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1047
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Desig
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t
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ri
th
m
s
re
late
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to
G
a
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ss
ian
m
ix
t
u
r
e
m
o
d
e
ls
(G
M
M
)
:
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M
M
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q
u
a
l
a
n
d
G
M
M
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n
e
q
u
a
l
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h
e
y
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re
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p
a
re
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ra
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k
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e
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NN
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e
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l,
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n
d
th
e
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c
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sWh
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li
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th
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h
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v
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sh
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ro
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ti
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g
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istri
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v
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m
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r
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ly
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si
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o
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il
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tes
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o
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ro
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rp
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o
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tco
m
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h
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n
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ly
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a
t
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M
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icie
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fro
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ly
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ry
fa
il
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.
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c
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in
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ti
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th
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se
re
su
lt
s
in
d
ica
te
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a
t
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M
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q
u
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l
is
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lan
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h
th
e
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re
li
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sc
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lab
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it
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a
p
p
li
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tern
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t
o
f
t
h
i
n
g
s a
n
d
sm
a
rt
h
o
m
e
s.
K
ey
w
o
r
d
s
:
C
en
tr
ality
Gau
s
s
ian
m
ix
tu
r
e
mode
Gr
ap
h
n
e
u
r
al
n
etwo
r
k
L
u
ca
s
m
o
d
el
Mo
d
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lar
ity
Netwo
r
k
clu
s
ter
in
g
R
an
d
o
m
n
o
d
e
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ailu
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es
Su
r
v
iv
ab
ilit
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W
ien
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in
d
ex
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Sh
an
m
u
k
Srin
i
v
as Am
ir
ip
alli
Dep
ar
tm
en
t o
f
C
o
m
p
u
ter
Scie
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ce
an
d
E
n
g
in
ee
r
in
g
,
GSC
SE
,
GI
T
AM
Un
iv
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s
ity
Vis
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h
ap
atn
am
,
I
n
d
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E
m
ail:
s
am
ir
ip
a@
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itam
.
ed
u
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
in
cr
ea
s
in
g
c
o
m
p
lex
ity
o
f
s
m
ar
t
h
o
m
e
e
n
v
ir
o
n
m
en
ts
r
eq
u
ir
es
ef
f
icien
t
a
n
d
ef
f
ec
tiv
e
n
etwo
r
k
clu
s
ter
in
g
s
t
r
a
t
e
g
ies,
wh
ich
ar
e
ca
p
ab
le
of
m
ain
tain
i
n
g
th
eir
p
e
r
f
o
r
m
an
ce
ev
en
in
th
e
e
v
en
t
o
f
n
o
d
e
f
ailu
r
es.
T
h
is
p
ap
er
p
r
o
p
o
s
es
two
n
ew
clu
s
ter
in
g
m
o
d
els,
Gau
s
s
ian
m
ix
tu
r
e
m
o
d
els
(
GM
M
)
e
q
u
al
an
d
GM
M
u
n
eq
u
al,
b
ased
o
n
GM
M
,
an
d
co
m
p
a
r
es
th
em
with
g
r
a
p
h
n
eu
r
al
n
etwo
r
k
(
GNN
)
e
q
u
al,
GNN
u
n
eq
u
al,
an
d
th
e
L
u
ca
s
Me
s
h
to
p
o
lo
g
y
.
M
ain
tain
in
g
th
e
co
n
n
ec
tiv
it
y
in
a
s
m
ar
t
h
o
m
e
in
ter
n
et
o
f
th
in
g
s
(
I
o
T
)
n
etwo
r
k
,
ev
en
wh
en
n
o
d
es
f
ail
r
an
d
o
m
l
y
,
is
n
o
t
an
in
s
ig
n
if
ican
t
task
.
W
e
co
n
s
id
er
ed
th
e
c
o
m
b
in
atio
n
o
f
L
u
ca
s
n
u
m
b
e
r
th
eo
r
y
a
n
d
tr
im
et
g
r
ap
h
o
p
tim
izatio
n
,
wh
ich
p
r
o
d
u
ce
s
g
r
a
p
h
s
/to
p
o
lo
g
ies
th
at
ar
e
m
o
r
e
f
au
lt
-
to
ler
an
t
th
an
th
e
s
tan
d
a
r
d
clu
s
ter
in
g
o
r
m
esh
alg
o
r
ith
m
s
.
I
n
o
u
r
ea
r
lier
s
im
u
latio
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s
,
L
u
ca
s
-
T
GO
p
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f
o
r
m
ed
9
-
12
r
o
u
n
d
s
of
k
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in
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th
e
n
etwo
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k
r
u
n
n
in
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co
m
p
ar
ed
to
6
-
8
r
o
u
n
d
s
in
s
tan
d
ar
d
m
o
d
els
[
1
]
.
T
h
is
d
i
f
f
er
en
ce
h
elp
ed
u
s
r
ea
lize
th
at
th
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e
was
s
co
p
e
f
o
r
th
e
ap
p
licatio
n
of
n
u
m
b
e
r
th
eo
r
y
in
telec
o
m
,
h
ea
lth
ca
r
e,
an
d
in
d
u
s
tr
y
I
o
T
.
W
h
en
n
o
d
es
ar
e
g
r
o
u
p
ed
b
y
th
eir
s
tr
u
ctu
r
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p
r
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p
er
ties
,
th
e
s
ize
an
d
d
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s
ity
o
f
clu
s
ter
s
s
tar
t
to
im
p
ac
t
all
asp
ec
ts
of
co
n
n
ec
tiv
ity
,
co
m
m
u
n
icatio
n
,
an
d
h
o
w
v
u
ln
e
r
ab
le
th
ey
ar
e
wh
en
th
in
g
s
g
o
wr
o
n
g
[
2
]
.
L
o
w
-
d
en
s
ity
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
2
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I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
0
4
7
-
1
0
5
7
1048
g
r
ap
h
s
m
ak
e
s
tr
u
ctu
r
e
more
v
is
ib
le
an
d
allo
w
f
o
r
ea
s
ier
is
o
latio
n
o
f
ef
f
ec
ts
as
th
ey
ar
e
s
p
ar
s
er
.
Me
d
iu
m
-
d
en
s
ity
co
n
f
ig
u
r
atio
n
s
tr
y
to
b
alan
ce
ef
f
icien
t
co
m
m
u
n
ic
atio
n
an
d
h
u
b
r
esil
ien
ce
.
H
i
g
h
-
d
e
n
s
ity
g
r
ap
h
s
illu
s
tr
ate
th
e
r
is
k
s
of
h
av
i
n
g
all
e
g
g
s
in
o
n
e
b
ask
et
[
3
]
.
W
e
in
ten
tio
n
ally
ch
o
s
e
th
e
L
u
ca
s
-
b
ased
alg
o
r
ith
m
as
th
e
clu
s
ter
s
izes
ar
e
b
ased
o
n
L
u
ca
s
s
eq
u
en
cin
g
;
th
e
r
ef
o
r
e
,
t
h
e
s
izes
ar
e
h
eter
o
g
en
e
o
u
s
,
wh
ich
l
o
o
k
e
d
p
r
o
m
is
in
g
f
o
r
r
ed
u
n
d
an
c
y
an
d
s
ca
lab
ilit
y
.
C
o
lo
r
d
if
f
er
en
tia
tio
n
an
d
s
p
r
in
g
lay
o
u
t
alg
o
r
ith
m
s
wer
e
u
s
ed
f
o
r
v
is
u
aliza
tio
n
as th
ey
ar
e
s
im
p
le
to
ev
alu
ate
asp
ec
ts
lik
e
s
tr
u
ctu
r
e
an
d
r
o
b
u
s
tn
ess
[
4
]
.
T
h
e
id
ea
f
o
r
th
e
ad
ap
tiv
e
s
am
p
lin
g
u
s
in
g
L
u
ca
s
s
eq
u
en
cin
g
ca
m
e
u
p
af
ter
we
r
ea
lize
d
th
at
th
e
m
ath
em
atica
l
p
r
o
p
e
r
ties
co
u
ld
h
elp
u
s
o
p
tim
ize
s
am
p
lin
g
in
ter
v
als.
GNN
e
q
u
al
clu
s
ter
in
g
attem
p
t
s
to
d
iv
id
e
th
e
n
o
d
es
s
u
ch
th
at
th
eir
s
izes
ar
e
e
q
u
al.
