I
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Adv
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s
(
I
J
AAS)
Vo
l.
4
,
No
.
4
,
Dec
em
b
er
201
5
,
p
p
.
130
~
134
I
SS
N:
2252
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T
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p
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p
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b
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h
ed
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cr
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2
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3
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[
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[
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[
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1
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[
8
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.
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„
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f
icie
n
c
y
w
it
h
co
n
v
en
t
io
n
al
k
-
m
ea
n
s
cl
u
s
ter
i
n
g
alg
o
r
it
h
m
[
1
0
]
.
Hen
ce
,
i
n
th
is
p
ap
er
,
w
e
i
n
tr
o
d
u
ce
a
m
o
d
i
f
i
ca
tio
n
o
f
K
-
m
ea
n
s
al
g
o
r
ith
m
th
at
e
f
f
icie
n
tl
y
s
ea
r
c
h
es
d
ata
to
clu
s
ter
p
o
in
ts
b
y
co
m
p
u
te
t
h
e
s
u
m
o
f
s
q
u
ar
es
w
it
h
i
n
ea
c
h
cl
u
s
ter
,
w
h
ic
h
m
ak
es
th
e
p
r
o
g
r
a
m
to
s
elec
t
th
e
m
o
s
t
p
r
o
m
is
i
n
g
s
u
b
s
et
o
f
class
e
s
f
o
r
cl
u
s
ter
i
n
g
.
T
h
e
h
-
a
n
d
g
-
in
d
ice
s
o
f
f
e
w
a
u
th
o
r
s
w
h
o
h
a
v
e
p
u
b
lis
h
ed
s
c
i
en
ti
f
ic
p
ap
er
s
o
f
e
x
ce
lle
n
ce
i
n
th
e
f
ield
s
o
f
co
m
p
u
ter
s
cie
n
ce
[
1
1
]
ar
e
s
eg
r
eg
ated
.
I
n
o
r
d
er
to
co
lle
ct
an
d
ca
lcu
l
ate
m
an
u
all
y
,
a
r
eliab
le
to
o
l
f
r
o
m
Go
o
g
le
Sch
o
lar
[
1
2
]
w
as
u
s
ed
to
p
er
f
o
r
m
th
e
tas
k
.
Go
o
g
le
C
h
r
o
m
e
h
as
d
ev
e
lo
p
ed
an
in
tu
i
tiv
e
H
-
i
n
d
ex
ca
lcu
lato
r
ad
d
-
o
n
to
C
h
r
o
m
e
b
r
o
w
s
er
.
2
.
M
AT
E
RIAL
S AN
D
M
E
T
H
O
DS
2
.
1
.
h
-
a
nd
g
-
ind
ices
T
h
e
h
-
a
n
d
g
-
in
d
ice
s
o
f
f
e
w
a
u
th
o
r
s
w
h
o
h
a
v
e
p
u
b
lis
h
ed
s
c
i
en
ti
f
ic
p
ap
er
s
o
f
e
x
ce
lle
n
ce
i
n
th
e
f
ield
s
o
f
co
m
p
u
ter
s
cie
n
ce
ar
e
s
e
g
r
eg
ated
.
I
n
o
r
d
er
to
co
llect
a
n
d
ca
lc
u
late
m
a
n
u
al
l
y
,
w
h
ich
is
a
m
o
r
e
ted
io
u
s
p
r
o
ce
s
s
th
a
n
e
x
p
ec
ted
;
a
m
o
r
e
r
eliab
le
to
o
l
f
r
o
m
Go
o
g
le
C
h
r
o
m
e
w
as
u
s
ed
to
p
er
f
o
r
m
t
h
e
tas
k
.
Go
o
g
le
C
h
r
o
m
e
h
as d
e
v
elo
p
ed
an
in
t
u
itiv
e
H
-
i
n
d
ex
ca
lc
u
lato
r
ad
d
-
on
.
Fig
u
r
e
1
.
I
n
d
ex
v
a
l
u
es c
o
m
p
u
t
ed
b
y
th
e
ca
lc
u
lato
r
B
o
th
th
e
h
-
a
n
d
g
-
i
n
d
ices
ar
e
co
n
s
eq
u
e
n
ce
to
s
o
m
e
s
co
p
e
b
y
th
e
n
u
m
b
er
o
f
p
ap
er
s
p
u
b
l
is
h
ed
i
n
a
j
o
u
r
n
al.
