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g
r
ea
t
h
elp
.
F
in
g
e
r
p
r
in
t
cla
s
s
i
f
icat
io
n
cla
s
s
i
f
ie
s
f
in
g
er
p
r
in
ts
in
to
a
s
e
t
o
f
p
r
ed
ef
in
ed
s
ets,
a
n
d
th
e
n
m
ak
es t
h
e
id
en
tical
ta
s
k
p
o
s
s
ib
l
e
[
1
0
]
.
Fin
g
er
p
r
in
t
clas
s
i
f
icatio
n
i
s
a
g
r
an
u
lar
lev
el
ap
p
o
r
tio
n
in
g
o
f
a
lar
g
e
f
in
g
er
p
r
in
t
d
atab
ase,
w
h
er
e
th
e
class
o
f
t
h
e
in
p
u
t
f
i
n
g
er
p
r
in
t
i
s
p
r
i
m
ar
il
y
p
er
s
is
te
n
t
a
n
d
t
h
er
ef
o
r
e,
a
s
ea
r
ch
i
s
co
n
d
u
cted
i
n
s
id
e
t
h
e
g
r
o
u
p
o
f
f
i
n
g
er
p
r
in
t
s
s
u
itab
le
to
th
e
s
i
m
ilar
class
as
t
h
e
i
n
p
u
t
f
i
n
g
er
p
r
i
n
t
[
1
1
]
.
T
h
e
au
th
e
n
ticatio
n
p
r
o
ce
s
s
is
s
ec
u
r
ed
b
y
d
ec
r
ea
s
in
g
th
e
n
u
m
b
er
o
f
co
m
p
ar
is
o
n
s
t
h
at
ar
e
e
s
s
e
n
tiall
y
a
ch
iev
ed
.
I
t
is
at
tain
ed
b
y
i
s
o
latin
g
t
h
e
f
i
n
g
er
p
r
in
t
d
atab
ase
in
to
a
n
u
m
b
er
o
f
class
es.
F
in
g
er
p
r
in
t
r
ec
o
g
n
iti
o
n
is
p
r
er
eq
u
is
ite
to
b
e
ass
o
ciate
d
o
n
l
y
to
th
e
f
i
n
g
er
p
r
in
t
s
in
a
s
in
g
le
clas
s
o
f
th
e
d
atab
ase
o
n
t
h
e
b
asis
o
f
its
f
ea
t
u
r
es.
Fi
n
g
er
p
r
in
t
id
en
ti
f
icatio
n
is
b
r
o
ad
l
y
u
s
ed
d
u
e
to
ea
s
e
in
th
e
ch
ar
ac
ter
is
tic
ac
q
u
is
i
tio
n
;
t
h
e
ten
f
i
n
g
er
s
ar
e
ac
ce
s
s
ib
le
f
o
r
co
llectio
n
an
d
th
eir
u
s
a
g
e
an
d
ass
o
r
t
m
e
n
t
s
o
f
la
w
i
m
p
le
m
en
tatio
n
a
n
d
i
m
m
i
g
r
atio
n
[
1
2
]
.
Fin
g
er
p
r
in
t
clas
s
i
f
icatio
n
a
n
d
ac
k
n
o
w
led
g
m
en
t
s
ch
e
m
es
ar
e
in
s
p
i
r
in
g
m
is
s
io
n
s
f
o
r
h
ac
k
er
s
as
it
i
n
clu
d
e
s
u
n
iq
u
e
id
en
ti
f
icatio
n
tech
n
iq
u
e,
in
co
r
p
o
r
atin
g
Data
Min
i
n
g
m
et
h
o
d
s
s
u
c
h
as
Ne
u
r
al
Net
w
o
r
k
s
an
d
K
Nea
r
est
Neig
h
b
o
r
alg
o
r
ith
m
s
,
th
e
i
n
tel
lig
e
n
ce
s
ta
g
e
o
f
th
e
f
i
n
g
er
p
r
in
t id
e
n
ti
f
icatio
n
i
s
en
h
an
ce
d
w
h
ich
s
af
e
g
u
ar
d
ac
c
u
r
ac
y
an
d
p
r
o
tecte
d
r
ec
o
g
n
itio
n
[
1
3
]
.
