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Vo
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6
,
No
.
6
,
Dec
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b
er
201
6
,
p
p
.
30
4
7
~
30
5
1
I
SS
N:
2088
-
8708
,
DOI
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0
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1
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as
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Mi
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[
3
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.
T
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k
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.
T
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
.
6
,
Dec
em
b
er
201
6
:
30
4
7
–
30
5
1
3048
w
ell
-
d
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f
in
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s
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io
n
o
f
o
u
r
w
o
r
k
.
2.
E
SS
E
N
T
I
A
L
T
E
CH
NO
L
O
G
I
E
S
C
lu
s
ter
i
n
g
is
t
h
e
p
r
o
ce
s
s
o
f
g
r
o
u
p
in
g
th
e
d
ata
in
to
class
es
o
r
clu
s
ter
s
,
s
o
th
at
o
b
j
ec
ts
w
ith
i
n
a
clu
s
ter
h
av
e
h
ig
h
s
i
m
ilar
it
y
in
co
m
p
ar
is
o
n
to
o
n
e
an
o
th
e
r
b
u
t
ar
e
v
er
y
d
is
s
i
m
ilar
to
o
b
j
ec
ts
in
o
th
er
clu
s
ter
s
[
3
]
.
Dis
s
i
m
ilar
i
ties
b
et
w
ee
n
o
b
j
ec
ts
ca
n
b
e
ca
lcu
lated
b
y
th
e
v
ar
iet
y
o
f
attr
ib
u
te
s
ass
o
ciate
d
with
th
e
o
b
j
ec
ts
.
I
n
g
en
er
al
cl
u
s
ter
i
n
g
alg
o
r
it
h
m
is
ca
teg
o
r
ized
in
to
P
ar
titi
o
n
b
ased
,
Hier
ar
ch
ical
m
et
h
o
d
,
Den
s
it
y
b
ased
m
et
h
o
d
s
,
Gr
id
b
ased
m
e
th
o
d
s
,
Mo
d
el
b
ased
m
eth
o
d
s
etc.
I
n
p
ar
titi
o
n
b
ased
clu
s
ter
in
g
k
m
ea
n
s
clu
s
ter
i
n
g
an
d
it
s
v
ar
iatio
n
s
ar
e
m
o
s
t
w
id
el
y
u
s
e
d
.
2
.
1
.
K
M
ea
ns
Clus
t
er
ing
a
lg
o
rit
hm
T
h
e
co
r
e
o
b
j
ec
tiv
e
o
f
K
Me
a
n
s
clu
s
ter
i
n
g
alg
o
r
it
h
m
is
to
d
i
v
id
e
g
iv
e
n
n
n
u
m
b
er
o
f
d
ata
o
b
j
ec
ts
in
to
k
n
u
m
b
er
o
f
cl
u
s
ter
s
u
c
h
t
h
at
i
n
tr
a
clu
s
ter
s
i
m
i
lar
it
y
is
h
i
g
h
b
u
t t
h
e
i
n
ter
clu
s
ter
s
i
m
i
lar
it
y
is
lo
w
.
T
h
e
d
etailed
alg
o
r
ith
m
is
a
s
b
elo
w
:
Alg
o
rit
h
m
:
T
h
e
k
-
m
ea
n
s
al
g
o
r
ith
m
f
o
r
p
ar
titi
o
n
i
n
g
,
w
h
er
e
ea
c
h
clu
s
ter
‟
s
ce
n
ter
i
s
r
ep
r
esen
ted
b
y
th
e
m
ea
n
v
al
u
e
o
f
th
e
o
b
j
ec
ts
in
th
e
cl
u
s
ter
.
I
np
ut:
k
: th
e
n
u
m
b
er
o
f
cl
u
s
ter
s
,
D
: a
d
ata
s
et
co
n
tain
i
n
g
n
o
b
j
ec
ts
.
O
utput
:
A
s
et
o
f
k
clu
s
ter
s
.
M
e
t
ho
d:
(
1
)
ar
b
itra
r
ily
c
h
o
o
s
e
k
o
b
j
ec
ts
f
r
o
m
D
as t
h
e
in
itial c
l
u
s
ter
c
en
ter
s
;
(
2
)
r
e
p
ea
t
(
3
)
(
r
e)
ass
ig
n
ea
ch
o
b
j
ec
t
to
th
e
cl
u
s
ter
to
w
h
ich
t
h
e
o
b
j
ec
t
is
t
h
e
m
o
s
t
s
i
m
ilar
b
ased
o
n
th
e
m
ea
n
v
al
u
e
o
f
th
e
o
b
j
ec
ts
in
th
e
cl
u
s
ter
;.
(
4
)
u
p
d
ate
th
e
clu
s
ter
m
ea
n
s
,
i.e
.
,
ca
lcu
late
th
e
m
ea
n
v
al
u
e
o
f
th
e
o
b
j
ec
ts
f
o
r
ea
ch
clu
s
ter
;
(
5
)
u
n
til n
o
c
h
a
n
g
e;[
3
]
T
h
is
alg
o
r
ith
m
is
r
ea
s
o
n
ab
l
y
p
r
o
f
icien
t
f
o
r
lar
g
e
d
ata
s
ets b
ec
au
s
e
t
i
m
e
co
m
p
lex
it
y
is
O(
n
k
t
)
,
w
h
er
e
n
is
n
u
m
b
er
o
f
o
b
j
ec
ts
in
d
ata
s
et,
k
is
th
e
n
u
m
b
er
o
f
cl
u
s
ter
an
d
t
is
th
e
n
u
m
b
er
o
f
iter
atio
n
s
.
