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n
in
g
tech
n
iq
u
e
h
ig
h
ly
v
alu
ab
le.
C
lu
s
ter
an
aly
s
is
r
ev
ea
ls
p
o
ten
tial
h
id
d
en
p
atter
n
s
,
s
tr
u
ctu
r
es,
o
r
co
n
n
ec
tio
n
s
in
th
e
d
ata
th
r
o
u
g
h
th
e
co
m
b
i
n
atio
n
o
f
s
im
ilar
d
ata
p
o
in
ts
.
T
h
is
v
er
s
atile
ap
p
r
o
ac
h
is
u
tili
ze
d
in
a
wid
e
r
an
g
e
o
f
in
d
u
s
tr
ies,
s
u
c
h
as
m
ar
k
et
r
esear
ch
,
p
h
o
to
id
en
tific
atio
n
,
an
o
m
aly
d
etec
t
io
n
,
an
d
c
u
s
to
m
er
s
eg
m
en
tatio
n
.
T
h
e
g
o
al
o
f
clu
s
ter
in
g
is
to
ef
f
icien
tly
d
iv
i
d
e
th
e
d
ata
i
n
to
cl
u
s
ter
s
b
ased
s
o
lely
o
n
in
ter
n
a
l
ch
ar
ac
ter
is
tics
s
u
ch
as
d
en
s
it
y
o
r
p
r
o
x
im
ity
.
Var
io
u
s
clu
s
ter
in
g
s
tr
ateg
ies
in
v
o
lv
e
alg
o
r
i
th
m
s
lik
e
k
-
m
ea
n
s
,
h
ier
ar
ch
ical
clu
s
ter
in
g
,
an
d
d
en
s
ity
-
b
ased
s
p
atial
clu
s
ter
i
n
g
o
f
ap
p
licatio
n
s
with
n
o
is
e
(
DB
S
C
AN)
.
B
y
d
is
r
eg
ar
d
in
g
ex
ter
n
al
in
f
o
r
m
a
tio
n
an
d
co
m
b
in
in
g
d
if
f
e
r
en
t
clu
s
ter
in
g
m
eth
o
d
s
,
th
e
o
b
ject
iv
e
is
to
p
i
n
p
o
in
t
a
s
in
g
u
lar
d
ata
p
ar
titi
o
n
th
at
ac
cu
r
ately
r
ep
r
esen
ts
th
e
in
h
er
en
t
s
tr
u
ctu
r
e
o
f
th
e
d
ata.
W
h
en
it
co
m
es
to
in
d
iv
id
u
al
clu
s
ter
in
g
,
th
er
e
ar
e
ce
r
tain
f
ac
to
r
s
th
at
ca
n
af
f
ec
t its
ac
cu
r
ac
y
,
s
u
c
h
as n
o
is
e,
in
i
tializatio
n
,
an
d
th
e
s
elec
tio
n
o
f
clu
s
ter
in
g
p
a
r
am
e
ter
s
.
I
n
th
ese
s
itu
atio
n
s
,
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
tr
a
d
itio
n
al
clu
s
te
r
in
g
m
eth
o
d
s
m
ay
b
e
co
m
p
r
o
m
is
ed
,
lead
in
g
to
l
ess
-
th
an
-
o
p
tim
al
r
esu
lts
.
E
n
s
em
b
le
clu
s
ter
in
g
h
as
g
a
r
n
er
e
d
s
ig
n
if
ican
t
in
ter
est
am
o
n
g
d
ata
m
i
n
in
g
an
d
m
ac
h
i
n
e
lear
n
in
g
r
esear
c
h
er
s
as a
s
o
lu
tio
n
to
th
e
ch
allen
g
e
o
f
lo
ca
t
in
g
ac
tu
al
clu
s
ter
s
.
E
n
s
em
b
le
clu
s
ter
in
g
h
as
e
m
e
r
g
ed
as
a
p
o
wer
f
u
l
to
o
l
th
at
co
m
b
in
es
m
u
ltip
le
clu
s
ter
in
g
r
esu
lts
to
c
r
ea
te
a
m
o
r
e
r
eliab
le
an
d
ef
f
ec
tiv
e
co
n
s
en
s
u
s
clu
s
ter
in
g
.
T
h
is
is
ac
h
iev
ed
b
y
m
er
g
in
g
r
esu
lts
f
r
o
m
d
if
f
er
en
t
alg
o
r
ith
m
s
o
r
th
e
s
am
e
alg
o
r
i
th
m
with
d
if
f
er
en
t
p
ar
am
eter
s
ettin
g
s
.
Un
lik
e
th
e
ty
p
ical
a
p
p
r
o
ac
h
th
at
u
s
es
a
s
in
g
le
alg
o
r
ith
m
to
g
en
er
ate
o
n
e
clu
s
ter
in
g
r
esu
lt,
th
e
r
e
h
as
b
ee
n
a
g
r
o
win
g
in
ter
est
in
e
n
s
em
b
le
clu
s
ter
in
g
,
wh
ich
in
v
o
l
v
es e
m
p
lo
y
in
g
m
u
ltip
le
clu
s
ter
in
g
ap
p
r
o
ac
h
es to
p
r
o
d
u
ce
m
o
r
e
ac
cu
r
ate
r
esu
lts
[
4
]
.
T
h
is
r
esear
ch
is
m
o
tiv
ated
b
y
th
e
n
ee
d
to
en
h
a
n
ce
t
h
e
p
r
ec
is
io
n
an
d
r
eliab
ilit
y
o
f
clu
s
ter
a
n
aly
s
is
in
m
an
y
a
p
p
licatio
n
s
lik
e
wea
th
er
f
o
r
e
ca
s
tin
g
.
C
o
r
r
ec
t
wea
th
er
esti
m
ates
ar
e
cr
u
cial
f
o
r
d
is
aster
awa
r
en
ess
,
r
eso
u
r
ce
s
h
ar
in
g
,
a
n
d
l
o
n
g
-
ter
m
wea
th
er
p
lan
n
in
g
.
T
r
a
d
itio
n
al
clu
s
ter
in
g
al
g
o
r
ith
m
s
o
f
te
n
s
tr
u
g
g
le
with
th
e
co
m
p
lex
ity
o
f
r
elatio
n
s
h
ip
s
an
d
p
atter
n
s
in
wea
th
er
f
o
r
e
ca
s
tin
g
d
atasets
.
T
o
ad
d
r
ess
th
is
,
th
is
r
esear
ch
p
r
o
p
o
s
es
lev
er
ag
in
g
en
s
em
b
le
lear
n
in
g
tech
n
iq
u
es
to
im
p
r
o
v
e
clu
s
ter
in
g
ac
cu
r
ac
y
a
n
d
elev
ate
th
e
q
u
ality
o
f
wea
th
er
p
r
ed
ictio
n
s
.
W
ea
th
er
f
o
r
ec
asti
n
g
in
v
o
lv
es
an
a
ly
zin
g
v
ar
io
u
s
m
eteo
r
o
lo
g
ical
attr
ib
u
tes
lik
e
tem
p
er
atu
r
e,
h
u
m
id
ity
,
win
d
s
p
ee
d
,
an
d
p
r
ec
ip
itatio
n
to
p
r
ed
ict
f
u
tu
r
e
co
n
d
itio
n
s
.
T
r
ad
itio
n
al
clu
s
ter
in
g
alg
o
r
ith
m
s
[
5
]
,
f
ac
e
ch
allen
g
es
in
ca
p
tu
r
i
n
g
in
tr
icate
,
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
s
b
etwe
en
th
ese
attr
ib
u
tes.
Ap
p
ly
in
g
en
s
em
b
le
lear
n
in
g
t
o
wea
th
er
f
o
r
ec
asti
n
g
d
atasets
aim
s
to
o
v
er
c
o
m
e
th
ese
lim
itatio
n
s
b
y
co
m
b
in
in
g
m
u
ltip
le
clu
s
ter
in
g
m
o
d
els,
p
r
o
d
u
cin
g
m
o
r
e
ac
cu
r
ate
an
d
r
o
b
u
s
t
r
esu
lts
.
T
h
is
ap
p
r
o
ac
h
m
itig
ates
th
e
im
p
ac
t
o
f
n
o
is
y
o
r
i
n
co
m
p
lete
d
ata,
im
p
r
o
v
es
clu
s
ter
s
ep
ar
a
b
ilit
y
,
an
d
im
p
r
o
v
es
in
clu
s
iv
e
clu
s
ter
in
g
p
e
r
f
o
r
m
an
ce
.
E
n
s
em
b
le
lear
n
in
g
,
a
p
r
o
m
in
e
n
t
m
ac
h
in
e
lear
n
in
g
a
p
p
r
o
ac
h
,
en
h
an
ce
s
p
r
e
d
ictiv
e
ac
cu
r
ac
y
an
d
g
e
n
er
aliza
tio
n
b
y
am
alg
am
atin
g
th
e
i
n
s
ig
h
ts
o
f
m
u
ltip
le
m
o
d
els.
T
h
e
f
u
n
d
a
m
en
tal
co
n
ce
p
t
in
v
o
l
v
es
ag
g
r
eg
atin
g
p
r
ed
ictio
n
s
f
r
o
m
d
i
v
er
s
e
m
o
d
els,
h
ar
n
ess
in
g
th
eir
co
llectiv
e
s
tr
en
g
t
h
to
y
ield
o
u
tco
m
es
th
at
s
u
r
p
ass
th
o
s
e
o
f
in
d
i
v
id
u
al
m
o
d
els
in
ter
m
s
o
f
ac
cu
r
ac
y
an
d
r
o
b
u
s
tn
ess
.
Dem
o
n
s
tr
atin
g
ef
f
icac
y
ac
r
o
s
s
d
iv
er
s
e
d
o
m
ain
s
s
u
ch
as
class
if
icatio
n
,
r
eg
r
ess
io
n
,
an
d
an
o
m
aly
d
etec
tio
n
,
en
s
em
b
le
lear
n
in
g
h
as p
r
o
v
en
its
v
er
s
atility
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
ap
e
r
i
s
o
r
g
an
ized
as
f
o
llo
ws.
I
n
s
e
ctio
n
2
,
r
elev
an
t
liter
atu
r
e
is
ex
h
ib
ited
.
