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[
1
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B
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alg
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m
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alo
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[
2
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.
An
o
th
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k
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ess
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f
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es
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alg
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r
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m
s
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th
at
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[
3
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.
Alth
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m
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[
4
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-
[
6
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T
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tain
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m
o
s
t p
o
p
u
lar
way
s
to
d
is
co
v
er
d
ata
k
n
o
wled
g
e
.
T
h
e
d
is
co
v
er
y
o
f
k
n
o
wled
g
e
is
b
r
o
ad
ly
d
iv
id
ed
in
to
two
ca
teg
o
r
ies:
s
u
p
er
v
is
ed
an
d
u
n
s
u
p
er
v
is
ed
.
A
s
u
p
er
v
is
ed
k
n
o
wled
g
e
d
is
co
v
er
y
p
r
o
ce
s
s
ty
p
ically
r
eq
u
ir
es
class
lab
els
th
at
ar
e
s
o
m
e
tim
es
n
o
t
av
ailab
le
in
th
e
d
ataset
.
T
h
is
m
ac
h
in
e
m
o
d
el
lear
n
s
u
s
in
g
lab
e
led
d
ata
an
d
h
av
in
g
th
e
r
ig
h
t
an
s
wer
s
.
Un
s
u
p
er
v
is
ed
m
ac
h
in
e
lear
n
in
g
is
th
e
p
r
o
ce
s
s
th
at
a
m
ac
h
in
e
lear
n
s
with
o
u
t
u
s
in
g
lab
eled
d
ata
an
d
an
y
teac
h
er
s
.
Kn
o
wn
d
is
co
v
er
y
k
n
o
wled
g
e
tech
n
iq
u
es
s
u
ch
as
clu
s
ter
in
g
ca
n
h
an
d
le
u
n
lab
eled
d
ataset
s
.
T
h
e
K
-
m
ea
n
s
alg
o
r
i
th
m
f
o
r
clu
s
ter
in
g
is
o
n
e
o
f
th
e
m
o
s
t
p
o
p
u
lar
an
d
wid
ely
u
s
ed
alg
o
r
ith
m
s
[
7
]
.
I
n
th
is
p
ap
er
,
af
ter
ex
ten
s
iv
e
r
esear
ch
,
we
h
av
e
co
n
clu
d
ed
th
at
th
e
s
elec
tio
n
o
f
th
e
in
itial
p
o
p
u
latio
n
f
o
r
ar
tific
ial
n
eu
r
al
n
etwo
r
k
tr
ain
in
g
alg
o
r
i
th
m
s
is
v
er
y
im
p
o
r
tan
t
.
So
in
s
tead
o
f
r
an
d
o
m
ly
s
elec
tio
n
an
in
itial
p
o
p
u
latio
n
in
a
s
m
all
s
ea
r
ch
s
p
ac
e,
we
d
ec
id
ed
to
u
s
e
r
esu
lt
o
f
clu
s
ter
in
g
in
a
lar
g
er
s
ea
r
ch
s
p
ac
e.
Sear
ch
in
g
in
a
lar
g
er
s
p
ac
e
in
cr
ea
s
es
th
e
ch
an
ce
s
o
f
f
in
d
in
g
a
g
lo
b
al
o
p
tim
al
o
r
ex
tr
em
ely
clo
s
e
to
o
p
tim
al
an
s
wer
s
.
Usi
n
g
th
e
m
o
d
if
ied
k
-
m
ea
n
alg
o
r
ith
m
,
we
d
iv
id
e
o
u
r
lar
g
e
in
itial
p
o
p
u
latio
n
in
to
a
lim
ited
n
u
m
b
er
o
f
clu
s
ter
s
,
an
d
th
en
co
n
s
id
er
th
e
b
est
clu
s
ter
ce
n
ter
s
as
th
e
in
itial
p
o
p
u
latio
n
o
f
o
u
r
tr
ain
in
g
alg
o
r
ith
m
.
W
e
th
en
u
s
e
an
im
p
r
o
v
ed
teac
h
in
g
-
lear
n
in
g
b
ased
o
p
tim
izatio
n
alg
o
r
ith
m
(
I
T
L
B
O)
as
th
e
tr
ain
in
g
alg
o
r
ith
m
.
T
h
is
alg
o
r
ith
m
s
o
lv
es
th
e
p
r
o
b
lem
o
f
tr
ap
p
in
g
in
th
e
lo
ca
l
o
p
tim
al
an
d
b
y
cr
ea
tin
g
a
p
r
o
p
er
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
,
it h
as b
ee
n
ab
le
to
g
et
clo
s
er
to
th
e
g
lo
b
al
o
p
tim
al
.
