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5
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Octo
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I
SS
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DOI
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1
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tr
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[
1
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[
2
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.
T
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[
3
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.
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[
4
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a
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5
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Data
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
5
,
Octo
b
e
r
2
0
2
1
:
4
3
8
1
-
4391
4382
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h
i
g
h
ex
p
ec
tatio
n
f
o
r
a
cc
u
r
ac
y
.
T
h
e
u
tili
za
t
io
n
o
f
t
h
e
li
n
ea
r
alg
o
r
it
h
m
i
s
u
n
ab
le
to
d
ed
u
ce
th
e
u
n
d
er
ly
i
n
g
n
o
n
-
l
in
ea
r
asp
ec
t
o
f
t
h
e
d
ata.
T
h
e
n
e
u
r
a
l
n
et
w
o
r
k
m
o
d
el
ap
p
licatio
n
f
o
r
ex
a
m
p
le,
tr
ad
itio
n
all
y
f
o
ll
o
w
s
th
e
b
lack
b
o
x
ap
p
r
o
ac
h
th
at
ar
e
n
o
t
m
ath
e
m
atica
ll
y
tr
ac
tab
le
an
d
ca
n
n
o
t
b
e
ea
s
ily
i
n
ter
p
r
eted
.
B
esid
e
s
th
at,
in
n
o
n
-
lin
ea
r
m
o
d
el
s
o
t
h
er
th
a
n
th
e
lo
n
g
s
h
o
r
t
-
ter
m
m
e
m
o
r
y
n
et
w
o
r
k
,
t
h
e
n
u
m
b
er
o
f
i
n
p
u
t
s
h
as
to
b
e
s
e
lecte
d
b
ef
o
r
eh
an
d
,
th
u
s
m
a
k
in
g
lear
n
i
n
g
i
m
p
o
s
s
i
b
le
f
o
r
f
u
n
ctio
n
s
t
h
at
d
ep
en
d
o
n
h
i
s
to
r
ical
i
n
p
u
t
th
at
to
o
k
p
l
ac
e
a
lo
n
g
ti
m
e
a
g
o
.
Sin
ce
s
ec
u
r
it
y
ac
ti
v
itie
s
f
o
r
s
o
f
t
w
ar
e
an
d
s
y
s
te
m
s
ar
e
h
i
g
h
l
y
r
eso
u
r
ce
s
av
v
y
,
th
e
m
o
d
els
ar
e
th
er
ef
o
r
e
ex
p
ec
ted
to
h
a
v
e
h
i
g
h
ac
c
u
r
ac
y
o
f
v
u
l
n
er
ab
ilit
y
p
r
ed
ictio
n
b
y
t
h
e
v
e
n
d
o
r
s
,
en
d
u
s
er
s
as
w
ell
a
s
b
u
s
i
n
es
s
e
s
[
1
6
]
.
I
n
th
is
r
esear
ch
,
th
e
p
r
e
d
ictio
n
o
f
th
e
n
u
m
b
er
o
f
f
u
t
u
r
e
v
u
l
n
er
ab
ilit
ie
s
is
tak
e
n
as
a
s
u
p
er
v
is
ed
s
eq
u
en
t
ial
ti
m
e
s
er
ie
s
f
o
r
ec
asti
n
g
p
r
o
b
lem
,
an
d
m
a
k
e
s
th
e
f
o
llo
w
in
g
c
o
n
tr
ib
u
tio
n
s
:
C
r
ea
tio
n
o
f
a
n
e
w
,
lar
g
er
d
ataset
f
o
r
ea
ch
s
elec
ted
v
e
n
d
o
r
(
Mic
r
o
s
o
f
t,
Or
ac
le
an
d
I
B
M
)
u
s
in
g
a
n
o
v
el
tech
n
iq
u
e
o
f
f
ea
t
u
r
e
a
g
g
r
e
g
ati
o
n
o
b
tain
ed
f
r
o
m
o
p
en
-
s
o
u
r
ce
d
atasets
w
h
ic
h
co
n
tai
n
s
a
lo
t
m
o
r
e
e
x
a
m
p
les
to
ef
f
icie
n
tl
y
tr
ai
n
th
e
L
ST
M
n
et
w
o
r
k
.