Sectio
n
3
s
p
ec
if
ies
an
o
u
tlin
e
o
f
th
e
r
ec
o
m
m
en
d
ed
clu
s
ter
in
g
en
s
em
b
le
ap
p
r
o
ac
h
wh
ich
o
u
tlin
in
g
its
d
is
tin
ct
p
h
ases
.
Mo
v
in
g
o
n
to
s
ec
tio
n
4
,
we
elab
o
r
ate
o
n
th
e
em
p
i
r
ical
in
v
esti
g
atio
n
s
an
d
ass
ess
p
er
f
o
r
m
an
ce
u
s
in
g
au
th
en
tic
d
atasets
.
C
o
n
clu
d
i
n
g
th
e
p
r
esen
tatio
n
in
s
ec
tio
n
5
,
we
u
ltima
tely
c
o
n
s
id
er
co
n
cl
u
s
io
n
s
an
d
p
o
s
s
ib
le
im
p
r
o
v
em
e
n
ts
f
o
r
t
h
e
f
u
tu
r
e.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
T
h
e
cu
r
r
e
n
t
liter
atu
r
e
o
n
clu
s
ter
an
aly
s
is
ca
n
b
e
b
r
o
ad
ly
c
h
a
r
ac
ter
izes
two
m
ajo
r
s
tr
ea
m
s
:
tr
ad
itio
n
al
clu
s
ter
in
g
ap
p
r
o
ac
h
es
a
n
d
co
m
m
o
n
ly
em
p
lo
y
ed
tec
h
n
iq
u
es.
T
r
ad
itio
n
al
ap
p
r
o
ac
h
es,
ex
e
m
p
lifie
d
b
y
k
-
m
ea
n
s
,
h
ier
ar
ch
ical
g
r
o
u
p
in
g
,
an
d
D
B
S
C
AN,
h
av
e
p
lay
ed
a
f
o
ca
l
r
o
le
in
th
e
f
ield
an
d
f
in
d
ex
ten
s
iv
e
ap
p
licatio
n
ac
r
o
s
s
d
iv
er
s
e
d
o
m
ain
s
.
T
h
e
ir
attr
ac
tiv
en
ess
s
tem
s
f
r
o
m
th
eir
s
im
p
licity
an
d
p
r
ac
ticality
,
m
ak
in
g
th
e
m
p
r
ef
er
r
e
d
s
elec
tio
n
s
f
o
r
clu
s
ter
in
g
task
s
.
No
tewo
r
th
y
with
in
th
ese
tr
ad
itio
n
al
m
eth
o
d
s
ar
e
s
p
ec
if
ic
tech
n
iq
u
es
ce
leb
r
ated
f
o
r
t
h
eir
u
n
i
q
u
e
ad
v
an
tag
es,
k
-
m
ea
n
s
f
o
r
its
ef
f
i
cien
cy
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
,
h
ier
ar
ch
ical
clu
s
ter
in
g
f
o
r
its
h
ier
ar
ch
ic
al
g
ath
er
in
g
illu
s
tr
atio
n
,
an
d
DB
SC
A
N
f
o
r
its
ex
p
er
tis
e
in
d
en
s
ity
-
b
ased
clu
s
ter
in
g
.
W
h
ile
th
ese
m
et
h
o
d
s
h
a
v
e
p
r
o
v
id
e
d
s
u
b
s
tan
tially
to
ad
d
r
ess
a
d
iv
er
s
e
ar
r
ay
o
f
clu
s
ter
in
g
ch
allen
g
es,
th
ey
a
r
e
n
o
t
with
o
u
t
lim
itatio
n
s
.
T
h
er
ef
o
r
e,
it
b
ec
o
m
es
im
p
er
ativ
e
t
o
s
tu
d
y
d
if
f
er
en
t
clu
s
ter
in
g
s
tr
ateg
ies
th
at
ca
n
s
u
r
m
o
u
n
t
th
ese
s
h
o
r
tco
m
in
g
s
an
d
au
g
m
en
t
th
e
ac
cu
r
ac
y
an
d
ad
a
p
tab
ilit
y
o
f
clu
s
ter
an
aly
s
is
.
A
clu
s
ter
in
g
en
s
em
b
le
tr
ies
to
m
er
g
e
s
ev
er
al
cl
u
m
p
in
g
m
o
d
els
to
g
e
n
er
ate
a
s
u
p
er
io
r
o
u
tco
m
e
co
m
p
ar
ed
to
d
is
tin
ctiv
e
clu
s
te
r
in
g
m
eth
o
d
s
in
ter
m
s
o
f
b
o
t
h
u
n
if
o
r
m
ity
an
d
s
u
p
er
io
r
ity
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
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m
p
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n
g
,
Vo
l.
1
4
,
No
.
5
,
Octo
b
e
r
2
0
2
4
:
5
8
0
2
-
5
8
1
2
5804
An
ad
v
a
n
ce
d
e
n
s
em
b
le
clu
s
te
r
in
g
m
et
h
o
d
o
lo
g
y
th
at
d
ep
en
d
s
o
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th
e
q
u
ick
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tr
ib
u
tio
n
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f
clu
s
ter
-
wis
e
co
m
p
ar
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o
n
s
th
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o
u
g
h
ca
s
u
al
walk
s
.
At
f
ir
s
t,
a
g
r
ap
h
i
s
g
en
er
ated
to
r
ep
r
esen
t
th
e
s
im
ilar
ities
b
etwe
en
clu
s
ter
s
.
T
h
e
clu
s
ter
s
ac
t
as
n
o
d
es,
an
d
th
e
J
ac
ca
r
d
c
o
ef
f
ici
en
t
is
u
s
ed
to
d
eter
m
in
e
th
e
weig
h
ts
o
f
th
e
e
d
g
es
co
n
n
ec
tin
g
th
em
.
W
ith
th
e
h
e
lp
o
f
a
s
tr
u
ctu
r
ed
g
r
a
p
h
,
a
p
a
s
s
ag
e
p
r
o
b
ab
ilit
y
m
at
r
ix
is
cr
ea
ted
to
s
u
p
p
o
r
t
th
e
r
an
d
o
m
walk
ac
tiv
ity
.
T
h
is
m
atr
ix
allo
ws
f
o
r
th
e
s
p
r
ea
d
o
f
s
tr
u
ctu
r
al
in
f
o
r
m
atio
n
th
r
o
u
g
h
o
u
t
th
e
g
r
a
p
h
.
T
h
r
o
u
g
h
an
an
aly
s
is
o
f
th
e
p
ath
s
o
r
ig
in
atin
g
f
r
o
m
d
if
f
er
en
t
p
o
in
ts
,
a
n
ew
m
atr
ix
f
o
r
co
m
p
ar
in
g
clu
s
ter
s
is
cr
ea
ted
b
y
co
n
s
id
er
i
n
g
th
e
r
el
atio
n
s
h
ip
s
b
etwe
en
th
ese
p
at
h
s
.
Af
ter
war
d
s
,
th
e
r
ec
e
n
tly
o
b
tain
ed
clu
s
ter
-
wis
e
s
im
ilar
ity
m
atr
ix
is
co
n
v
er
te
d
f
r
o
m
th
e
clu
s
ter
-
lev
el
to
th
e
o
b
ject
-
lev
el,
r
esu
ltin
g
in
an
im
p
r
o
v
ed
c
o
-
ass
o
ciatio
n
m
atr
ix
.
T
h
is
m
atr
ix
ef
f
ec
tiv
el
y
ca
p
tu
r
es
b
o
th
th
e
ass
o
ciatio
n
s
b
etwe
e
n
o
b
jects
an
d
th
e
r
elatio
n
s
h
ip
s
b
etwe
en
clu
s
ter
s
at
m
u
ltip
le
s
ca
les.
An
an
aly
s
i
s
is
co
n
d
u
cted
u
s
in
g
v
is
u
al
cl
u
s
ter
in
g
m
eth
o
d
s
to
d
eter
m
in
e
th
e
n
u
m
b
er
o
f
g
r
o
u
p
s
.
T
h
e
clu
s
ter
q
u
an
tity
is
v
is
u
ally
r
ep
r
esen
ted
b
y
th
ese
tech
n
iq
u
es
as
d
ar
k
b
lo
ck
s
with
s
q
u
ar
e
s
h
a
p
es
r
u
n
n
in
g
d
ia
g
o
n
ally
.
T
h
e
r
ep
r
esen
tatio
n
o
f
clu
s
ter
s
is
d
ep
icted
b
y
a
s
er
ies
o
f
b
lac
k
,
s
q
u
ar
e
b
lo
c
k
s
,
an
d
th
e
tec
h
n
i
q
u
es
wo
r
k
ex
ce
p
tio
n
ally
well
o
n
s
m
aller
d
atasets
.
Ho
wev
er
,
th
e
ac
c
u
r
ac
y
o
f
g
r
o
u
p
in
g
h
as d
ec
r
ea
s
ed
o
n
lar
g
e
d
atab
ases
,
an
d
t
h
e
p
r
o
ce
s
s
in
g
s
ize
h
as in
cr
ea
s
ed
[
6
]
.
B
y
an
aly
zin
g
v
ar
io
u
s
clu
s
ter
i
n
g
alg
o
r
ith
m
s
,
th
is
r
esear
ch
aim
ed
to
ass
is
t
v
en
d
o
r
s
in
id
en
t
if
y
in
g
an
d
p
r
io
r
itizin
g
th
e
m
o
s
t
p
r
o
f
itab
l
e
m
ar
k
et
s
eg
m
en
ts
,
wh
ile
d
is
r
eg
ar
d
in
g
t
h
e
less
lu
cr
ativ
e
o
n
es.
T
h
e
g
o
al
was
to
d
eter
m
in
e
th
e
m
o
s
t
p
r
ec
is
e
m
eth
o
d
f
o
r
clu
s
ter
in
g
c
u
s
to
m
er
b
eh
a
v
io
r
.
T
h
is
ty
p
e
o
f
s
tu
d
y
is
cr
u
cial
f
o
r
b
u
s
in
ess
g
r
o
wth
as
it
h
elp
s
i
n
r
etain
in
g
cu
s
to
m
er
s
an
d
in
c
r
ea
s
in
g
co
m
p
an
y
p
r
o
f
its
.
