i
n
s
ec
ti
o
n
4
.
w
h
er
ea
s
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
h
as
b
ee
n
tas
ted
an
d
an
al
y
ze
d
i
n
s
ec
tio
n
5
.
.
C
o
n
c
l
u
s
io
n
s
ar
e
g
iv
e
n
i
n
s
ec
tio
n
6
.
an
d
th
e
r
e
f
er
en
ce
s
c
o
m
e
at
t
h
e
e
n
d
.
2
.
T
H
E
M
AT
H
E
M
AT
I
CAL
B
ACK
G
RO
UND
S
Gen
etic
al
g
o
r
ith
m
is
a
s
ea
r
ch
b
ased
o
p
tim
iza
tio
n
tec
h
n
iq
u
e
f
o
r
NP
-
h
ar
d
p
r
o
b
lem
s
.
Gen
etic
alg
o
r
ith
m
is
i
n
s
p
ir
ed
b
y
t
h
e
b
io
lo
g
ical
g
e
n
etics
w
h
er
e
t
h
e
ch
r
o
m
o
s
o
m
e
o
f
th
e
p
ar
en
t
s
d
ec
id
es
th
e
n
a
tu
r
e
o
f
th
eir
o
f
f
s
p
r
i
n
g
.
I
t
is
al
s
o
b
eliev
ed
th
at
t
h
e
g
o
o
d
f
ea
tu
r
es
o
f
b
o
th
th
e
p
ar
en
t
s
in
h
er
it
to
th
e
o
f
f
s
p
r
in
g
a
n
d
th
e
o
f
f
s
p
r
in
g
m
a
y
s
u
p
er
io
r
th
an
it
s
p
ar
en
ts
.
T
h
e
ch
r
o
m
o
s
o
m
e
c
o
n
s
is
ts
o
f
s
e
v
er
al
g
e
n
e
s
.
E
ac
h
g
en
e
i
s
r
esp
o
n
s
ib
le
f
o
r
s
o
m
e
p
r
o
p
er
ty
o
f
t
h
e
o
f
f
s
p
r
in
g
.
P
r
o
p
er
ties
lik
e
h
air
co
lo
r
,
s
h
ap
e
o
f
n
o
s
e
etc
ar
e
d
u
e
to
g
e
n
e.
I
n
g
e
n
etic
alg
o
r
it
h
m
,
t
h
e
s
a
m
e
co
n
ce
p
t
h
a
s
b
ee
n
in
h
er
it
ed
.
E
v
er
y
i
n
d
iv
id
u
al
co
m
p
o
n
en
t
o
f
t
h
e
s
o
lu
tio
n
is
e
n
co
d
ed
in
a
g
e
n
e
an
d
ch
r
o
m
o
s
o
m
e
is
f
o
r
m
ed
f
r
o
m
th
e
g
e
n
e
s
et
s
.
E
ac
h
c
h
r
o
m
o
s
o
m
e
is
a
ca
n
d
id
ate
s
o
lu
tio
n
o
f
t
h
e
g
i
v
en
p
r
o
b
lem
.
I
n
g
en
et
ic
al
g
o
r
ith
m
,
a
n
u
m
b
er
o
f
s
u
c
h
s
o
l
u
tio
n
s
ar
e
cr
ea
ted
as
i
n
itia
l
p
o
p
u
latio
n
.
T
h
e
p
o
p
u
latio
n
i
s
allo
w
ed
f
o
r
cr
o
s
s
b
r
ee
d
in
g
,
ca
l
led
cr
o
s
s
o
v
er
.
I
n
s
u
c
h
ca
s
e,
p
a
ir
s
o
f
c
h
r
o
m
o
s
o
m
e
ar
e
ch
o
s
e
n
f
o
r
m
at
in
g
.
T
h
e
r
e
s
u
lt
is
t
h
e
cr
ea
tio
n
o
f
n
e
w
o
f
f
s
p
r
in
g
.
T
h
e
o
f
f
s
p
r
in
g
ar
e
th
e
n
p
ass
e
d
to
a
f
i
tn
e
s
s
f
u
n
ctio
n
f
o
r
th
eir
f
it
n
es
s
o
r
clo
s
en
e
s
s
to
w
ar
d
s
t
h
e
o
p
ti
m
al
s
o
lu
tio
n
.
Fo
r
t
h
is
,
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
d
eter
m
in
ed
an
d
th
e
ch
ar
ac
ter
i
s
tics
o
f
t
h
e
o
f
f
s
p
r
in
g
ar
e
m
ea
s
u
r
ed
.
Usi
n
g
th
e
r
u
le
o
f
s
u
r
v
i
v
al
o
f
th
e
f
itte
s
t,
th
e
elitis
m
m
o
d
el
o
f
t
h
e
G
A
s
e
lec
ts
b
est
n
ch
r
o
m
o
s
o
m
e
f
r
o
m
t
h
e
cu
r
r
en
t
p
o
o
l
an
d
r
est
f
r
o
m
t
h
e
o
f
f
s
p
r
i
n
g
.
I
n
th
is
w
a
y
th
e
s
o
lu
tio
n
s
et
ev
o
l
v
es.
Du
r
in
g
th
i
s
ev
o
l
u
tio
n
,
s
o
m
e
g
en
e
m
a
y
g
et
ch
a
n
g
ed
r
an
d
o
m
l
y
to
g
en
er
ate
an
en
tire
l
y
n
e
w
s
o
l
u
tio
n
.