W
h
en
tr
ain
in
g
,
th
e
co
n
s
tr
ain
ts
o
r
r
eg
u
lar
izatio
n
s
ar
e
m
ad
e
s
tr
ict
or
h
ar
d
c
o
r
e
to
en
s
u
r
e
th
at
th
ey
lear
n
to
b
alan
ce
th
e
ass
ig
n
m
en
ts
ev
en
if
th
e
y
ar
e
d
ea
lin
g
with
lo
ca
l
d
en
s
ities
th
at
ar
e
not
u
n
if
o
r
m
or
eq
u
al
[
5
]
.
T
h
is
is
ess
en
tial
f
o
r
lo
a
d
b
alan
cin
g
in
d
is
tr
ib
u
ted
s
y
s
te
m
s
o
r
co
m
m
u
n
ity
d
etec
tio
n
in
s
o
cial
n
etwo
r
k
s
.
T
h
e
m
ain
id
ea
is
to
k
ee
p
th
e
ca
r
d
in
ality
o
f
th
e
clu
s
ter
s
h
o
m
o
g
en
e
o
u
s
so
th
at
no
one
clu
s
ter
tak
es
up
all
th
e
n
o
d
es
[
6
]
.
Fig
u
r
e
1
s
h
o
w
s
GNN
e
q
u
al
f
ix
ed
-
s
ize
clu
s
ter
i
n
g
on
a
g
r
a
p
h
wh
e
r
e
each
cl
u
s
ter
h
ad
a
tar
g
et
of
100
n
o
d
es
each
.
Fig
u
r
e
1
.
GNN
eq
u
al
clu
s
ter
in
g
:
t
h
e
ev
en
s
p
lit ca
n
b
e
o
b
s
er
v
ed
On
th
e
lef
t
is
th
e
f
ea
tu
r
e
s
p
ac
e,
wh
ich
h
as
f
iv
e
clu
s
ter
s
with
1
0
0
n
o
d
es
ea
ch
,
s
o
th
at
th
ey
ar
e
p
er
f
ec
tly
b
alan
ce
d
.
T
h
e
ce
n
te
r
s
o
f
ea
ch
cl
u
s
ter
,
i.e
,
th
e
ce
n
tr
o
id
s
o
f
ea
ch
clu
s
ter
,
a
r
e
m
a
r
k
ed
with
b
lack
X
,
an
d
th
e
clu
s
ter
h
ea
d
o
f
ea
ch
o
f
th
e
clu
s
ter
is
cir
cled
with
r
ed
.
As
s
ee
n
,
th
e
clu
s
ter
s
ar
e
well
s
ep
ar
ated
with
v
er
y
litt
le
o
v
er
lap
.
T
h
is
r
ev
ea
l
ed
th
at
th
e
p
ar
titi
o
n
w
o
r
k
ed
b
etter
th
an
we
ex
p
ec
ted
it
to
w
o
r
k
.
On
t
h
e
r
ig
h
t
is
th
e
o
r
ig
in
al
g
r
a
p
h
f
o
r
th
e
k
-
n
ea
r
est
n
eig
h
b
o
r
(
k
NN
)
alg
o
r
ith
m
an
d
th
e
i
n
ter
co
n
n
ec
ted
n
e
two
r
k
.
As
s
ee
n
,
th
e
clu
s
ter
b
o
u
n
d
ar
ies
ar
e
p
r
eser
v
ed
wh
ile
en
h
a
n
cin
g
c
o
n
n
ec
tiv
ity
[
7
]
.
T
h
is
v
is
u
aliza
tio
n
s
h
o
ws
th
at
th
e
GNN
-
b
ased
alg
o
r
ith
m
s
p
er
f
ec
tly
a
ch
iev
e
s
ize
b
alan
ce
w
h
ile
e
f
f
ec
tiv
ely
o
p
tim
izin
g
th
e
n
et
wo
r
k
to
p
o
lo
g
y
b
y
s
im
u
ltan
eo
u
s
ly
co
n
s
id
er
in
g
th
e
lo
ca
l c
lu
s
ter
in
g
o
b
jectiv
es a
n
d
g
lo
b
al
co
n
n
ec
tiv
ity
p
atter
n
s
.
GNN
u
n
eq
u
al
clu
s
ter
in
g
is
th
e
ex
ac
t
o
p
p
o
s
ite
o
f
GNN
e
q
u
al,
in
th
e
s
en
s
e
th
at
t
h
er
e
is
n
o
co
n
s
tr
ain
t
o
n
th
e
d
is
tr
ib
u
tio
n
o
f
th
e
n
o
d
es.
T
h
e
clu
s
ter
s
will
b
e
o
f
v
a
r
y
in
g
s
izes
an
d
s
h
ap
es,
as
th
e
alg
o
r
ith
m
is
s
im
p
ly
f
o
llo
win
g
th
e
lead
o
f
th
e
g
r
ap
h
.
T
h
is
allo
ws
u
s
to
id
en
tify
c
lu
s
ter
s
o
f
all
s
izes
an
d
s
h
ap
es,
s
m
all
an
d
tig
h
t,
to
lar
g
e
an
d
lo
o
s
e,
with
in
th
e
s
a
m
e
g
r
ap
h
[
8
]
.
L
o
o
k
at
th
e
lef
t
p
an
el
o
f
Fig
u
r
e
2
,
we
h
av
e
f
iv
e
clu
s
ter
s
,
with
s
izes
r
an
g
in
g
f
r
o
m
5
8
to
2
7
6
.
T
h
e
g
eo
g
r
a
p
h
ical
lay
o
u
t
i
s
b
ased
o
n
ac
t
u
al
d
ata
d
e
n
s
ity
,
n
o
t
o
n
t
h
e
s
ize
co
n
s
tr
ain
ts
.
T
h
e
r
ig
h
t
p
an
els
illu
s
tr
ate
th
e
h
id
d
en
co
n
n
ec
tiv
ity
b
en
ea
th
th
e
s
u
r
f
ac
e.
T
h
e
l
ar
g
e
clu
s
ter
is
v
er
y
tig
h
tly
co
n
n
ec
ted
in
t
er
n
ally
,
a
n
d
th
e
s
m
aller
o
n
es
ar
e
v
er
y
tig
h
tly
co
n
n
ec
ted
,
with
ca
r
e
f
u
l
b
r
id
g
es
b
etwe
en
th
em
.
T
h
is
s
o
lv
ed
o
u
r
co
n
ce
r
n
ab
o
u
t
wh
et
h
er
GNN
clu
s
ter
in
g
with
n
o
b
alan
cin
g
ter
m
s
co
u
ld
id
en
tify
h
id
d
en
co
m
m
u
n
ity
s
tr
u
ctu
r
es [
9
]
.
I
n
L
u
ca
s
m
esh
clu
s
ter
in
g
b
u
ild
s
to
p
o
lo
g
y
f
r
o
m
th
e
L
u
ca
s
n
u
m
b
er
s
eq
u
e
n
ce
d
e
f
in
e
d
b
y
th
e
r
ec
u
r
r
en
ce
r
elatio
n
,
as
th
e
s
eq
u
en
ce
d
ictates
ev
er
y
th
i
n
g
,
lik
e
th
e
n
u
m
b
er
o
f
clu
s
ter
s
to
a
lay
er
,
th
e
n
u
m
b
e
r
o
f
n
o
d
es
o
n
ea
ch
co
n
ce
n
tr
ic
r
in
g
,
etc.
T
h
e
r
elatio
n
s
h
ip
s
ar
e
d
is
p
er
s
ed
ar
o
u
n
d
a
ce
n
tr
al
n
o
d
e
lik
e
a
wh
ee
l
[
1
0
]
.
W
e
s
elec
ted
th
i
s
m
o
d
el
s
in
ce
f
au
lt
to
ler
an
ce
an
aly
s
is
is
ea
s
ier
d
u
e
to
th
e
d
eter
m
in
is
tic
p
ath
len
g
th
s
.
T
h
e
m
u
lti
-
lay
er
h
ier
ar
c
h
ical
m
o
d
e
l
is
illu
s
tr
ated
in
Fig
u
r
e
3
.
T
h
e
r
ed
n
o
d
es
in
d
icate
th
e
c
lu
s
ter
h
ea
d
s
o
r
th
e
cr
itical
h
u
b
s
.