T
r
a
d
es
ca
teg
o
r
ize
th
eir
cu
s
to
m
er
s
b
ased
o
n
s
im
ilar
b
eh
av
io
r
al
ch
a
r
ac
ter
is
tics
.
T
h
is
m
eth
o
d
e
n
s
u
r
es
m
ax
im
u
m
e
x
p
o
s
u
r
e
o
f
o
n
lin
e
o
f
f
er
s
to
ca
p
tu
r
e
th
e
atten
ti
o
n
o
f
p
o
ten
tial
cu
s
to
m
er
s
.
T
wo
d
if
f
er
en
t
lear
n
in
g
m
et
h
o
d
s
,
k
-
m
ea
n
s
an
d
h
ier
ar
ch
ical
clu
s
ter
in
g
,
a
r
e
u
s
ed
o
n
a
cu
s
to
m
e
r
d
ataset
to
d
e
ter
m
in
e
wh
ich
ap
p
r
o
ac
h
y
ield
s
th
e
m
o
s
t
ac
cu
r
ate
clu
s
ter
in
g
r
esu
lts
.
Gr
o
u
p
in
g
p
lay
s
a
cr
u
cial
r
o
le
i
n
n
u
m
er
o
u
s
d
ata
-
d
r
iv
en
ap
p
licatio
n
s
an
d
is
co
n
s
id
er
ed
a
f
ascin
atin
g
an
d
s
ig
n
if
ican
t
task
in
m
ac
h
in
e
lear
n
in
g
.
I
t
is
also
s
tu
d
ied
in
s
tat
is
tic
s
,
p
att
er
n
d
if
f
er
e
n
tiatio
n
,
co
m
p
u
tatio
n
al
g
e
o
m
etr
y
,
b
io
-
in
f
o
r
m
atics,
o
p
tim
izatio
n
,
an
d
in
a
wid
e
r
an
g
e
o
f
o
th
e
r
d
is
cip
lin
es
[
7
]
,
[
8
]
.
C
lu
s
ter
in
g
tech
n
iq
u
es
s
u
ch
as
p
o
s
s
ib
ilis
tic
f
u
zz
y
C
-
m
ea
n
a
ch
iev
e
a
f
u
zz
y
s
u
b
d
iv
is
io
n
o
f
d
ata
p
o
in
ts
u
s
in
g
p
r
o
b
a
b
ilit
y
.
T
h
ese
tech
n
iq
u
es
f
in
d
ap
p
licatio
n
s
in
v
ar
io
u
s
a
r
ea
s
,
in
clu
d
in
g
im
a
g
e
s
u
b
d
iv
i
s
io
n
an
d
o
th
e
r
s
[
9
]
[
1
0
]
.
Ma
n
y
r
esear
ch
er
s
h
av
e
d
elv
ed
in
to
th
e
clu
s
ter
in
g
p
r
o
ce
s
s
es
f
o
r
lar
g
e
d
atasets
.
An
i
n
-
d
ep
th
a
n
aly
s
is
o
f
lar
g
e
d
atasets
is
co
n
d
u
cted
,
an
d
th
e
alg
o
r
ith
m
s
f
o
r
class
if
icat
io
n
an
d
clu
s
ter
in
g
t
h
at
ar
e
b
ased
o
n
Ma
p
R
ed
u
c
e
ar
e
d
is
cu
s
s
ed
an
d
ex
am
in
e
d
[
1
1
]
.
A
n
aly
zin
g
th
e
attr
ib
u
tes
o
f
d
if
f
er
en
t
cl
u
s
ter
in
g
alg
o
r
it
h
m
s
an
d
a
d
d
r
ess
in
g
th
e
ch
allen
g
es
o
f
h
an
d
lin
g
lar
g
e
d
atasets
,
co
n
d
u
ctin
g
a
co
m
p
r
eh
e
n
s
iv
e
an
aly
s
is
o
f
th
e
m
ain
clu
s
ter
in
g
p
r
o
ce
d
u
r
es
[
1
2
]
.
E
x
am
in
in
g
t
h
e
co
n
ce
p
t,
p
o
s
s
ib
ilit
ies,
an
d
ch
allen
g
es
o
f
la
r
g
e
d
atasets
an
d
p
r
o
v
id
i
n
g
a
b
r
ief
o
v
er
v
iew
o
f
th
e
c
u
ttin
g
-
ed
g
e
t
ec
h
n
iq
u
es u
s
ed
t
o
an
aly
ze
t
h
is
in
f
o
r
m
atio
n
[
1
3
]
.
T
h
e
s
tu
d
y
[
1
4
]
ca
teg
o
r
izes
th
e
p
r
esen
t
n
o
n
p
a
r
allel
clu
s
ter
f
o
r
m
atio
n
tech
n
iq
u
es
an
d
co
n
d
u
cts
ex
p
er
im
en
ts
to
ex
am
i
n
e
th
e
c
o
r
r
ec
tn
ess
,
s
ca
lab
ilit
y
,
an
d
e
f
f
icien
cy
o
f
v
ar
io
u
s
al
g
o
r
ith
m
ty
p
es
in
h
a
n
d
lin
g
h
u
g
e
d
atasets
.
T
h
e
p
u
r
p
o
s
e
o
f
e
n
s
em
b
le
clu
s
ter
in
g
is
to
in
teg
r
ate
th
e
d
ata
f
r
o
m
a
d
iv
er
s
if
ied
r
an
g
e
o
f
co
m
p
o
n
en
ts
in
o
r
d
e
r
to
cr
ea
te
a
p
r
esu
m
ab
ly
en
h
a
n
ce
d
p
ar
titi
o
n
.
T
h
e
f
u
n
d
am
e
n
tal
ap
p
r
o
ac
h
co
m
p
r
is
es
co
n
s
tr
u
ctin
g
a
clu
s
ter
o
f
alg
o
r
ith
m
s
=
{
_
(
1
)
,
_
(
2
)
,
…
…
_
(
)
}
,
d
esig
n
ated
as
en
s
em
b
le
m
em
b
er
s
,
an
d
co
n
s
o
lid
atin
g
th
e
r
esu
ltan
t
p
ar
titi
o
n
s
=
{
_
(
1
)
,
_
(
2
)
,
…
…
_
(
)
}
,
th
r
o
u
g
h
th
e
ap
p
licatio
n
o
f
a
co
n
s
en
s
u
s
f
u
n
ctio
n
[
1
5
]
,
[
1
6
]
.
I
t
is
cr
u
c
ial
to
s
tr
ess
th
at
co
n
s
en
s
u
s
cl
u
s
ter
in
g
is
n
o
t
ex
clu
s
iv
ely
a
p
p
lied
f
o
r
g
ettin
g
a
p
ar
titi
o
n
;
it
ca
n
also
s
er
v
e
g
o
als
s
u
ch
as
an
aly
zin
g
th
e
n
u
m
b
er
o
f
g
r
o
u
p
s
in
t
h
e
in
f
o
r
m
ati
o
n
[
1
7
]
,
e
x
am
in
in
g
th
eir
co
n
s
is
ten
cy
,
o
r
c
o
n
d
u
ctin
g
a
h
y
p
er
p
a
r
am
eter
in
v
esti
g
atio
n
[
1
8
]
.
An
alter
n
ate
n
am
e
s
y
n
o
n
y
m
o
u
s
with
en
s
em
b
le
clu
s
ter
in
g
is
"c
o
n
s
en
s
u
s
clu
s
ter
in
g
,
"
as r
ep
o
r
ted
[
1
9
]
,
an
d
p
r
o
v
id
ed
a
m
ar
g
in
all
y
d
if
f
er
e
n
t a
p
p
r
o
ac
h
.
T
h
ey
a
d
v
is
ed
e
m
p
lo
y
i
n
g
r
esam
p
lin
g
with
o
u
t
r
ep
lace
m
en
t
i
n
th
eir
in
v
esti
g
atio
n
.
T
h
is
co
n
ce
p
t
was
b
ased
o
n
th
e
p
r
e
m
is
e
th
at
clu
s
ter
s
th
at
d
em
o
n
s
tr
ated
b
etter
r
esis
tan
ce
to
r
esam
p
lin
g
m
ig
h
t
b
e
ac
tu
al
clu
s
ter
s
.
T
h
ey
also
p
r
o
p
o
s
ed
a
p
r
in
cip
le
f
o
r
id
e
n
tify
in
g
th
e
co
r
r
e
ct
n
u
m
b
er
o
f
g
r
o
u
p
s
.
Mü
ller
et
a
l.
[
2
0
]
p
r
o
v
id
e
ex
ten
s
iv
e
ass
es
s
m
en
ts
o
f
s
ev
er
al
clu
s
ter
in
g
tech
n
iq
u
es.
T
h
ey
d
escr
ib
e
th
e
v
a
r
io
u
s
q
u
alities
o
f
e
ac
h
alg
o
r
ith
m
an
d
co
n
d
u
ct
a
c
o
m
p
lete
s
tu
d
y
o
f
t
h
eir
b
elo
n
g
in
g
s
.
T
h
e
o
u
tc
o
m
e
s
ar
e
ass
es
s
ed
u
s
in
g
b
o
th
r
ea
l
-
wo
r
ld
an
d
s
im
u
lated
s
am
p
les.
Usi
n
g
n
u
m
er
o
u
s
clu
s
ter
in
g
ev
al
u
atio
n
c
r
iter
ia,
th
ey
co
n
tr
asted
t
h
ese
f
in
d
in
g
s
with
class
ic
clu
s
ter
in
g
alg
o
r
ith
m
s
ac
r
o
s
s
d
if
f
e
r
en
t a
r
e
as
[
2
1
]
,
[
2
2
]
.
T
h
e
in
n
o
v
ativ
e
m
eth
o
d
ca
lle
d
d
en
s
ity
c
o
n
s
cio
u
s
s
u
b
s
p
ac
e
clu
s
ter
in
g
(
DE
NC
OS)
T
h
i
s
m
eth
o
d
id
en
tifie
s
clu
s
ter
s
b
y
ex
am
in
in
g
th
e
r
elativ
e
d
en
s
ity
in
a
s
u
b
s
p
ac
e
a
n
d
r
ep
r
esen
ts
th
e
m
as
r
eg
i
o
n
s
.
