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1711
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8708
I
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t J
E
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&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
1
1
–
1719
1712
E
M,
C
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B
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lat
i
n
g
cl
u
s
ter
s
.
W
h
en
K
m
ea
n
s
i
s
m
i
g
r
ated
to
b
ig
d
at
a,
it
d
o
es
n
o
t
p
er
f
o
r
m
w
ell
a
s
co
m
p
ar
ed
to
o
th
er
clu
s
ter
i
n
g
alg
o
r
ith
m
s
[
4
]
.
T
h
e
m
ai
n
r
ea
s
o
n
is
t
h
at
K
m
ea
n
s
is
s
eq
u
e
n
tial
a
n
d
it
co
m
p
u
t
es
t
h
e
cl
u
s
ter
s
in
iter
at
io
n
s
.
K
m
ea
n
s
w
o
r
k
s
o
n
n
u
m
er
ical
d
ata
w
it
h
g
o
o
d
ac
cu
r
ac
y
.
W
ith
ca
teg
o
r
ical
a
ttrib
u
te
s
,
t
h
is
alg
o
r
i
t
h
m
ca
n
n
o
t
ca
lcu
late
t
h
e
ce
n
tr
o
id
d
ir
ec
tl
y
.
B
ig
d
ata
is
co
m
b
i
n
atio
n
o
f
n
u
m
er
ical
a
n
d
ca
teg
o
r
ical
d
at
a
[
2
]
.
Km
ea
n
s
ca
n
an
al
y
ze
n
u
m
er
ical
d
ataset
w
i
th
it
s
p
r
o
v
en
ac
c
u
r
ac
y
.
B
u
t
th
is
alg
o
r
it
h
m
ca
n
n
o
t
cl
u
s
te
r
ca
teg
o
r
ical
d
ata
.
Kp
r
o
to
ty
p
e
al
g
o
r
ith
m
is
u
s
ed
to
r
e
m
o
v
e
th
i
s
d
r
a
w
b
ac
k
o
f
K
m
ea
n
s
.
Kp
r
o
to
t
y
p
e
al
g
o
r
ith
m
ca
n
h
an
d
le
n
u
m
er
i
c
as
w
ell
as
ca
te
g
o
r
ical
d
ata
ef
f
ec
tiv
el
y
.
W
e
h
av
e
also
i
m
p
le
m
en
ted
Kp
r
o
to
ty
p
e
o
n
Ma
p
r
e
d
u
ce
s
o
th
at
it
ca
n
h
an
d
le
lar
g
e
s
ca
le
o
f
d
ata
a
s
w
ell.
As
p
er
o
u
r
k
n
o
w
led
g
e,
v
er
y
f
e
w
r
esear
c
h
w
o
r
k
s
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t
to
f
o
cu
s
o
n
en
h
a
n
ce
th
e
e
f
f
ec
tiv
e
n
es
s
o
f
Kp
r
o
to
t
y
p
e
alg
o
r
ith
m
.
B
ig
d
ata
is
co
m
b
in
a
tio
n
o
f
s
t
r
u
ctu
r
ed
,
u
n
s
tr
u
c
tu
r
ed
an
d
s
em
i
s
tr
u
ctu
r
ed
d
ata.
T
h
is
r
esear
ch
w
o
r
k
co
v
er
s
b
ig
d
ata
ch
ar
ac
ter
is
tic
s
lik
e
v
o
lu
m
e,
v
e
lo
cit
y
a
n
d
v
ar
iet
y
.
Vo
lu
m
e
is
i
m
p
o
r
tan
t
c
h
ar
ac
ter
is
tic
o
f
b
i
g
d
ata
as
t
h
is
r
eq
u
ir
es
c
h
an
g
es
in
s
to
r
ag
e
ar
ch
itectu
r
e
[
1
]
.
V
elo
cit
y
i
s
an
o
t
h
er
c
h
ar
ac
ter
is
t
ic
w
h
ic
h
s
h
o
u
ld
b
e
m
an
a
g
ed
b
y
cl
u
s
ter
i
n
g
alg
o
r
it
h
m
a
s
d
ata
f
lo
w
s
in
s
p
ee
d
an
d
r
esp
o
n
s
e
ti
m
e
s
h
o
u
ld
b
e
ac
cu
r
ate.
Var
iet
y
is
t
h
ir
d
ch
ar
ac
ter
is
tic
w
h
ic
h
is
co
m
b
i
n
atio
n
o
f
s
tr
u
ct
u
r
ed
,
s
e
m
i
s
tr
u
ctu
r
ed
an
d
u
n
s
tr
u
ct
u
r
ed
d
ata.
T
h
is
r
esear
ch
w
o
r
k
co
v
er
s
t
h
ese
c
h
ar
ac
ter
is
t
ics
w
it
h
th
e
u
s
e
o
f
b
ig
d
ata
tec
h
n
o
lo
g
ies.
I
n
K
m
ea
n
s
alg
o
r
it
h
m
w
it
h
th
e
u
s
e
o
f
h
ad
o
o
p
p
latf
o
r
m
b
i
g
d
ata
ca
n
b
e
p
r
o
ce
s
s
ed
ef
f
ec
ti
v
el
y
.
(
Ke
y
,
Val
u
e)
p
air
s
o
f
cl
u
s
ter
ed
d
at
a
is
p
r
o
ce
s
s
ed
w
it
h
th
e
u
s
e
o
f
Ma
p
[
5
]
.
R
ed
u
ce
c
o
m
b
i
n
es
th
e
r
es
u
lt
o
f
t
h
ese
p
air
s
o
f
d
if
f
er
e
n
t
clu
s
ter
s
.
T
h
is
ap
p
r
o
ac
h
r
ed
u
ce
s
ti
m
e
co
m
p
le
x
it
y
o
f
cl
u
s
ter
i
n
g
.
W
h
en
K
m
ea
n
s
is
d
is
tr
ib
u
ted
o
n
d
if
f
er
en
t
cl
u
s
ter
s
,
r
u
n
n
i
n
g
t
i
m
e
f
o
r
ca
lcu
lati
n
g
clu
s
ter
s
r
ed
u
ce
s
s
i
g
n
if
ican
t
l
y
.
I
n
Sectio
n
2
,
s
ev
er
al
r
ese
ar
ch
w
o
r
k
s
ar
e
d
escr
ib
ed
as
liter
atu
r
e
s
u
r
v
e
y
.
C
lu
s
er
in
g
al
g
o
r
ith
m
s
w
it
h
K
m
ea
n
s
a
n
d
Kp
r
o
to
ty
p
e
s
d
etail
ed
d
escr
ip
tio
n
is
i
n
Sect
io
n
3
.
P
r
o
p
o
s
ed
tech
n
iq
u
e
is
p
r
esen
ted
in
Sectio
n
4
.
E
x
p
er
im
e
n
tal
a
n
al
y
s
is
i
s
elab
o
r
a
ted
in
Sectio
n
5
.
P
a
p
er
is
c
o
n
clu
d
ed
in
Sectio
n
6
w
it
h
f
u
tu
r
e
d
ir
ec
tio
n
s
.
2.
L
I
T
E
R
AT
U
RE
SU
RVE
Y
T
h
er
e
ar
e
a
lo
t
o
f
r
esear
ch
w
o
r
k
s
w
h
ic
h
ar
e
b
ein
g
ca
r
r
ied
o
u
t
in
cl
u
s
ter
i
n
g
o
f
b
ig
d
ata.
A
F
ah
ad
et
a
l
[
1
]
in
tr
o
d
u
ce
s
a
ca
teg
o
r
izatio
n
f
r
a
m
e
w
o
r
k
f
o
r
clu
s
ter
i
n
g
a
lg
o
r
ith
m
s
.
I
n
t
h
i
s
r
esear
ch
wo
r
k
,
au
th
o
r
s
h
a
v
e
ca
teg
o
r
ized
d
if
f
er
en
t
clu
s
ter
in
g
alg
o
r
ith
m
s
b
ased
o
n
d
esi
g
n
e
r
p
er
s
p
ec
tiv
e.
P
a
r
titi
o
n
b
ased
,
h
ier
ar
ch
ical
b
ased
,
d
en
s
it
y
b
ased
,
g
r
id
b
ased
an
d
m
o
d
el
b
ased
a
lg
o
r
ith
m
ar
e
e
x
p
lain
ed
i
n
t
h
is
p
ap
er
.