T
h
ese
d
atasets
c
o
n
tain
a
lo
t
m
o
r
e
ex
a
m
p
les
co
m
p
ar
ed
to
th
e
p
r
ev
io
u
s
w
o
r
k
[
1
5
]
.
Ou
r
d
at
aset
(
cr
ea
ted
b
y
a
g
g
r
eg
ati
n
g
th
e
“
P
u
b
li
s
h
ed
Da
te
f
ea
t
u
r
e”
)
f
o
r
Mic
r
o
s
o
f
t
v
en
d
o
r
f
o
r
ex
a
m
p
le,
h
as
1
0
3
0
ex
a
m
p
le
s
co
m
p
ar
ed
to
[
1
5
]
w
h
er
e
th
e
d
ataset
w
as
p
r
ep
ar
ed
b
ased
o
n
a
m
o
n
t
h
l
y
a
g
g
r
eg
atio
n
a
n
d
h
as
ap
p
r
o
x
im
a
tel
y
2
5
2
ex
a
m
p
les
f
o
r
ea
ch
.
T
o
th
e
b
est
o
f
o
u
r
k
n
o
w
led
g
e,
t
h
e
s
e
ar
e
th
e
f
ir
s
t
d
ataset
s
w
i
th
s
u
c
h
f
ea
t
u
r
e
cr
ea
ted
b
y
g
r
o
u
p
i
n
g
b
ased
o
n
t
h
e
p
u
b
lis
h
ed
d
ate
t
o
b
e
u
tili
ze
d
f
o
r
v
u
l
n
er
ab
ilit
y
p
r
ed
ictio
n
m
o
d
el
.
Utilizatio
n
o
f
d
ee
p
lear
n
i
n
g
alg
o
r
ith
m
ca
lled
t
h
e
lo
n
g
s
h
o
r
t
-
ter
m
m
e
m
o
r
y
(
L
ST
M)
,
a
v
ar
ia
n
t
o
f
t
h
e
r
ec
u
r
r
en
t
n
e
u
r
al
n
et
w
o
r
k
(
R
N
N)
,
k
n
o
w
n
f
o
r
h
a
v
in
g
th
e
u
n
i
q
u
e
ca
p
ab
ilit
y
i
n
r
etai
n
i
n
g
p
as
t
in
f
o
r
m
a
tio
n
o
f
s
er
ies
in
ca
lc
u
lati
n
g
th
e
ac
ti
v
a
tio
n
f
u
n
c
tio
n
s
a
n
d
w
e
ig
h
ts
i
n
m
ac
h
in
e
lear
n
in
g
m
o
d
elli
n
g
t
o
f
o
r
ec
ast
f
u
t
u
r
e
v
alu
e
s
w
i
th
h
i
g
h
er
ac
cu
r
ac
y
.
T
o
th
e
b
est
o
f
o
u
r
k
n
o
w
led
g
e,
th
is
r
esea
r
ch
is
th
e
f
ir
s
t
to
u
til
ize
t
h
e
lo
n
g
s
h
o
r
t
-
ter
m
m
e
m
o
r
y
n
e
u
r
al
n
et
w
o
r
k
w
it
h
t
h
e
n
atio
n
al
v
u
ln
er
ab
ilit
y
d
ataset
in
d
ev
elo
p
in
g
a
m
ac
h
i
n
e
lear
n
in
g
m
o
d
el
to
f
o
r
ec
ast t
h
e
n
u
m
b
er
o
f
f
u
t
u
r
e
v
u
l
n
er
ab
ilit
i
es.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
in
th
i
s
r
esear
ch
h
as
ac
h
iev
ed
th
e
ac
c
u
r
ac
y
(
r
o
o
t
m
en
s
q
u
ar
ed
er
r
o
r
)
v
alu
e
o
f
as
lo
w
as
0
.