A
j
o
u
r
n
al
th
at
p
u
b
li
s
h
es
a
lar
g
er
n
u
m
b
er
o
f
p
ap
er
s
h
as
a
h
ig
h
er
p
o
s
s
ib
ilit
y
to
m
ak
e
a
h
ig
h
er
h
-
a
n
d
g
-
in
d
ices
s
i
n
ce
e
v
er
y
ar
ticle
p
r
e
s
en
t
s
a
n
o
th
er
c
h
a
n
ce
f
o
r
citati
o
n
s
[
1
6
]
.
T
h
e
v
al
u
e
f
o
r
t
h
e
i
n
d
ices d
ep
en
d
s
o
n
t
h
e
r
an
g
e
o
f
p
ap
er
s
b
ein
g
e
x
a
m
i
n
ed
,
an
d
h
o
w
co
m
p
r
eh
e
n
s
iv
e
l
y
t
h
e
citatio
n
s
f
o
r
ea
ch
h
a
v
e
b
ee
n
in
d
ex
ed
.
T
h
e
m
ai
n
in
te
n
s
it
y
o
f
th
e
h
-
in
d
e
x
i
s
th
at
it
m
ea
s
u
r
es
q
u
a
n
ti
t
y
a
n
d
im
p
ac
t
b
y
t
h
e
m
ea
n
s
o
f
s
i
n
g
le
in
d
icato
r
.
E
g
g
h
e
[
1
3
]
,
[
1
6
]
s
ay
s
g
-
in
d
e
x
is
“
t
h
e
h
i
g
h
er
r
an
k
,
s
u
ch
t
h
at
t
h
e
to
p
g
p
ap
er
s
h
av
e
at
lea
s
t
g
2
citat
io
n
s
.
I
t
al
s
o
m
ea
n
s
,
th
at
t
h
e
to
p
g
+
1
h
av
e
les
s
th
a
n
(
g
+
1
)
2
p
ap
er
s
”.
T
h
e
g
-
in
d
e
x
is
al
w
a
y
s
g
r
ea
ter
th
a
n
o
r
eq
u
al
to
h
-
i
n
d
ex
.
Da
t
a
s
et
s
:
I
r
is
is
a
s
e
t
o
f
to
tal
1
5
0
d
ata,
ea
ch
h
a
v
i
n
g
f
o
u
r
attr
ib
u
tes,
s
u
c
h
a
s
„
s
ep
tal
‟
len
g
t
h
a
n
d
b
r
ea
d
th
a
n
d
„
p
ed
al‟
le
n
g
t
h
an
d
b
r
ea
d
th
[
1
4
]
.
T
h
e
d
ataset
is
d
iv
id
ed
in
to
th
r
ee
class
lab
els
(
e.
g
.
,
ir
is
s
et
o
s
a;
ir
is
v
er
s
ico
lo
r
;
an
d
ir
is
v
er
g
i
n
ica)
ea
ch
h
av
in
g
eq
u
al
d
ata
d
is
tr
ib
u
tio
n
s
,
i.e
.
,
f
ir
s
t
5
0
b
elo
n
g
s
to
ir
is
s
eto
s
a
,
n
ex
t
5
0
ar
e
ir
is
ve
r
s
ico
lo
r
,
an
d
t
h
e
r
e
m
ai
n
i
n
g
5
0
d
ata
b
elo
n
g
to
ir
is
ve
r
g
in
ica
).
2
.
2
.
P
a
ra
m
et
er
s
t
o
M
e
a
s
ure
t
he
Clus
t
er
ing
P
er
f
o
r
m
a
nce
Da
t
a
dis
cr
epa
ncy
f
a
ct
o
r
(
DDF
)
:
Data
d
is
cr
ep
an
cy
i
s
m
ea
s
u
r
ed
b
y
n
o
ti
n
g
th
e
p
o
s
itio
n
al
d
is
cr
ep
an
cies
a
m
o
n
g
t
h
e
d
ata
p
o
in
ts
d
u
r
in
g
cl
u
s
ter
i
n
g
.