Ou
r
ap
p
r
o
ac
h
at
DE
NC
OS
in
v
o
lv
es
u
s
in
g
a
s
p
lit
-
an
d
-
co
n
q
u
e
r
s
tr
ateg
y
to
ef
f
ec
tiv
ely
id
e
n
tify
clu
s
ter
s
with
d
if
f
er
en
t
d
en
s
ity
th
r
esh
o
l
d
s
an
d
s
u
b
s
p
ac
e
ca
r
d
in
als.
B
ased
o
n
ex
te
n
s
iv
e
r
esear
ch
a
n
d
a
n
aly
s
is
,
it
h
as
b
ee
n
p
r
o
v
e
n
th
at
DE
NC
OS
is
h
ig
h
ly
ac
cu
r
ate
in
id
en
tify
i
n
g
g
r
o
u
p
s
in
v
ar
io
u
s
s
u
b
s
p
ac
es.
I
n
f
ac
t,
it
o
u
tp
er
f
o
r
m
s
o
th
er
clu
s
ter
in
g
tec
h
n
iq
u
es
in
ter
m
s
o
f
p
r
ec
is
io
n
.
R
esear
ch
er
s
h
av
e
ch
o
s
en
s
p
ec
if
ic
ap
p
r
o
ac
h
es
f
o
r
en
s
em
b
le
clu
s
ter
in
g
b
ased
o
n
th
e
in
t
en
d
ed
a
p
p
licatio
n
s
,
p
a
r
ticu
la
r
ly
wh
en
d
ea
lin
g
with
h
ig
h
-
d
im
en
s
io
n
al
d
ata
.
A
f
ea
tu
r
e
s
u
b
s
et
[
2
3
]
was
g
en
er
ated
b
y
s
elec
tin
g
v
ar
io
u
s
s
ets
o
f
o
b
jects,
an
d
th
is
a
p
p
r
o
ac
h
was
ca
lled
"o
b
ject
d
is
tr
ib
u
tio
n
"
.
T
h
e
p
r
o
ce
s
s
o
f
p
r
o
jectin
g
th
in
g
s
in
to
d
if
f
e
r
en
t
s
u
b
s
p
ac
es
is
ca
r
r
ied
o
u
t
in
a
s
ee
m
in
g
ly
r
an
d
o
m
m
an
n
er
,
lac
k
in
g
a
n
y
d
is
ce
r
n
i
b
le
p
atter
n
o
r
r
atio
n
ale
[
2
4
]
.
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
-
8
7
0
8
A
n
o
ve
l
co
m
p
r
eh
en
s
ive
in
ve
s
tig
a
tio
n
fo
r
en
h
a
n
cin
g
clu
s
ter a
n
a
lysi
s
a
cc
u
r
a
cy
th
r
o
u
g
h
…
(
H.
N
.
La
ksh
mi)
5805
3.
P
RO
P
O
SE
D
M
E
T
H
O
D
E
n
s
em
b
le
clu
s
ter
in
g
m
er
g
es
a
g
r
o
u
p
o
f
clu
s
ter
in
g
m
et
h
o
d
s
u
s
in
g
th
e
s
am
e
d
ataset,
r
es
u
ltin
g
in
a
f
in
al
clu
s
ter
in
g
.
T
h
e
o
b
jectiv
e
o
f
en
s
em
b
le
clu
s
ter
in
g
is
to
en
h
an
ce
th
e
q
u
ality
o
f
i
n
d
iv
id
u
al
d
ata
clu
s
ter
in
g
.
I
n
th
is
s
tu
d
y
,
m
ajo
r
ity
v
o
tin
g
-
b
ased
en
s
em
b
le
clu
s
ter
in
g
a
p
p
r
o
ac
h
is
u
tili
ze
d
;
to
ac
h
ie
v
e
th
is
,
we
em
p
lo
y
s
p
ec
if
ic
clu
s
ter
in
g
tech
n
iq
u
es
o
n
d
ef
in
e
d
d
atasets
to
o
b
tain
in
d
i
v
id
u
al
o
u
tco
m
es.
Fo
llo
win
g
th
e
im
p
lem
en
tatio
n
,
th
e
e
n
s
em
b
le
clu
s
ter
in
g
o
u
tco
m
es
ar
e
co
n
t
r
asted
with
th
o
s
e
o
f
in
d
i
v
id
u
al
tech
n
iq
u
es.
T
h
e
f
in
d
in
g
s
f
r
o
m
e
n
s
em
b
le
clu
s
ter
in
g
in
d
icate
im
p
r
o
v
ed
clu
s
t
er
in
g
r
esu
lts
an
d
Fig
u
r
e
1
,
p
r
o
v
id
es
a
d
etailed
s
u
m
m
ar
y
o
f
a
r
esear
ch
s
tu
d
y
aim
ed
at
im
p
r
o
v
in
g
th
e
ac
cu
r
ac
y
o
f
clu
s
ter
id
en
tific
atio
n
.
Data
co
llectio
n
is
th
e
f
ir
s
t
s
tep
,
an
d
th
en
th
er
e
ar
e
m
an
y
s
tag
es
o
f
d
ata
p
r
e
p
ar
ati
o
n
an
d
o
r
g
a
n
izatio
n
b
ef
o
r
e
cl
u
s
ter
in
g
.
I
n
th
e
p
r
e
-
p
r
o
ce
s
s
in
g
p
h
ase,
ir
r
elev
a
n
t
elem
en
ts
s
u
ch
as
n
u
ll
e
n
tr
ie
s
,
u
n
id
en
tifie
d
v
alu
es,
a
n
d
n
eg
lig
ib
le
attr
ib
u
tes,
wh
ich
ex
er
t
litt
le
o
r
n
o
n
o
ticea
b
le
in
f
lu
en
ce
o
n
th
e
r
esu
lts
,
ar
e
ex
clu
d
ed
,
an
d
an
o
m
alie
s
ar
e
f
ilter
ed
o
u
t
to
co
n
s
tr
u
ct
a
p
r
o
f
icien
t c
lu
s
ter
in
g
m
o
d
el.
Fig
u
r
e
1
.
Ar
c
h
itectu
r
e
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
Fin
d
in
g
th
e
id
ea
l
n
u
m
b
er
o
f
g
r
o
u
p
s
n
ee
d
ed
to
s
p
lit
th
e
d
ataset
in
to
m
ea
n
in
g
f
u
l
g
r
o
u
p
s
is
th
e
f
ir
s
t
s
tep
in
u
s
in
g
d
if
f
er
e
n
t
clu
s
ter
in
g
alg
o
r
ith
m
s
to
tr
ain
t
h
e
d
a
taset
[
2
5
]
.
T
h
e
d
ataset
is
s
u
b
jecte
d
to
co
m
m
o
n
clu
s
ter
in
g
m
eth
o
d
s
s
u
ch
as
k
-
m
ea
n
s
clu
s
ter
in
g
,
af
f
in
ity
p
r
o
p
a
g
atio
n
,
m
ea
n
s
h
if
t,
B
I
R
C
H
clu
s
ter
in
g
,
an
d
o
th
er
s
b
ef
o
r
e
th
e
clu
s
ter
in
g
m
o
d
els
ar
e
co
m
p
ar
ed
.
B
asic
clu
s
ter
in
g
r
esu
lts
ar
e
p
r
o
d
u
ce
d
u
s
in
g
th
ese
tech
n
iq
u
es,
a
n
d
th
e
s
u
g
g
ested
s
tr
ateg
y
is
t
h
en
co
n
tr
asted
with
th
em
.
T
o
cr
ea
te
an
e
m
b
ed
d
ed
m
o
d
el
f
o
r
th
is
s
tu
d
y
,
B
I
R
C
H
clu
s
ter
in
g
an
d
m
ea
n
s
h
if
t
clu
s
ter
in
g
,
th
e
t
wo
d
is
tin
ct
clu
s
ter
in
g
tech
n
iq
u
es
ar
e
m
er
g
ed
t
o
cr
ea
te
a
c
o
m
b
in
e
d
m
o
d
el.
T
h
i
s
co
m
b
in
atio
n
s
tr
ateg
y
im
p
r
o
v
es
th
e
o
v
er
all
s
tr
en
g
th
a
n
d
ac
c
u
r
ac
y
o
f
clu
s
ter
in
g
b
y
u
s
in
g
t
h
e
b
en
e
f
its
o
f
ea
ch
g
r
o
u
p
in
g
tech
n
i
q
u
e.
3
.
1
.
M
ea
n
s
hift
clus
t
er
ing
A
n
o
n
-
p
ar
am
etr
ic
g
r
o
u
p
in
g
a
p
p
r
o
ac
h
n
a
m
ed
m
ea
n
s
h
if
t
d
o
es
not
n
ec
ess
itate
a
g
r
asp
o
n
t
h
e
n
u
m
b
er
o
f
clu
s
ter
s
b
ef
o
r
eh
an
d
.
I
t
o
p
er
ates
b
y
r
e
p
ea
ted
ly
m
o
v
in
g
d
ata
p
o
i
n
ts
in
th
e
d
ir
ec
tio
n
o
f
th
e
s
u
p
p
o
r
tin
g
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
'
s
m
o
d
e,
o
r
p
ea
k
.
T
h
e
f
o
llo
win
g
is
a
d
etailed
p
r
o
ce
s
s
f
o
r
m
ea
n
s
h
if
t
clu
s
ter
in
g
:
−
I
n
p
u
t:
c
o
n
s
id
er
th
e
d
ata
p
o
in
t
s
=
{
1
,
2
…
.
}
,
k
er
n
el
f
u
n
ctio
n
with
b
an
d
wid
th
ℎ
an
d
co
n
v
er
g
e
n
ce
th
r
esh
o
ld
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
4
,
No
.
5
,
Octo
b
e
r
2
0
2
4
:
5
8
0
2
-
5
8
1
2
5806
−
I
n
itializatio
n
: I
n
itialize
clu
s
ter
ce
n
ter
s
=
an
d
s
h
if
t
v
ec
to
r
ℎ
=
.