M.
Haj
Kac
em
et
a
l
[
2
]
i
m
p
r
o
v
es
b
ig
d
ata
clu
s
ter
i
n
g
b
y
p
r
o
p
o
s
in
g
Ma
p
r
ed
u
ce
b
ased
K
-
P
r
o
to
ty
p
es
(
MR
-
KP
)
.
I
n
th
i
s
w
o
r
k
,
it
is
d
ef
in
ed
t
h
at
b
i
g
d
ata
i
s
co
llect
io
n
o
f
n
u
m
er
ical
an
d
ca
te
g
o
r
ic
al
d
ata.
I
n
v
ar
io
u
s
r
esear
c
h
w
o
r
k
s
,
f
e
w
cl
u
s
ter
i
n
g
m
et
h
o
d
s
ca
n
d
ea
l
w
i
th
m
ix
e
d
t
y
p
e.
P
r
o
p
o
s
ed
MR
-
KP
ca
n
p
r
o
ce
s
s
n
u
m
er
ical
a
s
w
e
ll
a
s
ca
te
g
o
r
ical
d
ata.
E
x
p
er
i
m
e
n
ts
w
er
e
co
n
d
u
cted
o
n
m
an
y
i
n
s
tan
ce
s
o
f
c
h
e
s
s
d
ataset.
I
t
is
p
r
o
v
ed
in
t
h
i
s
r
esear
ch
w
o
r
k
t
h
at
p
r
o
p
o
s
ed
K
-
P
r
o
to
ty
p
e
s
h
o
w
s
g
o
o
d
ac
cu
r
ac
y
a
n
d
s
ca
lab
ili
t
y
.
X.
W
u
et
al
[
3
]
d
em
o
n
s
t
r
ates
1
0
alg
o
r
ith
m
s
w
h
ic
h
ar
e
m
o
s
t
in
f
l
u
e
n
tial
b
y
I
E
E
E
I
n
ter
n
atio
n
al
C
o
n
f
er
e
n
c
e
o
n
Data
Min
in
g
(
I
C
DM
)
.
C
4
.
5
,
K
-
m
ea
n
s
,
SVM,
A
p
r
io
r
i,
E
M,
P
ag
eRan
k
,
A
d
a
B
o
o
s
t,
k
NN,
Naïv
e
B
ay
es,
an
d
C
AR
T
alg
o
r
ith
m
s
ar
e
ex
p
la
in
ed
in
t
h
i
s
r
esear
ch
w
o
r
k
.
W.
Z
h
ao
et
al
[
4
]
h
av
e
p
r
o
p
o
s
ed
a
p
ar
allel
K
m
ea
n
s
alg
o
r
ith
m
b
ased
o
n
Ma
p
R
ed
u
ce
.
I
n
th
is
r
esear
ch
w
o
r
k
s
p
ee
d
u
p
,
s
ize
u
p
an
d
s
ca
l
eu
p
is
s
h
o
w
n
as
b
etter
w
it
h
t
h
e
u
s
e
o
f
P
KM
ea
n
s
al
g
o
r
ith
m
.
Ma
p
r
ed
u
ce
is
u
s
ed
to
i
m
p
le
m
en
t
m
ac
h
in
e
lear
n
i
n
g
an
d
d
ata
m
i
n
i
n
g
al
g
o
r
ith
m
s
in
[
6
]
.
Had
o
o
p
an
d
Ma
p
r
ed
u
ce
f
r
a
m
e
w
o
r
k
ar
e
ex
p
lain
ed
i
n
t
h
i
s
p
ap
er
.
Km
ea
n
s
,
E
M
etc.
d
ata
m
i
n
i
n
g
al
g
o
r
ith
m
s
ar
e
i
m
p
le
m
e
n
t
ed
in
p
ar
allel
u
s
i
n
g
Ma
p
r
ed
u
ce
in
th
is
p
ap
er
.
X
C
u
i
et
a
l
[
7
]
p
r
o
p
o
s
ed
a
n
o
v
e
l
p
r
o
ce
s
s
in
g
m
o
d
el
to
r
e
m
o
v
e
th
e
d
ep
e
n
d
en
ce
o
n
iter
atio
n
s
.
I
n
Ma
p
r
ed
u
ce
t
h
er
e
is
li
m
i
tatio
n
o
f
r
es
tar
tin
g
j
o
b
s
.
I
n
t
h
is
w
o
r
k
,
t
h
i
s
is
r
e
m
o
v
ed
an
d
r
es
u
lt
ed
i
n
h
ig
h
p
er
f
o
r
m
an
ce
.
I
n
[
8
]
,
au
t
h
o
r
s
h
a
v
e
u
s
ed
d
is
s
i
m
ilar
it
y
m
ea
s
u
r
es
b
et
w
ee
n
p
r
o
to
t
y
p
e
o
f
clu
s
ter
s
a
n
d
d
ata
o
b
j
ec
ts
.
Fo
u
r
d
atasets
ar
e
u
s
e
d
f
o
r
co
m
p
ar
is
o
n
o
f
p
r
o
p
o
s
ed
m
et
h
o
d
an
d
tr
ad
itio
n
al
tec
h
n
i
q
u
es.
A
.
Ah
m
ad
et
al
[
9
]
p
r
o
p
o
s
ed
a
c
o
s
t
f
u
n
cti
o
n
b
ased
o
n
co
-
o
cc
u
r
r
en
ce
o
f
v
al
u
es.
T
h
is
co
s
t
f
u
n
ctio
n
im
p
r
o
v
es
t
h
e
clu
s
ter
ce
n
ter
ac
cu
r
ac
y
f
o
r
k
-
m
ea
n
s
cl
u
s
ter
i
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
N
o
ve
l A
p
p
r
o
a
ch
fo
r
C
lu
s
teri
n
g
B
ig
Da
t
a
b
a
s
ed
o
n
Ma
p
R
e
d
u
ce
(
Go
u
r
a
v
B
a
th
la
)
1713
3.
CL
US
T
E
RIN
G
A
L
G
O
RI
T
H
M
S
T
h
er
e
ar
e
d
if
f
er
e
n
t
cl
u
s
ter
in
g
alg
o
r
ith
m
s
h
av
i
n
g
s
p
ec
if
ic
ap
p
licatio
n
s
in
t
h
e
f
ield
o
f
d
ata
m
i
n
in
g
.
I
n
Fi
g
u
r
e
1
,
ca
teg
o
r
ies o
f
clu
s
ter
i
n
g
al
g
o
r
ith
m
s
ar
e
e
x
p
lain
ed
with
ex
a
m
p
le.
Fig
u
r
e
1
.
C
ateg
o
r
ies o
f
cl
u
s
ter
in
g
al
g
o
r
it
h
m
P
ar
titi
o
n
B
ased
: I
n
t
h
e
s
e
t
y
p
e
s
o
f
al
g
o
r
ith
m
s
,
d
ata
o
b
j
ec
ts
ar
e
d
iv
id
ed
in
to
d
if
f
er
en
t p
ar
titi
o
n
s
.
T
h
ese
d
i
f
f
er
en
t
p
ar
titi
o
n
s
ar
e
clu
s
ter
s
w
h
er
e
d
ata
o
b
j
ec
ts
ar
e
h
av
in
g
h
i
g
h
in
t
r
a
-
s
i
m
ilar
it
y
.
K
m
ea
n
s
w
h
ich
i
s
a
p
ar
titi
o
n
b
ased
alg
o
r
ith
m
w
h
ic
h
d
ec
id
e
s
clu
s
t
er
m
e
m
b
er
s
h
ip
b
y
ca
lcu
latin
g
ce
n
t
r
o
id
v
alu
e
s
.
Hier
ar
ch
ical
B
ased
:
C
o
m
p
let
e
d
ata
s
et
is
ass
u
m
ed
as
o
n
e
clu
s
ter
.
T
h
is
d
ata
s
et
is
d
i
v
i
d
ed
in
to
clu
s
ter
s
i
n
h
ier
ar
ch
ical
m
a
n
n
er
(
u
p
to
k
n
u
m
b
er
o
f
cl
u
s
ter
s
)
.