I
t
is
co
m
p
u
ted
b
y
ad
d
in
g
t
h
e
n
u
m
b
er
o
f
(
i)
„
w
r
o
n
g
‟
d
ata
p
o
in
ts
g
r
o
u
p
ed
in
s
id
e
(
W
I
)
,
(
ii)
th
e
„
co
r
r
ec
t‟
d
ata
p
o
in
ts
l
y
i
n
g
o
u
ts
id
e
(
W
O)
o
f
an
y
k
th
c
l
u
s
ter
an
d
(
iii)
n
u
m
b
er
o
f
d
ata
p
o
in
ts
,
w
h
i
ch
co
u
ld
n
o
t
b
e
clu
s
ter
ed
i
.
e.
th
e
o
u
tlier
s
(
O
L
)
w
h
en
m
atc
h
ed
w
ith
t
h
e
r
ep
r
esen
tativ
e
d
ata
(
C
k
)
.
Fi
n
all
y
,
it
is
ex
p
r
ess
ed
as
a
p
er
ce
n
tag
e
o
f
t
h
e
to
tal
n
u
m
b
er
o
f
d
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p
o
in
ts
(
N)
.
I
d
ea
lly
,
t
h
e
DDF
m
u
s
t
b
e
0
%,
i.e
.
a
ll
th
e
d
ata
p
o
in
ts
ar
e
clu
s
ter
ed
as
it
s
h
o
u
ld
b
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an
d
th
er
e
is
n
il
o
u
t
lier
.
I
ts
s
ig
n
i
f
ica
n
ce
is
to
e
v
al
u
ate
th
e
„
u
n
d
er
‟
a
n
d
„
o
v
er
‟
f
itt
in
g
o
f
t
h
e
d
ata.
A
n
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x
a
m
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le
o
f
D
DF c
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in
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I
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2
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Dec
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er
201
5
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3
0
–
1
3
4
132
Co
m
pu
t
a
t
io
na
l
T
i
m
e:
T
h
e
co
m
p
u
tatio
n
al
ti
m
e,
th
a
t
i
s
,
an
a
v
e
r
ag
e
u
s
er
ti
m
e
v
al
u
es
o
f
o
r
ig
i
n
al
v
er
s
u
s
m
o
d
i
f
ied
K
-
Me
a
n
s
alg
o
r
ith
m
h
a
v
e
b
ee
n
co
m
p
ar
ed
w
h
ile
ca
r
r
y
i
n
g
o
u
t
cl
u
s
ter
i
n
g
o
f
th
e
th
r
ee
d
ataset
s
u
s
ed
in
t
h
e
s
t
u
d
y
i
n
a
C
o
r
e
i3
,
6
4
-
b
it o
p
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s
y
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m
w
it
h
4
GB
R
A
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a
n
d
2
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2
GHz
p
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o
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s
s
o
r
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3
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RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
K
-
m
ea
n
s
s
u
f
f
er
s
f
r
o
m
d
r
a
w
b
a
ck
o
n
t
h
e
n
u
m
b
er
o
f
cl
u
s
ter
s
k
as
an
i
n
p
u
t
p
ar
a
m
eter
.
T
h
is
is
b
ec
au
s
e
o
f
an
in
ap
p
r
o
p
r
iate
ch
o
ice
o
f
k
w
h
ic
h
m
i
g
h
t
y
ield
s
p
u
r
io
u
s
r
esu
lt
s
.
He
n
ce
,
it
i
s
al
w
a
y
s
a
n
i
m
p
o
r
tan
t
tas
k
to
r
u
n
d
ia
g
n
o
s
tic
c
h
ec
k
s
w
h
e
n
u
s
in
g
k
-
m
ea
n
s
cl
u
s
t
er
i
n
g
to
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es
o
lv
e
t
h
e
n
u
m
b
er
o
f
cl
u
s
ter
s
i
n
th
e
g
i
v
en
d
ataset.