No
r
m
all
y
,
k
≤
n
an
d
t ≤
n
.
2
.
2
.
M
a
pReduce
P
a
rdig
m
T
h
e
p
ar
allel
p
r
o
g
r
am
m
i
n
g
o
n
s
i
n
g
le
m
ac
h
in
e
is
n
o
t
ef
f
i
cien
t
f
o
r
p
r
o
ce
s
s
in
g
th
e
B
ig
Data
.
Fo
r
P
ar
allel
p
r
o
g
r
am
m
i
n
g
f
r
a
m
e
w
o
r
k
o
n
m
u
ltip
le
m
ac
h
i
n
es
Ma
p
R
ed
u
ce
is
a
n
e
s
s
e
n
tial
p
r
ef
er
en
ce
.
Ma
p
R
ed
u
ce
is
a
p
r
o
g
r
a
m
m
in
g
m
o
d
el
f
o
r
B
ig
d
ata
an
al
y
zin
g
a
n
d
p
r
o
ce
s
s
i
n
g
.
T
h
e
co
r
e
id
ea
is
to
d
iv
i
d
e
b
u
lk
y
tas
k
s
i
n
to
m
an
y
s
m
all
ta
s
k
s
an
d
co
n
q
u
e
r
th
e
m
a
f
ter
p
r
o
ce
s
s
ed
.
Ma
p
an
d
R
ed
u
ce
ar
e
t
w
o
p
h
a
s
es
o
f
th
e
p
r
o
g
r
a
m
m
i
n
g
p
ar
ad
ig
m
.
T
h
e
co
m
p
u
tat
io
n
ta
k
es
a
s
et
o
f
i
n
p
u
t
k
e
y
/
v
al
u
e
p
air
s
,
an
d
p
r
o
d
u
ce
s
a
s
et
o
f
o
u
tp
u
t
k
e
y
/
v
al
u
e
p
air
s
.
Th
e
u
s
er
o
f
th
e
Ma
p
R
ed
u
ce
li
b
r
ar
y
ex
p
r
es
s
es t
h
e
co
m
p
u
ta
ti
o
n
as t
w
o
f
u
n
c
tio
n
s
:
m
ap
an
d
r
ed
u
ce
.
Ma
p
Fu
n
ctio
n
is
co
m
p
o
s
ed
b
y
t
h
e
u
s
er
a
n
d
ac
ce
p
ts
in
p
u
t
a
s
a
<
k
e
y
,
v
al
u
e>
p
air
a
n
d
p
r
o
d
u
ce
s
a
s
et
o
f
in
ter
m
ed
iate
<k
e
y
,
v
al
u
e>
p
air
s
.
Fro
m
all
t
h
e
in
ter
m
ed
i
ate
<k
e
y
,
v
alu
e>
p
air
s
v
alu
e
s
ass
o
ciate
d
w
ith
t
h
e
s
a
m
e
in
ter
m
ed
iate
k
e
y
ar
e
c
o
m
b
i
n
ed
<
k
e
y
,
lis
t
o
f
v
al
u
e>
an
d
p
ass
e
s
to
t
h
e
r
ed
u
ce
f
u
n
ctio
n
.
T
h
e
r
ed
u
ce
f
u
n
ctio
n
,
al
s
o
co
m
p
o
s
ed
b
y
t
h
e
u
s
er
,
ac
ce
p
ts
an
i
n
ter
m
ed
i
ate
r
esu
lt
<
k
e
y
,
lis
t
o
f
v
a
lu
e
>.
I
t
m
er
g
es
th
e
s
e
v
alu
e
s
to
g
et
h
er
to
f
o
r
m
a
co
n
ce
iv
ab
l
y
r
ed
u
ce
d
s
et
o
f
v
a
l
u
es.
T
h
e
in
ter
m
ed
iate
v
al
u
es
ar
e
s
u
p
p
lied
to
th
e
u
s
er
‟
s
r
ed
u
ce
f
u
n
ctio
n
v
ia
an
iter
ato
r
.
T
h
is
allo
w
s
u
s
to
h
an
d
le
lis
t
s
o
f
v
al
u
es
t
h
at
ar
e
to
o
lar
g
e
to
f
it
in
m
e
m
o
r
y
[
4
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
I
s
s
u
es o
f K Mea
n
s
C
lu
s
teri
n
g
W
h
ile
Mig
r
a
tin
g
to
Ma
p
R
ed
u
ce
P
a
r
a
d
ig
m
w
ith
B
ig
Da
ta
.
.
.
.
(
K
.
R
.
N
i
r
ma
l)
3049
3.
RE
L
AT
E
D
WO
RK
B
ig
d
ata
an
a
l
y
s
is
n
ee
d
s
m
er
g
in
g
o
f
tec
h
n
iq
u
e
s
f
o
r
B
ig
Data
an
d
Ma
c
h
i
n
e
L
ea
r
n
in
g
.
K
Me
a
n
s
C
lu
s
ter
i
n
g
is
th
e
o
n
e
o
f
s
u
c
h
alg
o
r
ith
m
o
f
f
er
in
g
s
in
to
g
e
th
e
r
th
e
f
ield
s
.