T
h
e
r
est
o
f
th
e
d
o
cu
m
en
t
is
o
r
g
an
ized
as
f
o
llo
w
s
:
Sectio
n
2
d
ef
in
es
a
co
n
cise
d
escr
ip
tio
n
o
f
th
e
latest
r
esear
c
h
w
o
r
k
;
Sec
tio
n
3
r
ef
er
s
to
t
h
e
p
r
o
ce
s
s
es
t
h
at
a
r
e
p
ar
t
o
f
o
u
r
m
a
s
ter
p
iece
m
e
t
h
o
d
w
it
h
s
u
r
p
r
is
i
n
g
d
em
o
n
s
tr
atio
n
s
an
d
m
at
h
e
m
at
ical
f
o
r
m
u
la
tio
n
s
.
W
h
ile
Secti
o
n
4
elu
c
id
ates t
h
e
r
es
u
lt
s
o
f
t
h
e
e
x
p
er
i
m
e
n
tatio
n
,
Sectio
n
5
co
n
clu
d
e
s
th
e
w
o
r
k
.
2.
RE
L
AT
E
D
WO
RK
P
atil
an
d
Su
r
al
k
ar
d
escr
ib
ed
a
m
et
h
o
d
o
f
f
i
n
g
er
p
r
in
t
clas
s
if
icatio
n
s
c
h
e
m
e
o
n
t
h
e
b
asis
o
f
A
NN.
Fin
g
er
p
r
in
t
id
en
t
if
icatio
n
s
c
h
e
m
e
u
s
ag
e
s
p
r
io
r
o
r
g
an
izatio
n
o
f
f
in
g
er
p
r
in
t
w
it
h
m
i
n
u
t
i
ae
f
ea
tu
r
e
[
1
4
]
.
I
n
tr
ad
itio
n
al
m
eth
o
d
s
p
er
f
o
r
m
a
n
ce
o
f
m
in
u
tiae
ab
s
tr
ac
tio
n
s
d
ep
en
d
in
te
n
s
el
y
o
n
an
au
g
m
en
tatio
n
al
g
o
r
ith
m
.
T
h
u
s
s
e
v
er
al
f
i
n
g
er
p
r
in
t
s
ar
e
co
m
p
o
s
ed
,
ta
k
i
n
g
a
lo
n
g
ti
m
e
to
m
atc
h
an
d
a
u
t
h
en
t
icate
a
s
p
ec
if
ied
f
in
g
er
p
r
in
t.
So
as
an
alter
n
ativ
e
o
f
cla
s
s
i
f
i
ca
tio
n
w
ith
t
h
e
m
i
n
u
tiae
[
1
5
]
t
h
e
y
p
r
o
j
ec
ted
a
class
if
icatio
n
s
ch
e
m
e
th
at
w
a
s
o
n
th
e
b
asis
o
f
i
n
d
i
v
id
u
al
f
ea
tu
r
es
s
u
c
h
as
t
h
e
s
i
n
g
u
lar
p
o
in
t
.
Sin
g
u
lar
p
o
in
t
d
etec
tio
n
w
a
s
v
er
y
r
o
b
u
s
t
a
n
d
r
eliab
le
th
at
o
v
er
co
m
es t
h
e
i
s
s
u
e
ab
o
u
t r
o
tatio
n
an
d
tr
an
s
lati
o
n
.
Dar
a
m
o
la
et
al.
[
1
6
]
p
r
o
j
ec
ted
a
r
o
b
u
s
t
v
er
i
f
icatio
n
s
c
h
e
m
e
o
n
th
e
b
asis
o
f
f
ea
t
u
r
es
ab
s
tr
ac
ted
f
r
o
m
h
u
m
a
n
f
i
n
g
er
p
r
in
ts
a
n
d
a
p
atter
n
class
i
f
ier
k
n
o
w
n
a
s
Su
p
p
o
r
t
Vec
to
r
Ma
ch
in
e
(
SVM)
.
E
f
f
icien
t
f
i
n
g
er
p
r
in
t
v
er
if
ica
tio
n
s
c
h
e
m
e
w
as
d
esir
ed
in
n
u
m
er
o
u
s
p
lace
s
f
o
r
p
er
s
o
n
al
e
m
p
at
h
y
to
ac
ce
s
s
p
h
y
s
ical
f
ac
ilit
ie
s
,
d
ata
etc.