Mo
r
eo
v
er
,
ap
p
ly
i
n
g
k
-
m
ea
n
s
v
alu
e
w
it
h
v
al
u
es
r
an
g
i
n
g
f
r
o
m
k
=2
,
3
,
4
o
r
5
d
ep
en
d
s
o
n
t
h
e
n
u
m
b
er
o
f
o
b
j
ec
ts
in
th
e
d
ataset
a
n
d
to
av
o
id
ex
p
ec
ted
clu
s
ter
s
o
f
s
i
m
ilar
s
ize
,
s
o
th
at
th
e
ass
ig
n
m
en
t
o
f
o
b
j
ec
ts
to
th
e
n
ea
r
est
clu
s
ter
ce
n
ter
o
r
ce
n
tr
o
id
w
ill
r
esu
lt i
n
co
r
r
ec
t c
lu
s
ter
s
.
Alg
o
rit
h
m
:
K
-
M
ea
ns
1.
I
n
itializatio
n
: c
h
o
o
s
e
k
in
itial
ce
n
tr
o
id
s
ar
b
itra
r
il
y
(
o
r
r
an
d
o
m
l
y
)
.
2.
Ass
i
g
n
ea
ch
d
ata
p
o
in
t to
th
e
c
en
tr
o
id
th
at
is
clo
s
er
to
it.
3.
C
o
m
p
u
te
th
e
d
is
ta
n
ce
b
et
w
ee
n
th
e
ce
n
tr
o
id
s
an
d
o
b
j
ec
ts
u
s
i
n
g
th
e
E
u
clid
ea
n
D
is
ta
n
ce
eq
u
a
tio
n
4.
Up
d
ate
all
th
e
ce
n
tr
o
id
s
an
d
t
h
e
n
e
w
ce
n
tr
o
id
o
f
a
clu
s
ter
is
th
e
m
ea
n
o
f
all
th
e
p
o
in
ts
w
it
h
in
th
a
t
clu
s
ter
.
5.
R
ep
ea
t p
o
in
ts
2
an
d
3
u
n
t
il th
e
n
e
w
ce
n
tr
o
id
s
ar
e
th
e
s
a
m
e
a
s
th
e
p
r
ev
io
u
s
ce
n
tr
o
id
s
.
C
lu
s
ter
i
n
g
b
y
k
-
m
ea
n
s
alg
o
r
it
h
m
w
ill
r
es
u
lt
i
n
d
if
f
er
en
t
r
u
n
s
ea
ch
ti
m
e
t
h
e
p
r
o
g
r
a
m
is
r
u
n
.
T
h
o
u
g
h
th
e
d
if
f
er
en
ce
i
s
n
e
g
li
g
ib
le,
it
s
h
o
u
ld
b
e
n
o
ted
th
at
t
h
e
clu
s
ter
ass
ig
n
m
e
n
ts
c
h
an
g
e
s
li
g
h
tl
y
f
o
r
ea
ch
ti
m
e
t
h
e
alg
o
r
ith
m
i
s
r
u
n
.
T
h
is
is
b
ec
au
s
e
k
-
m
ea
n
s
tr
ie
s
to
f
in
d
th
e
lo
ca
ll
y
o
p
ti
m
al
s
o
l
u
tio
n
,
b
u
t
n
o
t
a
g
lo
b
ally
o
p
ti
m
al
o
n
e.
Hen
ce
,
th
e
k
-
m
ea
n
s
al
g
o
r
ith
m
w
as r
u
n
m
o
r
e
n
u
m
b
er
o
f
ti
m
e
s
to
r
ea
lize
a
co
n
s
is
te
n
tl
y
o
p
tim
a
l so
lu
tio
n
.
B
u
t
th
e
p
r
o
b
le
m
s
ti
ll
ex
i
s
ts
,
t
h
at
is
,
h
o
w
to
ch
o
o
s
e
t
h
e
b
est
s
o
lu
tio
n
a
m
o
n
g
t
w
o
cl
u
s
ter
i
n
g
s
o
lu
tio
n
s
?
Hen
ce
,
a
m
o
d
if
ied
k
-
m
ea
n
s
al
g
o
r
ith
m
w
a
s
p
r
ese
n
ted
w
h
er
e
a
m
etr
ic
w
as
u
s
ed
to
ca
lc
u
late
th
e
s
u
m
o
f
s
q
u
ar
e
s
w
it
h
i
n
-
cl
u
s
ter
to
c
h
o
o
s
e
t
h
e
b
est
o
n
e.