T
h
e
r
e
s
t
o
f
th
is
ar
ticle
is
b
ein
g
as
:
I
n
th
is
ar
ticle,
we
will
f
ir
s
t
g
iv
e
a
b
r
ief
d
escr
ip
tio
n
o
f
th
e
clu
s
ter
in
g
alg
o
r
ith
m
u
s
ed
in
s
ec
tio
n
2
,
an
d
th
en
we
p
r
esen
t
th
e
I
T
L
B
O
alg
o
r
ith
m
s
,
an
d
th
en
we
d
escr
ib
e
o
u
r
p
r
o
p
o
s
ed
m
eth
o
d
.
T
h
en
,
in
s
ec
tio
n
3
,
we
f
ir
s
t
p
r
o
v
id
e
a
b
r
ief
d
escr
ip
tio
n
o
f
c
ase
s
tu
d
y
d
ata
s
et
s
,
an
d
th
en
we
s
h
o
w
th
e
r
esu
lts
o
f
ex
p
er
im
en
ts
u
s
in
g
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ap
p
lied
to
th
e
n
eu
r
al
n
etwo
r
k
p
r
o
b
lem
.
T
h
e
co
n
clu
s
io
n
o
f
th
is
wo
r
k
is
p
r
esen
ted
in
th
e
last
s
ec
tio
n
.
2.
M
AT
E
RIAL
S
AND
M
E
T
H
O
DS
2
.
1
.
K
-
m
ea
n
c
lus
t
er
ing
No
wad
ay
s
,
clu
s
ter
in
g
is
o
n
e
o
f
th
e
m
o
s
t
wid
ely
u
s
ed
is
s
u
es
in
th
e
f
ield
o
f
ar
tific
ial
in
tellig
en
ce
.
T
h
e
is
s
u
e
o
f
clu
s
ter
in
g
h
as
p
ar
ticu
lar
im
p
o
r
tan
ce
d
u
e
to
th
e
g
r
o
win
g
v
o
lu
m
e
o
f
web
-
b
ased
tex
ts
,
tex
tu
al
s
tatu
es,
ar
ticles
,
an
d
ca
n
also
b
e
ef
f
ec
tiv
e
in
im
p
r
o
v
in
g
th
e
r
esu
lts
o
b
tain
ed
f
r
o
m
s
ea
r
ch
en
g
in
es
an
d
in
f
o
r
m
atio
n
class
if
icatio
n
.
Pro
p
er
clu
s
ter
in
g
m
ak
es
it
ea
s
ier
to
s
ea
r
ch
an
d
ac
ce
s
s
in
f
o
r
m
atio
n
m
o
r
e
ef
f
icien
tly
.
I
n
g
en
er
al,
clu
s
ter
in
g
alg
o
r
ith
m
s
ca
n
b
e
d
iv
id
ed
in
to
two
g
en
er
al
ca
teg
o
r
i
es:
O
v
er
lap
p
in
g
clu
s
ter
in
g
m
eth
o
d
an
d
ex
clu
s
iv
e
clu
s
ter
in
g
m
eth
o
d
.
I
n
th
e
o
v
er
lap
p
in
g
clu
s
ter
in
g
m
eth
o
d
,
a
d
ata
ca
n
b
elo
n
g
to
s
ev
er
al
clu
s
ter
s
with
d
if
f
er
en
t
r
atio
s
,
an
ex
am
p
le
o
f
wh
ich
is
f
u
zz
y
clu
s
ter
in
g
.
I
n
th
e
ex
clu
s
iv
e
clu
s
ter
in
g
m
eth
o
d
,
af
ter
clu
s
ter
in
g
,
ea
ch
d
ata
i
s
ass
ig
n
ed
ex
ac
tly
o
n
e
clu
s
ter
,
k
-
m
ea
n
alg
o
r
ith
m
b
elo
n
g
s
to
th
is
ca
teg
o
r
y
.
T
h
e
k
-
m
ea
n
clu
s
ter
in
g
is
th
e
p
r
o
ce
s
s
o
f
class
if
y
in
g
a
s
et
o
f
o
b
jects in
to
clu
s
ter
s
,
in
wh
ich
th
e
in
ter
n
al
m
em
b
er
s
o
f
ea
ch
clu
s
ter
ar
e
m
o
s
t
s
im
ilar
to
ea
ch
o
th
er
an
d
h
av
e
th
e
least
s
im
ilar
to
m
em
b
er
s
o
f
o
th
er
clu
s
ter
s
.
C
lu
s
ter
in
g
is
th
e
p
r
o
ce
s
s
o
f
s
ep
ar
atin
g
d
ata
o
r
o
b
jects
in
to
s
u
b
class
es
ca
lled
clu
s
ter
s
.