T
h
r
ee
g
r
o
u
p
o
f
f
ea
tu
r
es
a
r
e
attac
h
ed
to
g
eth
er
an
d
p
ass
e
d
to
th
e
class
if
ier
.
T
h
e
f
u
s
ed
f
ea
tu
r
e
w
a
s
u
til
ized
to
tr
ain
th
e
s
c
h
e
m
e
f
o
r
o
p
er
ativ
e
v
er
i
f
icatio
n
o
f
co
n
s
u
m
er
s
f
i
n
g
er
p
r
in
t i
m
a
g
es.
L
i
u
et
a
l.
[
1
7
]
d
escr
ib
ed
a
to
u
ch
less
m
u
l
titi
er
f
i
n
g
er
p
r
i
n
t
ca
p
t
u
r
e
s
c
h
e
m
e
t
h
at
ac
q
u
ir
es
th
r
ee
d
is
s
i
m
ilar
asp
ec
t
s
o
f
f
in
g
er
p
r
in
t
i
m
a
g
es
a
t
t
h
e
s
i
m
i
lar
ti
m
e.
T
h
is
g
ad
g
e
t
m
ig
h
t
h
a
v
e
b
ee
n
p
lan
n
ed
E
v
en
t
u
all
y
T
o
m
's
p
er
u
s
i
n
g
u
p
g
r
ad
in
g
p
ar
a
m
eter
s
in
r
eg
ar
d
s
to
t
h
o
s
e
ca
u
g
h
t
f
in
g
er
i
m
p
r
ess
io
n
p
ict
u
r
e
ca
lib
er
an
d
g
ad
g
e
t
m
ea
s
u
r
e.
T
h
is
m
ac
h
i
n
e
w
as
i
n
ten
d
ed
b
y
o
p
ti
m
iz
in
g
p
ar
a
m
eter
s
co
n
ce
r
n
i
n
g
t
h
e
ca
p
t
u
r
ed
f
i
n
g
er
p
r
in
t
i
m
a
g
e
e
m
i
n
en
ce
a
n
d
d
ev
ice
s
ize.
A
f
i
n
g
er
p
r
in
t
m
o
s
aic
k
i
n
g
m
et
h
o
d
w
as
an
t
icip
ated
to
s
p
lice
to
g
eth
er
t
h
e
ca
p
tu
r
ed
i
m
a
g
es
o
f
a
f
in
g
er
to
f
o
r
m
an
i
m
a
g
e
w
it
h
a
g
r
ea
ter
v
al
u
ab
le
p
r
in
t
ar
e
n
a.
Op
ti
m
izatio
n
d
e
s
ig
n
o
f
t
h
eir
d
e
v
ice
w
a
s
es
tab
lis
h
ed
b
y
f
a
m
iliar
i
zin
g
t
h
e
d
esi
g
n
p
r
o
ce
s
s
a
n
d
a
s
s
o
ciati
n
g
w
it
h
p
r
ese
n
t
to
u
ch
les
s
m
u
ltit
ie
r
f
i
n
g
er
p
r
in
t a
cq
u
ir
e
m
e
n
t d
ev
ic
es.
L
ate
n
t
p
r
in
ts
ar
e
h
ab
itu
al
l
y
i
m
p
r
o
v
ed
f
r
o
m
o
f
f
en
s
e
s
ce
n
es
an
d
ar
e
co
n
n
ec
ted
w
it
h
ac
ce
s
s
ib
le
d
atab
ases
o
f
r
ec
o
g
n
ized
f
i
n
g
er
p
r
in
ts
f
o
r
r
ec
o
g
n
izin
g
cr
i
m
in
als.
Ho
w
e
v
er
,
cu
r
r
en
t
p
r
o
c
e
d
u
r
es
to
co
m
p
ar
e
laten
t
p
r
i
n
ts
to
g
r
ea
t
d
atab
ases
o
f
ex
e
m
p
lar
(
r
o
lled
o
r
p
lain
)
p
r
in
t
s
ar
e
p
r
ed
is
p
o
s
ed
to
er
r
o
r
s
.