T
h
e
s
u
m
o
f
s
q
u
ar
es
w
it
h
i
n
t
h
e
c
lu
s
ter
r
ep
r
esen
ts
th
e
s
u
m
o
f
al
l
d
is
tan
ce
s
b
et
w
ee
n
ea
c
h
d
ata
p
o
in
t a
n
d
t
h
e
ce
n
tr
o
id
o
f
its
c
lu
s
ter
.
T
h
e
s
m
aller
t
h
e
v
al
u
e,
th
e
m
o
r
e
co
m
p
ac
t a
n
d
g
o
o
d
is
t
h
e
c
lu
s
ter
.
T
h
er
ef
o
r
e,
f
o
r
a
g
i
v
en
d
ataset,
clu
s
ter
s
w
it
h
th
e
s
m
aller
s
u
m
o
f
s
q
u
ar
es
w
it
h
i
n
a
cl
u
s
ter
ar
e
r
eg
ar
d
ed
as g
en
er
all
y
b
ette
r
.
T
h
e
ti
m
e
r
eq
u
ir
ed
to
p
er
f
o
r
m
b
o
th
th
e
al
g
o
r
it
h
m
s
ar
e
r
ep
o
r
ted
.
M
o
dified
K
-
M
ea
ns
Alg
o
rit
h
m
:
1.
I
n
itializatio
n
: c
h
o
o
s
e
k
in
itial
ce
n
tr
o
id
s
ar
b
itra
r
il
y
(
o
r
r
an
d
o
m
l
y
)
.
2.
Ass
i
g
n
ea
ch
d
ata
p
o
in
t to
th
e
c
en
tr
o
id
th
at
is
clo
s
er
to
it.
3.
C
o
m
p
u
te
th
e
d
is
ta
n
ce
b
et
w
ee
n
th
e
ce
n
tr
o
id
s
an
d
o
b
j
ec
ts
u
s
i
n
g
th
e
E
u
clid
ea
n
D
is
ta
n
ce
eq
u
a
tio
n
4.
Up
d
ate
all
th
e
ce
n
tr
o
id
s
an
d
t
h
e
n
e
w
ce
n
tr
o
id
o
f
a
clu
s
ter
is
th
e
m
ea
n
o
f
all
th
e
p
o
in
ts
w
it
h
in
th
a
t
clu
s
ter
.
5.
C
o
m
p
u
te
th
e
s
u
m
o
f
s
q
u
ar
es
w
it
h
i
n
-
cl
u
s
ter
to
o
b
tain
a
d
is
tan
ce
v
al
u
e
b
et
w
ee
n
ea
ch
d
ata
p
o
in
t
an
d
th
e
ce
n
tr
o
id
o
f
its
clu
s
ter
.
6.
R
ep
ea
t
k
-
m
ea
n
s
clu
s
ter
in
g
n
ti
m
es
(
n
=5
)
an
d
r
etu
r
n
t
h
e
clu
s
ter
i
n
g
w
it
h
th
e
s
m
allest
s
u
m
o
f
s
q
u
ar
es
w
it
h
i
n
-
clu
s
ter
.
7.
Up
d
ate
th
e
ce
n
tr
o
id
s
.
8.
Sto
p
th
e
p
r
o
ce
s
s
w
h
e
n
n
e
w
ce
n
tr
o
id
s
ar
e
s
a
m
e
as t
h
e
p
r
ev
io
u
s
ce
n
tr
o
id
s
.
Oth
er
w
i
s
e,
g
o
to
s
tep
3
.
3
.
1
.
Clus
t
er
ing
P
er
f
o
r
m
a
nce
o
n I
RIS
D
a
t
a
s
et
Da
t
a
dis
cr
epa
ncy
f
a
ct
o
r
(
D
DF
)
:
An
atte
m
p
t
w
a
s
m
ad
e
t
o
test
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
m
o
d
if
ied
K
-
m
ea
n
s
al
g
o
r
ith
m
,
w
h
ile
ca
r
r
y
i
n
g
o
u
t
clu
s
ter
i
n
g
o
n
I
R
I
S
[
1
0
]
an
d
h
-
in
d
e
x
an
d
g
in
d
e
x
es.