Ma
n
y
r
e
s
ea
r
ch
s
t
u
d
ies
h
a
v
e
alr
ea
d
y
d
o
n
e
o
n
th
is
ar
ea
,
th
is
s
ec
tio
n
s
u
r
v
e
y
ed
o
n
it
an
d
m
o
s
tl
y
f
o
c
u
s
o
n
th
r
ee
is
s
u
e
s
r
elate
d
to
K
Me
an
s
C
l
u
s
ter
i
n
g
w
h
ile
m
ig
r
ati
n
g
o
n
Ma
p
R
ed
u
ce
w
ith
B
ig
d
ata
–
Selectio
n
o
f
I
n
itial
Valu
e
o
f
K,
I
n
itial
C
en
tr
o
id
Selectio
n
,
Ma
n
ag
in
g
t
h
e
ca
teg
o
r
ical
d
ata
.
1.
Yu
j
j
ex
u
et.
al
[
5
]
h
as
p
r
o
p
o
s
ed
E
f
f
icien
t
k
-
m
ea
n
s
++
A
p
p
r
o
x
i
m
atio
n
w
it
h
Ma
p
R
ed
u
ce
,
c
h
o
o
s
e
th
e
i
n
itial
to
ac
h
ie
v
e
a
s
o
lu
tio
n
th
a
t
i
s
p
r
o
v
ab
ly
clo
s
e
to
o
p
ti
m
al
o
n
e.
Her
e
o
n
l
y
o
n
e
Ma
p
R
ed
u
ce
j
o
b
is
u
s
ed
to
in
itial
ize
k
ce
n
ter
s
,
t
h
at
av
o
i
d
s
m
u
ltip
le
r
o
u
n
d
o
n
Ma
p
R
e
d
u
ce
j
o
b
o
n
m
a
n
y
m
ac
h
i
n
e.
Her
e
th
e
i
n
it
ial
v
alu
e
o
f
k
i
s
t
p
u
t
o
n
a
s
p
r
er
eq
u
is
i
t
e
o
f
a
lg
o
r
it
h
m
,
s
o
i
m
p
r
o
p
er
v
alu
e
o
f
k
w
ill
m
a
y
a
f
f
ec
t
th
e
co
m
p
le
x
it
y
o
f
alg
o
r
ith
m
.
2.
Keh
e
W
u
et.
al
[
6
]
h
a
v
e
d
o
n
e
r
esear
ch
an
d
i
m
p
r
o
v
e
K
m
ea
n
s
alg
o
r
it
h
m
b
ased
o
n
Had
o
o
p
an
d
co
m
e
o
u
t
w
it
h
t
h
e
s
o
lu
tio
n
to
d
ef
in
e
i
n
i
tial
ce
n
tr
o
id
.
Usi
n
g
C
o
n
v
e
x
h
u
ll
an
d
o
p
p
o
s
it
e
C
h
u
n
g
p
o
in
ts
th
e
in
itial
t
w
o
clu
s
ter
ce
n
ter
s
ar
e
d
ef
in
ed
.
T
h
e
o
p
tim
al
n
u
m
b
er
o
f
clu
s
ter
k
is
d
ec
id
ed
u
s
in
g
d
is
tan
ce
co
s
t
f
u
n
ctio
n
.
T
h
e
tex
t
f
ile
s
ar
e
u
s
ed
to
ex
p
er
i
m
en
t
t
h
e
al
g
o
r
ith
m
,
s
o
in
r
ea
l
t
i
m
e
ap
p
licatio
n
th
e
n
e
w
s
tr
at
eg
y
h
a
s
to
b
e
d
ev
elo
p
th
at
w
i
ll
w
o
r
k
f
o
r
h
et
er
o
g
en
eo
u
s
d
ata
s
et.
3.
An
u
p
a
m
a
C
h
ad
h
a
a
n
d
S
u
r
es
h
Ku
m
ar
[
7
]
h
as
p
r
esen
ted
A
n
i
m
p
r
o
v
ed
K
-
m
ea
n
s
C
l
u
s
ter
i
n
g
A
lg
o
r
it
h
m
:
A
s
tep
f
o
r
w
ar
d
f
o
r
r
e
m
o
v
al
o
f
d
ep
en
d
en
c
y
o
n
K.
T
h
e
m
o
d
i
f
ied
K
–
m
ea
n
s
al
g
o
r
ith
m
d
o
es
n
o
t
r
eq
u
ir
e
n
u
m
b
er
o
f
cl
u
s
ter
(
k
)
a
s
i
n
p
u
t.
I
n
i
tiall
y
it
s
elec
ts
th
e
t
w
o
ce
n
tr
o
id
s
w
h
ic
h
ar
e
f
ar
t
h
est
ap
ar
t,
an
d
co
n
s
id
er
ed
as
t
w
o
i
n
itia
l
ce
n
tr
o
id
s
.
T
h
e
v
al
u
e
o
f
k
is
d
ec
id
ed
b
y
u
s
i
n
g
o
u
tlier
s
w
h
ic
h
ar
e
o
r
ig
in
ated
d
u
r
in
g
th
e
ca
lcu
latio
n
o
f
E
u
cl
id
ea
n
d
is
tan
ce
b
et
w
ee
n
e
v
er
y
tu
p
le
an
d
n
e
w
m
ea
n
s
o
f
th
e
c
lu
s
ter
ce
n
ter
s
.
A
cc
u
r
ac
y
ac
co
m
p
l
is
h
ed
b
y
th
i
s
alg
o
r
it
h
m
i
s
b
etter
th
a
n
t
h
e
o
r
ig
in
a
l K
-
m
ea
n
s
al
g
o
r
ith
m
.
T
h
e
d
o
w
n
s
id
e
o
f
th
is
al
g
o
r
ith
m
i
s
th
a
t it
is
n
o
t d
esig
n
ed
f
o
r
m
ap
r
ed
u
ce
p
ar
ad
ig
m
a
n
d
it
w
o
r
k
s
o
n
l
y
f
o
r
n
u
m
er
ic
d
atasets
.