0
7
2
w
h
ic
h
h
a
s
o
u
tp
er
f
o
r
m
ed
th
e
ex
i
s
ti
n
g
m
o
d
els
in
ter
m
s
o
f
p
r
ed
ictio
n
ac
cu
r
ac
y
a
n
d
f
o
llo
w
i
n
g
d
is
tr
ib
u
tio
n
tr
e
n
d
s
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
an
i
ze
d
is
b
ein
g
as
:
Sectio
n
2
d
escr
ib
es
th
e
r
elate
d
w
o
r
k
w
h
i
le
.
Sectio
n
3
d
escr
ib
es th
e
d
ataset
an
d
m
et
h
o
d
u
s
ed
i
n
t
h
e
a
n
al
y
s
i
s
.
Sec
tio
n
4
d
escr
ib
es
th
e
ad
v
a
n
ta
g
es
o
f
t
h
e
L
ST
M
m
o
d
el
in
ti
m
e
s
er
ies
p
r
ed
ictio
n
,
s
ec
tio
n
5
d
escr
ib
es
th
e
r
esu
lt
s
a
n
d
an
al
y
s
i
s
,
an
d
f
i
n
all
y
s
ec
ti
o
n
6
d
escr
ib
es
th
e
co
n
clu
s
io
n
a
n
d
f
u
tu
r
e
w
o
r
k
s
.
2.
RE
L
AT
E
D
R
E
SE
ARCH
L
y
u
an
d
L
y
u
[
9
]
s
u
r
v
e
y
ed
s
o
f
t
w
ar
e
d
ef
ec
t
d
etec
tio
n
p
r
o
ce
s
s
es
u
s
i
n
g
s
o
f
t
w
ar
e
r
eliab
ili
t
y
g
r
o
w
t
h
m
o
d
el
s
.
A
n
d
er
s
o
n
p
r
o
p
o
s
ed
t
h
e
An
d
er
s
o
n
T
h
er
m
o
d
y
n
a
m
ic
(
A
T
)
ti
m
e
-
b
a
s
ed
v
u
ln
er
ab
ilit
y
d
is
co
v
er
y
w
h
ic
h
i
s
co
n
s
id
er
ed
as
a
p
io
n
ee
r
in
s
u
ch
r
esear
ch
[
1
6
]
.
A
lh
az
m
i
a
n
d
Ma
lai
y
a
p
r
o
p
o
s
ed
a
tim
e
-
b
ased
ap
p
licatio
n
o
f
s
o
f
t
w
ar
e
r
eliab
ili
t
y
g
r
o
w
t
h
m
o
d
ellin
g
(
S
R
GM
)
i
n
p
r
ed
ictin
g
th
e
n
u
m
b
er
o
f
v
u
l
n
er
ab
ilit
ie
s
,
an
d
later
h
av
e
also
p
r
o
p
o
s
ed
an
o
th
er
lo
g
i
s
tic
r
e
g
r
ess
io
n
m
o
d
el
f
o
r
W
in
d
o
ws
9
8
an
d
NT
4
.
0
in
p
r
e
d
ict
in
g
th
e
n
u
m
b
er
o
f
u
n
d
i
s
co
v
er
ed
v
u
l
n
er
ab
ilit
ie
s
[
1
7
]
.
R
esco
la
p
r
o
p
o
s
ed
tw
o
ti
m
e
-
b
ased
tr
en
d
m
o
d
els,
n
a
m
e
l
y
th
e
li
n
ea
r
m
o
d
el
(
R
L
)
a
n
d
th
e
ex
p
o
n
e
n
tial
m
o
d
el
(
R
E
)
to
esti
m
ate
f
u
t
u
r
e
v
u
ln
er
ab
ilit
ie
s
[
1
8
]
.