E
ac
h
clu
s
ter
co
n
tain
s
d
ata
th
at
s
ee
m
s
to
b
e
m
o
r
e
s
im
ilar
to
ea
ch
o
th
er
,
an
d
d
ata
th
at
ap
p
ea
r
s
to
b
e
less
s
i
m
ilar
to
ea
ch
o
th
er
is
p
lace
d
in
d
if
f
er
en
t c
lu
s
ter
s
.
T
h
e
k
-
m
ea
n
alg
o
r
ith
m
is
o
n
e
o
f
th
e
m
o
s
t w
id
ely
u
s
ed
clu
s
ter
in
g
alg
o
r
ith
m
s
.
T
h
is
alg
o
r
ith
m
was
f
ir
s
t
in
tr
o
d
u
ce
d
b
y
Mc
Qu
ee
n
in
1
9
6
7
[
8
]
th
at
is
d
esig
n
ed
f
o
r
clu
s
ter
in
g
n
u
m
er
ical
d
ata.
I
n
th
e
k
-
m
ea
n
alg
o
r
i
th
m
,
f
ir
s
t
th
e
k
m
em
b
er
is
r
an
d
o
m
ly
s
elec
ted
f
r
o
m
th
e
n
m
em
b
er
s
as
th
e
clu
s
ter
ce
n
ter
s
(
k
<n
)
.
T
h
e
r
em
ain
in
g
n
-
k
m
em
b
er
s
ar
e
th
en
ass
ig
n
ed
to
th
e
n
ea
r
est
clu
s
ter
ce
n
ter
b
ased
o
n
E
u
clid
ea
n
d
is
tan
ce
.
Af
ter
allo
ca
tin
g
all
m
em
b
er
s
,
th
e
clu
s
ter
ce
n
ter
s
ar
e
r
ec
al
cu
lated
b
y
th
e
av
er
ag
e
v
alu
e
o
f
th
e
clu
s
ter
s
m
em
b
er
s
,
an
d
th
is
co
n
tin
u
es
u
n
til th
e
clu
s
ter
ce
n
ter
s
r
em
ain
s
tab
le.
Su
p
p
o
s
e
th
at
=
{
1
,
2
,
…
,
}
is
a
s
et
of
n
d
ata
an
d
1
,
2
,
…
,
k
ar
e
s
ep
ar
ate
clu
s
ter
s
o
n
D,
in
wh
ich
ca
s
e
th
e
er
r
o
r
f
u
n
ctio
n
is
d
ef
in
ed
is
b
ein
g
as
:
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:
2
0
8
8
-
8
7
0
8
Usi
n
g
th
e
mo
d
ified
k
-
mea
n
a
l
g
o
r
ith
m
w
ith
a
n
imp
r
o
ve
d
tea
ch
in
g
lea
r
n
in
g
b
a
s
ed
…
(
Mo
r
teza
Jo
u
yb
a
n
)
5279
=
∑
∑
(
,
(
)
)
∈
=
1
(
1
)
w
h
er
e
μ
(
)
is
th
e
ce
n
ter
o
f
th
e
clu
s
ter
an
d
d
(
x
,
μ
(
)
)
is
th
e
d
is
tan
ce
b
etwe
en
x
an
d
μ
(
)
.
E
u
clid
ea
n
d
is
tan
ce
s
ar
e
co
m
m
o
n
ly
u
s
ed
to
ca
lcu
late
d
is
tan
ce
in
th
is
f
o
r
m
u
la.
B
u
t
in
th
is
p
ap
er
,
we
u
s
e
Ma
n
h
attan
d
is
tan
ce
to
id
en
tify
m
em
b
er
s
b
elo
n
g
in
g
to
clu
s
ter
s
,
an
d
we
m
o
d
if
y
th
e
k
-
m
ea
n
alg
o
r
ith
m
in
th
is
way
.
T
h
is
m
o
d
if
ied
alg
o
r
ith
m
m
ain
tain
s
b
o
th
n
u
m
er
ical
an
d
ca
teg
o
r
ical
f
ea
tu
r
es
o
f
th
e
s
am
p
les.
T
h
e
d
is
tan
ce
in
o
u
r
m
eth
o
d
is
ca
lcu
lated
is
b
ein
g
as
in
(
2
)
.
(
,
(
)
)
=
∑
|
,
−
(
)
,
|
+
∑
(
,
−
(
)
,
)
=
+
1
=
1
|
|
(
2
)
T
h
e
Ma
n
h
attan
'
s
d
is
tan
ce
is
b
ased
o
n
t
h
e
s
u
m
a
b
s
o
lu
te
v
alu
es
er
r
o
r
s
an
d
is
less
s
en
s
i
tiv
e
th
an
th
e
s
u
m
s
q
u
ar
es e
r
r
o
r
s
.
2.
2
.