T
h
is
r
ec
o
m
m
e
n
d
ed
ca
u
tio
n
in
cr
ea
tin
g
co
n
cl
u
s
io
n
s
ab
o
u
t
a
s
u
s
p
ec
t’
s
id
en
tit
y
o
n
th
e
b
as
is
o
f
a
laten
t
f
i
n
g
er
p
r
in
t
co
m
p
ar
is
o
n
.
A
ca
r
d
i
n
al
o
f
ef
f
o
r
ts
ac
ce
p
t b
ee
n
f
ab
r
icate
d
to
s
tatis
t
icall
y
ar
ch
et
y
p
al
t
h
e
ac
c
o
u
n
t o
f
a
f
i
n
g
er
p
r
in
t
ap
p
r
aisal
in
au
th
o
r
itati
v
e
a
ac
tu
al
ac
ce
p
t/re
j
ec
t
ac
co
m
m
o
d
atio
n
o
r
its
ap
o
ca
ly
p
tic
v
al
u
e.
T
h
ese
m
et
h
o
d
s
,
th
o
u
g
h
,
eith
er
ac
co
m
p
lis
h
u
n
r
ea
li
s
tic
e
x
p
ec
tatio
n
s
ab
o
u
t
th
e
ar
c
h
e
t
y
p
al
o
r
th
e
y
ab
r
id
g
e
m
en
t
s
i
m
p
le
clar
if
icatio
n
.
Nag
ar
et
al.
[
1
8
]
h
av
e
co
n
ten
d
ed
th
at
th
e
p
o
s
ter
io
r
p
r
o
b
ab
ilit
y
o
f
t
w
o
f
in
g
er
p
r
in
t
s
f
itti
n
g
to
d
is
s
i
m
ilar
f
i
n
g
er
s
p
r
o
v
id
ed
th
eir
m
atc
h
s
co
r
e,
m
en
t
io
n
ed
to
as
th
e
n
o
n
m
atch
p
r
o
b
ab
ilit
y
(
NM
P
)
,
ef
f
icien
tl
y
d
eten
tio
n
s
an
y
a
s
s
o
ciati
n
g
i
n
d
icatio
n
o
f
th
e
co
m
p
ar
is
o
n
.
NM
P
w
a
s
ca
lc
u
lated
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p
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ticatio
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e
f
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a
u
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n
tica
tio
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r
eg
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e
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n
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a
n
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r
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e
to
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o
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ce
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p
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v
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d
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s
.
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p
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icatio
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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.
1
.
Pr
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m
def
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bje
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Fin
g
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p
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ize
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ased
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o
f
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t b
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d.
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e.
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t r
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ilit
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to
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it d
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p
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g.
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o
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k
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3
.
2
.
F
ing
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print
Cla
s
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T
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ith
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Fig
u
r
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1
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Fig
u
r
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1
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3
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No
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Re
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No
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I
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test
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p
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a
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3
.
6
.
1.
T
ra
ini
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P
ha
s
e
I
n
th
e
tr
ain
in
g
p
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a
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n
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ts
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As
t
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u
tp
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alr
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y
k
n
o
w
n
in
t
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1213
1202
3
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6
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2
.
T
esting
P
ha
s
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I
n
th
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test
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h
ase,
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h
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i
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p
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t
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A
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o
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it
h
m
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y
i
n
co
r
p
o
r
atin
g
t
h
e
o
p
tim
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p
r
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ce
s
s
,
th
e
ac
cu
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ac
y
o
f
t
h
e
clas
s
i
f
icatio
n
w
il
l
b
e
i
m
p
r
o
v
ed
t
h
er
e
b
y
p
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v
id
in
g
a
b
etter
class
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f
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n
o
f
t
h
e
i
m
a
g
es.
T
h
e
s
tr
u
ctu
r
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o
f
t
h
e
ar
ti
f
icial
n
e
u
r
al
n
e
t
w
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k
i
s
ill
u
s
tr
ated
i
n
F
ig
u
r
e
2.
3
.
6
.
3
.