Ki
m
[
1
9
]
p
r
o
p
o
s
ed
a
n
e
w
W
eib
u
ll
d
is
tr
ib
u
tio
n
-
b
a
s
ed
v
u
ln
er
ab
ilit
y
d
i
s
co
v
er
y
m
o
d
el
(
VDM
)
w
h
ic
h
w
as
co
m
p
ar
ed
w
it
h
[
2
0
]
,
an
d
f
o
u
n
d
th
at
th
e
ir
m
o
d
el
p
er
f
o
r
m
ed
b
etter
in
m
a
n
y
ca
s
e
s
.
T
h
er
e
ar
e
also
s
ev
er
al
o
th
er
s
tu
d
ies
t
h
at
w
o
r
k
ed
f
u
r
t
h
er
b
ased
o
n
th
e
e
x
i
s
ti
n
g
VDM
s
f
o
r
v
ar
io
u
s
s
o
f
t
w
ar
e
p
ac
k
a
g
es
w
it
h
t
h
e
ai
m
o
f
i
m
p
r
o
v
i
n
g
t
h
e
v
u
l
n
er
ab
ilit
y
d
is
co
v
er
y
r
ate
an
d
t
h
e
p
r
ed
ictio
n
o
f
f
u
t
u
r
e
v
u
ln
er
ab
ilit
y
co
u
n
t
[
2
1
]
-
[
2
8
]
.
Mo
v
ah
ed
i
et
a
l.
[
2
9
]
d
ev
elo
p
ed
n
in
e
co
m
m
o
n
v
u
l
n
er
ab
ilit
y
d
is
co
v
er
y
m
o
d
els
(
VDM
s
)
wh
ich
w
er
e
co
m
p
ar
ed
w
ith
a
n
o
n
li
n
ea
r
n
eu
r
al
n
et
w
o
r
k
m
o
d
el
(
NN
M)
o
v
er
a
p
r
e
d
ictio
n
p
er
io
d
o
f
th
r
ee
y
ea
r
s
.
T
h
e
co
m
m
o
n
VDM
s
ar
e
t
h
e
NHP
P
p
o
w
er
-
la
w
g
a
m
m
a
-
b
ased
V
DM
,
W
eib
u
ll
-
b
ased
VDM
,
AM
L
V
DM
,
n
o
r
m
al
-
b
ased
VDM
,
r
esco
r
la
ex
p
o
n
e
n
tial
(
R
E
)
,
r
esco
r
la
q
u
ad
r
atic
(
R
Q)
,
y
o
u
n
i
s
f
o
ld
ed
(
YF)
an
d
lin
ea
r
m
o
d
el
(
L
M)
.
T
h
ese
m
o
d
els
u
s
e
th
e
NVD
d
ataset
w
it
h
t
h
e
f
ee
d
f
o
r
w
ar
d
N
NM
w
it
h
a
s
in
g
le
h
id
d
en
la
y
e
r
in
f
o
r
ec
asti
n
g
f
o
u
r
w
ell
-
k
n
o
w
n
O
Ss
a
n
d
f
o
u
r
w
el
l
-
k
n
o
w
n
w
eb
b
r
o
w
s
er
s
a
n
d
as
s
ess
ed
t
h
e
m
o
d
els
in
ter
m
s
o
f
p
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I
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3.
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ite
[
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6
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p
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n
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et
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n
1
9
9
7
to
2
0
1
9
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F
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ch
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
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lec
&
C
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p
E
n
g
,
Vo
l.
11
,
No
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5
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Octo
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4391
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Fig
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3
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Fi
g
u
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4
.
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ter
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.
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,
i
n
m
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t
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s
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f
o
r
m
atio
n
o
f
a
f
u
n
ct
io
n
t
h
at
i
s
d
ep
en
d
en
t
o
n
d
ata
p
o
in
ts
o
f
lo
n
g
ti
m
e
a
g
o
in
a
s
eq
u
e
n
ce
.
Ho
w
e
v
er
,
th
e
R
N
N
ca
n
av
o
id
th
i
s
d
r
a
w
b
ac
k
s
i
n
ce
it
is
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le
to
s
to
r
e
in
f
o
r
m
a
tio
n
f
r
o
m
d
ata
p
o
in
ts
o
f
lo
n
g
ti
m
e
a
g
o
.