T
h
e
r
ig
h
t
-
h
an
d
f
ig
u
r
es
d
ep
ict
th
e
en
tire
n
etwo
r
k
,
th
e
c
o
n
s
o
lid
ated
f
o
r
m
,
w
ith
r
ed
u
n
d
an
t
p
ath
s
all
th
r
o
u
g
h
,
wh
ich
will b
e
h
an
d
y
in
ca
s
e
o
f
n
o
d
e
f
ailu
r
e
[
1
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Desig
n
a
Ga
u
s
s
ia
n
mixtu
r
e
-
b
a
s
ed
clu
s
teri
n
g
mo
d
el
fo
r
en
h
a
n
cin
g
a
cc
u
r
a
cy
…
(
K
a
n
a
k
a
R
a
ju
R
a
ja
n
a
)
1049
Fig
u
r
e
2
.
GNN
u
n
eq
u
al
clu
s
te
r
in
g
:
t
h
e
s
p
lit n
atu
r
all
y
v
ar
ies
Fig
u
r
e
3
.
L
u
ca
s
-
b
ased
u
n
eq
u
al
clu
s
ter
in
g
: th
e
s
p
lit is
o
r
g
an
iz
ed
in
lay
er
s
2.
L
I
T
E
R
AT
U
RE
SU
RVE
Y
I
n
th
e
ev
o
lu
tio
n
o
f
n
ew
tech
n
o
lo
g
ies,
c
o
m
m
u
n
icatio
n
n
et
wo
r
k
s
ar
e
co
n
s
tan
tly
ch
an
g
in
g
f
o
r
b
etter
ef
f
icien
cy
,
s
ca
lab
ilit
y
,
an
d
r
esil
ien
cy
,
wh
ich
ar
e
th
e
r
ec
u
r
r
in
g
p
atter
n
s
o
f
g
r
ap
h
th
e
o
r
y
.
I
n
th
e
p
ap
er
b
y
R
ajan
a
an
d
Am
ir
ip
alli
[
1
]
,
th
e
a
u
th
o
r
s
u
s
ed
th
e
L
u
ca
s
n
u
m
er
ical
s
eq
u
en
ce
an
d
tr
im
et
g
r
ap
h
o
p
tim
izatio
n
f
o
r
I
o
T
n
etwo
r
k
r
esil
ien
cy
f
o
r
s
m
ar
t
h
o
m
e
I
o
T
n
etwo
r
k
s
.
T
h
eir
m
esh
n
etwo
r
k
,
b
ased
o
n
th
e
L
u
ca
s
n
u
m
er
ica
l
s
eq
u
en
ce
,
p
e
r
f
o
r
m
ed
b
ett
er
wi
th
r
an
d
o
m
n
o
d
e
f
ailu
r
es.
I
n
a
n
o
th
er
p
a
p
er
,
C
h
en
a
n
d
Z
h
an
g
[
2
]
in
v
esti
g
ated
th
e
m
ath
em
atica
l
f
o
u
n
d
atio
n
s
o
f
clu
s
ter
in
g
th
eo
r
y
,
s
p
ec
if
ically
GM
M,
m
in
im
ax
lo
wer
b
o
u
n
d
s
,
an
d
alg
o
r
ith
m
s
.
W
e
ex
ten
d
ed
o
u
r
wo
r
k
b
ased
o
n
s
o
m
e
o
f
th
e
c
o
n
ce
p
ts
p
r
e
s
en
ted
.
Ho
wev
er
,
th
e
h
o
m
o
g
e
n
eo
u
s
p
r
o
p
er
ties
o
f
co
v
ar
ian
ce
ar
e
n
o
t
v
alid
f
o
r
r
a
n
d
o
m
n
o
d
e
f
ailu
r
es,
wh
ich
m
ig
h
t
lim
it
th
e
d
ir
ec
t
ap
p
licatio
n
f
o
r
I
o
T
n
etwo
r
k
s
with
d
is
r
u
p
ted
clu
s
ter
s
.
I
n
o
u
r
s
tu
d
y
,
th
is
was
r
ef
lecte
d
in
th
e
lo
w
f
au
lt
to
ler
an
ce
o
f
GNN
u
n
eq
u
al:
less
th
an
0
.
3
5
an
d
o
n
ly
u
p
to
2
0
iter
atio
n
s
.
So
n
g
a
n
d
Z
h
an
g
’
s
[
4
]
in
t
r
o
d
u
ce
d
wh
ee
l
an
d
s
tar
ar
ch
itectu
r
es
co
m
b
in
in
g
wav
ele
n
g
th
d
iv
is
io
n
m
u
ltip
lex
in
g
a
n
d
wir
eless
p
r
o
tectio
n
.
T
h
e
u
s
e
o
f
r
i
n
g
to
p
o
l
o
g
y
f
o
r
in
ter
c
o
n
n
ec
tio
n
s
,
alo
n
g
with
a
s
tar
to
p
o
lo
g
y
f
o
r
co
n
n
ec
tiv
ity
,
e
n
s
u
r
ed
h
ig
h
r
eliab
ilit
y
,
m
in
i
m
u
m
laten
cy
,
s
ca
lab
ilit
y
,
an
d
AI
-
ass
is
ted
f
au
lt
r
ec
o
v
er
y
.
T
s
its
u
lin
et
a
l.
[
8
]
to
o
k
u
n
s
u
p
e
r
v
is
ed
g
r
ap
h
n
eu
r
al
n
etwo
r
k
p
o
o
lin
g
to
th
e
n
ex
t
lev
el
u
s
in
g
m
o
d
u
lar
ity
o
p
tim
izatio
n
.
T
h
e
ir
DM
o
N
m
o
d
u
le
was
ef
f
ec
tiv
e
o
n
clu
s
ter
s
o
f
eq
u
al
s
i
ze
.
T
h
eir
s
tu
d
y
als
o
s
h
o
wed
th
e
lim
itatio
n
s
o
f
GNN
clu
s
ter
in
g
o
n
clu
s
ter
s
o
f
u
n
eq
u
al
s
ize:
th
e
im
p
o
r
tan
ce
o
f
t
h
e
r
o
b
u
s
tn
ess
o
f
th
e
alg
o
r
ith
m
was
m
o
r
e
s
ig
n
if
ican
t
th
an
p
r
ev
io
u
s
ly
ass
u
m
ed
.
Kir
m
an
i
et
a
l.
[
1
2
]
p
r
o
v
i
d
ed
an
ex
h
au
s
tiv
e
o
v
er
v
iew
o
f
I
o
T
-
b
ased
s
m
ar
t
g
r
id
s
y
s
tem
s
.
T
h
eir
w
o
r
k
in
cl
u
d
ed
th
r
ee
-
tier
e
d
a
r
ch
itectu
r
e,
clo
u
d
ar
c
h
itectu
r
e,
co
m
m
u
n
icatio
n
s
y
s
tem
s
,
an
d
s
ec
u
r
ity
s
y
s
tem
s
u
tili
zin
g
b
lo
ck
ch
ain
an
d
AI
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
0
4
7
-
1
0
5
7
1050
T
h
e
au
th
o
r
s
Kar
ak
o
c
an
d
Ko
n
ar
[
1
3
]
u
s
ed
c
o
m
p
lex
n
etwo
r
k
th
e
o
r
y
f
o
r
g
lo
b
al
tr
ad
e
n
et
wo
r
k
s
with
s
tar
t
o
p
o
lo
g
y
,
s
ca
le
-
f
r
ee
to
p
o
lo
g
y
,
an
d
r
in
g
to
p
o
lo
g
y
.
T
h
ey
f
o
u
n
d
co
r
e
-
p
er
ip
h
er
y
s
tr
u
ctu
r
es
an
d
lattice
s
tr
u
ctu
r
es
f
r
o
m
th
e
tr
ad
eo
f
f
b
etwe
en
ef
f
icien
cy
an
d
r
esil
ien
ce
.
T
h
eir
wo
r
k
is
in
s
ig
h
tf
u
l,
b
u
t
tr
ad
e
n
etwo
r
k
s
b
eh
av
e
d
if
f
e
r
en
tly
f
r
o
m
I
o
T
n
etwo
r
k
s
.
Nelso
n
et
a
l.
[1
4
]
p
r
o
v
ed
th
e
ap
p
licab
ilit
y
o
f
th
e
m
esh
to
p
o
lo
g
y
with
lo
w
-
p
o
wer
Z
i
g
b
ee
n
etwo
r
k
s
f
o
r
e
n
v
ir
o
n
m
en
tal
m
o
n
ito
r
i
n
g
.