−
Me
an
s
h
if
t iter
atio
n
s
:
r
ep
ea
t
u
n
til co
n
v
er
g
en
ce
:
(
ℎ
)
:
C
o
m
p
u
te
th
e
m
ea
n
s
h
if
t u
s
in
g
ℎ
(
)
=
∑
(
−
,
ℎ
)
∗
=
1
∑
(
−
,
ℎ
)
=
1
.
(
1
)
Up
d
ate
clu
s
ter
ce
n
ter
s
=
+
ℎ
(
2
)
−
C
o
n
v
er
g
en
ce
ch
ec
k
:
(
‖
ℎ
‖
<
)
,
en
d
t
h
e
f
o
r
lo
o
p
.
−
Ass
ig
n
ea
ch
d
ata
p
o
in
t
x
i
to
th
e
g
r
o
u
p
wh
o
s
e
ce
n
ter
it c
o
n
v
e
r
g
ed
.
−
R
etu
r
n
th
e
clu
s
ter
s
.
T
h
e
k
er
n
el
f
u
n
ctio
n
is
ty
p
ical
ly
a
Gau
s
s
ian
k
er
n
el,
b
u
t o
th
er
ch
o
ices c
an
b
e
u
s
ed
d
ep
en
d
in
g
o
n
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
d
ata.
T
h
e
b
an
d
wid
th
ℎ
co
n
tr
o
ls
th
e
s
ize
o
f
th
e
n
eig
h
b
o
r
h
o
o
d
u
s
ed
to
esti
m
ate
th
e
lo
ca
l
d
en
s
ity
an
d
in
f
l
u
en
ce
s
th
e
s
h
a
p
e
an
d
n
u
m
b
e
r
o
f
clu
s
ter
s
.
T
h
e
co
n
v
er
g
en
ce
th
r
esh
o
ld
d
ete
r
m
in
es
wh
en
th
e
m
ea
n
s
h
if
t
iter
atio
n
s
s
h
o
u
ld
s
to
p
.
T
h
e
s
h
if
t
v
ec
t
o
r
r
ep
r
esen
ts
th
e
d
ir
ec
tio
n
an
d
m
a
g
n
itu
d
e
o
f
th
e
m
ea
n
s
h
if
t
f
o
r
ea
c
h
d
ata
p
o
in
t.
T
h
e
al
g
o
r
i
th
m
alliter
ativ
ely
s
h
if
ts
d
ata
p
o
in
ts
to
war
d
s
th
e
m
o
d
e
o
f
t
h
e
u
n
d
er
ly
i
n
g
d
en
s
ity
u
n
til co
n
v
e
r
g
en
ce
.
3
.
2
.
B
I
RCH
c
lus
t
er
ing
T
h
e
B
I
R
C
H
clu
s
ter
in
g
tech
n
iq
u
e
is
a
p
r
o
ce
d
u
r
e
ap
p
lied
to
ar
r
a
n
g
e
a
n
d
g
r
o
u
p
d
ata
p
o
in
ts
in
to
clu
s
ter
s
.
I
t
h
an
d
les
lar
g
e
d
ata
s
ets
ef
f
ec
tiv
ely
b
y
ar
r
a
n
g
in
g
d
ata
in
to
h
ier
ar
c
h
ical
f
o
r
m
.
T
h
e
p
r
o
ce
s
s
in
v
o
lv
es
th
e
f
o
llo
win
g
s
tep
s
:
−
I
n
itializatio
n
:
B
eg
in
b
y
in
itializin
g
th
e
tr
ee
s
tr
u
ctu
r
e
a
n
d
s
e
ttin
g
p
ar
am
eter
s
s
u
c
h
as
th
e
b
r
an
ch
in
g
f
ac
to
r
an
d
th
e
th
r
esh
o
ld
f
o
r
th
e
n
u
m
b
er
o
f
p
o
in
ts
in
a
s
u
b
clu
s
ter
.
−
I
n
s
er
tio
n
:
Ad
d
d
ata
p
o
in
ts
to
th
e
tr
ee
s
tr
u
ctu
r
e,
cr
ea
tin
g
s
u
b
clu
s
ter
s
at
th
e
leaf
n
o
d
es.
I
f
a
s
u
b
clu
s
te
r
ex
ce
ed
s
th
e
s
p
ec
if
ied
th
r
esh
o
l
d
,
it is
s
p
lit to
m
ain
tain
th
e
h
ie
r
ar
ch
ical
s
tr
u
ctu
r
e.
−
C
lu
s
ter
in
g
:
As
d
ata
p
o
in
ts
ar
e
in
s
er
ted
,
th
e
tr
ee
s
tr
u
ctu
r
e
is
co
n
tin
u
o
u
s
ly
u
p
d
ate
d
,
an
d
cl
u
s
ter
s
ar
e
f
o
r
m
ed
at
d
if
f
er
en
t le
v
els o
f
th
e
h
ie
r
ar
ch
y
.
−
Me
r
g
in
g
:
Su
b
clu
s
ter
s
with
s
im
ilar
ch
ar
ac
ter
is
tics
ar
e
m
er
g
ed
to
cr
ea
te
a
m
o
r
e
co
m
p
ac
t
r
ep
r
esen
tatio
n
o
f
th
e
d
ata.
−
Ou
tp
u
t:
T
h
e
r
esu
ltin
g
h
ier
ar
c
h
y
o
f
clu
s
ter
s
r
e
p
r
esen
ts
th
e
o
r
g
an
ized
s
tr
u
ctu
r
e
o
f
th
e
d
at
a,
with
ea
ch
leaf
n
o
d
e
c
o
r
r
esp
o
n
d
in
g
to
a
s
u
b
cl
u
s
ter
.
T
h
e
B
I
R
C
H
clu
s
ter
in
g
p
r
o
ce
d
u
r
e
is
p
ar
ticu
lar
ly
u
s
ef
u
l
f
o
r
ap
p
licatio
n
s
wh
e
r
e
ef
f
icien
c
y
an
d
s
ca
lab
ilit
y
ar
e
ess
en
tial,
cr
ea
tin
g
it a
p
p
r
o
p
r
ia
te
f
o
r
b
i
g
an
d
h
ig
h
-
d
im
en
s
io
n
al
d
atab
ases
.
3
.
3
.
E
m
bedd
ed
a
pp
ro
a
ch
I
n
th
is
s
tr
ateg
y
,
g
en
u
in
e
g
r
o
u
p
in
g
s
ar
e
estab
lis
h
ed
b
y
in
co
r
p
o
r
atin
g
th
e
B
I
R
C
H
an
d
m
ea
n
s
h
if
t
m
eth
o
d
o
l
o
g
ies.
I
n
itially
,
th
e
a
s
s
o
ciatio
n
b
etwe
en
ea
ch
p
air
o
f
en
titi
es
in
th
e
d
atab
ase
is
v
er
if
ied
to
d
ete
r
m
in
e
if
th
ey
b
elo
n
g
to
th
e
id
e
n
tical
clu
s
ter
ac
r
o
s
s
all
m
eth
o
d
o
lo
g
ies.
I
f
th
ey
co
n
s
is
ten
tly
b
elo
n
g
to
th
e
s
am
e
clu
s
ter
in
ev
er
y
tech
n
i
q
u
e,
th
ey
a
r
e
g
r
o
u
p
e
d
in
to
th
at
clu
s
ter
;
o
th
er
wis
e,
an
ass
e
s
s
m
en
t
f
o
r
an
alter
n
ativ
e
clu
s
ter
is
co
n
d
u
cte
d
at
a
s
u
b
s
eq
u
en
t
s
tag
e.
Fo
llo
win
g
th
e
allo
ca
tio
n
o
f
d
ata
o
b
jects
to
a
p
r
ed
ef
i
n
ed
n
u
m
b
er
o
f
clu
s
ter
s
,
an
ex
am
i
n
atio
n
is
ca
r
r
ied
o
u
t
f
o
r
a
n
y
r
em
ain
in
g
e
n
titi
es
in
t
h
e
d
atab
ase.
Fo
r
an
y
o
b
jects
in
th
e
d
atab
ase
n
o
t
ass
ig
n
ed
to
a
n
y
cl
u
s
ter
s
,
th
ey
ar
e
allo
ca
te
d
to
o
n
e
o
f
th
e
e
x
is
tin
g
clu
s
ter
s
b
ased
o
n
t
h
e
r
esem
b
lan
ce
o
f
th
e
tu
p
les to
th
e
ce
n
tr
o
id
s
o
f
th
o
s
e
g
r
o
u
p
s
.
T
h
e
o
u
tlin
ed
a
p
p
r
o
ac
h
is
d
ep
icted
in
Alg
o
r
ith
m
1
.
According to the algorithm Let D be the dataset,
M
=
{
M
i
\
M
i
i
sa
c
lus
t
e
r
i
n
gm
e
t
ho
d
}
,
which is the set of clustering methods,
C be the set of all groups that is
C
=
{
C
ij
\
C
ij
is
j
th
t
h
c
lus
t
e
r
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n
i
th
m
e
t
ho
d
}
, and
K
=
{
K
l
\
l
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1
,
2
,
…
n
um
b
e
r
o
f
c
lust
e
r
s
}
,
be the set of resulting clusters.
I
n
th
is
r
esear
ch
,
k
-
m
ea
n
s
clu
s
ter
in
g
,
m
ea
n
s
h
if
t
clu
s
ter
in
g
,
ag
g
lo
m
er
ativ
e
clu
s
ter
in
g
,
s
p
ec
tr
al
,
OPTI
C
S
clu
s
ter
in
g
,
B
I
R
C
H
clu
s
ter
in
g
ar
e
em
p
lo
y
ed
an
d
o
b
tain
ed
r
esu
lts
in
d
iv
id
u
ally
o
n
th
e
d
escr
ib
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
A
n
o
ve
l
co
m
p
r
eh
en
s
ive
in
ve
s
tig
a
tio
n
fo
r
en
h
a
n
cin
g
clu
s
ter a
n
a
lysi
s
a
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u
r
a
cy
th
r
o
u
g
h
…
(
H.
N
.
La
ksh
mi)
5807
d
atasets
.
Fo
r
th
e
en
s
em
b
le
clu
s
ter
in
g
,
m
ea
n
s
h
if
t
clu
s
ter
in
g
an
d
B
I
R
C
H
clu
s
ter
in
g
ar
e
u
tili
ze
d
to
en
h
a
n
ce
th
e
clu
s
ter
in
g
ac
cu
r
ac
y
.
