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a
tte
r
n
r
e
c
o
g
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itio
n
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a
b
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ch
o
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h
i
n
e l
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n
i
n
g
,
w
h
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ch
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o
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s
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o
n
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z
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n
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d
i
f
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er
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t
p
at
t
er
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s
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at
t
er
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g
n
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t
i
o
n
p
r
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v
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d
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t
h
e s
o
l
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t
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o
n
t
o
s
p
eech
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eco
g
n
i
t
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o
n
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eco
g
n
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t
i
o
n
o
f
h
a
n
d
w
r
i
t
t
en
ch
ar
act
er
s
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f
ace
r
e
c
o
g
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itio
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a
n
d
m
e
d
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a
l d
ia
g
n
o
s
is
.
A
r
t
if
ic
ia
l N
e
u
r
a
l N
e
t
w
o
r
k
s
(
A
N
N
)
a
r
e
u
s
e
f
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l
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er
e
t
h
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m
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t
s
b
et
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ee
n
d
i
f
f
er
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n
t
p
at
t
er
n
s
ar
e n
o
t
d
ef
i
n
ed
p
r
eci
s
el
y
[
5
]
.
I
n
s
u
pe
r
v
i
s
e
d l
e
a
r
ni
ng
,
i
n
pu
t
p
a
t
t
e
r
n
s
a
n
d i
t
s
c
or
r
e
s
pon
di
ng
ou
t
pu
t
pa
t
t
e
r
ns
a
r
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pr
ov
i
de
d f
or
l
e
a
r
n
i
n
g
w
h
i
c
h i
s
us
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d
t
o
a
d
j
us
t
t
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ne
ur
o
n
w
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i
ght
s
w
he
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e
a
s
,
u
ns
up
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vi
s
e
d
l
e
a
r
n
i
ng
n
o t
r
a
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n
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ng
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a
m
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l
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s
a
r
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pr
ov
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de
d.
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n p
a
t
t
e
r
n r
e
c
o
gni
t
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o
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p
ut
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l
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s
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d
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o
n i
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e
t
s
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i
a
s
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g
ht
s
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nd
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ur
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n
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e
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gh
t
s
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up
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i
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i
cat
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n
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d
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t
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n
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p
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f
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tio
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i
n
d
s
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p
p
lic
a
tio
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in
th
e
a
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a
o
f
c
lu
s
te
r
in
g
.
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h
e
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e
in
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c
e
m
e
n
t le
a
r
n
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is
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ty
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in
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ai
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ax
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o
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c p
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co
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t
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x
t
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h
e
o
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t
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t
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et
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ep
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x
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ce
s
w
hi
c
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t
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h
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g
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ti
f
ic
ia
l
N
eu
r
al
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et
w
o
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k
s
.
I
n
S
ect
i
o
n
2
,
t
h
e b
as
i
cs
o
f
A
r
t
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f
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c
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al
N
e
u
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N
et
w
o
r
k
s
ar
e d
i
s
cu
s
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ed
.
I
n
S
ect
i
o
n
3
d
i
f
f
er
en
t
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ack
P
r
o
p
ag
at
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o
n
N
eu
r
al
N
et
w
o
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k
m
et
h
o
d
s
ar
e d
i
s
cu
s
s
ed
.
I
n
s
ect
i
o
n
4
,
R
es
ear
ch
M
et
h
o
d
t
o
ex
t
r
act
r
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f
l
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t
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r
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m
D
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R i
m
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e
s i
s
d
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ss
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d
.
I
n
s
e
c
t
i
o
n
5
r
e
s
u
l
t
s
a
n
d
d
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sc
u
s
s
i
o
n
a
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d
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sse
d
,
f
o
l
l
o
w
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d
b
y
co
n
cl
u
s
i
o
n
s
an
d
b
y
t
h
e r
ef
er
en
ces
.
2.
A
R
TI
F
IC
I
A
L N
EU
R
A
L
NE
T
W
O
RK
S
A
N
N
f
u
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c
tio
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s
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m
ila
r
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a
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t
h
a
t o
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th
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b
r
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in
.
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h
e
b
a
s
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s
tr
u
c
t
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r
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o
f
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ti
f
ic
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l
N
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u
r
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l N
e
t
w
o
r
k
(
A
N
N
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i
s
s
ho
w
n
i
n
F
i
g
ur
e
1
.