Fig
u
r
e
4
.
An
u
n
r
o
lled
r
ec
u
r
r
en
t n
eu
r
al
n
et
w
o
r
k
(
So
u
r
ce
: [
3
1
]
)
Ho
w
e
v
er
,
o
n
e
s
ig
n
i
f
ica
n
t
d
r
aw
b
ac
k
o
f
t
h
e
R
NN
s
is
t
h
at
wh
en
th
e
d
ata
s
eq
u
e
n
ce
s
tar
ts
t
o
in
cr
ea
s
e
,
th
e
n
et
w
o
r
k
ten
d
s
to
lo
s
e
i
n
f
o
r
m
atio
n
o
n
h
is
to
r
ical
co
n
te
x
t
o
v
er
ti
m
e.
A
v
ar
ian
t
o
f
t
h
e
R
NN,
ca
lled
th
e
lo
n
g
s
h
o
r
t
-
ter
m
m
e
m
o
r
y
n
et
w
o
r
k
(
L
ST
M)
ca
n
s
o
lv
e
th
is
p
r
o
b
l
em
s
in
ce
it
m
ai
n
tain
s
th
e
ce
lls
f
o
r
k
ee
p
in
g
in
f
o
r
m
atio
n
f
o
r
t
h
e
p
r
ev
io
u
s
n
o
d
es
ir
r
esp
ec
tiv
e
o
f
t
h
e
s
eq
u
e
n
ce
s
ize.
An
L
ST
M
n
et
w
o
r
k
m
ai
n
tai
n
s
[
3
2
]
th
r
ee
o
r
f
o
u
r
g
ates
w
h
er
e
th
e
i
n
p
u
t,
o
u
tp
u
t a
n
d
f
o
r
g
et
g
a
tes ar
e
co
m
m
o
n
as
s
h
o
w
n
in
Fig
u
r
e
5
.
T
h
e
n
o
tatio
n
s
t,
C
a
n
d
h
in
d
icate
o
n
e
s
tep
in
ti
m
e,
ce
l
l
s
tat
e
an
d
th
e
h
id
d
en
s
ta
te
r
esp
ec
tiv
el
y
.
T
h
e
g
ates
i
(
in
p
u
t)
,
f
(
f
o
r
g
et)
a
n
d
o
(
o
u
tp
u
t)
th
at
ar
e
m
o
s
t
u
s
u
al
l
y
m
o
d
elled
w
i
th
a
s
i
g
m
o
id
la
y
er
(
v
al
u
es
r
a
n
g
in
g
b
et
w
ee
n
0
-
1
)
h
elp
in
p
r
o
tecti
n
g
a
n
d
co
n
tr
o
llin
g
t
h
e
ad
d
itio
n
an
d
r
e
m
o
v
al
o
f
i
n
f
o
r
m
atio
n
in
a
ce
ll
s
tate.
T
h
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
-
8708
F
o
r
ec
a
s
tin
g
n
u
mb
er o
f v
u
ln
era
b
ilit
ies u
s
in
g
lo
n
g
s
h
o
r
t
-
term n
eu
r
a
l m
emo
r
y
…
(
Mo
h
a
mma
d
S
h
a
msu
l H
o
q
u
e
)
4385
L
ST
Ms
th
er
e
f
o
r
e
tr
y
to
o
v
er
c
o
m
e
t
h
e
s
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tco
m
i
n
g
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o
f
t
h
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R
NN
m
o
d
els
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e
g
ar
d
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g
t
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e
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a
n
d
lin
g
o
f
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ter
m
d
ep
en
d
en
cies
b
y
m
iti
g
ati
n
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th
e
is
s
u
e
w
h
e
n
t
h
e
w
ei
g
h
t
m
atr
i
x
o
f
th
e
n
e
u
r
o
n
s
b
ec
o
m
es
to
o
s
m
a
ll
(
w
h
ich
m
a
y
lead
to
th
e
v
an
is
h
in
g
o
f
th
e
g
r
ad
ien
ts
)
o
r
to
o
lar
g
e
(
w
h
ic
h
m
a
y
ca
u
s
e
t
h
e
g
r
ad
ien
t
s
to
ex
p
lo
d
e)
.