Den
s
i
t
y
B
ased
: D
ata
o
b
j
ec
ts
ar
e
ass
ig
n
ed
in
to
cl
u
s
ter
s
b
ased
o
n
d
en
s
it
y
o
r
co
n
n
ec
ti
v
it
y.
Gr
id
B
ased
: I
n
th
ese
t
y
p
e
s
o
f
alg
o
r
ith
m
s
,
cl
u
s
ter
s
ar
e
ass
i
g
n
ed
to
d
ata
o
b
j
ec
ts
b
ased
o
n
s
tatis
tical
v
al
u
es.
Mo
d
el
B
ased
: I
n
th
ese
t
y
p
es o
f
alg
o
r
it
h
m
s
,
cl
u
s
ter
s
ar
e
as
s
ig
n
ed
to
d
ata
o
b
j
ec
ts
b
ased
o
n
p
r
ed
ef
in
ed
m
o
d
el.
I
n
o
u
r
w
o
r
k
,
p
ar
ti
tio
n
b
ased
a
lg
o
r
it
h
m
i
s
u
s
ed
.
K
m
ea
n
s
w
h
ich
i
s
p
ar
titi
o
n
b
ased
al
g
o
r
ith
m
as
s
i
g
n
s
d
ata
attr
ib
u
ted
to
d
if
f
er
en
t
cl
u
s
ter
s
b
ased
o
n
co
s
t
f
u
n
ctio
n
.
E
u
clid
ea
n
d
is
ta
n
ce
is
u
s
ed
f
o
r
c
alcu
lati
n
g
d
is
tan
ce
f
u
n
ctio
n
.
T
h
e
d
r
a
w
b
ac
k
o
f
k
m
ea
n
s
i
s
t
h
at
it
ca
n
w
o
r
k
o
n
l
y
f
o
r
n
u
m
er
ic
d
ata.
Fo
r
ca
teg
o
r
ical
d
ata,
K
m
ea
n
s
ca
n
n
o
t
w
o
r
k
as
th
er
e
i
s
n
o
E
u
clid
ea
n
s
p
ac
e
f
o
r
t
h
is
t
y
p
e
o
f
d
ata.
K
-
p
r
o
to
t
y
p
e
i
s
u
s
ed
f
o
r
ca
lcu
la
tin
g
co
s
t
f
u
n
ctio
n
f
o
r
ca
teg
o
r
ical
d
ata
,
w
h
ic
h
is
e
x
p
lain
ed
i
n
n
e
x
t s
u
b
s
ec
tio
n
.
3
.
1
.
K
m
ea
n
s
a
nd
k
pro
t
o
t
y
pe
K
m
ea
n
s
i
s
t
h
e
m
o
s
t
p
o
p
u
lar
clu
s
ter
i
n
g
m
et
h
o
d
to
ch
ec
k
o
b
jects
s
i
m
i
lar
it
y
[
1
]
.
T
h
e
o
b
j
ec
t
s
w
it
h
i
n
a
clu
s
ter
h
a
v
e
h
i
g
h
s
i
m
ilar
it
y
a
n
d
d
if
f
er
e
n
t
cl
u
s
ter
s
h
av
e
h
ig
h
d
is
s
i
m
ilar
it
y
.
I
t
cla
s
s
i
f
y
o
b
j
ec
ts
b
ased
o
n
k
v
al
u
e
w
h
ic
h
ar
e
f
ix
ed
b
ef
o
r
e
clu
s
ter
in
g
,
I
n
v
ar
io
u
s
r
esear
ch
w
o
r
k
i
t
is
p
r
o
v
ed
th
at
r
esu
lts
co
n
v
er
g
e
to
lo
ca
l
s
o
lu
ti
o
n
an
d
n
o
t
o
n
g
lo
b
al
s
o
l
u
tio
n
[
4
]
.
T
h
is
alg
o
r
ith
m
ca
lc
u
late
s
ce
n
tr
o
id
v
alu
e
i
n
iter
ati
v
e
w
a
y
.
I
n
f
ir
s
t
s
tep
,
r
an
d
o
m
o
b
j
ec
ts
ar
e
ass
i
g
n
ed
to
cl
u
s
te
r
s
.
T
h
en
n
e
x
t
s
tep
ca
lcu
lates
n
e
w
ce
n
tr
o
id
v
al
u
e
b
ased
o
n
p
r
e
v
io
u
s
s
tep
.
T
h
e
v
alu
e
o
f
k
ce
n
tr
o
id
s
ch
a
n
g
e
u
n
til
las
t
s
tep
w
h
e
n
th
er
e
is
n
o
ch
an
g
e
in
v
al
u
e
o
f
ce
n
tr
o
id
.
T
h
is
i
s
f
i
n
al
ce
n
tr
o
id
s
v
alu
e
a
n
d
o
b
j
ec
ts
ass
ig
n
ed
to
clu
s
ter
s
[
6
]
.
In
al
g
o
r
ith
m
,
s
tep
2
ta
k
es
m
ax
i
m
u
m
ti
m
e.
I
n
th
i
s
s
tep
,
d
ata
i
s
tr
av
er
s
ed
f
o
r
ass
ig
n
i
n
g
to
cl
u
s
ter
.
T
h
e
r
u
n
n
i
n
g
ti
m
e
ca
n
b
e
r
ed
u
ce
d
b
y
u
s
in
g
o
u
r
tech
n
iq
u
e.
O
n
l
y
s
o
m
e
i
d
i
m
e
n
s
io
n
s
c
h
an
g
e
s
v
al
u
e
af
ter
s
o
m
e
iter
atio
n
.
T
h
er
e
is
n
o
n
ee
d
to
ca
lcu
late
K
d
i
m
en
s
io
n
s
in
e
v
er
y
iter
atio
n
.
I
n
t
h
is
o
p
ti
m
iz
ed
ap
p
r
o
ac
h
,
o
n
ly
i
d
i
m
en
s
io
n
s
o
u
t
o
f
K
d
i
m
en
s
i
o
n
s
ar
e
s
elec
ted
.
T
h
ese
i
d
i
m
en
s
io
n
s
ar
e
r
elev
a
n
t.
T
h
ese
d
im
en
s
io
n
s
ar
e
g
i
v
en
th
e
f
i
x
ed
p
r
io
r
it
y
.
O
n
l
y
d
i
m
e
n
s
io
n
s
w
h
ic
h
ar
e
g
i
v
e
n
p
r
io
r
it
y
ar
e
u
s
ed
in
ca
lcu
latio
n
o
f
E
u
clid
ea
n
d
is
ta
n
ce
f
r
o
m
ce
n
tr
o
id
.
T
h
is
r
ed
u
ce
s
ti
m
e
co
m
p
le
x
it
y
o
f
d
er
iv
i
n
g
cl
u
s
ter
s
f
r
o
m
b
i
g
d
ata.
Ou
r
tec
h
n
iq
u
e
i
s
ch
o
o
s
i
n
g
k
clu
s
ter
s
an
d
af
ter
s
o
m
e
iter
ati
o
n
s
elec
ti
n
g
o
n
l
y
o
b
j
ec
ts
w
h
i
ch
ch
a
n
g
e
s
clu
s
ter
s
.
T
h
er
e
is
n
o
n
ee
d
to
co
m
p
u
t
e
th
e
ce
n
tr
o
id
v
a
lu
e
f
o
r
t
h
e
o
b
j
ec
ts
w
h
o
r
e
m
ain
i
n
s
a
m
e
cl
u
s
ter
s
a
f
ter
s
o
m
e
f
i
x
ed
iter
ati
o
n
s
.
I
t
r
ed
u
ce
s
t
h
e
co
m
p
u
tatio
n
w
h
e
n
t
h
er
e
is
a
la
r
g
e
s
ca
le
o
f
d
ata
-
s
tr
u
ct
u
r
ed
as
w
ell
u
n
s
tr
u
ctu
r
ed
d
ata.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
1
1
–
1719
1714
Alg
o
rit
h
m
1
:
K
m
ea
ns
D
ata
: D
ata
s
et
N=
{n
1
……
…
….
.
n
n
);
K
n
u
m
b
er
o
f
clu
s
ter
s
R
es
u
lt
: C
lu
s
ter
C
e
n
tr
o
id
s
: C
1
………….