Alg
o
r
ith
m
1
.
Input:
Dataset, resulting clusters of all cluster methodologies.
Output
: Real clusters after embedded method.
Consider,
=
{
\
ℎ
}
=
{
\
ℎ
ℎ
ℎ
ℎ
}
,
=
{
\
=
1
,
2
,
…
}
,
1.
Initialize
=
1
,
=
0
.
//
Initialization of variables.
2.
ℎ
(
≠
|
|
)
3.
=
Ø
.
4.
(
ℎ
)
5.
(
ℎ
,
≠
)
//
Considering each pair of objects
6.
(
=
1
|
|
)
7.
(
=
1
|
|
)
// For each cluster from each method
8.
(
{
,
}
)
// checking for each pair of the objects belongs to same
cluster
9.
=
+
1
10.
8
.
11.
7
.
12.
6
.
13.
(
=
|
|
)
14.
=
Ս
{
,
}
. // Assigning couple of tuples to same cluster if they
belong
to
same cluster in all methods.
15.
13
.
16.
5
.
17.
4
.
18.
=
0
.
19.
=
+
1
.
20.
=
−
.
21.
2
.
22.
(
≠
Ø
)
23.
Find the centroid of each cluster
.
24.
(
ℎ
)
// Assigning the remaining objects to corresponding clusters
25.
=
{
Ս
\
ℎ
}
.
26.
24
.
27.
22
.
28.
Return the ensemble set of clusters,
29.
=
{
\
=
1
,
2
,
…
|
|
)
.
4.
E
XP
E
R
I
M
E
N
T
A
L
ANA
L
Y
SI
S AN
D
P
E
RF
O
R
M
ANC
E
E
VAL
UAT
I
O
N
T
h
is
s
eg
m
en
t
elab
o
r
ates
o
n
th
e
ex
p
er
im
e
n
tal
ex
am
in
atio
n
,
ch
o
s
en
d
atasets
,
an
d
r
esu
ltan
t
f
in
d
in
g
s
d
er
iv
ed
f
r
o
m
th
e
ass
ess
m
en
t.
T
h
e
co
m
p
r
e
h
en
s
iv
e
ex
p
er
im
e
n
ts
wer
e
co
n
d
u
cted
o
n
th
e
we
ath
er
h
is
to
r
y
d
ataset
an
d
wea
th
e
r
p
r
ed
ictio
n
d
atase
t.
I
n
th
is
r
esear
ch
th
e
r
esu
lts
c
ar
r
ied
o
u
t
u
s
in
g
a
m
ac
h
in
e
wi
th
an
I
n
tel
C
o
r
e
i3
C
PU
an
d
4
GB
o
f
R
AM
u
s
in
g
th
e
Py
th
o
n
p
r
o
g
r
a
m
m
in
g
la
n
g
u
ag
e
.
I
n
p
y
th
o
n
th
e
ex
is
tin
g
clu
s
ter
in
g
m
eth
o
d
m
ea
n
s
h
if
t
clu
s
ter
in
g
is
im
p
lem
en
ted
u
s
in
g
th
e
Me
an
Sh
i
f
t
class
an
d
th
e
m
eth
o
d
B
I
R
C
H
clu
s
ter
in
g
is
im
p
lem
en
ted
u
s
in
g
th
e
B
I
R
C
H
clas
s
f
r
o
m
s
cik
it
-
lear
n
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
f
en
s
em
b
le
clu
s
ter
in
g
is
im
p
lem
en
ted
ac
co
r
d
in
g
to
Alg
o
r
ith
m
1.
4
.
1
.
Da
t
a
s
et
des
cr
iptio
n
T
h
e
h
is
to
r
ical
wea
th
er
ar
ch
iv
e
f
u
r
n
is
h
es p
ast we
ath
er
in
f
o
r
m
atio
n
p
er
tain
in
g
to
d
i
f
f
er
en
t lo
ca
tio
n
s
.
I
t
en
co
m
p
ass
es
co
m
p
r
e
h
en
s
iv
e
d
etails
r
eg
ar
d
in
g
wea
th
er
cir
cu
m
s
tan
ce
s
d
o
cu
m
e
n
ted
t
h
r
o
u
g
h
o
u
t
a
p
ar
ticu
lar
tim
e
f
r
am
e.
C
o
m
p
r
is
in
g
a
g
r
an
d
to
tal
o
f
9
6
,
4
5
3
en
tr
ies,
ea
ch
s
ig
n
if
ies
a
d
is
tin
ct
ti
m
estam
p
alo
n
g
s
id
e
co
r
r
elate
d
wea
th
e
r
m
et
r
ics.
Af
ter
an
aly
zi
n
g
v
is
u
aliza
tio
n
s
a
n
d
e
x
tr
ac
tin
g
in
s
ig
h
ts
,
th
e
m
o
s
t
s
u
itab
le
n
u
m
b
e
r
o
f
clu
s
ter
s
f
o
r
th
is
d
ataset
h
as
b
ee
n
ascer
tain
ed
to
b
e
f
o
u
r
.
T
h
is
im
p
lies
th
at,
in
ac
co
r
d
an
ce
with
th
e
s
p
ec
if
ied
cr
iter
ia,
s
eg
m
en
tin
g
th
e
d
ata
i
n
to
f
o
u
r
clu
s
ter
s
y
ield
s
th
e
m
o
s
t sig
n
if
ican
t a
n
d
in
d
icativ
e
ca
teg
o
r
izatio
n
o
f
d
ata
p
o
in
ts
with
in
th
e
p
r
o
v
id
e
d
d
ataset
an
d
p
r
o
b
lem
d
o
m
ain
.
T
h
e
wea
th
er
p
r
ed
ictio
n
d
ataset
co
m
p
r
is
es
m
eteo
r
o
lo
g
ical
r
ec
o
r
d
s
s
o
u
r
ce
d
f
r
o
m
1
8
d
is
tin
ct
E
u
r
o
p
ea
n
l
o
ca
tio
n
s
.
Sp
an
n
in
g
th
e
y
ea
r
s
2
0
0
0
to
2
0
1
0
,
th
e
d
ataset
en
co
m
p
ass
es
3
,
6
5
4
d
aily
o
b
s
er
v
ati
o
n
s
.
I
t
in
v
o
lv
es
d
iv
er
s
e
v
ar
iab
les
s
u
c
h
as
av
er
ag
e
tem
p
er
atu
r
e,
m
ax
im
u
m
tem
p
er
at
u
r
e,
m
in
i
m
u
m
tem
p
er
atu
r
e
a
n
d
s
o
o
n
.
T
h
e
o
p
tim
al
clu
s
ter
co
u
n
t
f
o
r
th
e
d
ataset
h
as
b
ee
n
d
eter
m
in
ed
to
b
e
2
.
T
h
is
im
p
lies
th
at,
in
ac
co
r
d
an
ce
with
th
e
ch
o
s
en
cr
iter
ia,
p
ar
titi
o
n
in
g
th
e
d
ata
in
to
two
clu
s
ter
s
y
ield
s
th
e
m
o
s
t
m
ea
n
in
g
f
u
l
an
d
r
ep
r
esen
tativ
e
ca
teg
o
r
izatio
n
o
f
d
ata
p
o
in
ts
w
ith
in
th
e
s
p
ec
if
ied
d
ataset
an
d
p
r
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o
m
ain
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
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0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
4
,
No
.
5
,
Octo
b
e
r
2
0
2
4
:
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8
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4
.
2
.
Study
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n
p
er
f
o
r
m
a
nce
I
n
th
is
s
ec
tio
n
,
we
ex
am
in
e
th
e
r
esu
lts
o
f
th
e
ex
p
e
r
im
e
n
t
an
d
ev
al
u
ate
th
e
ad
v
a
n
ta
g
es
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
in
co
m
p
ar
is
o
n
with
o
th
er
cu
r
r
e
n
t
m
o
d
els
s
elec
ted
f
o
r
th
e
s
tu
d
ies.
T
wo
co
m
p
o
n
en
ts
o
f
th
e
ex
ten
s
iv
e
tr
ials
wer
e
ca
r
r
ied
o
u
t.
I
n
itially
,
an
ass
es
s
m
en
t
wa
s
co
n
d
u
cted
o
n
th
e
ac
cu
r
ac
y
o
f
clu
s
ter
in
g
u
s
in
g
well
-
k
n
o
wn
tech
n
iq
u
es
in
cl
u
d
in
g
k
-
m
ea
n
s
,
A
f
f
in
ity
p
r
o
p
ag
atio
n
,
m
ea
n
s
h
if
t,
an
d
B
I
R
C
H
clu
s
ter
in
g
.
T
o
ex
tr
ac
t
u
s
ef
u
l
in
f
o
r
m
atio
n
f
r
o
m
th
e
d
atab
ase,
th
is
ev
alu
atio
n
r
eq
u
ir
e
d
u
s
in
g
a
n
ap
p
r
o
p
r
iate
d
is
tan
ce
m
etr
ic.
T
h
e
clu
s
ter
in
g
p
r
o
ce
d
u
r
e
was
u
s
ed
in
th
e
s
ec
o
n
d
ex
p
er
im
e
n
t
to
em
p
h
asize
th
e
s
ig
n
if
ican
ce
o
f
th
e
s
u
g
g
ested
s
tr
ateg
y
.
T
h
is
r
eq
u
ir
ed
u
s
in
g
an
en
s
em
b
le
ap
p
r
o
ac
h
th
at
u
s
es
B
I
R
C
H
clu
s
ter
in
g
an
d
m
ea
n
s
h
if
t.
Me
tr
ics
lik
e
th
e
Sil
h
o
u
ette
s
co
r
e
an
d
clu
s
t
er
Dav
is
B
o
u
ld
in
s
co
r
e
wer
e
u
s
ed
to
ass
ess
th
e
r
elev
an
ce
o
f
th
e
clu
s
ter
s
th
at
wer
e
p
r
o
d
u
ce
d
b
y
th
e
s
u
g
g
e
s
ted
en
s
em
b
le
ap
p
r
o
ac
h
v
er
s
u
s
tr
ad
itio
n
al
clu
s
ter
in
g
m
et
h
o
d
s
.