B
o
th
I
R
I
S
as
w
el
l
as
h
an
d
g
i
n
d
ices
d
ataset
s
is
id
ea
ll
y
cl
u
s
ter
ed
i
n
to
th
e
ir
r
esp
ec
tiv
e
g
r
o
u
p
s
.
T
h
e
r
esu
l
ts
ar
e
g
i
v
en
in
T
ab
le
1
an
d
2.
T
ab
le
1
.
DDF
ca
lcu
latio
n
o
n
I
R
I
S d
ataset
u
s
i
n
g
k
-
m
ea
n
s
alg
o
r
ith
m
#
C
l
u
st
e
r
D
a
t
a
P
o
i
n
t
s
T
a
r
g
e
t
O
b
se
r
v
e
d
#
W
r
o
n
g
d
a
t
a
p
o
i
n
t
s
OL
P
r
o
p
o
se
d
D
D
F
(
%)
C
o
n
v
e
n
t
i
o
n
a
l
D
D
F
(
%)
1
1
-
50
50
61
14
0
{1
4
+
0
+
3
+
1
/
1
5
0
}*
1
0
0
=
1
2
%
1
1
+
1
+
1
1
+
1
/
1
5
0
}
*
1
0
0
=
1
6
%
2
51
-
1
0
0
50
49
0
1
3
1
0
1
-
150
50
39
3
0
T
ab
le
2
.
DDF
ca
lcu
latio
n
o
n
I
R
I
S d
ataset
u
s
i
n
g
k
-
m
ea
n
s
m
o
d
if
ied
alg
o
r
ith
m
#
C
l
u
st
e
r
D
a
t
a
P
o
i
n
t
s
T
a
r
g
et
O
b
se
r
v
e
d
#
W
r
o
n
g
d
a
t
a
p
o
i
n
t
s
OL
P
r
o
p
o
se
d
D
D
F
(
%)
C
o
n
v
e
n
t
i
o
n
a
l
D
D
F
(
%)
1
1
-
50
50
49
0
1
{0
+
1
4
+
2
+
1
/
1
5
0
}*
1
0
0
=
1
1
.
3
3
%
1
+
1
2
+
1
2
+
1
/
1
5
0
}*
1
0
0
=
1
7
.
3
3
%
2
51
-
1
0
0
50
62
14
0
3
1
0
1
-
150
50
38
2
0
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
AA
S
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8814
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va
lu
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tio
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f h
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f S
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th
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in
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S
.
Go
vin
d
a
R
a
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)
133
On
e
o
f
t
h
e
cl
u
s
ter
q
u
a
lit
y
m
ea
s
u
r
es
is
t
h
e
DDF
co
m
p
u
tat
io
n
.
I
t
is
ca
lc
u
lated
u
s
i
n
g
a
n
eq
u
at
io
n
g
iv
e
n
ab
o
v
e.
DDF
is
th
e
m
o
s
t
i
m
p
o
r
tan
t
m
ea
s
u
r
e
a
m
o
n
g
all
o
th
er
m
ea
s
u
r
es
to
j
u
d
g
e
th
e
p
er
f
o
r
m
an
ce
o
f
an
y
clu
s
ter
i
n
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tec
h
n
iq
u
e.
C
o
n
v
e
n
t
io
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all
y
,
g
o
o
d
clu
s
ter
in
g
i
s
as
s
ess
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b
y
co
u
n
ti
n
g
to
tal
n
u
m
b
er
o
f
d
ata
p
o
in
ts
w
it
h
i
n
a
cl
u
s
ter
.
I
f
th
e
n
u
m
b
er
eq
u
als
to
th
e
n
u
m
b
er
o
f
d
es
ir
ed
d
ata
p
o
in
ts
an
d
th
e
cl
u
s
ter
is
s
aid
to
b
e
p
er
f
ec
t
[
1
5
]
.