C
K
b
eg
in
Select
K
p
o
in
ts
i
n
n
-
E
u
clid
ea
n
s
p
ac
e
f
o
r
in
t
ial
ce
n
tr
o
id
s
r
ep
ea
t
P
lace
d
ata
o
b
j
ec
ts
in
th
e
s
e
K
p
o
in
ts
u
s
i
n
g
d
is
tan
ce
m
ea
s
u
r
es.
R
ec
alcu
late
ce
n
tr
o
id
s
v
a
lu
e
b
y
tak
in
g
m
ea
n
o
f
d
ata
o
b
j
ec
ts
u
n
ti
l
th
er
e
is
n
o
ch
an
g
e
i
n
ce
n
tr
o
id
p
o
s
itio
n
s
.
e
nd
I
n
u
n
s
tr
u
ct
u
r
ed
d
ata
th
er
e
ar
e
n
u
m
er
ical
at
tr
ib
u
tes
as
w
el
l
a
s
ca
teg
o
r
ical
attr
ib
u
tes.
I
n
t
h
is
p
r
o
p
o
s
e
d
w
o
r
k
,
co
s
t
f
u
n
ctio
n
w
ill
b
e
d
ef
i
n
ed
as
t
h
e
co
m
b
i
n
atio
n
o
f
d
is
tan
ce
m
ea
s
u
r
es
o
f
n
u
m
er
ic
al
v
al
u
es
a
s
w
ell
as
ca
teg
o
r
ical
v
al
u
es.
C
ate
g
o
r
ic
al
v
alu
e
s
ar
e
n
o
t
ca
lcu
lated
as
b
in
ar
y
v
a
lu
e
s
o
r
d
is
cr
ete
v
alu
e
s
,
r
ath
er
it
is
ca
lcu
lated
b
ased
o
n
o
v
er
all
d
is
tr
ib
u
tio
n
o
r
co
-
o
cc
u
r
r
en
ce
w
ith
o
th
er
attr
ib
u
tes.
T
h
e
s
i
m
i
lar
it
y
an
d
d
is
s
i
m
ilar
it
y
o
f
o
b
j
ec
ts
d
ep
en
d
o
n
h
o
w
clo
s
e
t
h
eir
v
al
u
es
ar
e
f
o
r
all
attr
ib
u
te
s
.
Fo
r
n
u
m
er
i
ca
l
d
ata
it
i
s
ea
s
ier
to
ca
lcu
late
t
h
e
d
is
ta
n
ce
b
et
wee
n
o
b
j
ec
ts
b
ased
o
n
E
u
clid
e
an
d
is
tan
ce
.
I
t
is
d
if
f
ic
u
lt
f
o
r
ca
teg
o
r
ical
d
ata
to
co
m
p
u
te
t
h
e
clo
s
en
e
s
s
b
et
w
e
en
o
b
j
ec
ts
.
B
in
ar
y
d
is
ta
n
ce
m
ea
s
u
r
es
i
s
n
o
t
ap
p
r
o
p
r
iate
f
o
r
ca
teg
o
r
ical
d
ata,
it
s
h
o
u
ld
g
i
v
e
s
o
m
e
v
al
u
e
to
ca
teg
o
r
ies o
f
d
ata
[
5
]
.
C
o
n
v
er
s
io
n
o
f
ca
teg
o
r
ical
d
ata
to
n
u
m
er
ical
d
ata:
a.
T
h
e
n
u
m
er
ical
d
is
tan
ce
ca
n
b
e
ap
p
lied
af
ter
co
n
v
er
s
io
n
o
f
ca
teg
o
r
ical
attr
ib
u
ted
i
n
to
n
u
m
er
ical
,
attr
ib
u
te
s
b
u
t it
is
v
er
y
d
if
f
ic
u
lt
.
b.
Nu
m
er
ical
d
ata
ca
n
b
e
d
is
cr
etize
d
to
ca
teg
o
r
ical
d
ata.
T
h
e
d
is
tan
ce
b
et
w
ee
n
a
d
ata
o
b
j
ec
t a
n
d
a
clu
s
ter
ce
n
ter
is
t
h
e
s
u
m
m
atio
n
o
f
t
h
e
d
is
ta
n
ce
s
b
et
w
ee
n
it
s
n
u
m
er
ic
a
n
d
ca
teg
o
r
ical
attr
ib
u
te
v
a
lu
e
s
.
Fo
r
n
u
m
er
ic
attr
ib
u
tes,
w
e
ta
k
e
t
h
e
E
u
clid
ea
n
d
is
tan
ce
b
et
w
ee
n
th
e
o
b
j
ec
t’
s
attr
ib
u
te
v
a
lu
e
a
n
d
th
e
m
ea
n
v
al
u
e
o
f
t
h
e
ce
n
te
r
.
Fo
r
ca
teg
o
r
ical
attr
ib
u
tes,
all
v
al
u
e
s
h
a
v
e
a
p
r
o
p
o
r
tio
n
al
p
r
esen
ce
in
t
h
e
d
ef
i
n
itio
n
o
f
clu
s
ter
ce
n
ter
.
I
t
is
p
r
esen
ted
in
m
a
n
y
s
t
u
d
ies
th
at
K
m
ea
n
s
ca
n
p
r
o
ce
s
s
n
u
m
er
ical
d
ata
o
n
l
y
.
K
p
r
o
to
t
y
p
e
is
ab
le
to
r
e
m
o
v
e
t
h
is
li
m
ita
tio
n
[
2
]
.
Kp
r
o
to
ty
p
e
is
p
r
o
p
o
s
ed
in
[
1
0
]
to
r
em
o
v
e
t
h
e
li
m
itat
io
n
o
f
K
m
ea
n
s
al
g
o
r
ith
m
.
Kp
r
o
to
ty
p
e
i
s
co
m
b
i
n
atio
n
o
f
K
m
ea
n
s
a
n
d
K
m
o
d
es
al
g
o
r
it
h
m
s
.
K
p
r
o
to
t
y
p
e
al
g
o
r
ith
m
ca
n
h
an
d
le
n
u
m
er
ica
l
an
d
ca
teg
o
r
ical
d
ata
[
1
1
]
.
E
u
clid
ea
n
d
i
s
tan
ce
i
s
u
s
ed
f
o
r
ca
lcu
lati
n
g
s
i
m
ilar
it
y
f
o
r
n
u
m
er
ica
l
attr
ib
u
te
s
.
Ha
m
m
i
n
g
d
is
ta
n
ce
i
s
u
s
ed
f
o
r
ca
lcu
lat
in
g
s
i
m
ilar
it
y
f
o
r
ca
te
g
o
r
ical
attr
ib
u
te
s
.
Sp
li
t
t
h
e
d
at
a
D
i
n
to
n
u
m
er
ical
an
d
ca
teg
o
r
ical
v
al
u
e.
(
)
∑
(
)
∑
(
)
(
1
)
I
n
th
i
s
eq
u
a
tio
n
,
d
is
ta
n
ce
b
et
wee
n
attr
ib
u
te
v
al
u
e
an
d
n
u
m
er
ic
ce
n
ter
is
ca
lcu
lated
.
Nu
m
er
ical
v
alu
e
s
d
i
s
tan
ce
is
ca
lc
u
lated
b
y
u
s
i
n
g
m
ea
n
s
o
f
d
ata
o
b
j
ec
ts
allo
tted
to
a
cl
u
s
ter
.
T
h
e
n
t
h
ese
cl
u
s
ter
s
ar
e
u
p
d
ated
b
ased
o
n
iter
atio
n
s
.
A
l
s
o
,
d
is
tan
ce
b
et
w
ee
n
att
r
ib
u
te
v
al
u
e
an
d
ca
teg
o
r
ical
ce
n
ter
is
ca
lcu
lated
.
C
ate
g
o
r
ical
v
al
u
e
s
d
is
tan
ce
is
ca
lc
u
lated
b
y
u
s
in
g
m
o
s
t
f
r
eq
u
en
tl
y
o
cc
u
r
r
in
g
v
al
u
e
as
cl
u
s
te
r
ce
n
ter
.
Dif
f
er
en
t d
is
ta
n
ce
m
ea
s
u
r
es c
a
n
b
e
u
s
ed
f
o
r
n
u
m
er
ic
al
as
w
e
ll a
s
ca
te
g
o
r
ical
d
ata.