I
m
pro
v
ing
t
ea
ching
-
lea
rning
o
ptim
iza
t
io
n a
lg
o
rit
hm
(
I
T
L
B
O
)
T
h
e
teac
h
in
g
-
lear
n
in
g
o
p
tim
izatio
n
(
T
L
B
O)
alg
o
r
ith
m
was
in
tr
o
d
u
ce
d
b
y
R
ao
.
I
n
2
0
1
1
[
9
]
th
is
alg
o
r
ith
m
is
a
p
o
p
u
lar
an
d
p
o
wer
f
u
l
o
p
tim
izatio
n
alg
o
r
ith
m
th
at
is
u
s
ed
in
m
an
y
en
g
in
ee
r
in
g
an
d
r
ea
l
-
wo
r
ld
p
r
o
b
lem
s
.
T
h
e
alg
o
r
ith
m
is
in
s
p
ir
ed
b
y
th
e
p
r
o
ce
s
s
o
f
teac
h
in
g
an
d
lear
n
in
g
in
a
ty
p
ical
class
r
o
o
m
.
Alth
o
u
g
h
T
L
B
O
o
f
f
er
s
h
ig
h
-
q
u
ality
s
o
lu
tio
n
s
in
th
e
s
h
o
r
test
p
o
s
s
ib
le
tim
e
an
d
h
as
co
n
s
is
ten
t
co
n
v
er
g
en
ce
[
9
]
,
in
th
e
lear
n
in
g
p
h
ase
o
f
th
is
alg
o
r
ith
m
,
ea
ch
lear
n
er
r
an
d
o
m
ly
s
elec
ts
an
o
th
er
lear
n
er
f
r
o
m
th
e
p
o
p
u
latio
n
.
T
h
is
p
r
o
b
lem
lead
s
to
an
im
b
alan
ce
b
etwe
en
th
e
two
co
n
ce
p
ts
o
f
d
iv
er
s
ity
an
d
co
n
v
er
g
en
ce
.
I
T
L
B
O
s
o
lv
es
th
is
p
r
o
b
lem
b
y
im
p
r
o
v
in
g
th
e
b
asic
T
L
B
O.
I
n
th
is
alg
o
r
ith
m
,
th
e
teac
h
in
g
p
h
ase
is
th
e
s
am
e
as
th
e
b
asic
T
L
B
O
alg
o
r
ith
m
,
an
d
th
e
lear
n
in
g
p
h
ase
is
d
escr
ib
ed
is
b
ein
g
as
.
At
th
is
s
tag
e,
all
lear
n
er
s
ar
e
r
an
d
o
m
ly
p
lace
d
in
a
r
ec
tan
g
u
lar
s
tr
u
ctu
r
e.
E
v
er
y
lear
n
er
h
av
e
to
lear
n
f
r
o
m
th
eir
n
eig
h
b
o
r
s
.
Her
e,
in
o
r
d
er
to
in
cr
ea
s
e
th
e
d
iv
er
s
ity
in
th
e
alg
o
r
ith
m
,
af
ter
a
ce
r
tain
n
u
m
b
er
o
f
iter
atio
n
s
,
th
e
m
em
b
er
s
ar
e
r
an
d
o
m
ly
r
ea
r
r
an
g
ed
in
a
r
ec
tan
g
u
lar
s
tr
u
ctu
r
e.
IT
L
B
O
h
as
b
ee
n
d
ev
elo
p
ed
to
im
p
r
o
v
e
th
e
T
L
B
O
alg
o
r
ith
m
.
I
n
T
L
B
O,
f
o
r
ex
am
p
le,
r
an
d
o
m
ch
o
ices m
ak
e
lo
w
lo
ca
l sear
ch
ab
ilit
ies,
b
u
t in
I
T
L
B
O,
alo
n
g
with
ad
d
in
g
th
e
co
n
ce
p
t o
f
n
eig
h
b
o
r
h
o
o
d
,
we
tr
y
to
r
ed
u
ce
r
an
d
o
m
ch
o
ices a
n
d
u
s
e
th
e
ca
p
ab
ilit
ies o
f
n
eig
h
b
o
r
s
.
T
h
is
in
cr
ea
s
es th
e
lo
ca
l
an
d
g
lo
b
al
s
ea
r
ch
ab
ilit
y
.
T
h
e
m
ain
s
ec
tio
n
s
o
f
I
T
L
B
O
ar
e:
2
.
2
.
1
.
I
T
L
B
O
lea
rning
ph
a
s
e
I
n
th
is
p
h
ase,
ea
ch
lear
n
er
is
k
n
o
wn
with
an
in
teg
er
an
d
p
lace
d
in
a
r
ec
tan
g
u
lar
ar
r
ay
.