“Self
-
h
ea
lin
g
,
co
s
t
-
ef
f
ec
tiv
e
,
an
d
r
eliab
le
d
ata
ac
q
u
is
itio
n
.
”
Ho
wev
er
,
th
e
n
etwo
r
k
s
ize
was
lim
ited
to
f
e
wer
th
an
5
0
n
o
d
es.
Nu
r
lan
e
t
a
l.
[1
5
]
cr
itically
an
aly
ze
d
th
e
in
ter
f
ac
es
f
o
r
W
SN
an
d
W
MN
s
in
ter
m
s
o
f
p
er
f
o
r
m
a
n
ce
,
p
r
o
t
o
co
ls
,
an
d
s
ec
u
r
ity
an
d
p
r
iv
ac
y
.
AI
an
d
ML
p
lay
an
im
p
o
r
ta
n
t
r
o
le
in
th
is
ar
ea
.
H
o
wev
e
r
,
th
er
e
was
n
o
q
u
an
tific
atio
n
o
f
th
e
r
esil
ien
cy
.
Om
p
al
et
a
l.
[1
6
]
p
r
o
v
id
e
d
a
n
o
v
e
r
v
iew
o
f
th
e
in
teg
r
atio
n
o
f
s
tar
to
p
o
lo
g
y
,
m
esh
to
p
o
lo
g
y
,
an
d
cl
u
s
ter
tr
ee
to
p
o
lo
g
y
with
FP
GA
an
d
I
E
E
E
8
0
2
.
1
5
.
4
.
T
h
eir
f
o
c
u
s
o
n
in
ter
n
o
d
e
co
m
m
u
n
icatio
n
,
en
er
g
y
ef
f
icien
c
y
,
an
d
AI
-
b
ased
o
p
tim
izatio
n
p
o
in
te
d
f
o
r
wa
r
d
.
Ho
wev
er
,
th
e
y
d
i
d
n
o
t
co
n
s
id
er
n
o
d
e
f
ailu
r
es.
W
h
at
is
m
is
s
in
g
ac
r
o
s
s
m
o
s
t
o
f
th
ese
r
ef
er
en
ce
s
is
an
h
o
n
est
d
is
cu
s
s
io
n
o
f
wh
at
f
ail
ed
o
r
u
n
d
er
p
e
r
f
o
r
m
ed
.
W
e
tr
ied
to
ad
d
r
ess
th
at
in
o
u
r
wo
r
k
.
3.
P
RO
P
O
SE
D
M
O
D
E
L
GM
M
e
q
u
al
an
d
GM
M
u
n
eq
u
al
clu
s
ter
in
g
s
tr
ateg
ies
p
r
o
p
o
s
e
a
d
if
f
er
en
t
a
p
p
r
o
ac
h
in
cl
u
s
ter
in
g
th
e
clu
s
ter
s
izes w
ith
u
n
if
o
r
m
ac
r
o
s
s
n
etwo
r
k
s
in
th
e
e
q
u
al
ca
s
e
an
d
v
a
r
iab
le
in
th
e
u
n
eq
u
al
ca
s
e
.
3
.
1
.
G
M
M
e
qu
a
l
GM
M
e
q
u
al
c
lu
s
ter
in
g
f
o
r
ce
s
ea
ch
Ga
u
s
s
ian
co
m
p
o
n
en
t
to
s
h
ar
e
a
n
id
e
n
tical
co
v
a
r
ian
ce
s
tr
u
ctu
r
e
an
d
p
u
s
h
es
b
alan
ce
d
m
em
b
er
s
h
ip
d
is
tr
ib
u
tio
n
Fig
u
r
e
3
.
E
ac
h
clu
s
ter
b
ec
o
m
es
s
p
h
e
r
ical
o
r
id
en
tically
o
r
ien
ted
ellip
s
o
id
al.
T
h
is
w
o
r
k
s
wh
en
y
o
u
ass
u
m
e
th
at
th
e
g
r
o
u
p
s
h
av
e
a
s
im
ilar
d
en
s
ity
an
d
s
p
ac
e.
W
e
h
av
e
test
ed
it
with
s
y
n
th
etic
d
ata
f
o
r
th
r
ee
co
m
p
o
n
e
n
ts
with
a
s
p
h
er
ical
co
v
ar
ian
ce
an
d
with
th
r
ee
well
-
s
ep
ar
ated
eq
u
al
-
s
ize
clu
s
ter
s
[
1
2
]
.
T
h
e
r
esu
lt
ca
m
e
o
u
t
with
a
u
n
if
o
r
m
s
h
ap
e
an
d
with
a
s
im
ilar
d
i
s
tr
ib
u
tio
n
o
f
p
o
in
ts
.
Ass
u
m
in
g
th
at
all
th
e
co
m
p
o
n
en
ts
h
av
e
eq
u
al
weig
h
ts
wh
i
le
in
itializin
g
p
r
esu
p
p
o
s
es
th
a
t
th
e
g
r
o
u
p
s
h
av
e
a
b
alan
ce
d
co
m
p
o
s
itio
n
,
w
h
ich
p
r
ev
e
n
ts
a
d
o
m
in
a
n
t
c
lu
s
ter
f
r
o
m
tak
in
g
o
v
er
th
e
as
s
ig
n
m
en
ts
[1
7
]
.
T
o
b
e
h
o
n
est,
th
is
wo
r
k
s
b
est
wh
e
n
y
o
u
s
p
ec
if
ically
wan
t
h
o
m
o
g
e
n
eity
b
etwe
en
clu
s
ter
s
[
1
3
]
.
W
e
h
av
e
co
n
d
u
cte
d
ex
ten
s
iv
e
an
aly
s
is
with
a
n
etwo
r
k
d
ataset,
wh
ic
h
h
as
f
o
u
r
clu
s
ter
s
,
with
ex
ac
tly
1
0
0
n
o
d
es
in
ea
ch
.
T
h
e
lef
t
p
an
el
in
Fig
u
r
e
4
s
h
o
ws
th
e
2
D
f
ea
tu
r
e
s
p
ac
e,
with
y
ello
w,
g
r
ee
n
,
p
u
r
p
le,
an
d
b
lu
e
clu
s
t
er
s
,
with
b
lack
X’
s
f
o
r
th
e
ce
n
tr
o
id
s
,
an
d
r
e
d
f
o
r
t
h
e
clu
s
ter
h
ea
d
s
[1
4
]
.
So
m
e
p
r
o
b
ab
ilis
tic
o
v
er
lap
,
wh
ich
we
wan
ted
,
is
s
h
o
wn
with
th
e
u
s
e
o
f
a
GM
M.
T
h
e
r
ig
h
t p
an
els s
h
o
w
th
e
en
tire
n
etwo
r
k
an
d
th
e
u
n
i
f
ied
v
er
s
io
n
with
in
ter
co
n
n
ec
ted
n
etwo
r
k
s
.
Fig
u
r
e
5
illu
s
tr
ates
th
e
f
lo
wch
ar
t,
an
d
T
a
b
les 1
an
d
2
s
h
o
w
th
e
n
o
tatio
n
tab
le
f
o
r
GM
M
.
Fig
u
r
e
4
.
Pro
p
o
s
ed
m
o
d
el
o
f
GM
M
e
q
u
al
v
is
u
aliza
tio
n
:
c
lu
s
ter
in
g
3
.
2
.
G
M
M
un
equa
l
T
h
is
f
lex
ib
ilit
y
is
p
ar
ticu
lar
l
y
u
s
ef
u
l
f
o
r
h
eter
o
g
en
e
o
u
s
d
ata
wh
er
e
th
e
clu
s
ter
s
v
ar
y
i
n
ter
m
s
o
f
s
p
r
ea
d
an
d
d
e
n
s
ity
[
1
5
]
.
As
s
h
o
wn
in
o
u
r
ex
p
er
im
e
n
ts
,
th
is
f
lex
ib
ilit
y
led
to
o
n
e
o
f
th
e
clu
s
ter
s
co
n
tain
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Desig
n
a
Ga
u
s
s
ia
n
mixtu
r
e
-
b
a
s
ed
clu
s
teri
n
g
mo
d
el
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r
en
h
a
n
cin
g
a
cc
u
r
a
cy
…
(
K
a
n
a
k
a
R
a
ju
R
a
ja
n
a
)
1051
m
o
r
e
th
a
n
3
0
.