T
h
e
g
o
o
d
n
ess
o
f
th
e
clu
s
ter
i
n
g
tec
h
n
iq
u
es
m
u
s
t
n
o
t
b
e
j
u
d
g
ed
b
ased
o
n
o
n
l
y
th
e
d
ata
co
u
n
t
in
s
id
e
a
clu
s
ter
,
r
at
h
er
t
h
e
g
o
o
d
n
es
s
o
f
a
clu
s
ter
m
u
s
t
b
e
te
s
ted
b
y
s
u
m
m
i
n
g
u
p
t
h
e
d
ata
p
o
in
ts
wh
ich
ar
e
(
i)
p
r
ese
n
t
w
it
h
i
n
a
clu
s
ter
w
h
er
e
it
s
h
o
u
ld
n
o
t
b
e
an
d
v
ice
v
er
s
a
an
d
(
ii)
n
o
t
clu
s
ter
ed
i.e
.
o
u
tlier
s
(
OL
)
.
Fro
m
T
ab
le
3
an
d
4
,
it
is
ev
id
e
n
ce
d
th
at
m
o
d
if
ied
k
-
m
ea
n
s
alg
o
r
it
h
m
p
r
esen
ted
i
n
th
is
p
ap
er
p
er
f
o
r
m
e
d
w
ell
t
h
a
n
n
o
r
m
a
l
alg
o
r
ith
m
.
3
.
2
.
Co
m
pu
t
a
t
io
na
l Ti
m
e
P
er
f
o
r
m
a
n
ce
o
f
th
e
m
o
d
i
f
ied
K
-
m
ea
n
s
al
g
o
r
it
h
m
w
as
a
s
s
ess
ed
b
y
co
m
p
u
ti
n
g
t
h
e
ti
m
e
tak
e
n
to
co
m
p
lete
t
h
e
r
u
n
u
s
i
n
g
I
R
I
S a
n
d
h
-
g
i
n
d
ices d
ataset
s
.
T
h
e
r
esu
lt
s
ar
e
s
u
m
m
ar
ized
in
T
ab
le
3
an
d
4
.
T
ab
le
3
.
C
o
m
p
u
ta
tio
n
al
ti
m
e
e
v
alu
a
tio
n
o
f
r
e
g
u
lar
a
n
d
m
o
d
if
ied
k
-
m
ea
n
s
al
g
o
r
ith
m
D
a
t
a
se
t
K
-
m
e
a
n
s o
r
i
g
i
n
a
l
(
R
u
n
t
i
me
i
n
se
c
s)
M
o
d
i
f
i
e
d
K
-
me
a
n
s (R
u
n
t
i
me
i
n
se
c
s)
I
R
I
S
R
u
n
1
:
5
.
8
2
R
u
n
2
:
5
.
6
6
R
u
n
3
:
5
.
6
4
R
u
n
1
:
3
.
4
9
R
u
n
2
:
3
.
3
0
R
u
n
3
:
3
.
4
7
h
-
g
i
n
d
i
c
e
s
R
u
n
1
:
1
5
.
2
1
R
u
n
2
:
1
4
.
2
5
R
u
n
3
:
1
5
.
2
2
R
u
n
1
:
0
.
4
0
R
u
n
2
:
0
.
3
7
R
u
n
3
:
0
.
3
7
T
ab
le
4
.
C
o
m
p
ar
is
o
n
o
f
ti
m
e
co
m
p
le
x
it
y
o
f
k
-
m
ea
n
s
o
r
ig
in
al
an
d
m
o
d
if
ied
al
g
o
r
ith
m
w
h
ile
a
v
ar
y
i
n
g
n
u
m
b
er
o
f
clu
s
ter
s
D
a
t
a
se
t
N
o
.
o
f
c
l
u
st
e
r
s
K
-
m
e
a
n
s o
r
i
g
i
n
a
l
(
R
u
n
t
i
me
i
n
se
c
s)
M
o
d
i
f
i
e
d
K
-
me
a
n
s (R
u
n
t
i
me
i
n
se
c
s)
I
R
I
S
1
2
.
4
4
2
.
8
1
2
3
.
5
2
3
.
0
6
3
6
.
6
3
3
.
3
0
4
7
.
7
0
3
.
7
2
5
8
.
8
4
4
.
1
1
H
-
G
i
n
d
i
c
e
s
1
2
.
1
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