T
h
is
is
ca
lled
m
u
tat
io
n
.
A
f
ter
f
i
n
ite
g
en
er
a
tio
n
s
,
an
ac
ce
p
ted
s
o
lu
tio
n
is
e
x
p
ec
ted
to
o
cc
u
r
[
1
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
2
5
2
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8938
IJ
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AI
Vo
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5
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2
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1
6
:
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4
–
71
66
T
h
e
v
alid
it
y
i
n
d
ex
e
s
h
av
e
an
i
m
p
o
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t
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r
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u
alit
y
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f
th
e
r
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u
lt
s
p
r
o
d
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ce
d
b
y
th
e
cl
u
s
ter
i
n
g
alg
o
r
ith
m
s
.
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h
er
e
ar
e
b
r
o
ad
ly
tw
o
t
y
p
es
o
f
v
alid
it
y
i
n
d
ex
e
s
,
n
a
m
e
l
y
,
i
n
ter
n
al
an
d
ex
ter
n
al.
A
l
m
o
s
t
all
i
n
ter
n
al
cr
iter
ia
co
n
s
id
er
s
th
e
w
it
h
in
clu
s
ter
s
ca
t
ter
an
d
b
et
w
ee
n
clu
s
ter
s
ep
ar
atio
n
i
n
s
o
m
e
w
a
y
o
r
o
th
er
.
T
h
e
p
r
ese
n
t
p
ap
er
co
n
s
id
er
s
o
n
e
o
f
th
e
in
ter
n
a
l
cl
u
s
ter
v
alid
it
y
i
n
d
ex
es,
ca
lled
B
all
-
Ha
ll
in
d
ex
[
1
7
]
as th
e
o
b
j
ec
t
iv
e
f
u
n
ctio
n
f
o
r
th
e
g
en
e
tic
alg
o
r
it
h
m
.
T
h
e
ex
ter
n
al
i
n
d
ex
es,
o
n
th
e
o
th
er
h
a
n
d
,
ass
u
m
e
s
o
m
e
p
r
io
r
k
n
o
w
led
g
e
ab
o
u
t t
h
e
s
a
m
p
le
d
is
tr
ib
u
tio
n
an
d
m
ea
s
u
r
es
th
e
cl
u
s
ter
p
r
o
d
u
ce
d
ac
co
r
d
in
g
l
y
.
A
g
o
o
d
d
is
cu
s
s
io
n
o
n
s
u
ch
i
n
d
ex
e
s
is
g
i
v
en
b
y
Des
g
r
au
p
e
s
[
1
8
]
an
d
Sah
a
et
al
[
1
9
]
.
3
.
T
H
E
P
RO
P
O
SE
D
M
O
DE
L
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
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SS
N:
2252
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8938
A
n
S
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b
a
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R
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)
67
4
.
RE
SE
AR
CH
M
E
T
H
O
DO
L
O
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T
o
test
th
e
p
er
f
o
r
m
a
n
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o
f
t
h
e
p
r
o
p
o
s
ed
m
o
d
el,
th
e
a
n
ex
p
er
i
m
en
tal
s
et
u
p
h
as
b
ee
n
ch
o
s
en
.
T
h
r
ee
th
i
n
g
s
ar
e
co
n
s
id
er
ed
f
o
r
th
is
s
etu
p
.
T
h
ese
ar
e
th
e
p
r
o
b
lem
t
o
co
n
s
id
er
,
th
e
d
ataset
co
n
tain
in
g
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u
c
h
p
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le
m
s
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ea
s
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r
e
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t scale
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h
ich
th
e
o
u
tp
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t
s
w
ill
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e
m
ea
s
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r
ed
.
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h
er
e
ar
e
m
ain
l
y
t
w
o
asp
ec
ts
th
at
th
e
cl
u
s
ter
i
n
g
p
r
o
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lem
s
ca
n
b
e
o
b
s
er
v
ed
.
On
e
is
o
n
th
e
b
asis
o
f
s
ep
ar
ab
ilit
y
an
d
th
e
o
th
er
is
o
n
th
e
b
asis
o
f
th
e
s
h
ap
e
o
f
th
e
clu
s
ter
s
.
T
h
e
p
r
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b
lem
o
f
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ep
ar
ab
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y
m
ea
n
s
w
h
et
h
er
th
e
cl
u
s
ter
s
ar
e
w
ell
s
ep
ar
at
ed
o
r
n
o
t.
I
f
t
h
e
cl
u
s
ter
s
ar
e
n
o
t
w
ell
s
ep
ar
ated
,
th
e
p
r
o
b
lem
i
s
to
u
ch
i
n
g
p
r
o
b
lem
.
T
h
e
s
h
ap
e
o
f
th
e
cl
u
s
ter
s
ar
e
o
f
t
w
o
t
y
p
es.
C
o
n
v
e
x
s
h
ap
ed
an
d
ar
b
itra
r
y
s
h
ap
ed
.
I
n
f
i
g
u
r
e
1
(
a)
,
a
co
n
v
ex
a
n
d
w
ell
s
ep
ar
ated
s
a
m
p
le
h
as
b
ee
n
s
h
o
w
n
w
h
er
ea
s
in
f
i
g
u
r
e
1
(
b
)
,
a
s
a
m
p
l
e
is
s
h
o
w
n
w
h
ic
h
is
w
ell
s
ep
ar
a
ted
b
u
t
clu
s
ter
s
h
ap
e
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
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tt
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//
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Evaluation Warning : The document was created with Spire.PDF for Python.