Neig
h
b
o
r
s
o
f
ea
ch
lear
n
er
ar
e
clea
r
ly
id
en
t
if
ied
in
Fig
u
r
e
1
.
At
th
is
s
tep
,
lear
n
er
s
m
ay
lear
n
f
r
o
m
n
eig
h
b
o
r
s
o
r
th
e
b
est
p
er
s
o
n
in
th
e
class
.
T
h
is
p
r
o
ce
s
s
is
b
ased
o
n
lo
ca
l
s
ea
r
ch
ca
p
ab
ilit
y
,
in
ad
d
itio
n
,
a
b
alan
ce
is
estab
lis
h
ed
b
etwe
en
lo
ca
l a
n
d
g
lo
b
al
s
ea
r
ch
.
I
n
a
lo
ca
l sear
ch
,
ea
ch
lear
n
er
u
p
d
ates
th
eir
p
o
s
itio
n
with
th
e
p
r
o
b
ab
ilit
y
o
f
a
Pc
b
y
th
e
b
est lea
r
n
er
in
th
eir
n
eig
h
b
o
r
h
o
o
d
o
r
b
y
th
e
teac
h
er
,
th
e
g
lo
b
al
b
est
,
in
th
e
p
o
p
u
latio
n
.
Fig
u
r
e
1
.
A
class
o
f
lear
n
er
s
a
r
r
an
g
e
d
in
a
r
ec
ta
n
g
le
,
=
,
+
2
.
(
,
ℎ
−
,
)
+
3
.
(
ℎ
−
,
)
(3
)
W
h
er
e
,
ℎ
is
th
e
teac
h
er
in
th
e
n
eig
h
b
o
r
h
o
o
d
o
f
an
d
ℎ
is
th
e
teac
h
er
o
f
th
e
wh
o
le
class
,
an
d
2
,
3
a
re
r
an
d
o
m
n
u
m
b
er
s
in
th
e
r
an
g
e
o
f
(
0
,
1
)
.
I
f
th
e
n
ew
p
o
s
itio
n
o
f
each
m
em
b
er
is
im
p
r
o
v
ed
,
th
e
n
ew
p
o
s
itio
n
will
b
e
ac
ce
p
ted
.
I
n
th
e
g
lo
b
al
s
ea
r
ch
,
if
th
e
p
r
o
b
ab
ilit
y
o
f
Pc
is
n
o
t
m
et,
ea
ch
lear
n
er
s
elec
ts
a
r
an
d
o
m
lear
n
er
lik
e
f
r
o
m
th
e
wh
o
le
class
to
p
r
o
v
id
e
lear
n
in
g
,
if
is
b
etter
th
an
,
o
r
else,
lear
n
in
g
estab
lis
h
b
ased
o
n
T
L
B
O
alg
o
r
ith
m
lear
n
in
g
p
h
ase
b
y
(
4
)
,
(
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
5
2
7
7
-
5
2
8
5
5280
=
+
.
(
−
)
(
)
>
(
)
(4
)
=
+
.
(
−
)
(
)
<
(
)
(5
)
T
h
er
ef
o
r
e,
u
s
in
g
th
is
o
p
er
atio
n
,
b
o
th
lo
ca
l
an
d
g
lo
b
al
s
ea
r
ch
ca
p
ab
ilit
ies
ar
e
o
b
tain
ed
.
I
n
th
is
alg
o
r
ith
m
,
we
im
p
r
o
v
e
ex
p
lo
itatio
n
ca
p
ab
ilit
y
b
y
th
is
co
n
ce
p
t
th
at
f
o
r
ea
ch
p
er
s
o
n
in
th
e
p
o
p
u
latio
n
th
er
e
ar
e
a
n
u
m
b
er
o
f
n
eig
h
b
o
r
s
wh
o
lear
n
f
r
o
m
th
e
b
est
o
f
th
em
.
T
o
m
ain
tain
d
iv
er
s
ity
af
ter
a
n
u
m
b
er
o
f
iter
at
io
n
s
,
eac
h
p
er
s
o
n
'
s
n
eig
h
b
o
r
in
g
m
em
b
er
s
ch
an
g
e.
T
h
is
m
ak
es
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
ca
p
ab
ilit
ies.
2
.
3
.
I
nv
estig
a
t
e
t
he
ra
ng
e
o
f
v
a
ria
ble c
ha
ng
es
I
n
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
,
wh
en
a
n
ew
p
o
s
itio
n
is
o
b
tain
ed
f
o
r
ea
ch
in
d
iv
id
u
al,
it
m
ay
lead
to
th
e
p
r
o
d
u
ctio
n
o
f
v
ar
iab
les
th
at
ar
e
o
u
ts
id
e
th
e
d
ef
in
ed
r
an
g
e.