Nu
m
er
ical
a
n
d
ca
te
g
o
r
ical
d
at
a
is
s
ep
ar
ated
as
s
h
o
w
n
in
A
l
g
o
r
ith
m
2
.
I
n
itial
v
a
lu
e
s
ar
e
s
elec
ted
an
d
th
en
s
i
m
i
lar
it
y
is
ca
lcu
la
ted
u
s
in
g
E
q
u
a
tio
n
(
1
)
.
T
h
ese
iter
a
tio
n
s
ar
e
ca
r
r
ied
o
u
t
u
n
t
il
t
h
e
r
e
is
n
o
ch
a
n
g
e
i
n
clu
s
ter
s
v
al
u
es i.
e
Old
ce
n
ter
C
is
eq
u
al
to
u
p
d
ated
ce
n
ter
C
u
.
K
m
ea
n
s
a
n
d
K
p
r
o
to
t
y
p
e
al
g
o
r
ith
m
w
o
r
k
s
o
n
s
m
all
s
ca
le
o
f
d
ata
w
i
th
g
o
o
d
ac
cu
r
ac
y
.
B
u
t
w
h
e
n
it
i
s
d
ep
lo
y
ed
o
n
b
ig
d
ata,
it
tak
es
u
n
r
ea
li
s
tic
d
u
r
atio
n
to
p
r
o
c
ess
th
i
s
lar
g
e
s
ca
le
o
f
d
ata.
W
e
h
av
e
d
ep
lo
y
ed
K
p
r
o
to
ty
p
e
o
n
Ma
p
r
ed
u
ce
in
th
is
p
ap
er
.
I
n
th
i
s
w
o
r
k
,
in
t
ellig
e
n
t
f
r
a
m
e
w
o
r
k
i
s
also
p
r
o
p
o
s
ed
f
o
r
b
ig
d
ata
clu
s
ter
i
n
g
.
Dif
f
er
en
t
v
ar
ieties
o
f
m
i
x
ed
d
ata
ar
e
s
ep
ar
ate
d
in
to
n
u
m
er
ical
a
n
d
ca
teg
o
r
ical
d
ata.
T
h
en
th
ese
d
if
f
er
e
n
t d
ata
o
b
j
ec
ts
ar
e
ass
i
g
n
ed
cl
u
s
ter
s
o
n
d
i
f
f
er
en
t
Ma
p
an
d
R
ed
u
ce
p
h
a
s
e.
Deta
iled
p
r
o
p
o
s
ed
f
r
a
m
e
w
o
r
k
is
ex
p
lai
n
ed
in
n
ex
t
s
ec
tio
n
.
Alg
o
rit
h
m
2
:
K
p
ro
t
o
t
y
pe
Data
:
Data
s
et
D
=
{x
1
…
….
x
n
)
an
d
clu
s
ter
y
n
f
o
r
n
u
m
er
ica
l a
n
d
y
c
f
o
r
ca
teg
o
r
ical
d
ata
R
es
u
lt:
C
l
u
s
ter
C
e
n
ter
C
f
o
r
n
u
m
er
ica
l a
n
d
ca
teg
o
r
ical
d
ata
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
N
o
ve
l A
p
p
r
o
a
ch
fo
r
C
lu
s
teri
n
g
B
ig
Da
t
a
b
a
s
ed
o
n
Ma
p
R
e
d
u
ce
(
Go
u
r
a
v
B
a
th
la
)
1715
b
eg
in
Select
K
p
o
in
ts
i
n
n
-
E
u
clid
ea
n
s
p
ac
e
f
o
r
in
tial c
e
n
tr
o
id
s
f
o
r
n
u
m
er
ical
d
ata
an
d
K
p
o
in
ts
f
o
r
h
a
m
m
i
n
g
d
is
ta
n
ce
f
o
r
ca
teg
o
r
ical
d
ata
r
ep
ea
t
C
o
m
p
u
te
d
is
tan
ce
u
s
in
g
co
s
t
f
u
n
ctio
n
p
r
o
p
o
s
ed
.
Up
d
ate
C
lu
s
ter
v
al
u
es C
to
C
u
u
n
t
il
C
=C
u
en
d
4.
P
RO
P
O
SE
D
T
E
CH
NI
Q
U
E
B
ig
d
ata
is
co
llectio
n
o
f
n
u
m
er
ical
an
d
ca
te
g
o
r
ical
d
ata.
T
r
ad
itio
n
al
K
m
ea
n
s
ca
n
n
o
t
w
o
r
k
o
n
th
e
s
e
t
y
p
es
o
f
d
ata
ef
f
icien
tl
y
.
It
wo
r
k
s
o
n
n
u
m
er
ical
d
ata
w
ith
p
r
o
v
en
ac
cu
r
ac
y
.
I
t
ca
lcu
late
s
ce
n
tr
o
id
v
alu
e
o
f
o
b
j
ec
ts
f
o
r
clu
s
t
er
i
n
g
.
Di
s
tan
c
e
is
ca
lcu
lated
b
et
w
ee
n
n
-
d
i
m
en
s
io
n
al
v
ec
to
r
s
u
s
i
n
g
E
u
clid
ea
n
d
is
tan
ce
.
T
h
en
ce
n
ter
i
s
ca
lc
u
lated
f
o
r
d
if
f
e
r
en
t
cl
u
s
ter
s
c1
,
c2
…c
k
.
a
n
d
av
er
a
g
e
d
i
s
tan
ce
is
m
ea
s
u
r
ed
u
s
in
g
s
a
m
p
le
p
o
in
ts
.
C
o
s
i
n
e
d
is
ta
n
ce
,
E
u
clid
ea
n
d
is
tan
ce
a
n
d
P
ea
r
s
o
n
co
r
r
elatio
n
ar
e
u
s
ed
f
o
r
ca
lcu
latio
n
o
f
s
i
m
ilar
it
y
[
1
3
]
.
T
h
ese
d
is
tan
ce
m
ea
s
u
r
es
w
o
r
k
s
f
o
r
n
u
m
er
ical
d
ata
w
it
h
a
cc
u
r
ac
y
b
ec
a
u
s
e
n
u
m
er
ical
d
ata
h
a
v
e
o
r
ig
i
n
i
n
C
ar
tesi
a
n
co
o
r
d
in
ate
’
s
v
al
u
e.
Ma
p
r
ed
u
ce
[
1
2
]
ca
n
p
r
o
ce
s
s
d
ata
in
p
ar
allel
b
y
th
e
u
s
e
o
f
m
ap
an
d
r
ed
u
ce
p
h
ase.
K
m
ea
n
s
i
s
d
ep
lo
y
ed
o
n
Ma
p
r
ed
u
ce
w
it
h
p
ar
allel
ca
lcu
latio
n
o
f
clu
s
ter
s
f
o
r
p
r
o
ce
s
s
in
g
lar
g
e
s
ca
le
o
f
d
ata
[
4
]
,
[1
4]
,
[
1
5
]
.
Si
m
i
lar
it
y
b
et
w
ee
n
d
ata
o
b
j
ec
ts
an
d
cl
u
s
ter
s
ar
e
d
if
f
er
e
n
t
f
o
r
ev
er
y
o
b
j
ec
t.
So
,
d
is
tan
ce
ca
n
b
e
ca
lcu
lated
in
p
a
r
allel
b
y
t
h
e
u
s
e
o
f
m
ap
a
n
d
d
is
tan
ce
f
r
o
m
ea
ch
n
o
d
es
is
co
m
b
i
n
ed
to
f
o
r
m
g
lo
b
al
r
esu
lt i
n
r
ed
u
ce
.
Fig
u
r
e
2
.
C
lu
s
ter
in
g
o
f
n
u
m
er
i
ca
l d
ata
As
ex
p
lai
n
ed
in
Fig
u
r
e
2
,
o
n
l
y
n
u
m
er
ical
p
ar
t
o
f
b
ig
d
ata
ca
n
b
e
ass
ig
n
ed
in
o
n
e
clu
s
ter
u
s
in
g
K
m
ea
n
s
o
n
Ma
p
r
ed
u
ce
.