4.
P
r
a
j
esh
An
ch
alia
[
8
]
h
as
i
m
p
r
o
v
ed
k
-
m
ea
n
s
cl
u
s
ter
i
n
g
al
g
o
r
ith
m
b
y
i
n
tr
o
d
u
cin
g
co
m
b
in
er
.
T
h
e
co
m
b
in
er
r
ea
d
s
th
e
o
u
tp
u
t
p
r
o
d
u
ce
d
b
y
m
ap
p
er
an
d
ca
lcu
late
s
th
e
c
en
tr
o
id
f
o
r
ea
ch
m
ap
p
er
.
No
w
t
h
e
r
ed
u
ce
r
ca
lcu
late
t
h
e
g
lo
b
al
ce
n
tr
o
id
u
s
i
n
g
th
e
v
alu
e
o
f
lo
ca
l
ce
n
tr
o
id
r
ea
d
f
r
o
m
ea
c
h
m
ap
p
er
.
T
h
e
p
er
f
o
r
m
an
c
e
o
f
Had
o
o
p
ca
n
b
e
in
cr
ea
s
ed
b
y
c
u
tti
n
g
d
o
w
n
th
e
r
ea
d
an
d
w
r
ite
o
p
er
atio
n
f
r
o
m
m
ap
p
er
an
d
r
ed
u
ce
r
r
esp
ec
tiv
el
y
.
Her
e
Sar
t
u
p
alg
o
r
ith
m
i
s
u
s
ed
to
ca
lcu
late
th
e
in
itial
s
e
t
o
f
ce
n
tr
o
id
w
h
ic
h
ag
ain
r
eq
u
ir
e
s
th
e
n
u
m
b
er
o
f
cl
u
s
ter
(
k
)
as in
p
u
t.
5.
A
r
s
h
ad
M.
Me
h
ar
et.
al
[
9
]
h
a
s
i
n
tr
o
d
u
ce
d
k
m
ea
n
s
cl
u
s
ter
i
n
g
al
g
o
r
ith
m
f
o
r
d
eter
m
i
n
i
n
g
o
p
ti
m
al
v
al
u
e
o
f
k
.
Mo
s
tl
y
d
is
tan
ce
b
ased
m
eth
o
d
ar
e
u
s
ed
to
ca
lcu
late
th
e
v
alu
e
o
f
k
.
I
n
co
n
tr
ast
w
i
th
o
th
er
m
et
h
o
d
o
lo
g
ies
i
n
t
h
i
s
al
g
o
r
it
h
m
t
h
e
j
o
in
t
p
r
o
b
ab
ilit
y
is
u
s
ed
.
T
h
e
f
u
n
d
a
m
e
n
tal
id
ea
i
s
to
an
al
y
ze
t
h
e
m
o
v
e
m
e
n
t o
f
o
b
j
ec
ts
b
et
w
ee
n
clu
s
ter
s
.
T
h
e
d
iag
o
n
all
y
d
o
m
i
n
an
t
p
r
o
b
ab
ilit
y
m
atr
i
x
i
s
p
r
o
d
u
ce
d
u
s
in
g
t
h
e
m
o
v
e
m
e
n
t o
f
m
e
m
b
er
s
h
ip
w
il
l b
e
u
s
ed
to
d
ec
id
e
th
e
s
et
o
f
r
an
g
e
o
f
o
p
ti
m
al
v
al
u
e
f
o
r
k
cl
u
s
ter
s
.
Her
e
t
h
e
alg
o
r
ith
m
f
o
cu
s
o
n
s
y
n
th
e
tic
d
ata
s
et
f
o
r
t
w
o
d
i
m
e
n
s
io
n
s
an
d
it
i
s
n
o
t
p
r
o
p
o
s
ed
f
o
r
Ma
p
R
ed
u
ce
p
r
o
g
r
am
m
i
n
g
.
6.
J
in
g
Z
h
a
n
g
et.
al
[1
0
]
h
as
d
esig
n
ed
a
2
tier
clu
s
ter
in
g
alg
o
r
ith
m
w
it
h
Ma
p
-
R
ed
u
ce
f
o
r
d
is
tr
ib
u
ted
clu
s
ter
i
n
g
e
n
v
ir
o
n
m
e
n
t.
T
h
e
e
n
tire
p
r
o
ce
d
u
r
e
is
d
is
tr
ib
u
ted
i
n
f
o
u
r
p
ar
ts
.
Sp
lit
p
h
ase
d
iv
id
es th
e
in
p
u
t
f
ile
in
m
p
ar
ts
,
w
h
er
e
m
is
u
s
er
d
ef
i
n
ed
.
T
h
e
o
n
e
s
p
lit
clu
s
ter
i
n
g
u
s
i
n
g
k
m
ea
n
s
alg
o
r
it
h
m
i
s
p
er
f
o
r
m
ed
in
m
ap
p
h
ase
f
o
r
ea
ch
m
ap
p
er
an
d
in
ter
m
ed
iate
r
es
u
lt
i
s
g
en
er
ated
.
T
h
e
in
ter
m
ed
iate
r
esu
lt
ar
e
ag
a
i
n
p
ar
titi
o
n
ed
in
to
r
r
eg
io
n
i
n
P
ar
titi
o
n
p
h
ase
a
n
d
as
s
ig
n
ed
to
r
ed
u
ce
r
.
Fin
al
r
es
u
lt
i
s
ca
lcu
l
ated
in
r
ed
u
ce
r
p
h
ase
b
y
u
s
i
n
g
i
n
te
g
r
atio
n
s
tr
ateg
y
o
f
t
w
o
tier
clu
s
ter
in
g
.