T
h
e
f
o
llo
w
i
n
g
s
tep
s
s
h
o
w
s
t
h
e
m
at
h
e
m
atica
l
f
u
n
ctio
n
s
[
3
3
]
,
[
3
4
]
o
f
a
lo
n
g
s
h
o
r
t
-
ter
m
m
e
m
o
r
y
n
eu
r
al
n
et
w
o
r
k
f
o
r
t
y
p
ical
u
s
a
g
e,
s
u
ch
as
f
o
r
th
i
s
r
esear
ch
ex
p
er
i
m
en
t
:
Stag
e
1
Fo
r
a
f
o
r
w
ar
d
p
ass
i
n
a
n
L
ST
M
b
lo
ck
,
if
x
t
is
co
n
s
id
er
ed
as
an
i
n
p
u
t
v
ec
to
r
at
a
ti
m
e
t,
N
an
d
M
ar
e
th
e
L
ST
M
b
lo
ck
n
u
m
b
er
an
d
in
p
u
t
n
u
m
b
er
r
esp
ec
tiv
el
y
,
an
L
ST
M
la
y
er
ca
n
h
av
e
f
o
u
r
w
e
ig
h
ts
:
W
eig
h
t
s
f
o
r
in
p
u
t: W
z,
W
i,
W
f
,
W
o
∈
R
N×
M
W
eig
h
t
s
f
o
r
p
ee
p
h
o
le:
p
i,
p
f
,
p
o
∈
R
N
W
eig
h
t
s
f
o
r
r
ec
u
r
r
en
t:
R
z,
R
i,
R
f
,
R
o
∈
R
N×
N
an
d
W
eig
h
t
s
f
o
r
b
ias:
b
z,
b
i,
b
f
,
b
o
∈
R
N
W
ith
r
ef
er
en
ce
to
t
h
e
w
ei
g
h
t
s
ab
o
v
e,
th
e
f
o
r
m
u
la
f
o
r
v
ec
to
r
in
a
f
o
r
w
ar
d
p
ass
f
o
r
an
L
ST
M
la
y
er
ar
e
as f
o
llo
w
s
,
(
e
σ
,
g
an
d
h
a
r
e
ac
tiv
atio
n
f
u
n
ctio
n
s
)
:
z
-
t =
W
z
x
t +
R
z
y
t−1
+
b
z
zt
=
g
(
z
-
t)
[
b
lo
ck
f
o
r
in
p
u
t]
i
-
t =
W
i x
t +
R
i
y
t−1
+
p
i •
c
t
−1
+
b
i
it =
σ (
¯
i
t)
[
g
ate
f
o
r
in
p
u
t]
t
-
t =
W
f
x
t+R
f
y
t
-
1
+
p
f
•
ct
-
1
+
b
f
f
t =
σ
(
f
-
t)
[
g
ate
f
o
r
f
o
r
g
et]
ct
=
zt
•
it +
ct
-
1
•
f
t [
L
ST
M
ce
ll]
o
-
t =
W
o
x
t +
R
o
y
t
-
1
+p
o
•
ct
+
b
o
o
t =
σ (
o
-
t)
[
g
ate
f
o
r
o
u
tp
u
t]
y
t =
h
(
ct)
•
o
t [
o
u
tp
u
t f
o
r
b
lo
ck
]
T
y
p
icall
y
,
lo
g
is
t
ic
s
i
g
m
o
id
is
th
e
ac
ti
v
atio
n
f
u
n
ctio
n
at
th
e
L
ST
M
g
ate
w
h
ile
th
e
h
y
p
er
b
o
lic
tan
g
e
n
t
is
th
e
ac
ti
v
atio
n
f
u
n
ctio
n
at
t
h
e
b
lo
ck
in
p
u
t
a
n
d
o
u
tp
u
t.