B
a
t
Alg
o
ri
t
h
m
f
o
r
O
pti
m
izi
ng
Weig
hts in A
NN
T
h
e
b
at
alg
o
r
ith
m
i
s
a
m
eta
h
e
u
r
is
tic
al
g
o
r
ith
m
,
e
x
cited
b
y
t
h
e
b
eh
av
io
r
o
f
ec
h
o
lo
ca
tio
n
o
f
m
icr
o
b
ats
[2
6
-
34
]
.
T
h
e
b
at
alg
o
r
ith
m
(
B
A
)
is
u
s
ed
to
o
p
ti
m
ize
t
h
e
w
ei
g
h
t o
f
h
id
d
en
la
y
er
n
e
u
r
o
n
s
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e
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e
t
w
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T
h
e
B
A
t
h
at
ex
p
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h
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tio
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en
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s
o
n
s
o
m
e
o
f
th
e
i
m
p
o
r
ta
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t
p
ar
a
m
eter
s
,
s
u
c
h
as
f
r
eq
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en
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y
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v
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,
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l
s
e
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ate
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d
lo
u
d
n
es
s
.
T
h
e
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A
c
h
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g
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al
s
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w
h
e
n
u
p
d
atin
g
t
h
e
cu
r
r
en
t
p
o
s
it
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n
w
i
th
t
h
e
v
e
lo
cit
y
o
f
t
h
e
m
o
s
t
s
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itab
le
s
o
lu
t
io
n
s
.
No
w
,
t
h
e
p
u
ls
e
e
m
is
s
io
n
r
ate,
as
w
el
l
as
th
e
lo
u
d
n
es
s
,
is
al
s
o
ef
f
icie
n
t
i
n
e
ac
h
iter
atio
n
.
I
n
th
e
d
e
m
a
n
d
t
o
ac
h
iev
e
t
h
e
B
A
s
o
m
e
o
f
t
h
e
ex
p
ec
tatio
n
s
w
er
e
p
r
ed
ef
in
ed
d
ep
en
d
in
g
o
n
t
h
e
c
h
ar
ac
ter
is
ti
c
c
h
ar
ac
ter
is
tic
s
o
f
th
e
b
ats.
Ass
u
m
p
t
io
n
:
Sev
er
al
o
f
t
h
e
ass
u
m
p
tio
n
s
m
u
s
t b
e
m
ad
e
w
ith
in
t
h
e
B
at
(
B
A)
A
l
g
o
r
ith
m
.
E
x
p
ec
tatio
n
s
ar
e
ir
r
eg
u
lar
h
er
e,
a.
A
ll b
at
s
ar
e
ab
le
to
d
is
tin
g
u
is
h
b
et
w
ee
n
b
ac
k
g
r
o
u
n
d
an
d
P
r
ey
.
b.
A
ll b
at
s
u
s
e
ec
h
o
lo
ca
tio
n
p
r
o
p
er
t
y
to
d
etec
t
d
is
tan
ce
.
c.
A
ll
b
ats
f
l
y
u
n
s
y
s
te
m
a
ticall
y
w
i
th
v
elo
cit
y
i
v
in
p
o
s
itio
n
i
x
an
d
r
elea
s
es
p
u
ls
e
s
o
f
s
o
u
n
d
w
it
h
f
r
eq
u
en
c
y
i
f
,
f
lu
c
tu
at
in
g
w
a
v
ele
n
g
t
h
an
d
lo
u
d
n
es
s
i
l
.
d.
Fre
q
u
en
c
y
(
o
r
)
w
av
ele
n
g
th
v
a
r
ies estab
lis
h
ed
in
t
h
e
v
ic
in
i
t
y
o
f
th
e
tar
g
e
t p
ar
ticle.
e.
Fu
r
t
h
er
m
o
r
e,
th
e
p
u
l
s
e
e
m
i
s
s
i
o
n
r
ate
ca
n
also
b
e
v
ar
ied
b
et
w
ee
n
th
e
r
an
g
e
o
f
0
an
d
1
b
a
s
ed
o
n
th
e
tar
g
et
lo
ca
tio
n
.
f.