He
r
e
also
th
e
s
ize
o
f
r
is
d
ef
in
ed
b
y
u
s
er
.
7.
Mo
h
a
m
m
ad
Ka
k
o
o
ei
an
d
Ha
d
i
S.Sh
a
h
h
o
s
ein
i
[1
1
]
h
av
e
p
r
esen
ted
a
p
ar
allel
k
-
m
ea
n
s
c
lu
s
ter
i
n
g
i
n
itial
ce
n
ter
s
e
lectio
n
an
d
d
y
n
a
m
ic
ce
n
ter
co
r
r
ec
tio
n
o
n
GP
U.
I
n
t
h
i
s
al
g
o
r
ith
m
in
itiall
y
g
r
o
u
p
o
f
i
n
itia
l
ce
n
ter
s
ar
e
s
elec
ted
w
h
ic
h
s
h
o
u
ld
b
e
les
s
t
h
a
n
t
h
e
p
ar
allel
s
tr
ea
m
e
x
ec
u
t
io
n
p
r
o
v
id
ed
b
y
m
ac
h
in
e.
I
t
ca
lcu
late
s
t
h
e
i
n
n
er
d
is
ta
n
ce
b
et
w
ee
n
d
ata
p
o
in
ts
an
d
ce
n
ter
o
f
ea
c
h
g
r
o
u
p
.
T
h
e
g
r
o
u
p
h
a
v
in
g
m
in
i
m
u
m
d
is
tan
ce
is
s
elec
ted
a
s
i
n
it
ial
ce
n
ter
.
Fo
r
th
e
m
ain
cl
u
s
ter
i
n
g
t
h
e
al
g
o
r
ith
m
ap
p
lies
t
w
o
as
y
n
c
h
r
o
n
o
u
s
s
tr
ea
m
s
.
T
h
e
in
n
er
d
is
ta
n
ce
o
f
m
ai
n
cl
u
s
ter
i
n
g
is
ca
lc
u
late
d
b
y
f
ir
s
t
s
tr
ea
m
a
n
d
o
th
er
s
t
r
ea
m
ca
lc
u
lates
th
e
i
n
n
er
d
is
ta
n
ce
o
f
n
e
w
i
n
iti
al
ce
n
ter
s
.
T
h
e
n
t
h
ese
t
w
o
d
is
tan
ce
s
ar
e
co
m
p
ar
ed
an
d
i
f
n
e
w
l
y
g
e
n
er
ated
d
is
tan
ce
is
les
s
th
a
n
m
ai
n
d
is
t
an
ce
th
e
n
m
ai
n
clu
s
ter
an
d
n
ew
l
y
g
e
n
er
ated
clu
s
ter
s
ar
e
co
m
b
in
ed
i
n
to
o
n
e
g
r
o
u
p
.
T
h
e
s
tr
ea
m
o
f
m
ain
cl
u
s
ter
i
n
g
p
r
o
ce
d
u
r
e
g
o
es
o
n
co
n
ti
n
u
o
u
s
l
y
.
I
n
th
i
s
alg
o
r
it
h
m
i
n
itial
t
h
e
v
al
u
e
o
f
k
is
s
elec
ted
ar
b
itra
r
y
,
t
h
e
i
m
p
r
o
p
er
s
elec
tio
n
f
o
r
v
al
u
e
o
f
k
w
ill
m
a
y
b
e
d
eg
r
ad
e
th
e
p
er
f
o
r
m
a
n
ce
.
8.
P
o
o
n
am
G
h
u
li
et.
al
[1
2
]
h
as
d
o
n
e
a
co
m
p
r
eh
e
n
s
i
v
e
s
u
r
v
e
y
o
n
ce
n
tr
o
id
s
elec
tio
n
s
tr
ateg
ies
f
o
r
d
is
tr
ib
u
ted
k
-
m
ea
n
s
clu
s
ter
i
n
g
al
g
o
r
ith
m
.
T
h
e
ex
ec
u
tio
n
is
d
iv
id
ed
in
to
f
o
u
r
m
o
d
u
le
s
.
I
n
So
r
tin
g
Mo
d
u
le
th
e
d
ata
s
e
t is p
r
o
ce
s
s
ed
an
d
s
i
m
p
li
f
y
it
f
o
r
s
elec
ti
n
g
th
e
i
n
itial c
e
n
tr
o
id
.
Her
e
f
o
r
i
n
itiali
za
tio
n
o
f
ce
n
tr
o
id
th
r
ee
d
if
f
er
en
t
s
tr
ateg
ies
ar
e
p
r
o
p
o
s
ed
.
1
)
W
eig
h
ted
Av
er
ag
e
So
r
tin
g
m
o
d
u
l
e
ca
lcu
la
te
t
h
e
s
co
r
es
u
s
i
n
g
u
n
i
f
o
r
m
l
y
a
s
s
i
g
n
ed
w
eig
h
t
s
to
attr
ib
u
tes
o
f
d
a
taset.
T
h
e
s
o
r
tin
g
o
f
d
ata
p
o
in
ts
i
s
d
o
n
e
in
r
ed
u
ce
r
ac
co
r
d
in
g
to
th
e
av
e
r
ag
e
v
alu
e
an
d
w
r
ite
r
es
u
lt
i
n
to
i
n
ter
m
ed
iate
f
ile.