I
f
C
l
u
s
ter
s
v
al
u
es
d
o
n
o
c
h
a
n
g
e
t
h
en
clu
s
ter
s
ar
e
f
in
al
ized
,
o
th
er
w
i
s
e
m
ap
a
n
d
r
ed
u
ce
p
h
ase
is
r
ep
ea
ted
in
n
ex
t
ite
r
atio
n
.
I
n
th
is
w
o
r
k
,
th
e
li
m
i
tatio
n
o
f
K
m
ea
n
s
u
s
i
n
g
n
u
m
er
ical
d
ata
o
n
ly
is
r
e
m
o
v
ed
b
y
u
s
i
n
g
p
r
o
p
o
s
ed
f
r
a
m
e
w
o
r
k
.
C
ateg
o
r
ical
d
ata
ca
n
b
e
co
n
v
e
r
ted
in
to
n
u
m
er
ical
f
o
r
m
a
s
p
r
o
v
ed
b
y
v
ar
io
u
s
r
esear
c
h
w
o
r
k
s
.
B
u
t
it
r
esu
lt
s
in
a
lo
t
o
f
ti
m
e
co
n
s
u
m
p
tio
n
an
d
lo
s
s
o
f
i
n
f
o
r
m
atio
n
.
I
n
t
h
is
p
r
o
p
o
s
ed
f
r
a
m
e
w
o
r
k
,
in
te
lli
g
en
t
alg
o
r
ith
m
is
u
s
ed
w
h
ich
c
h
e
ck
t
y
p
e
o
f
d
ata
in
f
ir
s
t
p
h
a
s
e.
T
h
en
d
ataset
is
d
ep
lo
y
ed
o
n
m
ap
o
n
l
y
a
f
ter
d
ec
id
in
g
t
y
p
e
o
f
d
ata.
Sp
litt
er
p
r
o
p
o
s
ed
in
th
is
w
o
r
k
s
ep
ar
ate
m
ix
ed
d
ataset
an
d
th
e
n
ass
i
g
n
it
to
co
r
r
ec
t
s
p
lit
as
s
h
o
w
n
in
F
i
g
u
r
e
3
.
K
p
r
o
to
t
y
p
e
alg
o
r
ith
m
ca
n
ca
lcu
late
s
i
m
ilar
it
y
b
et
w
ee
n
o
b
j
ec
ts
f
o
r
b
ig
d
ata
b
y
u
s
in
g
e
u
clid
ea
n
d
is
ta
n
ce
an
d
h
a
m
m
i
n
g
d
is
ta
n
ce
.
T
h
is
alg
o
r
it
h
m
r
e
m
o
v
e
s
th
e
d
r
a
w
b
ac
k
o
f
k
m
ea
n
s
al
g
o
r
ith
m
w
h
ic
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
1
1
–
1719
1716
is
w
o
r
k
i
n
g
o
n
l
y
o
n
n
u
m
er
ical
d
ata.
T
h
is
alg
o
r
ith
m
p
r
o
d
u
ce
s
v
er
y
i
n
ter
esti
n
g
r
es
u
lts
o
n
m
i
x
ed
d
ata.
I
n
o
u
r
p
r
o
p
o
s
ed
f
r
a
m
e
w
o
r
k
,
t
h
is
al
g
o
r
ith
m
i
s
d
ep
lo
y
ed
o
n
Ma
p
R
ed
u
ce
m
o
d
el
to
m
a
n
ag
e
lar
g
e
s
ca
le
d
ata
.
I
n
th
i
s
alg
o
r
ith
m
,
ca
lc
u
latio
n
o
f
o
b
j
e
ct
w
it
h
cl
u
s
ter
ce
n
ter
i
s
i
n
d
ep
en
d
en
t
o
f
a
n
o
th
er
o
b
j
ec
t
ca
lc
u
latio
n
o
f
d
is
ta
n
ce
w
it
h
r
ele
v
an
t
cl
u
s
er
ce
n
ter
.
S
o
,
Kp
r
o
t
o
ty
p
e
al
g
o
r
ith
m
f
its
w
ell
to
b
e
i
m
p
le
m
e
n
ted
in
p
ar
allel
o
n
Ma
p
r
ed
u
ce
.
I
n
Fi
g
u
r
e
4
,
it
i
s
clea
r
l
y
ex
p
lain
ed
t
h
at
m
ix
ed
d
ata
i
s
d
is
tr
ib
u
ted
in
n
u
m
er
ical
a
n
d
ca
t
eg
o
r
ical
d
ata.
On
n
u
m
er
ical
p
ar
t,
E
u
cl
id
ea
n
d
is
t
an
ce
is
u
s
ed
f
o
r
ca
lcu
lat
in
g
d
i
s
tan
ce
w
i
th
ce
n
ter
.
O
n
ca
te
g
o
r
ical
p
ar
t,
h
a
m
m
i
n
g
d
is
tan
ce
m
ea
s
u
r
e
is
u
s
ed
.
T
h
en
r
es
u
lt
s
o
f
b
o
th
n
u
m
er
ical
a
n
d
ca
te
g
o
r
ical
d
at
a
ar
e
co
m
b
i
n
ed
to
f
o
r
m
c
lu
s
ter
ce
n
ter
s
.
Fig
u
r
e
3
.
Sp
litt
er
f
o
r
d
is
tr
ib
u
ti
n
g
n
u
m
er
ical
a
n
d
ca
teg
o
r
ical
d
ata
o
n
clu
s
ter
s
Fig
u
r
e
4
.
P
r
o
p
o
s
ed
f
r
am
e
w
o
r
k
f
o
r
clu
s
ter
i
n
g
m
i
x
ed
d
ataset
o
n
Ma
p
r
ed
u
ce
I
n
m
ap
p
h
a
s
e
o
b
j
ec
t
d
is
tan
ce
w
it
h
cl
u
s
ter
ce
n
ter
is
ca
lc
u
lated
an
d
i
n
r
ed
u
ce
p
h
ase
r
esu
lt
s
ar
e
co
m
b
i
n
ed
.
E
x
is
tin
g
ap
p
r
o
ac
h
es
u
s
e
m
ap
an
d
r
ed
u
ce
f
o
r
n
u
m
er
ical
d
ata
an
d
th
e
n
a
f
ter
g
e
ttin
g
in
p
u
t
f
r
o
m
it,
d
is
tan
ce
i
s
ca
lcu
lated
f
o
r
ca
t
eg
o
r
ical
d
ata.
Ou
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
r
u
n
s
p
ar
allel
f
o
r
p
a
r
allel
co
m
p
u
tatio
n
.
Nu
m
er
ical
a
n
d
C
a
tr
g
o
r
ical
d
a
ta
clu
s
ter
s
ar
e
ca
lcu
lated
i
n
p
ar
allel
an
d
i
n
th
e
s
e
p
r
o
ce
s
s
e
s
,
clu
s
ter
ce
n
ter
s
ar
e
ca
lcu
lated
i
n
d
iv
id
u
all
y
u
s
i
n
g
m
ap
an
d
r
ed
u
ce
a
ls
o
.
Sp
litt
er
ch
ec
k
s
t
h
e
m
i
x
ed
d
ataset
a
n
d
s
en
d
s
d
ata
to
clu
s
ter
s
et
w
h
ic
h
is
ap
p
r
o
p
r
iate.
T
h
is
r
ed
u
ce
s
p
r
o
ce
s
s
in
g
ti
m
e
as
in
itial
l
y
m
ap
p
er
h
as
co
r
r
ec
t
d
ata
to
p
r
o
ce
s
s
.
On
m
ap
p
er
,
d
is
tan
ce
ca
lcu
latio
n
i
s
s
ep
ar
ate
f
o
r
ca
teg
o
r
ical
an
d
n
u
m
er
ical
d
ata.
W
h
e
n
clu
s
ter
s
ar
e
f
in
alize
d
a
f
ter
u
s
i
n
g
E
q
u
atio
n
(
1
)
,
p
r
o
p
o
s
ed
tech
n
iq
u
e
co
m
b
i
n
es t
h
e
clu
s
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
N
o
ve
l A
p
p
r
o
a
ch
fo
r
C
lu
s
teri
n
g
B
ig
Da
t
a
b
a
s
ed
o
n
Ma
p
R
e
d
u
ce
(
Go
u
r
a
v
B
a
th
la
)
1717
5.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
A
k
e
y
m
o
ti
v
atio
n
f
o
r
th
i
s
ex
p
er
im
e
n
t
i
s
to
p
r
o
v
e
th
at
K
p
r
o
to
ty
p
e
w
o
r
k
s
b
etter
w
it
h
t
h
e
u
s
e
o
f
h
ad
o
o
p
an
d
Ma
p
r
ed
u
ce
.