L
o
u
d
n
ess
i
l
co
n
g
r
e
g
ates a
m
o
n
g
th
e
m
a
x
i
m
u
m
lo
u
d
n
e
s
s
m
a
x
l
to
co
n
s
tan
t
m
i
n
i
m
u
m
lo
u
d
n
es
s
m
i
n
l
T
h
e
f
o
llo
w
i
n
g
f
lo
w
ill
u
s
tr
atio
n
f
o
r
t
h
e
b
at
al
g
o
r
ith
m
u
s
ed
to
o
p
ti
m
ize
t
h
e
w
h
o
le
v
a
l
u
e
is
a
s
s
u
m
ed
b
y
th
e
Fi
g
u
r
e
3
.
Ste
p
1
:
I
n
p
u
t
m
icr
o
-
b
ats
(
i
B
)
p
o
p
u
latio
n
is
r
a
n
d
o
m
l
y
g
e
n
er
at
ed
.
A
cc
o
r
d
in
g
to
o
u
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
,
th
e
w
ei
g
h
ts
o
f
n
e
u
r
o
n
s
ar
e
co
n
s
id
er
ed
as
th
e
m
icr
o
-
b
ats.
E
a
ch
m
icr
o
-
b
at
h
a
s
t
h
e
v
elo
cit
y
v
ec
to
r
)
(
i
v
an
d
p
o
s
itio
n
v
ec
to
r
)
(
i
x
,
w
h
ic
h
is
d
e
s
cr
ib
ed
by
t
h
e
f
o
llo
w
in
g
E
q
u
atio
n
(
1
2
)
.
I
n
itiall
y
,
t
h
e
v
a
lu
es
o
f
th
e
s
e
cr
ed
en
tials
ar
e
ass
i
g
n
ed
r
an
d
o
m
l
y
to
a
p
ar
ticu
lar
r
an
g
e.
bn
mn
mn
b
m
m
b
m
m
bn
n
n
b
b
bn
n
n
b
b
i
x
v
x
v
x
v
x
v
x
v
x
v
x
v
x
v
x
v
B
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
2
2
2
1
1
1
2
2
2
22
22
2
22
21
1
1
2
12
12
1
11
11
(
1
2
)
Ste
p
2
:
T
o
allo
ca
te
th
e
ec
h
o
lo
ca
tio
n
p
ar
a
m
eter
s
,
t
h
e
m
icr
o
-
b
at
p
o
p
u
latio
n
s
ar
e
in
cl
u
d
ed
w
i
th
th
e
ec
h
o
lo
ca
tio
n
p
ar
a
m
e
ter
s
l
ik
e
f
r
eq
u
e
n
c
y
)
(
i
f
,
p
u
ls
e
r
ate
)
(
i
pr
,
an
d
th
e
lo
u
d
n
ess
p
ar
a
m
eter
s
)
(
i
l
.
T
h
ese
p
ar
am
eter
s
a
r
e
n
o
n
-
n
e
g
ati
v
e
r
ea
l v
alu
e
s
w
it
h
t
h
e
f
o
llo
w
i
n
g
r
an
g
e
s
.
m
a
x
m
i
n
f
f
f
i
,
m
a
x
m
i
n
pr
pr
pr
i
,
m
a
x
m
i
n
l
l
l
i
(
1
3
)
Her
e,
w
e
allo
ca
te
t
h
e
f
r
eq
u
e
n
c
y
r
a
n
g
e
0
m
in
f
an
d
1
m
a
x
f
,
th
e
p
u
ls
e
r
ate
m
i
n
i
m
u
m
v
al
u
e
5
.
0
m
in
pr
is
an
d
th
e
lo
u
d
n
es
s
m
a
x
i
m
u
m
v
al
u
e
is
1
m
a
x
l
.