T
h
e
wea
th
er
h
is
to
r
y
d
ataset
is
s
h
o
w
n
in
Fig
u
r
e
2
u
s
in
g
th
e
elb
o
w
m
et
h
o
d
an
d
C
alin
s
k
i
-
Har
ab
asz
s
co
r
e
.
T
h
e
d
ata
was
s
eg
m
en
ted
in
to
f
o
u
r
clu
s
ter
s
,
wh
ich
p
r
o
d
u
ce
d
t
h
e
m
o
s
t
s
ig
n
if
ican
t
an
d
s
u
g
g
esti
v
e
g
r
o
u
p
in
g
o
f
d
ata
p
o
i
n
ts
with
in
th
e
g
iv
en
d
ataset
an
d
is
s
u
e
ar
ea
.
I
n
a
s
im
ilar
v
ein
,
F
ig
u
r
e
3
illu
s
tr
ates
th
e
wea
th
er
p
r
ed
ictio
n
d
ataset
u
s
in
g
th
e
elb
o
w
ap
p
r
o
ac
h
a
n
d
s
ilh
o
u
ette
s
co
r
e.
Div
id
in
g
th
e
d
ata
in
to
two
clu
s
ter
s
p
r
o
d
u
ce
s
th
e
m
o
s
t
r
ep
r
esen
tativ
e
an
d
s
ig
n
if
ican
t
g
r
o
u
p
in
g
o
f
d
ata
p
o
in
ts
.
Gr
o
u
n
d
e
d
o
n
th
e
co
n
cl
u
s
io
n
s
ex
is
tin
g
in
T
ab
le
1
,
it
is
ap
p
ar
en
t
th
at
th
e
co
llectiv
e
clu
s
ter
in
g
ap
p
r
o
ac
h
h
as
p
r
o
d
u
ce
d
a
r
ed
u
ce
d
Dav
ies
-
B
o
u
ld
in
s
co
r
e
[
2
6
]
,
an
d
an
elev
ated
Sil
h
o
u
et
te
s
co
r
e
[
2
7
]
,
wh
en
co
n
tr
asted
with
all
alter
n
ativ
e
co
n
v
en
tio
n
al
clu
s
ter
in
g
alg
o
r
ith
m
s
f
o
r
wea
th
er
h
is
to
r
y
d
atas
et.
T
h
ese
o
u
tco
m
es
in
d
icate
th
at
th
e
co
llectiv
e
m
o
d
el
ap
p
lied
to
th
e
wea
th
er
h
is
to
r
y
d
ataset
d
em
o
n
s
tr
ates
s
u
p
er
io
r
clu
s
ter
in
g
ef
f
icac
y
co
n
ce
r
n
in
g
b
o
t
h
th
e
d
is
tin
ctiv
en
ess
an
d
co
h
er
en
ce
o
f
clu
s
ter
s
,
as a
s
s
es
s
ed
th
r
o
u
g
h
th
ese
m
etr
ics.
B
ased
o
n
th
e
f
in
d
in
g
s
p
r
ese
n
ted
in
T
ab
le
2
,
th
e
en
s
em
b
le
clu
s
ter
in
g
ap
p
r
o
ac
h
h
as
p
r
o
d
u
ce
d
a
s
ig
n
if
ican
tly
r
e
d
u
ce
d
Dav
ies
-
B
o
u
ld
in
s
co
r
e
wh
en
co
m
p
ar
ed
to
v
ar
io
u
s
co
n
v
en
tio
n
al
clu
s
t
er
in
g
al
g
o
r
ith
m
s
f
o
r
wea
th
er
p
r
ed
ictio
n
d
ataset.
T
h
ese
o
u
tco
m
es
in
d
icate
th
at,
wh
en
ass
ess
ed
with
th
ese
m
e
tr
ics,
th
e
en
s
em
b
le
m
o
d
el
ap
p
lied
to
th
e
wea
th
e
r
p
r
ed
ictio
n
d
ataset
d
em
o
n
s
tr
ates
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
b
o
th
th
e
s
ep
ar
atio
n
an
d
co
h
esio
n
o
f
clu
s
ter
s
.
Fig
u
r
e
2
.
Op
tim
al
n
u
m
b
e
r
o
f
c
lu
s
ter
s
id
en
tifie
d
b
y
elb
o
w
m
e
th
o
d
an
d
C
alin
s
k
i
-
Har
ab
asz
s
co
r
e
Fig
u
r
e
3
.
Op
tim
al
n
u
m
b
e
r
o
f
c
lu
s
ter
s
id
en
tifie
d
b
y
elb
o
w
m
e
th
o
d
an
d
s
ilh
o
u
ette
s
co
r
e
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
-
8
7
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A
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T
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C
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tr
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A
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T
ab
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2
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C
o
m
p
a
r
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n
s
em
b
le
clu
s
ter
in
g
to
tr
ad
itio
n
al
m
o
d
e
ls
o
n
wea
th
er
p
r
e
d
ictio
n
d
atas
et
C
l
u
st
e
r
i
n
g
a
l
g
o
r
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t
h
m
N
u
mb
e
r
o
f
c
l
u
s
t
e
r
s
D
a
v
i
s
B
o
u
l
d
i
n
s
c
o
r
e
S
i
l
h
o
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e
t
t
e
s
c
o
r
e
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e
a
n
s
2
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3
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4
1
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M
e
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T
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f
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at
th
e
en
s
em
b
le
m
o
d
el
is
f
o
r
m
ed
b
y
co
m
b
in
in
g
th
e
r
esu
lts
o
f
two
well
-
estab
lis
h
ed
clu
s
ter
in
g
m
o
d
els,
n
am
ely
m
ea
n
s
h
if
t
an
d
B
I
R
C
H
,
u
til
izin
g
a
v
o
tin
g
tech
n
iq
u
e
to
o
b
tain
th
e
u
ltima
te
o
u
tco
m
es.
T
h
ese
two
m
o
d
els
ar
e
f
a
v
o
r
ed
f
o
r
p
r
o
f
icien
cy
in
r
ec
o
g
n
izin
g
d
en
s
e
r
eg
io
n
s
with
in
th
e
d
ata
an
d
p
er
f
o
r
m
ex
ce
p
tio
n
ally
well
in
s
ce
n
ar
io
s
c
h
ar
ac
ter
ized
b
y
clu
s
ter
s
with
d
iv
er
s
e
s
h
ap
es
an
d
s
izes,
r
en
d
er
in
g
it
a
f
itti
n
g
o
p
tio
n
f
o
r
ca
p
tu
r
i
n
g
c
o
m
p
lex
s
tr
u
ctu
r
es
p
r
esen
t
in
th
e
d
ata
b
y
th
e
m
ea
n
s
h
if
t
m
eth
o
d
a
n
d
B
I
R
C
H
wh
ich
p
r
o
v
id
es
s
ca
la
b
ilit
y
an
d
co
m
p
u
tatio
n
al
e
f
f
ec
tiv
en
ess
.
I
t
ad
ep
tly
m
a
n
ag
es
s
izab
le
d
atasets
an
d
ex
h
ib
its
lo
wer
co
m
p
u
tatio
n
al
in
ten
s
ity
in
co
m
p
ar
is
o
n
to
ce
r
tain
alter
n
ativ
e
alg
o
r
ith
m
s
.
T
h
is
r
en
d
er
s
a
p
r
ag
m
atic
o
p
tio
n
f
o
r
s
ce
n
ar
io
s
wh
er
e
th
er
e
is
a
co
n
s
id
er
atio
n
f
o
r
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
.
W
e
p
r
o
v
id
e
a
m
o
d
el
o
f
a
n
e
n
s
em
b
le
clu
s
ter
in
g
alg
o
r
ith
m
to
s
o
lv
e
th
e
is
s
u
e
th
at
th
e
co
n
v
en
tio
n
al
clu
s
ter
in
g
alg
o
r
ith
m
s
h
av
e
tr
o
u
b
le
h
a
n
d
lin
g
th
e
s
et
-
b
ased
d
ata
alo
n
g
with
n
o
n
lin
ea
r
d
ata
b
ased
o
n
th
e
Dav
is
B
o
u
ld
in
s
co
r
e
an
d
th
e
Sil
h
o
u
ette
s
co
r
e
.
I
n
itially
,
we
estab
lis
h
th
e
ca
teg
o
r
ies
b
ased
o
n
h
o
w
co
m
p
ar
ab
le
th
e
d
ata
is
.
Dete
r
m
in
in
g
th
e
id
ea
l
n
u
m
b
e
r
o
f
g
r
o
u
p
s
n
ee
d
ed
t
o
s
p
lit
th
e
d
ataset
in
to
m
ea
n
i
n
g
f
u
l
g
r
o
u
p
s
is
th
e
p
r
o
b
lem
at
h
an
d
[
2
8
]
.
T
h
e
d
ataset
is
s
u
b
jecte
d
to
co
m
m
o
n
c
lu
s
ter
in
g
m
eth
o
d
s
s
u
ch
as
af
f
i
n
ity
p
r
o
p
ag
atio
n
,
k
-
m
ea
n
s
clu
s
ter
in
g
,
B
I
R
C
H
clu
s
ter
in
g
,
m
ea
n
s
h
if
t,
an
d
o
th
e
r
s
b
ef
o
r
e
th
e
clu
s
ter
in
g
m
o
d
els
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r
e
co
m
p
ar
ed
.
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asic
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s
ter
in
g
r
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lts
ar
e
p
r
o
d
u
ce
d
u
s
in
g
th
ese
tech
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iq
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es,
an
d
th
e
s
u
g
g
ested
s
tr
ateg
y
is
th
en
co
n
tr
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with
th
em
.
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o
c
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ea
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an
em
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ed
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ed
m
o
d
el
f
o
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t
h
is
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tu
d
y
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B
I
R
C
H
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s
ter
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g
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d
m
ea
n
s
h
if
t
clu
s
ter
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,
th
e
two
d
is
tin
ct
clu
s
ter
in
g
tech
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iq
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es
ar
e
m
er
g
ed
t
o
cr
ea
te
a
c
o
m
b
i
n
ed
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o
d
el,
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s
h
o
wn
.