Stag
e
2
Af
ter
t
h
e
f
o
r
w
ar
d
p
as
s
f
u
n
cti
o
n
s
ar
e
co
m
p
u
ted
,
th
e
f
o
llo
win
g
d
elta
f
u
n
ctio
n
s
ar
e
co
m
p
u
ted
i
n
s
id
e
th
e
L
ST
M
b
lo
ck
f
o
r
b
ac
k
p
r
o
p
ag
atio
n
t
h
r
o
u
g
h
t
i
m
e
s
ta
m
p
s
:
Δy
-
t =
∆t
+
R
z
T
δzt+1
+
R
t T
δit+1
+
R
f
T
δf
t+1
+
R
o
T
δo
t
+1
Δo
-
t =
δ
y
t
•
h
(
ct)
•
σ
/(
o
-
t)
Δ
ct
=
δ
y
t
•
o
t •
h
/(
ct)
+
p
o
•
δo
-
t +
p
i •
δi
-
t+1
+
p
f
•
δ
f
-
t+1
+
δct+1
•
f
t+1
Δf
-
t =
δct
•
ct
-
1
•
σ
/(
f
-
t)
Δ
it =
δct
•
zt
•
σ
/(
i
-
t)
Δz
-
t =
δc
t
•
it
•
g
/(
z
-
t)
Her
e
∆t
d
en
o
tes
th
e
v
ec
to
r
o
f
d
eltas
p
r
o
p
ag
ated
f
r
o
m
th
e
u
p
p
er
lay
er
s
to
th
e
d
o
w
n
w
ar
d
la
y
er
s
.
T
h
e
v
alu
e
E
co
r
r
esp
o
n
d
s
to
∂E
/∂y
t
w
h
en
tr
ea
ted
as
a
lo
s
s
f
u
n
ct
i
o
n
.
I
n
p
u
t
d
eltas
ar
e
o
n
l
y
r
eq
u
i
r
ed
w
h
e
n
th
e
lo
w
er
la
y
er
o
f
th
e
i
n
p
u
t la
y
er
r
eq
u
ir
e
s
tr
ain
i
n
g
,
a
n
d
in
s
u
c
h
s
it
u
atio
n
th
e
v
al
u
e
o
f
t
h
e
d
elta
f
o
r
th
e
in
p
u
t i
s
:
Δ
x
t =
W
zT
δz
-
t +
W
iT
δi
-
t +
W
f
T
δf
-
t +
W
o
T
δo
-
t
Stag
e
3
A
t
th
e
f
in
al
s
ta
g
e,
t
h
e
g
r
ad
ien
ts
to
ad
j
u
s
t
t
h
e
w
ei
g
h
ts
ar
e
co
m
p
u
ted
w
it
h
t
h
e
f
o
llo
w
i
n
g
f
u
n
ct
io
n
s
,
w
h
er
ea
s
¤
d
en
o
tes
an
y
o
f
t
h
e
v
ec
to
r
s
z,
I
,
f
an
d
o
,
an
d
(
¤
1
.
¤
2
)
ar
e
th
e
o
u
ter
p
r
o
d
u
cts
o
f
th
e
co
r
r
esp
o
n
d
in
g
t
w
o
v
ec
to
r
s
:
δW
*
=
∑t
=0
T
(
δ¤
t,
x
t)
δp
i =
∑t
=0
T
-
1
ct
•
δi
-
t+1
δR
*
=
∑t
=0
T
(
δ¤
t+1
,
y
t)
δp
f
=
∑t
=0
T
-
1
ct
•
δf
-
t+1
δb
*
=
∑t
=0
T
δ¤
t δp
o
=
∑t
=0
T
-
1
ct
•
δo
-
t+1
T
h
e
R
NNs,
u
n
li
k
e
t
h
e
AR
I
M
A
,
h
a
v
e
t
h
e
ca
p
ab
ilit
y
to
lear
n
n
o
n
li
n
ea
r
itie
s
i
n
a
d
ata
s
eq
u
en
ce
,
a
n
d
s
p
ec
ialized
n
o
d
es
s
u
c
h
a
s
t
h
e
L
ST
M
n
o
d
es
co
u
ld
h
a
n
d
le
t
h
at
ev
e
n
m
o
r
e
e
f
f
icie
n
tl
y
.