2
)
He
u
r
is
tic
So
r
ti
n
g
Mo
d
u
le,
I
n
th
i
s
m
o
d
u
le
t
h
e
at
tr
ib
u
te
h
av
in
g
h
i
g
h
est
r
ag
e
i
s
s
elec
ted
a
n
d
r
ed
u
ce
r
s
o
r
ts
th
e
d
ata
p
o
in
t
s
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
.
6
,
Dec
em
b
er
201
6
:
30
4
7
–
30
5
1
3050
in
cr
ea
s
i
n
g
o
r
d
er
an
d
w
r
ites
r
esu
lt
s
i
n
in
ter
m
ed
iate
f
ile.
3
)
P
r
in
cip
al
C
o
m
p
o
n
e
n
t
An
al
y
s
i
s
,
I
n
th
i
s
v
al
u
e
th
e
attr
ib
u
te
h
a
v
i
n
g
h
i
g
h
est
v
ar
ian
ce
is
s
elec
ted
an
d
t
h
e
r
ed
u
ce
r
s
o
r
ts
t
h
e
d
ata
p
o
in
t
s
i
n
i
n
cr
ea
s
i
n
g
o
r
d
er
o
f
v
ar
ian
ce
an
d
w
r
ites
t
h
e
r
esu
lts
i
n
in
ter
m
ed
iate
f
ile.
I
n
it
ia
l
ce
n
tr
o
id
s
elec
tio
n
m
o
d
u
le
s
p
lits
th
e
d
ata
s
et
in
to
k
s
u
b
s
e
ts
.
No
w
m
ed
ian
o
f
t
h
e
d
ata
s
et
is
ca
lc
u
lated
a
n
d
th
at
w
il
l
ac
t
as
an
in
itial
ce
n
t
r
o
id
.
T
h
is
w
i
l
l
ac
t a
s
in
p
u
t
f
ile
to
Ma
p
R
ed
u
c
e
A
lg
o
r
it
h
m
.
I
ter
ati
v
e
C
lu
s
ter
i
n
g
an
d
clu
s
ter
a
s
s
i
g
n
m
e
n
t
m
o
d
u
le
w
il
l a
ct
i
n
r
eg
u
lar
m
a
n
n
er
to
d
i
v
id
e
an
d
c
ateg
o
r
ize
th
e
d
ataset
i
n
to
k
cl
u
s
t
er
s
.
A
ll o
v
er
ag
ai
n
I
n
s
ec
o
n
d
m
o
d
u
le
t
h
e
k
is
n
o
t a
u
to
m
ated
an
d
s
t
ill it is
u
s
er
d
ep
en
d
ed
.
9.
Mu
g
d
h
a
J
ain
an
d
C
h
ak
r
ad
h
ar
Ver
m
a
[1
3
]
h
as
ad
o
p
ted
k
-
m
ea
n
s
f
o
r
clu
s
ter
in
g
in
B
i
g
Dat
a.
Her
e
d
ataset
is
r
ep
r
esen
ted
u
s
in
g
m
atr
i
x
w
h
er
e
d
ata
p
o
in
ts
ar
e
r
ep
r
esen
ted
b
y
r
o
w
s
an
d
attr
ib
u
tes
o
f
d
ata
p
o
in
ts
r
ep
r
esen
ted
b
y
co
lu
m
n
s
.
I
n
t
h
e
s
it
u
atio
n
w
h
er
e
s
o
m
e
at
tr
ib
u
te
v
al
u
e
f
o
r
d
ata
p
o
in
t
is
m
is
s
i
n
g
,
m
atr
i
x
w
i
ll
n
o
t
d
ef
i
n
e
a
n
y
v
al
u
es.
Data
p
o
in
ts
ar
e
ar
r
a
n
g
ed
ac
co
r
d
in
g
t
o
d
ec
r
ea
s
in
g
o
r
d
er
o
f
p
r
io
r
it
y
o
f
d
i
m
en
s
io
n
s
an
d
v
ar
ia
n
ce
o
f
d
i
m
e
n
s
io
n
s
i
s
ca
lcu
lated
.
A
s
s
ig
n
m
e
n
t
o
f
d
ata
s
et
ac
co
r
d
in
g
to
p
r
im
ar
y
d
i
m
e
n
s
io
n
is
f
o
llo
w
ed
b
y
all
s
ec
o
n
d
ar
y
d
im
en
s
io
n
s
an
d
o
u
tlier
s
ar
e
ca
lcu
lated
.
Dis
ta
n
ce
b
et
w
ee
n
ce
n
t
r
o
id
an
d
o
u
tlier
is
u
s
ed
to
ca
teg
o
r
ize
th
e
d
ata
s
et
in
to
cl
u
s
ter
s
.
T
h
e
n
u
m
b
er
o
f
clu
s
ter
k
is
p
r
ed
ef
in
ed
it
i
s
n
o
t
th
e
p
ar
t
o
f
alg
o
r
ith
m
a
n
d
t
h
e
p
r
io
r
ities
ar
e
d
ec
id
ed
b
y
u
s
er
i
n
s
tead
m
a
ch
in
e
lear
n
i
n
g
ap
p
r
o
ac
h
ca
n
b
e
in
te
g
r
ated
to
d
ec
id
e
p
r
io
r
ities
.
10.
Yiu
-
Mi
n
g
C
h
e
u
n
g
[1
4
]
h
as
p
r
o
p
o
s
ed
k
*
-
m
ea
n
s
:
A
n
e
w
g
en
er
alize
d
k
-
m
ea
n
s
cl
u
s
ter
i
n
g
al
g
o
r
ith
m
.