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he
ne
t
w
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ho
w
n
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n
F
i
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1
ha
s
m
i
np
ut
s
a
m
p
l
e
s
,
n o
ut
p
ut
s
a
m
p
l
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s
,
a
nd
k
h
i
dde
n
l
a
y
e
r
s
.
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h
e
n
e
t
w
or
k
i
s
pr
ov
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de
d w
i
t
h
s
a
m
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l
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i
np
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a
nd
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t
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s
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o
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r
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nd
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s
a
m
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l
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p
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t
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t
r
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n a
nd
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d
j
us
t
t
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p
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nd
hi
d
d
e
n
l
a
y
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r
ne
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n
w
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g
ht
s
[
6
]
.
E
a
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h i
np
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x2
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.
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1
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w
n.
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m
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gh
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th
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tio
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tio
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m
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t d
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s
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a b
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as
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h
e b
as
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c A
N
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eq
u
at
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o
n
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ar
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s
ho
w
n i
n
E
q
ua
t
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n
1 a
n
d 2.
T
h
er
e ar
e a
w
i
d
e v
ar
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et
y
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f
act
i
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n
ct
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ch
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s
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d
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s
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a
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e
r
m
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f
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n
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lo
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is
tic
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n
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tio
n
)
,
h
y
p
e
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b
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ta
n
g
e
n
t e
tc
.
,
a
v
a
ila
b
l
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i
n t
he
l
i
t
e
r
a
t
ur
e
.
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he
t
hr
e
s
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l
d
i
ng
f
unc
t
i
o
n
w
i
l
l
b
e
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ho
s
e
n d
e
p
e
nd
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n t
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na
t
ur
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o
f
t
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p
r
o
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l
e
m
.
F
ig
u
r
e
1
.
A
r
ti
f
ic
ia
l N
e
u
r
a
l N
e
t
w
o
r
k
s
Ne
t
=
∑
∗
=
1
+ b
i
as
(1
)
O
u
t
put
=
f (
N
e
t
)
(2
)
A
N
N
h
a
s
p
r
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v
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t
o
b
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e
f
f
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ci
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t
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t
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n
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t
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al
m
et
h
o
d
s
o
f
d
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s
t
an
ce
m
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s
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r
es
[
7
,
8
,
9
]
.
T
h
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ack
p
r
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at
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l
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m
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T
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In
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a
m
p
l
e
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s
m
or
e
t
h
a
n
t
h
e
m
i
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i
m
um
n
um
be
r
of
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n
put
s
a
m
pl
e
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r
e
qui
r
e
d f
or
t
r
a
i
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l
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a
ds
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o ov
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r
f
i
t
t
i
n
g
.
T
h
e
num
b
e
r
of
h
i
dd
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l
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er
n
eu
r
o
n
s
r
eq
u
i
r
ed
f
o
r
a p
r
o
b
l
em
i
s
2/
3r
d t
h
e
s
um
o
f
t
h
e
num
be
r
of
i
n
pu
t
a
n
d ou
t
put
n
e
u
r
on
s
[
12]
.
I
n
or
de
r
t
o
s
a
v
e
c
om
p
u
t
a
t
i
on
t
i
m
e
a
n
d
m
e
m
o
r
y
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t
h
e n
u
m
b
er
o
f
h
i
d
d
en
l
a
y
er
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i
n
f
i
r
s
t
a
n
d
s
eco
n
d
l
a
y
er
s
h
o
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l
d
b
e al
m
o
s
t
s
a
m
e.
T
h
er
e ar
e d
i
f
f
er
en
t
a
lg
o
r
ith
m
s
u
s
e
d
i
n t
hi
s
p
a
p
e
r
f
o
r
t
r
a
i
ni
n
g
t
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ne
ur
a
l
ne
t
w
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r
k i
s
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e
r
g
-
M
a
r
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r
d
t
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o
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a
d
i
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d
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i
l
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e
n
t
b
ack
p
r
o
p
ag
at
i
o
n
al
g
o
r
i
t
h
m
[
1
3
]
.
T
h
e er
r
o
r
o
f
t
h
e
n
et
w
o
r
k
i
s
d
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i
n
ed
as
t
h
e
d
i
f
f
er
e
n
ce b
et
w
ee
n
d
es
i
r
ed
t
ar
g
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d
n
et
w
o
r
k
r
es
p
o
n
s
e.