O
n
e
r
eq
u
ir
e
m
en
t
o
f
th
e
L
ST
M
n
et
w
o
r
k
is
t
h
at
a
lo
n
g
s
eq
u
e
n
ce
is
n
ee
d
ed
in
lear
n
in
g
p
ast
d
ep
en
d
en
cie
s
an
d
f
o
r
th
is
r
ea
s
o
n
th
i
s
r
esear
ch
th
er
e
f
o
r
e
ai
m
s
to
cr
ea
te
a
lo
n
g
s
eq
u
en
ce
as d
escr
ib
e
d
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
5
,
Octo
b
e
r
2
0
2
1
:
4
3
8
1
-
4391
4386
Fig
u
r
e
5
.
An
L
ST
M
n
o
d
e
(
So
u
r
ce
: [
3
1
]
)
5.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
P
r
io
r
to
ap
p
ly
i
n
g
a
ti
m
e
s
er
ies
d
ataset
in
to
th
e
m
ac
h
in
e
lear
n
in
g
al
g
o
r
ith
m
,
it
is
i
m
p
o
r
tan
t
to
an
al
y
s
e
th
e
s
tatio
n
ar
it
y
.
T
h
e
in
itial
n
u
ll
h
y
p
o
th
e
s
is
is
t
h
at
th
e
ti
m
e
s
er
ies
at
h
an
d
is
n
o
n
-
s
ta
tio
n
ar
y
.
Fig
u
r
es
6
-
8
s
h
o
w
th
e
r
o
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E
Co
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ter
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c
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0
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A
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1
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3
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M
a
laiy
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,
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5
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6
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7
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M
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8
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9
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J.
Kim
,
Y.
K.
M
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I.
Ra
y
,
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h
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p
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.
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1
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M
.
Xie
,
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R
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M
o
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,
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u
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Co
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P
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L
td
,
S
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l.
1
,
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.
10
-
11
,
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2
]
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O.
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A
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i
,
a
n
d
Y.
K.
M
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a
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“
As
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A
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ter
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3
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.
M
a
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c
c
i
a
n
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V.
H.
Ng
u
y
e
n
,
“
A
n
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M
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to
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[2
4
]
A
.
K.
S
h
riv
a
sta
v
a
,
R.
S
h
a
r
m
a
a
n
d
P
.
K.
Ka
p
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r,
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Vu
l
n
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o
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f
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Fu
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T
re
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Co
m
p
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t
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a
l
A
n
a
lys
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a
n
d
Kn
o
wled
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(
AB
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,
G
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ter
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[2
5
]
H.
C.
Jo
h
a
n
d
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.
K.
M
a
laiy
a
,
“
M
o
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n
g
S
k
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w
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e
ss
in
Vu
ln
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Disc
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ra
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Disc
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Qu
a
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n
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Reli
a
b
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E
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g
I
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rn
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ti
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a
l
,
v
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l.
3
0
,
n
o
.
8
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p
p
.
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5
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0
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4
,
doi
:
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rg
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1
0
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re
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1
5
6
7
.
[2
6
]
A
.
A
.
Yo
u
n
is,
H.
Jo
h
,
a
n
d
Y.
M
a
laiy
a
,
“
M
o
d
e
li
n
g
L
e
a
rn
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g
les
s
V
u
l
n
e
ra
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il
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y
Disc
o
v
e
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u
sin
g
a
F
o
ld
e
d
Distrib
u
ti
o
n
,
”
In
:
Pro
c
e
e
d
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NIST
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