T
h
i
s
alg
o
r
ith
m
ac
h
ie
v
es
i
m
p
r
o
v
ed
clu
s
ter
i
n
g
w
it
h
o
u
t
p
r
ed
eter
m
i
n
in
g
p
r
ec
is
e
c
lu
s
ter
n
u
m
b
er
i
n
t
w
o
s
tep
s
.
B
y
ass
i
g
n
in
g
s
ee
d
p
o
in
t
to
ev
er
y
cl
u
s
ter
a
n
d
u
s
in
g
lear
n
in
g
r
u
le
w
it
h
p
an
el
ized
m
ec
h
an
is
m
t
h
e
i
n
p
u
t
i
s
ca
teg
o
r
ized
in
p
ar
ticu
lar
clu
s
ter
.
T
h
e
s
h
o
r
tco
m
i
n
g
o
f
th
e
alg
o
r
ith
m
is
t
h
at
it
i
s
n
o
t
d
es
ig
n
ed
f
o
r
Ma
p
R
ed
u
ce
p
ar
ad
ig
m
.
4.
P
RO
P
O
SE
D
O
B
J
E
CT
I
VE
T
h
e
p
r
o
p
o
s
ed
o
b
j
e
ctiv
e
o
f
t
h
is
p
ap
er
is
to
ap
p
ly
cl
u
s
ter
i
n
g
o
n
B
ig
Da
ta
s
et
u
s
i
n
g
Ma
p
R
ed
u
ce
P
ar
ad
ig
m
.
W
h
ile
co
n
s
id
er
in
g
ab
o
v
e
m
e
n
tio
n
ed
i
s
s
u
es,
o
u
tlin
e
i
s
p
lan
n
ed
.
T
h
e
b
elo
w
F
ig
u
r
e
1
d
is
p
la
y
s
o
u
tlin
e
o
f
th
e
p
r
o
p
o
s
ed
o
b
j
ec
ti
v
e.
Fig
u
r
e
1
.
Ou
tli
n
e
o
f
t
h
e
p
r
o
p
o
s
ed
Ob
j
ec
tiv
e
P
r
ep
r
o
ce
s
s
in
g
:
A
t
all
ti
m
e
s
th
e
B
ig
d
ata
is
al
w
a
y
s
in
t
h
e
f
o
r
m
o
f
ca
teg
o
r
ical
d
ata.
Stan
d
ar
d
k
m
ea
n
s
w
il
l
m
a
y
d
eg
r
ad
e
in
p
er
f
o
r
m
an
ce
w
h
e
n
co
n
s
id
er
ed
f
o
r
m
u
ltid
i
m
e
n
s
io
n
al
d
ata
s
o
P
r
e
P
r
o
ce
s
s
in
g
o
n
ca
teg
o
r
ical
d
ata
s
et
is
ta
k
en
i
n
to
th
e
p
r
o
p
o
s
ed
o
b
j
ec
tiv
e.
Ma
p
R
ed
u
ce
P
ar
a
d
ig
m
:
T
o
h
an
d
le
th
e
B
ig
Data
Ma
p
R
ed
u
ce
p
ar
ad
ig
m
i
s
ad
o
p
ted
to
i
m
p
r
o
v
e
i
n
p
er
f
o
r
m
a
n
ce
a
n
d
to
i
m
p
r
o
v
e
s
ca
lab
ilit
y
o
f
d
ata.
K
s
elec
tio
n
m
o
d
u
le:
T
h
e
tim
e
co
m
p
le
x
it
y
o
f
k
m
ea
n
s
al
g
o
r
ith
m
is
d
ep
en
d
ed
o
n
p
r
e
d
icate
d
n
u
m
b
er
o
f
cl
u
s
ter
,
s
o
m
et
i
m
e
s
i
m
p
r
o
p
er
s
elec
tio
n
o
f
v
alu
e
o
f
k
w
i
ll
d
eg
r
ad
e
t
h
e
p
er
f
o
r
m
an
ce
s
o
it
i
s
es
s
e
n
tial
to
au
to
m
ate
i
t.
C
en
tr
o
id
Selectio
n
Mo
d
u
le:
An
o
th
er
is
s
u
e
w
h
ile
ad
o
p
tin
g
k
m
ea
n
s
is
to
s
elec
t
i
n
itial
ce
n
tr
o
id
,
w
h
ic
h
w
il
l
h
u
d
d
le
to
ad
o
p
t
k
m
ea
n
s
cl
u
s
ter
i
n
g
.
I
n
p
r
o
p
o
s
ed
o
b
j
ec
tiv
e
th
e
in
it
ial
c
en
tr
o
id
w
il
l
b
e
d
ec
id
ed
in
alg
o
r
ith
m
o
n
l
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
I
s
s
u
es o
f K Mea
n
s
C
lu
s
teri
n
g
W
h
ile
Mig
r
a
tin
g
to
Ma
p
R
ed
u
ce
P
a
r
a
d
ig
m
w
ith
B
ig
Da
ta
.
.
.
.
(
K
.
R
.
N
i
r
ma
l)
3051
5.
CO
NCLU
SI
O
N
K
Me
an
s
C
l
u
s
ter
in
g
is
ef
f
icie
n
t
alg
o
r
it
h
m
to
ca
teg
o
r
ize
th
e
B
ig
Data
in
to
ap
p
r
o
p
r
iate
c
lu
s
ter
s
.
K
Me
an
s
cl
u
s
ter
h
a
s
s
o
m
e
i
s
s
u
es
li
k
e
i
n
itial
n
u
m
b
er
o
f
clu
s
ter
,
in
it
ial
s
elec
tio
n
o
f
ce
n
t
r
o
id
s
.