T
h
e
p
er
f
o
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a
n
ce
o
f
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e
n
et
w
o
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s
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al
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at
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s
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f
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et
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cs
s
u
c
h
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s
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s
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r
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R
MS
E
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ea
n
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b
s
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l
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e E
r
r
o
r
(
M
A
E
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Mea
n
A
b
s
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t
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D
ev
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at
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M
A
D
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a
s
s
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n i
n
E
q
ua
t
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o
n
3,
4 a
n
d 5.
T
h
e
m
a
i
n
f
oc
us
of
t
h
i
s
ba
c
k
pr
opa
g
a
t
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on
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l
g
or
i
t
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s
t
o r
e
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c
e
t
h
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l
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l
e
r
r
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r
a
s
m
i
n
i
m
u
m
a
s p
o
ss
i
b
l
e
.
RM
S
E
=
∑
(
−
)
2
=
1
(3
)
M
AE
=
1
∑
|
−
|
=
1
(4
)
M
AD
=
1
∑
|
−
|
=
1
(5
)
3.
TH
E D
I
F
F
ER
EN
T B
A
C
K
P
R
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P
A
G
A
TIO
N
N
EU
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L
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ETH
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T
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er
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s
B
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f
t
h
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m
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ad
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R
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t
h
M
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t
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m
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D
X
)
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e
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r
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t
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C
G
P
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,
Q
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s
i
-
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e
w
t
o
n
(B
F
G
S
),
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e
v
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b
e
rg
-
M
ar
q
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ar
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t
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L
M
)
,
a
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R
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s
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t b
a
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k
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B
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t
t
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ei
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h
t
s
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h
e N
eu
r
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n
et
w
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k
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I
n
t
h
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g
r
ad
i
en
t
d
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ce
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t
B
ack
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r
o
p
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t
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m
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b
i
as
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s
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n
d
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w
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t
s
ar
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p
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at
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i
n t
he
d
i
r
e
c
t
i
o
n o
f
ne
ga
t
i
ve
gr
a
d
i
e
nt
p
e
r
f
o
r
m
a
nc
e
f
u
nc
t
i
o
n [
1
4
,
1
5
]
.
T
h
e
p
ar
am
et
er
η
i
s
t
h
e
l
ear
n
i
n
g
r
at
e
p
ar
am
et
er
w
h
i
ch
h
a
s
a
d
i
r
ect
i
n
f
l
u
e
n
ce o
n
t
h
e
t
r
ai
n
i
n
g
t
h
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n
et
w
o
r
k
.
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k
i
s
t
h
e er
r
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r
g
r
ad
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t
w
i
t
h
r
es
p
ect
t
o
t
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w
e
i
g
ht
ve
c
t
o
r
.
T
he
up
d
a
t
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d
w
e
i
g
ht
ve
c
t
o
r
i
s
gi
ve
n i
n
E
q
ua
t
i
o
n
6
[
1
6
]
.
G
r
ad
i
en
t
D
es
cen
t
s
u
f
f
er
s
f
r
o
m
t
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l
l
o
w
l
o
c
a
l
m
i
ni
m
u
m
.
G
D
M
c
a
n s
k
i
p
s
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h
m
i
n
i
m
u
m
va
l
ue
s
b
y
up
d
a
t
i
n
g t
he
w
e
i
ght
va
l
ue
s
e
q
ua
l
t
o
t
he
s
u
m
of
m
odi
f
i
e
d
w
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i
gh
t
i
n
G
r
a
di
e
n
t
de
s
c
e
n
t
a
n
d t
h
e
f
r
a
c
t
i
on of
pr
e
v
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ou
s
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e
i
g
h
t
v
a
l
u
e
s
a
s
gi
v
e
n i
n
E
q
ua
t
i
o
n
7
.
T
h
e
p
ar
am
et
er
μ
i
s
t
h
e
co
ef
f
i
ci
en
t
o
f
m
o
m
e
n
t
um
a
n
d i
t
v
a
r
i
e
s
be
t
w
e
e
n
0 a
n
d 1.
W
k+
1
=
W
k
–
η
*
G
k
(6
)
Wk
+1
=
W
k
–
η
*
G
k
-
μ
*
W
k
-
1
(7
)
T
h
e G
D
an
d
G
D
M
m
et
h
o
d
s
u
f
f
er
s
f
r
o
m
t
h
e p
r
o
b
l
em
o
f
l
o
w
co
n
v
er
g
e
n
ce r
at
e.