T
h
is
s
ec
tio
n
p
r
o
v
es
th
a
t
o
n
b
ig
d
a
ta,
p
r
o
p
o
s
ed
w
o
r
k
g
iv
e
s
ac
cu
r
ate
r
es
u
lts
f
o
r
clu
s
ter
i
n
g
.
T
h
e
i
m
p
o
r
tan
t
p
ar
am
eter
s
f
o
r
ch
ec
k
in
g
t
h
e
p
er
f
o
r
m
an
ce
ar
e
s
ca
leu
p
,
s
p
ee
d
u
p
a
n
d
C
P
U
u
ti
lizatio
n
.
E
x
p
er
i
m
e
n
ts
p
r
o
v
e
t
h
at
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ati
s
f
ies
th
e
s
e
p
ar
a
m
eter
s
w
i
th
cl
u
s
ter
ac
cu
r
ac
y
.
W
h
en
th
is
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
s
d
ep
lo
y
e
d
o
n
m
u
l
tip
le
n
o
d
es th
e
n
p
er
f
o
r
m
an
ce
i
m
p
r
o
v
es i
n
ter
m
s
o
f
r
esp
o
n
s
e
ti
m
e.
T
h
is
s
ca
leu
p
i
s
i
m
p
r
o
v
ed
b
y
co
m
p
ar
in
g
K
1
w
it
h
K
m
.
W
e
h
av
e
u
s
ed
C
h
es
s
d
ataset
w
h
ich
h
as
co
m
b
in
a
tio
n
o
f
n
u
m
er
ical
as
w
ell
a
s
ca
teg
o
r
ical
attr
ib
u
tes.
T
h
is
d
at
aset
i
s
co
m
b
in
atio
n
o
f
ch
e
s
s
p
o
s
it
io
n
s
as
s
h
o
w
n
i
n
Fig
u
r
e
5
.
D
a
t
a
se
t
S
t
a
t
i
s
t
i
c
s
N
u
mb
e
r
o
f
d
a
t
a
o
b
j
e
c
t
s
2
8
0
5
6
N
u
me
r
i
c
a
l
A
t
t
r
i
b
u
t
e
s
6
C
a
t
e
g
o
r
i
c
a
l
A
t
t
r
i
b
u
t
e
s
10
Fig
u
r
e
5
.
C
h
es
s
d
ataset
s
tatis
t
i
cs
I
n
o
u
r
e
x
p
er
i
m
e
n
t,
h
ad
o
o
p
1
.
2
.
1
u
s
i
n
g
VM
W
ar
e
is
u
s
ed
.
R
esu
lt
s
s
h
o
w
th
a
t
cl
u
s
ter
ac
cu
r
ac
y
i
s
v
er
y
g
o
o
d
w
h
e
n
o
u
r
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
i
m
p
le
m
en
ted
o
n
Ma
p
r
ed
u
ce
.
Usi
n
g
h
ad
o
o
p
p
latf
o
r
m
,
th
e
i
n
p
u
t
d
ata
is
p
r
o
ce
s
s
ed
o
n
Ma
p
.
T
h
en
u
s
i
n
g
HD
FS
,
Kp
r
o
to
ty
p
e
w
o
r
k
s
o
n
s
e
m
is
tr
u
ct
u
r
ed
an
d
u
n
s
tr
u
ctu
r
ed
d
ata.
P
ar
t
-
0
0
0
0
0
f
ile
co
n
tain
s
th
e
f
i
n
al
cl
u
s
ter
s
f
r
o
m
b
i
g
d
ata.
Ma
p
r
ed
u
ce
p
r
o
ce
s
s
th
is
lib
r
ar
y
as
f
o
llo
w
s
[
1
6
]
,
[
1
7
]
:
I
n
p
u
t
-
T
h
is
lib
r
ar
y
i
s
d
iv
id
ed
in
to
s
ev
er
al
d
ata
b
lo
ck
s
f
o
r
w
o
r
k
in
g
o
n
m
ap
f
u
n
ctio
n
.
a
b
s
tr
ac
t
class
es a
r
e
d
ef
i
n
ed
at
th
is
s
tep
o
f
p
r
o
ce
s
s
in
g
.
Ke
y
-
Val
u
e
p
air
-
I
n
th
i
s
s
tep
<k
e
y
,
v
a
lu
e>
p
air
i
s
d
ef
i
n
ed
f
o
r
ea
ch
k
e
y
-
v
al
u
e
p
air
s
.
Sh
u
f
f
le
-
I
n
th
i
s
s
tep
all
i
n
p
u
t o
f
<
k
e
y
,
v
alu
e>
p
air
s
ar
e
s
o
r
ted
.
R
ed
u
ce
-
I
n
r
ed
u
ce
s
tep
,
<k
e
y
,
{l
is
t}>
p
air
s
ar
e
tr
av
er
s
ed
to
<k
e
y
,
v
a
lu
e>
.
Ou
tp
u
t
-
T
h
is
s
tep
co
m
b
in
es t
h
e
o
u
tp
u
t
o
f
d
if
f
er
en
t c
l
u
s
ter
s
an
d
co
m
b
i
n
es
f
i
n
al
o
u
tp
u
t.
Fig
u
r
e
6
.
C
o
m
p
ar
is
o
n
o
f
Kp
r
o
to
t
y
p
e
o
n
1
,
3
an
d
5
clu
s
ter
s
I
n
Fi
g
u
r
e
6
,
it
is
elab
o
r
ated
th
at
Kp
r
o
to
t
y
p
e
i
s
d
ep
lo
y
ed
o
n
s
i
n
g
le
n
o
d
e
an
d
m
u
l
tip
le
n
o
d
es
to
an
al
y
s
e
t
h
e
d
if
f
er
en
ce
i
n
C
P
U
ti
m
e.
I
t
i
s
clea
r
th
at
w
h
e
n
it
is
d
ep
lo
y
ed
o
n
m
u
lt
ip
le
n
o
d
es
u
s
i
n
g
in
telli
g
en
t
s
p
litt
er
o
f
o
u
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
,
C
P
U
ti
m
e
r
ed
u
ce
s
ig
n
i
f
ic
an
tl
y
.
S
p
ee
d
u
p
is
also
u
s
ed
to
p
r
o
v
e
b
etter
r
esu
lts
f
r
o
m
o
u
r
p
r
o
p
o
s
e
d
ap
p
r
o
ac
h
.
Sp
ee
d
u
p
=
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
1
1
–
1719
1718
w
h
er
e
T
1
is
s
p
ee
d
o
n
s
in
g
le
n
o
d
e
an
d
T
m
is
s
p
ee
d
o
n
m
n
o
d
es.
Fig
u
r
e
7
.
Kp
r
o
to
ty
p
e
s
p
ee
d
u
p
o
n
m
u
ltip
le
n
o
d
es
Fro
m
Fi
g
u
r
e
7
,
it
is
clea
r
t
h
at
w
h
e
n
t
h
is
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
d
ep
lo
y
ed
o
n
m
u
ltip
le
n
o
d
es
,
s
p
ee
d
u
p
is
g
ai
n
ed
w
it
h
th
e
i
n
cr
ea
s
e
o
f
n
u
m
b
er
o
f
n
o
d
es.
E
x
p
er
i
m
e
n
t
s
p
r
o
v
e
th
at
lin
ea
r
s
p
ee
d
u
p
is
n
o
t
g
ai
n
ed
as
s
o
m
e
C
P
U
ti
m
e
i
s
co
n
s
u
m
ed
in
d
ata
tr
an
s
f
er
an
d
f
i
n
al
r
es
u
lt a
f
ter
m
er
g
i
n
g
o
f
d
ata
f
r
o
m
d
i
f
f
er
en
t
n
o
d
es
.
6.
CO
NCLU
SI
O
N
C
lu
s
ter
i
n
g
i
s
u
s
ed
in
o
u
r
w
o
r
k
to
p
r
o
ce
s
s
b
ig
d
ata
e
f
f
icien
tl
y
.