I
n
th
is
ca
s
e,
m
o
s
t
r
esear
ch
er
s
u
s
e
f
r
o
m
co
n
v
er
g
en
ce
ap
p
r
o
ac
h
b
ased
o
n
alg
o
r
ith
m
1
,
b
u
t
th
is
m
eth
o
d
is
an
o
ld
an
d
o
b
s
o
lete
m
eth
o
d
th
at
ca
u
s
es
th
e
alg
o
r
ith
m
to
tr
ap
p
in
g
in
th
e
lo
ca
l
m
in
im
u
m
.
T
o
o
v
er
co
m
e
th
ese
p
r
o
b
lem
s
,
we
h
av
e
p
r
o
p
o
s
ed
a
n
ew
m
eth
o
d
in
a
lg
o
r
ith
m
2
to
d
eter
m
in
e
th
e
r
an
g
e
o
f
v
ar
iab
le
ch
an
g
es
,
as
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
is
alg
o
r
ith
m
p
r
ev
en
ts
th
e
alg
o
r
ith
m
f
r
o
m
tr
ap
p
in
g
in
th
e
lo
ca
l
o
p
tim
a
l
an
d
also
p
r
ev
en
t
f
r
o
m
m
ak
in
g
th
e
b
est
an
s
wer
s
in
h
ig
h
n
u
m
b
er
of
iter
atio
n
.
Alg
o
r
ith
m
1
.
B
asic
bound
c
o
n
s
tr
ain
ts
h
an
d
lin
g
1.
For j=
1
→
dim
2.
If
(
)
>
(
)
3.
(
)
=
(
)
4.
Else if
(
)
<
(
)
5.
(
)
=
(
)
6.
End if
7.
End for
(
a)
Alg
o
r
ith
m
2
.
Mo
d
if
ied
b
o
u
n
d
co
n
s
tr
ain
ts
h
an
d
lin
g
1.
For j=
1
→
dim
2.
If
(
)
<
(
)
3.
(
)
=
(2*
(
)
)
–
(
)
4.
Else if
(
)
>
(
)
5.
(
)
=
(2*
(
)
)
–
(
)
6.
End if
7.
End for
(
b
)
Fig
u
r
e
2
.
T
h
e
r
an
g
e
o
f
v
ar
iab
l
e
ch
an
g
es
;
(
a)
a
l
g
o
r
ith
m
1
:
b
a
s
ic
b
o
u
n
d
c
o
n
s
tr
ain
ts
h
an
d
li
n
g
,
(
b
)
alg
o
r
ith
m
2
:
m
o
d
if
ie
d
b
o
u
n
d
co
n
s
tr
ain
ts
h
a
n
d
lin
g
3.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
e
b
asic T
L
B
O
alg
o
r
ith
m
,
lik
e
o
th
er
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
,
s
u
f
f
er
s
f
r
o
m
lo
w
co
n
v
er
g
en
ce
s
p
ee
d
.
I
n
o
r
d
er
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
alg
o
r
ith
m
we
m
o
d
if
ied
th
e
lear
n
in
g
p
h
ase
o
f
T
L
B
O
alg
o
r
ith
m
an
d
th
en
we
p
r
esen
ted
I
T
L
B
O
alg
o
r
ith
m
with
b
alan
ce
b
etwe
en
lo
ca
l
an
d
g
lo
b
al
s
ea
r
ch
.
An
d
also
,
we
u
s
ed
f
r
o
m
a
d
ata
m
in
in
g
tech
n
iq
u
e
ca
lled
M
k
-
m
ea
n
to
m
ak
e
m
o
r
e
ef
f
icien
t
u
s
e
o
f
th
e
h
id
d
en
in
f
o
r
m
atio
n
in
th
e
s
ea
r
ch
s
p
ac
e
to
cr
ea
te
a
m
o
r
e
s
u
itab
le
in
itial
p
o
p
u
latio
n
.
C
lu
s
ter
in
g
m
e
an
s
p
lacin
g
d
ata
in
ea
ch
clu
s
ter
th
at
h
as
th
e
least
d
is
tan
ce
an
d
th
e
m
o
s
t similar
ity
.
T
h
e
im
p
o
r
tan
ce
o
f
in
itial
p
o
p
u
latio
n
s
in
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
h
as
lo
n
g
b
ee
n
d
eb
ated
.
T
h
e
in
itial
p
o
p
u
latio
n
is
th
e
s
tar
tin
g
p
o
in
t
o
f
an
y
alg
o
r
ith
m
,
an
d
alg
o
r
ith
m
s
th
at
s
tar
t
at
a
p
r
o
p
er
s
tar
tin
g
p
o
in
t
m
ay
h
av
e
b
etter
r
esu
lts
th
an
o
th
er
s
.