T
h
e
r
em
ai
n
i
n
g
v
a
lu
es
ar
e
d
eter
m
i
n
ed
b
y
t
h
e
s
u
b
s
eq
u
en
t
E
q
u
a
tio
n
(
1
4
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
E
fficien
t F
in
g
erp
r
in
t I
d
e
n
tifi
ca
tio
n
u
s
in
g
N
eu
r
a
l Netw
o
r
k
a
n
d
B
A
T A
lg
o
r
ith
m
(
S
u
b
b
a
R
ed
d
y
B
o
r
r
a
)
1203
s
e
c
m
i
n
1
n
l
(
1
4
)
1
1
1
m
a
x
d
n
pr
(
1
5
)
W
h
er
e,
s
e
c
n
is
th
e
n
u
m
b
er
o
f
s
ec
ti
o
n
s
i
n
th
e
d
i
s
cr
ete
s
et
u
s
ed
f
o
r
s
izin
g
t
h
e
d
esi
g
n
v
ar
iab
le
a
n
d
s
e
c
n
is
t
h
e
n
u
m
b
er
o
f
d
is
cr
ete
d
esi
g
n
v
ar
i
ab
les.
Ste
p
3
:
C
alc
u
late
t
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
o
f
t
h
e
i
n
itial
p
o
p
u
l
atio
n
s
;
th
e
r
eq
u
ir
ed
f
it
n
es
s
f
u
n
ctio
n
is
d
escr
ib
ed
by
t
h
e
f
o
llo
w
in
g
E
q
u
atio
n
(
1
6
)
.
M
S
E
F
i
m
i
n
(
1
6
)
A
cc
o
r
d
in
g
to
E
q
u
atio
n
(
1
6
)
,
t
h
e
f
r
eq
u
en
c
y
o
f
ea
c
h
cla
s
s
lab
el
is
u
s
ed
to
d
ef
i
n
e
f
itn
e
s
s
v
al
u
e
f
o
r
ea
c
h
m
icr
o
b
at
.
T
h
e
f
itn
e
s
s
f
u
n
ct
io
n
o
f
th
e
m
icr
o
b
ats
i
s
d
eter
m
i
n
ed
b
ased
o
n
th
e
m
ea
n
s
q
u
ar
e
er
r
o
r
(
MSE
)
.
W
h
en
th
e
o
b
tain
ed
MSE
o
f
a
m
icr
o
b
at
is
f
o
u
n
d
lo
w
,
t
h
e
n
th
e
m
icr
o
b
at
is
r
an
k
ed
as a
b
est
m
icr
o
b
at.
Ste
p 4
:
Sto
r
e
th
e
cu
r
r
en
t p
o
p
u
latio
n
an
d
au
g
m
e
n
t th
e
i
ter
atio
n
co
u
n
t a
s
t+1
,
i.e
.
,
iter
atio
n
t =
t+1
.
Ste
p
5
:
T
h
e
cu
r
r
en
t
p
o
p
u
l
atio
n
o
f
r
u
le
s
is
r
a
n
d
o
m
l
y
u
p
d
ated
b
ased
o
n
th
e
f
r
eq
u
e
n
c
y
an
d
th
e
v
elo
cit
y
.
I
n
itiall
y
,
th
e
f
r
eq
u
e
n
c
y
ca
n
b
e
ev
alu
a
ted
,
w
h
ic
h
is
d
escr
ib
ed
by
t
h
e
f
o
llo
w
in
g
E
q
u
atio
n
(
1
7
)
.
i
t
i
u
f
f
f
f
)
(
m
i
n
m
a
x
m
i
n
(
1
7
)
W
h
er
e,
i
u
is
th
e
r
an
d
o
m
n
u
m
b
e
r
o
f
v
alu
es,
w
h
ic
h
is
s
elec
ted
f
r
o
m
0
to
1
,
th
en
t
h
e
f
r
eq
u
e
n
c
y
is
ap
p
lied
to
th
e
v
elo
cit
y
eq
u
at
io
n
,
w
h
ich
c
an
b
e
d
escr
ib
ed
by
th
e
f
o
llo
w
i
n
g
E
q
u
a
tio
n
(
1
8
)
.
]
)
(
[
1
1
t
i
t
i
t
i
t
i
f
x
x
v
r
o
u
n
d
v
(
1
8
)
t
i
t
i
t
i
v
x
x
1
(
1
9
)
W
h
er
e,
t
i
v
an
d
1
t
i
v
ar
e
th
e
v
elo
cit
y
v
ec
to
r
s
o
f
th
e
m
icr
o
-
b
ats
at
th
e
ti
m
e
s
tep
s
t
an
d
,
t
i
x
an
d
1
t
i
x
ar
e
th
e
p
o
s
itio
n
v
ec
to
r
s
o
f
t
h
e
m
icr
o
-
b
ats
at
ti
m
e
s
tep
s
t
an
d
,
x
is
t
h
e
cu
r
r
e
n
t
g
lo
b
al
b
est
s
o
lu
t
i
o
n
.