T
h
is
ar
ticle
p
r
esen
ts
s
o
m
e
is
s
u
es
to
s
o
lv
e
t
h
ese
is
s
u
e
s
w
h
ic
h
ar
e
h
elp
f
u
l
t
o
p
r
e
d
ef
in
e
th
e
d
ec
lar
ed
p
ar
a
m
eter
s
.
F
u
r
th
er
th
is
s
tu
d
y
a
ls
o
ad
d
r
ess
es
th
e
i
s
s
u
e
s
to
ad
o
p
t
k
m
ea
n
s
cl
u
s
ter
i
n
g
f
o
r
ca
teg
o
r
ical
d
atasets
an
d
b
ased
o
n
th
is
s
tu
d
y
o
n
e
o
u
tlin
e
o
f
o
b
j
ec
ti
v
es
is
p
r
o
p
o
s
ed
.
P
r
o
p
o
s
ed
m
o
d
el
w
il
l
ap
p
ly
s
elec
ted
s
tr
ateg
ie
s
to
p
r
ed
ef
in
e
th
e
p
ar
am
eter
s
w
h
i
le
h
a
n
d
lin
g
t
h
e
ca
teg
o
r
ical
d
ata
s
et.
RE
F
E
R
E
NC
E
S
[1
]
G
a
n
tz
J
.
a
n
d
Re
in
se
l
D.
,
“
T
h
e
d
ig
it
a
l
u
n
iv
e
rse
in
2
0
2
0
:
Big
d
a
ta,
b
ig
g
e
r
d
ig
it
a
l
sh
a
d
o
ws
,
a
n
d
b
ig
g
e
st
g
ro
w
th
in
th
e
f
a
r
e
a
st
,”
IDC i
Vi
e
w:
IDC A
n
a
lyz
e
th
e
fu
t
u
re
,
v
o
l.
2
0
0
7
,
p
p
.
1
-
6
,
2
0
1
2
.
[2
]
W
u
X
.
,
e
t
a
l
.
,
“
Da
ta
m
in
in
g
w
it
h
b
ig
d
a
ta
,”
Kn
o
wled
g
e
a
n
d
Da
t
a
En
g
in
e
e
rin
g
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
,
v
o
l/
issu
e
:
2
6
(
1
)
,
p
p
.
97
-
1
0
7
,
2
0
1
4
.
[3
]
J
.
Ha
n
a
n
d
M
.
Ka
m
b
e
r,
“
Da
ta M
in
in
g
:
C
o
n
c
e
p
ts
a
n
d
T
e
c
h
n
iq
u
e
s
,
”
2
nd
Ed
it
io
n
,
p
u
b
li
s
h
e
d
b
y
El
se
v
ier
.
[4
]
De
a
n
J
.
a
n
d
G
h
e
m
a
wa
t
S
.
,
“
M
a
p
Re
d
u
c
e
:
sim
p
li
f
ied
d
a
ta
p
ro
c
e
ss
in
g
o
n
larg
e
c
lu
ste
rs
,”
Co
mm
u
n
ica
ti
o
n
s
o
f
th
e
ACM
,
v
o
l/
issu
e
:
5
1
(1
)
,
p
p
.
1
0
7
-
13
,
2
0
0
8
.
[5
]
X
u
Y
.
,
e
t
a
l.
,
“
Ef
f
icie
n
t
-
m
e
a
n
s
+
+
A
p
p
ro
x
im
a
ti
o
n
w
it
h
M
a
p
Re
d
u
c
e
,”
Pa
r
a
ll
e
l
a
n
d
Distrib
u
ted
S
y
ste
ms
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
,
v
o
l/
iss
u
e
:
2
5
(1
2
)
,
p
p
.
3
1
3
5
-
44
,
2
0
1
4
.
[6
]
W
u
K
.
,
e
t
a
l.
,
“
Re
se
a
rc
h
a
n
d
i
m
p
ro
v
e
o
n
K
-
m
e
a
n
s
a
lg
o
rit
h
m
b
a
se
d
o
n
h
a
d
o
o
p
,”
i
n
S
o
ft
w
a
re
En
g
i
n
e
e
rin
g
a
n
d
S
e
rv
ice
S
c
ien
c
e
(
ICS
ES
S
),
2
0
1
5
6
th
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
,
p
p
.
3
3
4
-
3
3
7
,
2
0
1
5
.
[7
]
Ch
a
d
h
a
A
.
a
n
d
Ku
m
a
r
S
.
,
“
A
n
imp
ro
v
e
d
K
-
M
e
a
n
s
c
lu
ste
rin
g
a
lg
o
ri
th
m
:
A
ste
p
f
o
rwa
rd
f
o
r
re
m
o
v
a
l
o
f
d
e
p
e
n
d
e
n
c
y
o
n
K
,”
i
n
Op
t
imiza
ti
o
n
,
Rel
ia
b
il
t
y
,
a
n
d
I
n
fo
rm
a
ti
o
n
T
e
c
h
n
o
lo
g
y
(
ICROIT
),
2
0
1
4
I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
,
p
p
.
136
-
1
4
0
,
2
0
1
4
.
[8
]
A
n
c
h
a
li
a
P
.
P.
,
“
Im
p
ro
v
e
d
M
a
p
Re
d
u
c
e
k
-
M
e
a
n
s
Clu
ste
rin
g
A
lg
o
rit
h
m
w
it
h
Co
m
b
in
e
r
,”
in
Co
m
p
u
ter
M
o
d
e
ll
i
n
g
a
n
d
S
im
u
la
ti
o
n
(
UKS
im),
2
0
1
4
U
KS
im
-
AM
S
S
1
6
th
I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
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