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h
is
co
m
b
in
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n
s
tr
ateg
y
im
p
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o
v
es
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h
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o
v
er
all
s
tr
en
g
th
an
d
ac
c
u
r
ac
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o
f
clu
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ter
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g
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y
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s
in
g
th
e
b
e
n
ef
its
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f
ea
ch
g
r
o
u
p
in
g
tech
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i
q
u
e.
in
co
n
tr
ast
to
th
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m
ea
n
s
h
if
t
tec
h
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iq
u
e,
wh
ich
is
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ased
o
n
th
e
ab
s
o
lu
te
an
d
r
elativ
e
d
is
tan
ce
s
o
f
th
e
g
r
an
u
lar
v
ec
to
r
s
[
2
9
]
.
I
n
co
n
clu
s
io
n
,
o
u
r
s
u
g
g
ested
en
s
em
b
le
clu
s
ter
in
g
m
eth
o
d
o
u
tp
er
f
o
r
m
s
co
n
v
en
tio
n
al
clu
s
ter
in
g
alg
o
r
ith
m
s
,
as
s
h
o
wn
b
y
th
e
t
r
ials
,
wh
ich
s
h
o
w
an
av
er
a
g
e
en
h
an
ce
m
e
n
t
o
f
6
.
8
%
an
d
4
.
2
%
in
th
e
m
o
d
elin
g
r
esu
lts
,
r
esp
ec
tiv
ely
.
4
.
3
.
Dis
cus
s
io
n
I
n
th
is
s
tu
d
y
,
en
s
em
b
le
clu
s
ter
in
g
p
er
f
o
r
m
s
b
etter
at
c
lu
s
ter
in
g
o
n
n
u
m
er
o
u
s
d
ata
s
ets
th
an
Me
an
Sh
if
t
alo
n
g
with
ad
d
itio
n
al
clu
s
ter
in
g
m
eth
o
d
s
.
Me
an
s
h
if
t
p
er
f
o
r
m
s
s
o
m
ewh
at
wo
r
s
e
in
th
e
wea
th
er
d
ataset
th
an
th
e
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r
itis
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m
ix
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r
e
alo
n
g
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g
lo
m
er
ativ
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lu
s
ter
in
g
m
eth
o
d
s
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alth
o
u
g
h
t
h
e
d
if
f
er
e
n
ce
is
n
o
t
v
er
y
g
r
ea
t.
I
n
co
n
tr
ast
to
th
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c
o
n
v
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tio
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clu
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ter
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ith
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o
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r
h
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o
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g
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a
n
u
latio
n
tech
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lo
g
y
.
T
h
is
en
h
a
n
ce
s
th
e
alg
o
r
ith
m
'
s
clu
s
ter
in
g
p
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o
r
m
an
ce
a
n
d
y
ield
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u
p
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io
r
r
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lts
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o
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v
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atasets
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Ov
er
all,
it
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d
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v
er
ed
th
at
f
r
o
m
T
ab
les
1
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d
2
,
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n
s
em
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le
clu
s
ter
in
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p
e
r
f
o
r
m
s
b
etter
an
d
is
m
o
r
e
a
d
ap
tab
le.
T
h
e
m
e
asu
r
em
en
ts
u
s
ed
f
o
r
ac
cu
r
ac
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co
m
p
ar
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o
n
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r
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h
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Sil
h
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ette
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r
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Dav
is
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o
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ld
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e
s
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wn
p
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is
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tco
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wh
en
co
m
b
in
ed
with
en
s
em
b
le
clu
s
ter
in
g
.
T
h
is
ca
n
b
e
f
u
r
th
e
r
u
s
ed
to
im
p
r
o
v
e
th
e
ac
c
u
r
ac
y
o
f
th
e
r
esear
c
h
[
3
0
]
,
[
3
1
]
.
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
p
r
esen
ts
an
en
s
em
b
le
m
o
d
el
th
at
is
in
ten
d
ed
to
h
a
n
d
le
th
e
co
m
p
le
x
ity
an
d
s
ize
o
f
m
o
d
er
n
d
atasets
,
to
s
o
lv
e
th
e
is
s
u
e
th
at
class
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clu
s
ter
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alg
o
r
ith
m
s
s
tr
u
g
g
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a
n
d
le
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-
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ased
d
ata
a
n
d
n
o
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lin
ea
r
d
ata.
T
o
cr
ea
te
th
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m
o
d
el,
th
e
r
esu
lts
o
f
th
e
m
ea
n
s
h
if
t
an
d
B
I
R
C
H
alg
o
r
ith
m
s
wer
e
c
a
r
ef
u
lly
c
o
m
b
in
e
d
.
A
v
o
tin
g
a
p
p
r
o
ac
h
was
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s
ed
to
en
s
u
r
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th
at
ea
ch
al
g
o
r
ith
m
'
s
ad
v
an
tag
es
wer
e
ef
f
ec
tiv
ely
in
clu
d
e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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A
co
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s
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e
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aly
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is
w
as
ca
r
r
ied
o
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s
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b
le
m
o
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el
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er
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k
n
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co
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v
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tio
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em
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ate
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h
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icac
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p
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o
v
in
g
clu
s
ter
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g
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cu
r
ac
y
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n
d
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esil
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ce
wh
ich
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ak
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u
s
e
o
f
th
e
m
ea
n
s
h
if
t
an
d
B
I
R
C
H
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
lin
es
its
s
ig
n
i
f
ican
ce
.
T
h
ese
r
ev
elatio
n
s
f
u
r
t
h
er
ai
d
i
n
d
ec
is
io
n
-
m
ak
in
g
,
m
a
k
e
d
at
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ex
p
lo
r
atio
n
ea
s
ier
,
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d
p
r
o
m
o
te
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d
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er
e
x
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atio
n
o
f
th
e
b
asic
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atter
n
s
in
th
e
d
ataset
th
at
is
s
u
p
p
lied
.
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h
e
g
o
al
o
f
th
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f
ea
tu
r
e
is
to
cr
ea
te
a
s
y
s
tem
th
at
is
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ap
tab
le
an
d
f
lex
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le
e
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o
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g
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to
b
e
u
s
ed
with
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s
e
ac
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ar
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s
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atasets
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d
d
o
m
ain
s
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s
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r
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g
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r
elev
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f
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n
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n
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g
in
a
r
an
g
e
o
f
d
ata
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aly
s
is
s
ce
n
ar
io
s
.
I
n
th
e
f
u
tu
r
e,
we
wan
t
to
ad
d
m
o
r
e
co
m
p
lex
au
to
m
at
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ca
p
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to
m
ak
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th
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y
c
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m
p
atib
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with
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g
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o
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ty
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es,
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cr
ea
s
e
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s
ca
lab
ilit
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to
h
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le
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ig
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atasets
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d
m
a
k
e
it
ea
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ier
f
o
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er
s
to
ad
o
p
t
b
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a
d
d
in
g
th
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f
ea
tu
r
es.
I
n
f
u
tu
r
e,
t
o
en
h
a
n
ce
th
e
clu
s
ter
in
g
alg
o
r
ith
m
'
s
p
er
f
o
r
m
an
ce
,
we
wan
t
to
cr
ea
te
m
o
r
e
s
o
p
h
is
ticated
g
r
an
u
lar
v
ec
to
r
d
is
tan
ce
m
etr
i
cs
as
d
is
tan
ce
m
ea
s
u
r
es.
Ap
p
ly
in
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g
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ested
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r
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n
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lar
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s
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te
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etr
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d
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t c
l
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s
ter
in
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m
eth
o
d
s
is
also
an
in
tr
ig
u
in
g
p
iece
o
f
wo
r
k
.
ACK
NO
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E
DG
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M
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ex
p
r
ess
m
y
s
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ce
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e
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at
itu
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e
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m
y
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to
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s
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VR
C
o
lleg
e
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f
E
n
g
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in
g
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Hy
d
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ad
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Dep
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tm
en
t
o
f
DS
at
Gee
th
an
j
ali
co
lleg
e
o
f
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n
g
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ee
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in
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T
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h
n
o
lo
g
y
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Hy
d
er
ab
a
d
,
an
d
th
e
Dep
ar
tm
en
t
o
f
AI
at
An
u
r
a
g
Un
iv
er
s
ity
f
o
r
th
eir
u
n
wa
v
er
in
g
s
u
p
p
o
r
t
an
d
v
alu
ab
le
in
s
ig
h
ts
.
T
h
eir
co
llab
o
r
ativ
e
ef
f
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r
ts
h
av
e
s
ig
n
if
ican
tly
s
h
ap
ed
th
e
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ch
d
ir
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tio
n
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h
a
n
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g
th
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q
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ality
an
d
d
e
p
th
o
f
th
is
s
tu
d
y
.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
T.
M
e
h
r
y
a
r
M
o
h
r
i
,
A
f
s
h
i
n
R
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a
m
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d
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,
F
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d
a
t
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o
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o
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m
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c
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e
l
e
a
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n
i
n
g
.
C
a
m
b
r
i
d
g
e
,
M
A
,
U
S
A
,
2
0
1
2
.
[
2
]
C
.
M
.
B
i
sh
o
p
,
N
e
u
r
a
l
n
e
t
w
o
r
k
s f
o
r
p
a
t
t
e
r
n
r
e
c
o
g
n
i
t
i
o
n
.
O
x
f
o
r
d
,
U
K
:
O
x
f
o
r
d
U
n
i
v
e
r
si
t
y
P
r
e
ss,
1
9
9
5
.
[
3
]
D
.
H
u
a
n
g
,
C
.
-
D
.
W
a
n
g
,
H
.
P
e
n
g
,
J.
La
i
,
a
n
d
C
.
-
K
.
K
w
o
h
,
“
E
n
h
a
n
c
e
d
e
n
semb
l
e
c
l
u
st
e
r
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v
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a
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t
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c
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st
e
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-
w
i
s
e
si
mi
l
a
r
i
t
i
e
s,”
I
EE
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
S
y
st
e
m
s
,
Ma
n
,
a
n
d
C
y
b
e
r
n
e
t
i
c
s:
S
y
st
e
m
s
,
v
o
l
.
5
1
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n
o
.
1
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p
p
.
5
0
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–
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2
0
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Ja
n
.
2
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1
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:
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[
4
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[
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[
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[
7
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[
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[
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[
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[
1
7
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