Fig
u
r
e
6
:
u
n
e
x
p
ec
ted
d
en
s
ity
co
n
ce
n
tr
atio
n
o
f
C
lu
s
ter
1
an
d
s
u
b
s
eq
u
e
n
t
r
ap
id
in
cr
ea
s
e
in
b
etwe
en
n
ess
ce
n
tr
ality
.
L
ef
t:
2
D
f
ea
tu
r
e
s
p
ac
e
s
h
o
win
g
th
e
d
is
tr
ib
u
tio
n
o
f
t
h
e
f
o
u
r
clu
s
ter
s
with
v
ar
y
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g
s
izes.
C
lu
s
ter
in
g
r
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lts
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C
lu
s
t
er
0
:
5
2
n
o
d
es
(
b
lu
e)
.
C
lu
s
ter
1
:
1
6
6
n
o
d
es
(
teal)
.
C
lu
s
ter
2
:
9
0
n
o
d
es
(
y
ello
w)
.
C
lu
s
ter
s
3
an
d
4
:
1
1
5
an
d
7
7
n
o
d
es
(
g
r
ee
n
a
n
d
p
u
r
p
le)
.
R
ig
h
t:
c
o
m
p
lete
n
etwo
r
k
a
n
d
c
o
m
b
in
ed
v
iew.
T
h
e
u
n
eq
u
al
clu
s
ter
in
g
r
esu
lted
f
r
o
m
th
e
h
eter
o
g
e
n
eo
u
s
d
ata
an
d
is
ex
p
ec
ted
to
b
e
n
atu
r
al
[
1
6
]
.
T
h
is
im
b
alan
ce
p
r
o
v
es
t
h
e
ef
f
ec
tiv
en
ess
o
f
GM
M
in
d
ea
lin
g
with
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
wh
e
r
e
n
atu
r
al
g
r
o
u
p
in
g
s
ar
e
n
o
t
alwa
y
s
b
alan
ce
d
.
As
s
h
o
wn
b
y
th
e
d
is
tin
ct
b
o
u
n
d
ar
ies
o
f
th
e
clu
s
ter
s
with
p
r
o
m
in
e
n
t
ce
n
t
r
o
id
s
an
d
h
ea
d
s
o
f
th
e
clu
s
ter
s
,
th
e
alg
o
r
ith
m
was
s
u
cc
ess
f
u
l
in
d
is
co
v
e
r
in
g
s
tr
u
ctu
r
al
p
atter
n
s
with
in
th
e
d
ata
s
et.
T
h
e
p
an
els
o
n
th
e
r
ig
h
t
p
o
r
tio
n
o
f
t
h
e
g
r
ap
h
s
h
o
w
ad
d
itio
n
al
in
f
o
r
m
atio
n
r
eg
ar
d
in
g
t
h
e
s
tr
u
ctu
r
e
o
f
t
h
e
n
etwo
r
k
,
wh
ich
ca
n
b
e
u
s
ed
to
f
u
r
th
er
u
n
d
er
s
tan
d
t
h
e
d
ata
s
et
p
r
esen
ted
[
1
8
]
.
T
h
e
“Fu
ll
Netwo
r
k
Stru
ctu
r
e”
o
f
Fig
u
r
e
6
s
h
o
ws
th
e
co
m
p
lex
i
n
ter
co
n
n
ec
ted
n
ess
o
f
th
e
d
ata
s
et,
with
th
e
lar
g
est
clu
s
ter
(
C
lu
s
ter
1
)
s
h
o
win
g
d
en
s
e
co
n
n
ec
tiv
ity
with
in
th
e
g
r
o
u
p
wh
ile
estab
li
s
h
in
g
s
tr
ateg
ic
co
n
n
ec
tio
n
s
with
o
th
er
clu
s
ter
s
[
1
9
]
.
T
h
e
s
in
g
le
in
ter
co
n
n
ec
ted
n
etwo
r
k
(
Un
if
ied
View)
”
s
h
o
ws
th
e
g
l
o
b
al
s
tr
u
ct
u
r
e
o
f
th
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titi
o
n
in
g
s
tr
ateg
y
ass
ig
n
s
ex
ac
tly
[
n
_
s
am
p
les/
n
_
clu
s
ter
s
]
n
o
d
es
to
ea
ch
clu
s
ter
b
y
iter
ativ
ely
s
elec
tin
g
th
e
clo
s
est
u
n
ass
ig
n
ed
n
o
d
es,
th
er
e
b
y
en
s
u
r
i
n
g
a
u
n
if
o
r
m
en
e
r
g
y
lo
a
d
d
is
tr
ib
u
tio
n
ac
r
o
s
s
th
e
n
etwo
r
k
.
W
ith
in
ea
ch
clu
s
ter
,
th
e
ce
n
tr
o
id
is
r
ec
o
m
p
u
ted
as
th
e
m
ea
n
p
o
s
iti
o
n
o
f
ass
ig
n
ed
n
o
d
es,
an
d
th
e
n
o
d
e
ly
in
g
clo
s
est
to
th
is
ce
n
tr
o
id
is
elec
ted
as
th
e
clu
s
ter
h
ea
d
(
C
H)
,
d
esig
n
ated
to
p
er
f
o
r
m
l
o
c
al
d
ata
ag
g
r
eg
atio
n
an
d
in
te
r
-
clu
s
ter
f
o
r
war
d
in
g
.
A
k
NN
g
r
ap
h
G
is
s
u
b
s
eq
u
en
t
ly
co
n
s
tr
u
cted
o
v
e
r
all
n
o
d
es
to
estab
lis
h
lo
ca
l
c
o
m
m
u
n
icatio
n
lin
k
s
r
e
f
lectin
g
p
h
y
s
ical
p
r
o
x
im
ity
,
u
p
o
n
wh
i
ch
a
f
u
ll
m
esh
o
v
er
lay
.
G
combined
is
f
o
r
m
ed
b
y
in
ter
c
o
n
n
ec
tin
g
all
C
Hs,
en
ab
lin
g
d
ir
ec
t
s
in
g
le
-
h
o
p
c
o
m
m
u
n
icatio
n
b
etwe
en
an
y
two
cl
u
s
ter
s
an
d
s
ig
n
if
ican
tly
r
e
d
u
cin
g
r
o
u
tin
g
o
v
e
r
h
ea
d
.
T
o
f
u
r
th
er
en
h
a
n
ce
n
etwo
r
k
r
esil
ien
ce
,
s
to
ch
asti
c
in
ter
-
cl
u
s
ter
b
r
id
g
e
e
d
g
es
ar
e
in
tr
o
d
u
ce
d
b
y
r
an
d
o
m
l
y
s
elec
tin
g
n
o
d
e
p
air
s
f
r
o
m
n
eig
h
b
o
r
in
g
clu
s
ter
s
an
d
co
n
n
ec
tin
g
th
e
m
,
y
ield
in
g
t
h
e
f
in
al
u
n
if
ied
g
r
ap
h
G
unified
,
wh
o
s
e
to
p
o
lo
g
y
is
th
en
v
is
u
alize
d
to
v
alid
ate
clu
s
ter
f
o
r
m
ati
o
n
,
lo
c
al
co
n
n
ec
tiv
ity
,
a
n
d
i
n
ter
-
clu
s
ter
m
esh
s
tr
u
ctu
r
e,
m
ak
in
g
th
e
o
v
er
all
f
r
am
ewo
r
k
well
-
s
u
ited
f
o
r
en
e
r
g
y
-
co
n
s
tr
ain
ed
W
SN a
n
d
I
o
T
n
etwo
r
k
d
esig
n
.
Alg
o
r
ith
m
1
.
GM
M
eq
u
al
Input: n_samples, n_clusters, k
Output:
Combined network with cluster
head connections of a Mesh
Step 1: Start
Step 2: Generate X = {
1
, ...,
} in
2
Step 3: Fit GMM with n_clusters to X → initial_centroids
Step 4: For each x_i:
Compute distances to all centroids
Step 5: For each cluster j:
Assign n_samples/
n_clusters closest unassigned points to cluster j
Step 6: For each cluster j:
centroid_j = mean
(points in cluster j)
cluster_head_j = argmin_x ||x
-
centroid_j||
Step 7: Build k
-
NN graph G from X
Step 8: G_combined = G + edges between all cluste
r heads
Step 9: For each cluster pair (i, j):
Randomly select nodes from i and j
Add inter
-
cluster edges in G_unified
Step 10:
Visualize clusters, G, and G_unified
Step 11:
Stop
T
h
e
A
lg
o
r
ith
m
2
GM
M
u
n
eq
u
al
b
eg
in
s
with
th
e
r
an
d
o
m
d
ep
lo
y
m
en
t
o
f
n
_
s
am
p
les
s
en
s
o
r
n
o
d
es
in
a
two
-
d
im
en
s
io
n
al
r
eg
io
n
.