I
n
th
is
ar
ticle
,
we
h
av
e
tr
ied
to
s
tar
t
o
f
a
s
tr
o
n
g
er
in
itial
p
o
p
u
latio
n
b
y
b
etter
an
aly
zin
g
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
r
o
u
tin
e
is
to
u
s
e
f
r
o
m
clu
s
ter
ce
n
ter
s
o
f
a
lar
g
e
p
o
p
u
latio
n
as
in
itial
p
o
p
u
latio
n
in
s
tead
o
f
r
an
d
o
m
ly
s
elec
t
th
e
lim
ited
in
itial p
o
p
u
latio
n
.
W
e
co
n
s
id
er
th
e
b
est clu
s
ter
in
g
ce
n
ter
s
a
s
th
e
in
itial
p
o
p
u
latio
n
o
f
o
u
r
alg
o
r
ith
m
.
T
h
e
p
s
e
udo
co
d
e
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
f
o
r
m
o
r
e
d
etails
is
s
h
o
wn
in
Fig
u
r
e
3
.
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:
2
0
8
8
-
8
7
0
8
Usi
n
g
th
e
mo
d
ified
k
-
mea
n
a
l
g
o
r
ith
m
w
ith
a
n
imp
r
o
ve
d
tea
ch
in
g
lea
r
n
in
g
b
a
s
ed
…
(
Mo
r
teza
Jo
u
yb
a
n
)
5281
Alg
o
r
ith
m
3
.
Pro
p
o
s
ed
alg
o
r
it
h
m
Clustering section:
Input: Dataset D, Number of Clusters k, Dimensions d:
{
is the
ith
cluster}
{% Initialization Phase for Clustering algorithm}
1: (
1
,
2
,
…
,
)
=Initial partition of D.
{% Iteration Phase for Clustering algorithm}
2: While (Iter < Max_Iter)
3:
=distance between case i and cluster j;
4:
=
min (
)
;
5: Assign case i to cluster
;
6: Re
-
compute the cluster means of any changed clusters above;
7: End While
Training section:
8: Training algorithm population = Clustering Output results.
{% Initialization Phase for Training
algorithm}
9: Objective function
(
)
=
(
1
,
2
,
…
,
)
d = number of design variables
{% Iteration Phase for Training algorithm}
10:
While (
Iter < Max_Iter
)
{%Teacher Phase}
11:
Calculate the mean of each design variable
12:
Identify the best solution (
ℎ
)
13: For i
=
1
→
pop size
14: Calculate teaching factor
using
=
[
1
+
(
0
,
1
)
]
15: Modify solution based on best solution (teacher) using
=
+
.
(
ℎ
−
.
)
16: Calculate objective function for new mapped student
(
)
17: If
is better than
18:
=
19: End If %End of Teac
her Phase
{% Learner Phase}
20: finding neighbors for each learner
21: If rand<P_c
22: Update the solution using Eq. (
3
);
23: Else
24: Randomly select another learner
, such that
25: If
is better than
26: Update the solution
using Eq. (
5
);
27: Else
28: Update the solution using Eq. (
4
);
29: End If
30: If
is better than
31:
=
32:
End If
33: End If
29: End For
30: End While
Fig
u
r
e
3
.
Su
g
g
ested
m
eth
o
d
4.
E
XP
E
RIM
E
NT
S
4
.
1
.
Def
ini
ng
cla
s
s
if
ica
t
io
n pro
blem
s
a
nd
predict
ing
t
im
e
s
er
ies
In
th
is
s
ec
tio
n
,
we
ev
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
u
s
in
g
ten
cl
ass
if
icatio
n
p
r
o
b
lem
s
a
n
d
two
tim
e
s
er
ies
p
r
ed
ictio
n
p
r
o
b
lem
s
,
a
n
d
to
p
r
o
v
e
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
,
it
s
r
esu
lts
ar
e
co
m
p
ar
ed
with
o
th
er
alg
o
r
ith
m
s
s
u
ch
as
b
asic
T
L
B
O
an
d
I
T
L
B
O.
I
n
a
d
d
itio
n
,
th
e
r
esu
lts
o
f
th
e
im
p
r
o
v
e
d
tr
ain
i
n
g
al
g
o
r
ith
m
h
av
e
b
e
en
c
o
m
p
ar
e
d
with
th
e
b
asic
n
eu
r
al
n
etwo
r
k
tr
ai
n
in
g
alg
o
r
ith
m
s
f
r
o
m
o
th
er
ar
ticles,
an
d
th
en
in
an
o
th
er
s
tep
,
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
h
as
b
ee
n
co
m
p
ar
ed
with
o
th
er
m
eth
o
d
s
av
ailab
le
in
th
e
r
esear
ch
liter
atu
r
e
,
t
h
e
f
o
llo
win
g
e
x
p
er
im
e
n
ts
ca
n
b
e
s
ee
n
in
d
etail
.