T
h
e l
e
ar
n
i
n
g
r
at
e
p
ar
am
et
er
v
al
u
e
h
as
a d
i
r
ect
r
el
at
i
o
n
t
o
t
h
e co
n
v
er
g
e
n
ce.
A
s
t
h
e l
ear
n
i
n
g
r
at
e i
n
cr
eas
es
co
n
v
er
g
e
n
ce v
a
l
u
e
i
n
cr
eas
es
.
T
h
e al
g
o
r
i
t
h
m
t
ak
e
s
a l
o
n
g
t
i
m
e t
o
co
n
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er
g
e i
f
t
h
e
v
al
u
e o
f
t
h
e l
ear
n
i
n
g
r
at
e p
ar
a
m
et
er
i
s
h
i
g
h
an
d
i
t
l
ead
s
t
o
an
u
n
s
t
ab
l
e
n
et
w
o
r
k
.
T
o
o
v
er
co
m
e t
h
i
s
p
r
o
b
l
e
m
,
v
ar
i
ab
l
e l
ear
n
i
n
g
r
at
e b
a
ck
p
r
o
p
ag
at
i
o
n
wi
t
h
m
o
m
e
n
t
u
m
i
s
u
s
e
d
.
I
n
t
h
i
s
a
l
g
o
r
i
t
h
m
,
t
h
e
v
a
l
u
e
o
f
η
i
s
l
a
r
g
e
i
n
i
t
i
a
l
l
y
a
n
d
i
t
d
e
c
r
e
a
s
e
s
a
s
t
i
m
e
p
r
o
g
r
e
s
s
e
s
.
T
h
e
w
e
i
g
ht
a
d
j
us
t
m
e
nt
i
n G
D
X
i
s
gi
ve
n b
y
e
q
ua
t
i
o
n 8
.
Wk
+1
=
W
k
-
η
k
+
1
*
g
k
+
μ
*
W
k
-
1
(8
)
T
h
e
m
e
t
h
o
d
s d
i
s
c
u
ss
e
d
t
i
l
l
n
o
w
u
s
e
s
t
h
e
s
t
e
e
p
e
st
d
e
s
c
e
nt
m
e
t
ho
d
w
hi
c
h
w
o
r
ks
a
t
t
he
d
i
r
e
c
t
i
o
n o
f
t
he
ne
ga
t
i
ve
gr
a
d
i
e
nt
f
o
r
m
o
d
i
f
yi
ng t
he
ne
ur
o
n
w
e
i
g
ht
s
.
T
he
c
o
nve
r
ge
nc
e
r
a
t
e
o
f
t
he
s
e
m
e
t
h
o
d
s
i
s
ve
r
y
s
l
o
w
.
I
n
o
r
d
er
t
o
i
m
p
r
o
v
e t
h
e co
n
v
er
g
e
n
ce r
at
e,
t
h
e co
n
j
u
g
at
e d
i
r
ect
i
o
n
o
f
t
h
e s
ear
ch
i
s
p
r
ef
er
r
ed
o
v
er
s
t
eep
es
t
d
es
cen
t
m
e
t
ho
d
.
C
o
nj
uga
t
e
gr
a
d
i
e
nt
d
e
s
c
e
nt
b
a
c
k
-
pr
opa
g
a
t
i
on
a
l
g
or
i
t
hm
(
C
G
D
-
B
P
)
i
s
u
s
e
d
f
or
t
r
a
i
n
i
n
g pu
r
pos
e
.
I
n
C
G
P
s
ear
ch
i
s
p
er
f
o
r
m
ed
al
o
n
g
t
h
e co
n
j
u
g
at
e
g
r
ad
i
en
t
d
i
r
ect
i
o
n
w
h
i
c
h
w
i
l
l
m
i
n
i
m
i
ze t
h
e
co
s
t
f
u
n
ct
i
o
n
al
o
n
g
t
he
l
i
ne
b
y
a
d
j
us
t
i
n
g t
he
s
t
e
p
s
i
z
e
.
T
he
w
e
i
gh
t
up
d
a
t
e
i
n
t
h
e
c
o
nj
uga
t
e
gr
a
d
i
e
nt
m
e
t
ho
d
i
s
g
i
ve
n
i
n
e
q
ua
t
i
o
n
9[
17]
.
T
h
e
di
r
e
c
t
i
on
of
C
on
j
ug
a
t
e
g
r
a
di
e
n
t
s
e
a
r
c
h
i
s
g
i
v
e
n
i
n
e
qu
a
t
i
on
10.