Su
b
s
eq
u
en
tly
,
a
GM
M
was
f
itted
to
th
e
n
o
d
e
co
o
r
d
in
ates,
g
en
er
atin
g
p
r
o
b
a
b
ilis
tically
in
f
o
r
m
ed
in
it
ial
ce
n
tr
o
id
p
o
s
itio
n
s
th
at
m
o
r
e
ac
cu
r
ately
r
ef
lect
th
e
s
p
atial
d
is
tr
ib
u
tio
n
o
f
t
h
e
n
o
d
es th
an
tr
a
d
itio
n
al
s
ee
d
in
g
m
eth
o
d
s
.
At
th
is
p
o
i
n
t,
a
n
in
iti
al
clu
s
ter
lab
el
is
ass
ig
n
ed
to
ea
ch
n
o
d
e
b
ased
o
n
th
e
o
u
tp
u
t
o
f
th
e
GM
M,
an
d
th
e
n
u
m
b
er
o
f
n
o
d
es
p
er
clu
s
ter
is
r
ec
o
r
d
ed
to
q
u
an
tif
y
th
e
in
itial
d
is
tr
ib
u
tio
n
b
ef
o
r
e
r
eb
alan
ci
n
g
.
T
h
en
a
b
a
lan
ce
d
p
a
r
titi
o
n
in
g
s
tep
is
p
er
f
o
r
m
ed
in
w
h
ich
ea
c
h
clu
s
ter
is
ass
ig
n
ed
ex
ac
tly
[
n
_
s
am
p
les/
n
_
clu
s
ter
s
]
n
o
d
es
b
y
iter
ativ
ely
s
elec
tin
g
th
e
clo
s
est
u
n
ass
ig
n
ed
n
o
d
es.
T
h
is
en
s
u
r
es
u
n
if
o
r
m
clu
s
ter
s
izes
an
d
s
im
ilar
en
er
g
y
lo
a
d
d
is
tr
ib
u
tio
n
o
v
e
r
th
e
n
etwo
r
k
.
CH
j
=
ar
g
m
in
x
∥
x
−c
en
tr
o
i
d
j
∥
.
T
h
e
ce
n
tr
o
id
is
th
en
r
ec
alcu
lated
a
s
th
e
m
ea
n
p
o
s
itio
n
o
f
all
ass
ig
n
ed
n
o
d
es,
a
n
d
th
e
n
o
d
e
cl
o
s
est
to
th
e
r
ef
in
e
d
ce
n
tr
o
id
is
elec
ted
as
th
e
C
H.
T
h
e
C
H
i
s
r
esp
o
n
s
ib
le
f
o
r
lo
ca
l
d
ata
ag
g
r
eg
atio
n
an
d
in
ter
-
cl
u
s
ter
f
o
r
war
d
in
g
.
A
k
NN
g
r
ap
h
G
,
is
th
en
c
o
n
s
tr
u
cted
o
v
er
all
n
o
d
es
to
m
o
d
el
lo
ca
l
co
m
m
u
n
icatio
n
lin
k
s
,
an
d
a
f
u
ll
m
es
h
o
v
er
lay
G
combined
is
f
o
r
m
ed
b
y
in
ter
co
n
n
ec
tin
g
all
C
Hs
f
o
r
d
ir
ec
t
s
in
g
le
-
h
o
p
in
ter
-
clu
s
t
er
co
m
m
u
n
icatio
n
.
T
o
f
u
r
th
er
im
p
r
o
v
e
n
etwo
r
k
r
e
s
ilien
ce
,
we
in
tr
o
d
u
ce
all
p
o
s
s
ib
le
ed
g
es
b
etwe
en
r
an
d
o
m
ly
c
h
o
s
en
n
o
d
e
s
u
b
s
ets
f
r
o
m
ea
ch
p
air
o
f
n
ei
g
h
b
o
r
in
g
clu
s
ter
s
an
d
s
to
r
e
th
ese
n
ewly
ad
d
ed
in
ter
-
clu
s
ter
ed
g
es
ex
p
licitly
in
n
ewly
_
ad
d
e
d
_
in
ter
_
clu
s
ter
_
ed
g
es
f
o
r
tr
ac
ea
b
ilit
y
,
y
ield
in
g
th
e
f
in
al
u
n
if
ie
d
g
r
ap
h
G
unified
.
T
h
e
r
esu
ltin
g
to
p
o
lo
g
y
is
th
en
v
is
u
alize
d
with
clu
s
ter
an
n
o
tatio
n
s
,
ce
n
tr
o
id
s
,
an
d
C
H
d
esig
n
atio
n
s
to
en
ab
le
r
ig
o
r
o
u
s
v
alid
atio
n
an
d
p
er
f
o
r
m
a
n
ce
an
aly
s
is
in
W
S
N
an
d
I
o
T
r
esear
ch
co
n
tex
ts
.
Alg
o
r
ith
m
2
.
GM
M
u
n
eq
u
al
Output: Combined
network with cluster head connections of a Mesh
Step 1: Start
Step 2: Generate X = {
1
, ...,
} in
2
Step 3: Fit GMM with n_clusters to X → initial_centroids
Step 4: For each
:
Store in labels;
count nodes in each cluster
Step 5: For
each cluster j:
Assign n_samples/n_clusters closest unassigned points to cluster j
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
0
4
7
-
1
0
5
7
1054
Step 6: For each cluster j:
centroid_j = mean
(points in cluster j)
cluster_head_j = argmin_x ||x
-
centroid_j||
Step 7: Build k
-
NN graph G from X
Step 8: G
c
ombined
= G + edges between all cluster heads
Step 9: For each cluster pair (i, j):
Randomly select nodes from i and j
Add all possible edges between these nodes in G
unified
Store new edges in newly_added _inter_cluster_edges
Step 10:
Visualize:
Clusters with node counts,
centroids, and
cluster heads
Full k
-
NN network structure
Unified network with inter
-
cluster edges
Step 11:
Stop
4.
RE
SU
L
T
AND
DI
SCUS
SS
I
O
N
Netwo
r
k
s
cien
ce
e
v
alu
atio
n
h
as
r
esu
lted
i
n
th
e
cr
ea
tio
n
o
f
to
o
ls
th
at
e
n
ab
le
u
s
to
m
ea
s
u
r
e
th
e
p
er
f
o
r
m
an
ce
o
f
a
n
alg
o
r
ith
m
in
th
r
ee
o
v
e
r
lap
p
in
g
d
i
m
en
s
io
n
s
:
s
tr
u
ctu
r
al
r
o
b
u
s
tn
ess
,
c
o
m
m
u
n
icatio
n
e
f
f
icien
cy
,
a
n
d
r
o
b
u
s
tn
ess
ag
ain
s
t
f
ailu
r
e
[
2
0
]
.
T
h
er
e
ar
e
s
ev
er
al
m
etr
ics
in
ea
ch
c
ateg
o
r
y
/d
im
e
n
s
io
n
.
Stru
ctu
r
al
r
o
b
u
s
tn
ess
d
escr
ib
es
th
e
ex
ten
t
to
wh
ich
th
e
n
etwo
r
k
s
tay
s
co
n
n
ec
ted
d
u
r
in
g
a
d
is
r
u
p
tio
n
[
2
1
]
.
T
h
e
n
u
m
b
er
o
f
c
o
n
n
ec
te
d
co
m
p
o
n
e
n
ts
is
ca
lled
f
r
ag
m
e
n
tatio
n
[
2
2
]
.
T
h
e
d
e
g
r
ee
o
f
r
e
d
u
n
d
an
cy
o
f
p
ath
s
is
m
ea
s
u
r
ed
b
y
th
e
av
e
r
ag
e
d
e
g
r
ee
[
2
3
]
.
C
lu
s
ter
in
g
co
ef
f
icien
t
is
a
m
ea
s
u
r
e
o
f
lo
ca
l
co
h
esio
n
.