Her
e
af
ter
p
er
f
o
r
m
in
g
t
h
e
lo
ca
l
s
ea
r
ch
in
t
h
e
r
a
n
d
o
m
l
y
s
elec
ted
p
o
p
u
latio
n
,
th
i
s
i
s
d
escr
ib
ed
b
y
th
e
f
o
llo
w
i
n
g
E
q
u
atio
n
(
2
0
)
.
A
s
o
lu
t
io
n
is
s
elec
ted
a
m
o
n
g
c
u
r
r
en
t
b
est
s
o
lu
tio
n
s
an
d
th
e
n
r
an
d
o
m
w
a
lk
is
i
n
tr
o
d
u
ce
d
to
o
b
tain
n
e
w
s
o
l
u
tio
n
t
a
v
g
j
i
o
l
d
n
e
w
l
x
x
,
(
2
0
)
W
h
er
e,
j
i
,
is
a
r
an
d
o
m
n
u
m
b
er
b
et
w
ee
n
1
an
d
1
,
t
a
v
g
l
is
th
e
a
v
er
ag
e
v
a
l
u
e
o
f
lo
u
d
n
ess
at
t
i
m
e
s
tep
.
Ste
p
6
:
Fi
n
d
t
h
e
f
it
n
e
s
s
o
f
t
h
e
n
e
w
m
icr
o
-
b
ats
p
o
p
u
latio
n
u
s
i
n
g
t
h
e
E
q
u
atio
n
(
1
6
)
.
Af
ter
e
v
al
u
atio
n
,
th
e
m
icr
o
-
b
ats
ec
h
o
lo
ca
tio
n
p
ar
am
eter
s
ar
e
u
p
d
ated
f
o
r
b
etter
m
o
v
i
n
g
o
f
t
h
e
m
icr
o
-
b
ats,
w
h
ich
ca
n
b
e
d
escr
ib
ed
by
t
h
e
f
o
llo
w
in
g
E
q
u
atio
n
(
2
1
)
.
)]
e
x
p
(
1
[
.
m
a
x
1
1
t
pr
pr
and
l
a
l
t
i
t
i
t
i
(
2
1
)
W
h
er
e,
1
t
i
l
an
d
t
i
l
ar
e
th
e
u
p
d
ated
an
d
p
r
ev
io
u
s
v
alu
e
s
o
f
t
h
e
lo
u
d
n
es
s
1
t
pr
is
t
h
e
p
u
l
s
e
r
ate
o
f
t
h
e
m
icr
o
-
b
ats in
t
h
e
ti
m
e
s
tep
,
a
an
d
ar
e
t
h
e
ad
ap
tatio
n
p
ar
a
m
eter
s
o
f
t
h
e
lo
u
d
n
es
s
an
d
p
u
ls
e
r
ate.
Ste
p 7
:
T
o
f
in
d
th
e
b
est
m
icr
o
-
b
ats,
w
h
ich
s
atis
f
ie
s
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
Ste
p 8
:
T
h
e
s
tep
s
4
to
7
is
co
n
tin
u
ed
u
n
til t
h
e
ter
m
i
n
atio
n
cr
iter
ia
ar
e
attain
ed
.
Her
e
th
e
in
p
u
t
w
ill
b
e
t
h
e
w
ei
g
h
t
s
o
f
Ne
u
r
o
n
,
b
ased
o
n
t
h
e
f
it
n
es
s
;
th
e
o
p
ti
m
al
w
ei
g
h
ts
o
f
a
n
e
u
r
o
n
ar
e
s
elec
ted
.
T
h
e
o
p
tim
al
w
e
i
g
h
t
s
w
ill
h
elp
th
e
A
N
N
to
class
i
f
y
t
h
e
f
in
g
er
p
r
in
t
s
m
o
r
e
ac
cu
r
atel
y
.
T
h
e
f
it
n
es
s
Evaluation Warning : The document was created with Spire.PDF for Python.