D
if
f
er
en
t
t
y
p
es
o
f
clu
s
ter
i
n
g
alg
o
r
ith
m
s
ar
e
ex
p
lai
n
ed
in
t
h
is
p
ap
er
.
K
m
ea
n
s
w
h
ic
h
i
s
p
ar
titi
o
n
in
g
b
ased
al
g
o
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e
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tellig
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ical
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s
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.
RE
F
E
R
E
NC
E
S
[1
]
A
.
F
a
h
a
d
,
N.
A
lsh
a
tri
,
Z.
T
a
ri,
A
.
A
l
a
m
ri,
I.
Kh
a
li
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A
.
Y.
Zo
m
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.
F
o
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n
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A
.
Bo
u
ra
s,
“
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S
u
rv
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f
Clu
ste
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g
A
lg
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rit
h
m
s
f
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r
Big
D
a
ta:
Tax
o
n
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m
y
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n
d
Em
p
iri
c
a
l
An
a
ly
sis
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Eme
rg
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t
o
p
ics
in
Co
m
p
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t
in
g
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v
o
l.
2
n
o
.
3,
p
p
.
2
6
7
-
2
7
9
,
2
0
1
4
.
[2
]
M
.
Ha
jKa
c
e
m
,
C.
Be
n
N’
c
ir
a
n
d
N.
Esso
u
ss
i,
“
M
a
p
Red
u
c
e
-
b
a
se
d
K
-
Pro
to
typ
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s
Clu
ste
rin
g
M
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th
o
d
fo
r
Bi
g
Da
ta
”
,
In
P
r
o
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e
d
in
g
s o
f
In
tern
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ti
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n
a
l
C
o
n
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re
n
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o
n
DSA
A
,
IE
EE
,
p
p
.
1
-
7,
2
0
1
5
.
[3
]
X
.
W
u
,
V
.
K
u
m
a
r,
J.
Ro
ss
Qu
i
n
i
a
n
,
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G
h
o
s
h
,
Q.
Ya
n
g
,
H.
M
o
to
d
a
,
G
.
J.
M
c
L
a
c
h
lan
,
A
.
Ng
.
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iu
,
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.
S
.
Yu
,
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Zh
o
u
,
M
.
S
tein
b
a
c
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,
D.J.
Ha
n
d
a
n
d
D.
S
tei
n
b
e
rg
,
“
T
o
p
1
0
a
lg
o
r
it
h
m
s
in
d
a
ta
m
in
in
g
”
,
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o
wled
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e
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n
d
I
n
f
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rm
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1
4
,
no.
1
,
p
p
.
1
-
3
7
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2
0
0
7
.
[4
]
W
.
Zh
a
o
,
H.
M
a
a
n
d
Q.
He
,
“
P
a
ra
ll
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l
K
-
M
e
a
n
s
Cl
u
ste
rin
g
Ba
se
d
o
n
M
a
p
Re
d
u
c
e
”
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in
Cl
o
u
d
C
o
m
L
NCS
5
9
3
1
,
p
p
.
6
7
4
-
6
7
9
,
2
0
0
9
.
[5
]
J.
He
e
r
a
n
d
S
.
Ka
n
d
e
l,
“
I
n
tera
c
ti
v
e
a
n
a
ly
sis o
f
b
ig
d
a
ta”
,
XR
DS
AC
M
,
v
o
l.
1
9
n
o
.
1
,
p
p
.
5
0
-
5
4
,
2
0
1
2
.
[6
]
K.
S
h
im
,
“
M
a
p
Re
d
u
c
e
A
lg
o
rit
h
m
s
f
o
r
Big
Da
ta
A
n
a
l
y
sis”
,
Da
ta
b
a
se
s
in
Ne
two
rk
e
d
I
n
fo
rm
a
ti
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n
S
y
ste
ms
,
L
NCS
,
v
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l.
7
8
1
3
,
p
p
.
4
4
-
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8
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0
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3
.
[7
]
X
.
Cu
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P
.
Z
h
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,
X.
Ya
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g
,
K.
L
i
a
n
d
C.
Ji,
“
Op
ti
m
ize
d
b
ig
d
a
ta
K
-
m
e
a
n
s
c
lu
ste
rin
g
u
sin
g
M
a
p
Re
d
u
c
e
”
,
J
o
u
rn
a
l
o
f
S
u
p
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p
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ti
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g
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r
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l.
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o
.
3
,
p
p
.
1
2
4
9
-
1
2
5
9
,
2
0
1
4
.
[8
]
M
.
Ha
jKa
c
e
m
,
C.
N’c
ir
a
n
d
N.
Esso
u
ss
i,
“
P
a
ra
ll
e
l
K
-
P
r
o
to
ty
p
e
s
f
o
r
Clu
ste
rin
g
Big
Da
ta”
,
ICCCI
L
NCS
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3
3
0
,
p
p
.
6
2
8
-
6
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,
2
0
1
5
.
[9
]
A
.
A
h
m
a
d
a
n
d
L
.
D
e
y
,
“
A
k
-
m
e
a
n
c
lu
ste
rin
g
a
lg
o
rit
h
m
f
o
r
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x
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d
n
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m
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ric
a
n
d
c
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te
g
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rica
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d
a
ta”
,
J
o
u
rn
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l
o
f
d
a
ta
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n
d
k
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o
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led
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ACM
,
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l.
6
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.
2
,
p
p
.
5
0
3
-
5
2
7
,
2
0
0
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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Z
Hu
a
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Clu
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larg
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tas
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ts
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it
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[1
1
]
J.
Ji,
T
.
B
a
i,
C.
Zh
o
u
,
C.
M
a
a
n
d
Z.
W
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g
,
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n
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m
p
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k
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ro
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1
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p
p
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5
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6
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3
.
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2
]
J.
De
a
n
a
n
d
S
.
G
h
e
m
a
wa
t,
“
M
a
p
Re
d
u
c
e
:
S
im
p
li
f
ied
Da
ta
P
r
o
c
e
ss
in
g
o
n
L
a
r
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3
]
R.
X
u
a
n
d
D.
W
u
n
sc
h
,
“
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u
rv
e
y
o
f
Clu
ste
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g
A
lg
o
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h
m
”
,
IEE
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n
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ra
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tw
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s
,
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l.
1
6
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o
.
3
,
2
0
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5
.
[1
4
]
Z.
Hu
a
n
g
,
“
A
f
a
st
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lu
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rin
g
a
lg
o
rit
h
m
to
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rg
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c
a
te
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o
rica
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d
a
tas
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ts
in
d
a
ta
m
in
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9
9
8
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[1
5
]
K.R
.
Nirm
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l
a
n
d
K.
V
.
V
S
a
ty
a
n
a
ra
y
a
n
a
,
“
Iss
u
e
s
o
f
K
M
e
a
n
s
c
lu
ste
in
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w
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p
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c
e
p
a
ra
d
ig
m
w
it
h
Big
Da
ta:
A
S
u
rv
e
y
”
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l.
6
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o
.
6
,
p
p
.
3
0
4
7
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0
5
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0
1
6
.
[1
6
]
X
.
Ya
n
,
Z
.
W
a
n
g
,
D.
Ze
n
g
,
C.
Hu
a
n
d
H.
Ya
o
,
“
De
sig
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a
n
d
a
n
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ly
sis
o
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f
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r
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Da
ta Cl
a
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sif
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n
”
,
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EE
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S
,
v
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1
2
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.
1
1
,
p
p
.
7
9
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4
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7
]
S
.
A
.
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h
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n
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S
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ra
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.
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Ba
g
w
a
n
,
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A
stu
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M
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p
Re
d
u
c
e
:
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ll
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Tren
d
s”
,
IJ
EE
CS
,
v
o
l.
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o
.
1
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p
p
.
1
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6
-
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6
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,
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,
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h
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s
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tern
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s
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n
d
jo
u
rn
a
ls.
His
a
re
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o
f
in
tere
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Big
Da
ta,
Da
ta
m
in
in
g
,
P
r
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g
ra
m
m
in
g
lan
g
u
a
g
e
s.
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is
m
e
m
b
e
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o
f
IEE
E
c
lo
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d
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m
p
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g
,
CS
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n
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IS
T
E.
Dr
.
H
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