β
k
i
s
t
h
e
r
a
t
i
o
of
n
or
m
s
q
u
a
r
e
d
of
t
h
e cu
r
r
en
t
g
r
ad
i
en
t
t
o
n
o
r
m
s
q
u
ar
ed
o
f
t
h
e p
r
ev
i
o
u
s
g
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ad
i
en
t
as
s
h
o
w
n
i
n t
he
e
q
ua
t
i
o
n i
n 1
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
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8708
In
t
J
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l
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&
C
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V
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8
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279
5
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2798
W
k+
1
=
W
k
+
η
*
P
k
(9
)
W
he
r
e,
P
k
=
-
g
k
+
β
k
*
P
k
-
1
(
10)
β
k
=
∆
g
k
−
1
T
∗
g
k
g
k
−
1
T
∗
g
k
−
1
(
11)
L
e
ve
nb
e
r
g
-
M
a
r
q
ua
r
d
t
a
l
go
r
i
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a
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p
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o
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g t
he
H
e
s
s
i
a
n
m
a
t
r
i
x
d
i
r
e
c
t
l
y
.
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he
H
e
s
s
i
a
n
m
a
t
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i
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m
p
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s
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ng
t
he
J
a
c
o
b
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a
n
m
a
t
r
i
x
a
s
s
ho
w
n
i
n
E
q
ua
t
i
o
n
12.
T
h
e
p
r
i
n
ci
p
al
d
i
ag
o
n
al
el
e
m
e
n
t
s
o
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H
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i
a
n
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at
r
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ar
g
er
t
h
a
n
zer
o
.
T
h
e
w
ei
g
h
t
u
p
d
at
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u
l
e i
n
t
h
e
L
ev
e
n
b
er
g
-
M
a
r
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a
r
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o
r
ith
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te
d
in
E
q
ua
t
i
o
n
13.
H
=
J
T J
+
μ
I
(
12)
W
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k
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(
J
k
T
J
k
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I
)
-
1
J
k e
k
(
13)
T
he
L
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ve
nb
e
r
g
-
M
ar
q
u
ar
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t
s
w
i
t
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h
e
s
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et
w
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t
d
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t
a
l
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t
h
m
an
d
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au
s
s
N
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t
o
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al
g
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r
i
t
h
m
d
u
r
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n
g
t
h
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t
r
ai
n
i
n
g
p
h
as
e.
T
h
e co
n
v
er
g
e
n
ce r
at
e
o
f
t
h
e G
a
u
s
s
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e
w
t
o
n
m
et
h
o
d
i
s
f
as
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an
d
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n
s
t
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l
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w
h
er
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e
v
en
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er
g
-
M
ar
q
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ar
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t
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v
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es
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h
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r
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e
m
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n
s
t
ab
i
l
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t
y
b
y
m
ai
n
t
ai
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n
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h
e co
n
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er
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ce
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at
e f
a
s
t
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A
G
a
u
s
s
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t
o
n
al
g
o
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t
h
m
i
s
u
s
ed
w
h
en
t
h
e
co
e
f
f
i
ci
en
t
μ
i
s
v
er
y
s
m
a
l
l
.
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h
e
S
t
eep
es
t
D
e
s
c
en
t
m
et
h
o
d
i
s
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s
ed
w
h
e
n
μ
i
s
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er
y
l
ar
g
e.
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h
e
r
el
at
i
o
n
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et
w
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l
ear
n
i
n
g
r
at
e
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n
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t
h
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m
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n
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o
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c
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en
t
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s
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v
e
n
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y
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h
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llo
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la
tio
n
a
s
s
h
o
w
n
i
n
E
q
ua
t
i
o
n
14.
η
=
1
/μ
(
14)
T
h
e
a
c
tiv
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tio
n
f
u
n
c
t
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ic
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ll
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m
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lt
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t
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tio
n
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h
e
p
r
im
a
r
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r
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le
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c
ti
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t r
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f
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te
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o
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g
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t
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p
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ach
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s
u
s
ed
t
o
ex
t
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act
t
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I
an
d
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f
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t
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e D
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h
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m
ag
e
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t
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d
f
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D
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A
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(
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m
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m
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19t
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s
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n
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g
u
r
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[
1
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]
.
T
h
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l
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f
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h
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gh
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s
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m
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e [
1
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,
2
0
]
.
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h
e r
ef
l
ect
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t
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s
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r
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ab
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AND D
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