Netwo
r
k
d
en
s
ity
is
u
s
ed
to
m
ea
s
u
r
e
g
lo
b
a
l
co
n
n
ec
tiv
ity
.
W
ien
er
in
d
ex
i
s
a
m
ea
s
u
r
e
o
f
ef
f
icien
c
y
in
r
er
o
u
tin
g
o
f
p
ath
s
.
C
o
m
m
u
n
icatio
n
ef
f
icien
cy
s
tu
d
ies
th
e
ef
f
icien
c
y
o
f
in
f
o
r
m
atio
n
tr
a
v
el.
T
h
e
d
en
s
ity
o
f
th
e
n
etwo
r
k
is
n
e
g
ativ
ely
ass
o
ciate
d
with
p
at
h
len
g
th
s
.
B
etwe
en
n
ess
ce
n
tr
ality
id
en
tifie
s
k
ey
in
te
r
m
ed
iar
ies
wh
o
s
e
f
ailu
r
e
p
r
o
p
a
g
ates
r
o
u
tin
g
.
Failu
r
e
r
esil
ien
ce
co
m
b
in
es
r
o
b
u
s
tn
ess
with
ef
f
icien
c
y
to
k
ee
p
f
u
n
ctio
n
i
n
g
i
n
th
e
f
ac
e
o
f
p
r
o
g
r
ess
iv
e
n
o
d
e
f
ailu
r
e
[
2
4
]
.
T
h
e
p
o
s
t
-
f
ailu
r
e
r
elate
d
co
m
p
o
n
e
n
ts
s
h
o
w
th
e
in
ten
s
ity
o
f
f
r
a
g
m
en
tatio
n
.
R
em
ain
in
g
alter
n
ate
p
ath
s
ar
e
m
ea
s
u
r
ed
b
y
s
u
r
v
i
v
al
o
f
th
e
av
er
ag
e
d
e
g
r
ee
an
d
g
r
ap
h
d
e
n
s
ity
.
E
ig
en
v
ec
to
r
ce
n
tr
ality
is
u
s
ed
to
ev
alu
ate
th
e
s
ig
n
if
ican
ce
o
f
s
tr
o
n
g
ly
in
f
l
u
en
tial
n
o
d
es
[
2
5
]
.
All
th
ese
m
etr
ics
ar
e
in
d
icato
r
s
o
f
n
etwo
r
k
s
u
r
v
iv
ab
ilit
y
ac
r
o
s
s
f
ailu
r
e
r
at
es;
th
e
r
o
b
u
s
tn
ess
s
co
r
e
s
h
o
wn
in
Fig
u
r
e
8
r
e
v
ea
led
L
u
ca
s
W
h
ee
l
d
o
m
in
ated
all,
with
s
co
r
es
o
v
er
(
~4
6
)
at
ze
r
o
f
ailu
r
e
b
u
t
d
ec
lin
ed
s
teep
ly
with
in
cr
ea
s
in
g
f
ailu
r
es.
GM
M
e
q
u
al
s
u
s
tain
s
b
etter
r
esil
ien
ce
th
a
n
GM
M
u
n
eq
u
al,
wh
ile
GNN
e
q
u
al
a
n
d
GNN
u
n
eq
u
al
b
e
h
av
e
s
im
ilar
ly
th
r
o
u
g
h
o
u
t
.
B
ey
o
n
d
4
5
%
f
ailu
r
e
,
all
to
p
o
lo
g
ies
co
n
v
e
r
g
e
n
ea
r
a
s
co
r
e
o
f
4
to
6
,
in
d
icatin
g
th
at
s
tr
u
ctu
r
al
ad
v
an
tag
es
d
im
in
is
h
u
n
d
er
s
ev
er
e
n
o
d
e
d
eg
r
ad
atio
n
.
T
h
e
ef
f
icien
cy
s
c
o
r
e
s
h
o
wn
in
Fig
u
r
e
9
r
e
v
ea
le
d
a
g
r
ad
u
al
u
p
war
d
tr
en
d
,
as
n
etwo
r
k
co
n
tr
ac
tio
n
r
ed
u
ce
s
av
e
r
ag
e
p
ath
le
n
g
th
s
am
o
n
g
s
u
r
v
iv
in
g
n
o
d
es.
GM
M
e
q
u
al
s
u
s
tain
s
th
e
h
ig
h
est
ef
f
icien
cy
th
r
o
u
g
h
o
u
t (
~0
.
5
9
to
0
.
6
5
)
,
wh
e
r
ea
s
GNN
e
q
u
al
e
x
h
ib
its
th
e
s
teep
est
r
is
e,
p
ea
k
in
g
at
~
0
.
7
0
at
5
0
%
f
ailu
r
e.
GM
M
u
n
e
q
u
al
co
n
s
is
ten
tly
r
ec
o
r
d
s
th
e
l
o
west
ef
f
icien
cy
,
wh
ile
L
u
ca
s
W
h
ee
l
an
d
GNN
u
n
eq
u
al
f
o
llo
w
m
o
d
er
ate
ascen
d
in
g
tr
en
d
s
,
co
n
v
er
g
in
g
n
e
ar
0
.
5
8
to
0
.
6
5
at
h
ig
h
e
r
f
ailu
r
e
r
ates.
Fig
u
r
e
10
co
m
p
ar
es
th
e
m
o
d
u
lar
ity
s
co
r
es
o
f
f
iv
e
to
p
o
lo
g
ies
ac
r
o
s
s
n
o
d
e
f
ail
u
r
e
r
ates
f
r
o
m
0
%
to
5
0
%.
GNN
e
q
u
al
ac
h
iev
es
th
e
h
ig
h
est
m
o
d
u
lar
ity
(
~0
.
6
5
)
,
wh
ile
GM
M
e
q
u
a
l,
GM
M
u
n
eq
u
al,
an
d
GNN
u
n
eq
u
al
m
ain
tai
n
co
m
p
ar
ab
le
s
co
r
es
b
etwe
e
n
0
.
5
6
to
0
.
6
5
,
all
s
h
o
win
g
a
s
lig
h
t
d
ec
lin
e
as
th
e
f
ail
u
r
e
r
ate
in
cr
ea
s
es.
L
u
ca
s
W
h
ee
l
r
ec
o
r
d
s
a
n
ea
r
-
ze
r
o
m
o
d
u
lar
ity
ac
r
o
s
s
all
f
ailu
r
e
co
n
d
itio
n
s
,
co
n
f
ir
m
in
g
its
h
u
b
-
ce
n
tr
i
c
ar
ch
itectu
r
e
la
ck
s
an
y
m
ea
n
in
g
f
u
l c
o
m
m
u
n
ity
s
tr
u
ct
u
r
e.
T
h
ese
r
esu
lts
s
u
g
g
est
th
at
G
MM
an
d
GNN
-
b
ased
to
p
o
lo
g
ies
p
r
eser
v
e
s
tr
o
n
g
er
clu
s
ter
o
r
g
an
izatio
n
u
n
d
er
n
o
d
e
f
ailu
r
es
c
o
m
p
ar
e
d
to
L
u
ca
s
W
h
ee
l.
C
en
tr
ality
B
alan
ce
,
s
h
o
wn
i
n
Fig
u
r
e
11
,
r
ev
ea
led
th
e
s
tr
u
ctu
r
al
d
if
f
er
en
ce
s
a
m
o
n
g
th
e
m
eth
o
d
s
.
E
x
ce
p
t
at
ze
r
o
f
ailu
r
e,
G
NN
e
q
u
al
an
d
GM
M
u
n
eq
u
al
ex
h
ib
it
t
h
e
h
ig
h
est
v
alu
es
(
~0
.
1
2
an
d
~0
.
1
1
)
,
wh
er
ea
s
GNN
u
n
eq
u
al
s
tar
ts
n
ea
r
ze
r
o
,
r
ef
lectin
g
h
i
g
h
ly
s
k
ew
ed
lo
ad
d
is
tr
ib
u
tio
n
.
All
to
p
o
lo
g
ies
d
r
o
p
s
h
ar
p
ly
b
y
5
%
in
f
ailu
r
e
an
d
s
u
b
s
eq
u
e
n
tl
y
s
tab
ilize
with
in
a
n
ar
r
o
w
b
an
d
o
f
0
.
0
1
–
0
.
0
3
,
with
n
o
t
o
p
o
lo
g
y
co
n
s
is
ten
tly
o
u
tp
e
r
f
o
r
m
in
g
o
th
er
s
.
T
h
is
c
o
n
v
er
g
en
ce
im
p
lies
th
at
p
r
o
g
r
ess
iv
e
n
o
d
e
f
ailu
r
es
n
atu
r
ally
r
ed
is
tr
ib
u
te
t
r
af
f
ic
lo
ad
am
o
n
g
s
u
r
v
iv
in
g
n
o
d
es,
r
ed
u
cin
g
ce
n
t
r
ality
im
b
ala
n
ce
r
eg
ar
d
less
o
f
th
e
in
itial
to
p
o
lo
g
y
d
esig
n
.
Failu
r
e
r
esil
ien
ce
p
er
f
o
r
m
an
ce
o
f
a
ll
f
iv
e
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
n
o
d
e
f
ailu
r
es
ar
e
s
h
o
wn
in
Fig
u
r
e
12
.
L
u
ca
s
W
h
ee
l
s
tar
ts
with
a
p
er
f
ec
t
s
co
r
e
o
f
1
.
0
b
u
t
d
eg
r
a
d
es
m
o
s
t
s
ev
er
ely
,
d
r
o
p
p
in
g
to
~0
.
0
8
at
5
0
%
f
ailu
r
e,
m
ak
i
n
g
i
t
th
e
least
f
au
lt
-
to
ler
a
n
t
to
p
o
lo
g
y
o
v
e
r
all.
GM
M
e
q
u
al
e
x
h
ib
its
th
e
s
tr
o
n
g
est
r
esil
ien
ce
th
r
o
u
g
h
o
u
t,
d
ec
lin
i
n
g
g
r
ad
u
ally
f
r
o
m
~0
.
8
8
at
1
0
%
to
~0
.
3
9
at
5
0
%
f
ailu
r
e.
GM
M
u
n
eq
u
al,
GNN
e
q
u
al,
an
d
GNN
u
n
eq
u
al
f
o
llo
w
co
m
p
ar
ab
le
d
escen
d
in
g
tr
en
d
s
,
co
n
v
er
g
i
n
g
n
ea
r
0
.
2
5
to
0
.
3
1
at
5
0
%
f
ailu
r
e,
co
n
f
ir
m
in
g
t
h
at
GM
M
an
d
GNN
b
ased
to
p
o
lo
g
ies
s
u
s
tain
b
etter
co
n
n
ec
tiv
ity
th
a
n
L
u
ca
s
W
h
ee
l
u
n
d
er
p
r
o
g
r
ess
iv
e
n
o
d
e
d
e
g
r
ad
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Desig
n
a
Ga
u
s
s
ia
n
mixtu
r
e
-
b
a
s
ed
clu
s
teri
n
g
mo
d
el
fo
r
en
h
a
n
cin
g
a
cc
u
r
a
cy
…
(
K
a
n
a
k
a
R
a
ju
R
a
ja
n
a
)
1055
Fig
u
r
e
8
.
R
o
b
u
s
tn
es
s
s
co
r
e
p
er
f
o
r
m
a
n
ce
o
f
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
n
o
d
e
f
ailu
r
es
Fig
u
r
e
9
.
E
f
f
icien
cy
s
co
r
e
p
er
f
o
r
m
an
ce
o
f
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
n
o
d
e
f
ailu
r
es
Fig
u
r
e
10
.
Mo
d
u
la
r
ity
s
co
r
e
p
er
f
o
r
m
a
n
ce
o
f
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
n
o
d
e
f
ailu
r
es
Fig
u
r
e
11
.
C
en
tr
ality
b
alan
ce
p
er
f
o
r
m
an
ce
o
f
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
n
o
d
e
f
ailu
r
es
Fig
u
r
e
1
2
.
Failu
r
e
r
esil
ien
ce
p
er
f
o
r
m
a
n
ce
o
f
clu
s
ter
in
g
alg
o
r
ith
m
s
u
n
d
er
n
o
d
e
f
ailu
r
es
5.
CO
NCLU
SI
O
N
Af
ter
test
in
g
all
th
e
alg
o
r
ith
m
s
o
n
8
4
3
n
o
d
es
with
t
h
e
f
ailu
r
e
r
ate
o
f
5
0
p
er
ce
n
tag
e,
t
h
e
G
MM
e
q
u
al
alg
o
r
ith
m
p
r
o
v
ed
th
e
m
o
s
t
w
ell
-
r
o
u
n
d
ed
p
er
f
o
r
m
er
with
s
u
s
tain
in
g
co
m
p
etitiv
e
ef
f
icien
cy
an
d
th
e
s
lo
west
r
esil
ien
ce
d
e
ca
y
ac
r
o
s
s
all
te
s
ted
co
n
d
itio
n
s
.
L
u
ca
s
W
h
ee
l,
d
esp
ite
its
s
u
p
er
io
r
in
itial
r
o
b
u
s
tn
ess
,
d
eg
r
ad
e
d
s
h
ar
p
ly
u
n
d
e
r
p
r
o
g
r
ess
iv
e
n
o
d
e
f
ailu
r
e
s
with
n
eg
lig
ib
le
m
o
d
u
lar
ity
,
lim
itin
g
its
p
r
ac
tical
a
p
p
licab
ilit
y
.
GNN
e
q
u
al
ex
h
ib
ited
th
e
s
tr
o
n
g
est
m
o
d
u
lar
ity
a
n
d
e
f
f
icien
cy
g
ain
s
at
elev
ated
f
ailu
r
e
r
ate
s
,
wh
ile
ce
n
tr
ality
b
alan
ce
co
n
v
e
r
g
ed
ac
r
o
s
s
all
to
p
o
lo
g
ies
b
ey
o
n
d
cr
itical
f
ailu
r
e
th
r
esh
o
ld
s
.
T
h
ese
o
u
tc
o
m
es
v
alid
ate
th
at
GM
M,
GNN
b
ased
clu
s
ter
in
g
f
r
am
ewo
r
k
s
a
r
e
m
o
r
e
r
esil
ien
t
,
an
d
s
tr
u
ctu
r
ally
s
tab
le,
p
o
s
itio
n
in
g
GM
M
e
q
u
al
as th
e
o
p
tim
al
ar
ch
itectu
r
e
f
o
r
wir
eless
s
en
s
o
r
n
etwo
r
k
d
esig
n
u
n
d
e
r
ad
v
er
s
e
co
n
d
itio
n
s
.
6.
F
UT
UR
E
WO
RK
Fu
tu
r
e
r
esear
ch
s
h
o
u
ld
b
u
ild
u
p
o
n
th
is
an
aly
s
is
b
y
ap
p
l
y
in
g
th
e
s
am
e
alg
o
r
ith
m
s
o
n
lar
g
er
n
etw
o
r
k
s
th
at
s
u
r
p
ass
th
e
s
ize
o
f
1
0
,
0
0
0
n
o
d
es,
wh
ile
co
n
s
id
er
in
g
d
y
n
am
ic
f
ailu
r
e
s
ce
n
ar
io
s
s
u
ch
as
ca
s
ca
d
in
g
f
ailu
r
es
an
d
ad
v
er
s
ar
y
attac
k
s
to
m
im
ic
th
e
r
ea
l
-
life
co
n
d
itio
n
s
with
in
ess
en
tial sy
s
tem
s
.
I
n
ad
d
itio
n
,
th
er
e
is
s
co
p
e
f
o
r
s
tu
d
y
in
g
h
y
b
r
id
alg
o
r
ith
m
s
wh
er
e
th
e
r
esil
ien
ce
o
f
GM
M
e
q
u
al
is
co
m
b
in
ed
with
th
e
m
o
d
u
lar
ity
o
f
GNN
e
q
u
al
u
s
in
g
e
n
s
em
b
le
lear
n
in
g
tech
n
iq
u
es o
r
r
ein
f
o
r
ce
m
en
t l
ea
r
n
in
g
tech
n
iq
u
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
0
4
7
-
1
0
5
7
1056
ACK
NO
WL
E
DG
M
E
N
T
S
W
e
wo
u
ld
lik
e
to
e
x
p
r
ess
o
u
r
g
r
atitu
d
e
to
GI
T
AM
(
Dee
m
ed
to
b
e
Un
iv
er
s
ity
)
f
o
r
p
r
o
v
id
in
g
th
e
h
ig
h
-
en
d
co
m
p
u
tatio
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al
f
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