C
las
s
if
icatio
n
p
r
o
b
lem
s
i
n
clu
d
e
I
r
is
,
d
iab
etes
d
iag
n
o
s
is
,
t
h
y
r
o
id
d
is
ea
s
e
,
b
r
ea
s
t
ca
n
ce
r
,
cr
ed
it
ca
r
d
,
g
lass
,
h
ea
r
t,
win
e,
p
ag
e
b
lo
c
k
s
,
an
d
liv
er
d
is
o
r
d
er
s
.
T
im
e
s
er
ies
p
r
ed
ictio
n
p
r
o
b
lem
s
in
clu
d
e
Ma
ck
ey
-
Glass
[1
0
]
an
d
g
as
f
u
r
n
ac
es
[
1
1
]
.
T
h
e
n
u
m
b
e
r
o
f
f
ea
tu
r
es
in
th
e
class
if
icatio
n
p
r
o
b
lem
,
th
e
n
u
m
b
e
r
o
f
cl
ass
es
an
d
th
e
to
tal
n
umbe
r
o
f
s
am
p
les
lis
ted
in
T
ab
le
1
.
C
las
s
if
icatio
n
p
r
o
b
lem
s
ar
e
tak
en
f
r
o
m
th
e
UC
I
m
ac
h
in
e
lear
n
in
g
r
ep
o
s
it
or
y
[1
2
]
.
T
h
e
Ma
c
k
ey
-
Glass
i
s
a
d
ataset
th
at
o
b
tain
ed
f
r
o
m
th
e
(
6
)
,
wh
ich
is
td
=1
7
.
(
)
=
−
(
)
+
(
−
)
1
+
10
(
−
)
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
5
2
7
7
-
5
2
8
5
5282
Fo
r
th
e
Ma
ck
ey
-
Glass
d
ata
s
et,
we
co
n
s
id
er
ed
th
e
x
(
t+
6
)
o
u
t
p
u
t
with
th
e
in
p
u
t
v
ar
iab
les
x
(
t
)
,
x
(
t
-
6
)
,
x
(
t
-
1
2
)
an
d
x
(
t
-
1
8
)
.
Fo
r
g
as
f
u
r
n
ac
e
d
ata
s
et
,
th
e
in
p
u
t
v
ar
iab
les
ar
e
u
(
t
-
3
)
,
u
(
t
-
2
)
,
u
(
t
-
1
)
,
y
(
t
-
3
)
,
y
(
t
-
2
)
,
y
(
t
-
1
)
an
d
th
e
o
u
tp
u
t
v
ar
iab
le
is
y
(
t)
,
as
r
ep
o
r
te
d
in
p
r
ev
io
u
s
wo
r
k
s
[
1
3
].
W
e
im
p
lem
en
t
ed
th
is
alg
o
r
ith
m
b
y
MA
T
L
AB
.
W
e
u
s
ed
3
0
r
u
n
s
t
o
ev
alu
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
is
m
o
d
el.
T
h
e
d
ata
s
ets
wer
e
r
an
d
o
m
l
y
d
iv
id
e
d
in
to
two
s
ets:
T
h
e
tr
ain
in
g
s
et
an
d
th
e
test
s
et
f
o
r
ea
ch
r
u
n
.
7
0
%
o
f
th
e
to
tal
d
ata
was
u
s
ed
f
o
r
th
e
tr
ain
in
g
s
et
an
d
th
e
r
est
o
f
th
e
d
ata
was
u
s
ed
as
a
test
s
et
to
ex
a
m
in
e
t
h
e
m
o
d
el.
Data
s
et
s
ar
e
n
o
r
m
ali
ze
d
to
th
e
in
ter
v
al
[
-
1
]
,
[
1
]
u
s
in
g
th
e
m
i
n
-
m
ax
n
o
r
m
aliza
tio
n
m
eth
o
d
.
T
ab
le
1
.
E
x
p
lain
th
e
d
ata
s
et
s
u
s
ed
f
o
r
th
e
p
r
o
p
o
s
ed
m
eth
o
d
D
a
t
a
s
e
t
I
n
st
a
n
c
e
s
F
e
a
t
u
r
e
s
C
l
a
s
ses
1
.
I
r
i
s
2
.
D
i
a
b
e
t
e
s
3
.
Th
y
r
o
i
d
4
.
C
a
n
c
e
r
5
.
C
a
r
d
6
.
G
l
a
ss
7
.
H
e
a
r
t
8
.
W
i
n
e
9
.
P
a
g
e
-
b
l
o
c
k
s
1
0
.
L
i
v
e
r
1
1
.
M
a
c
k
e
y
-
G
l
a
ss
1
2
.
G
a
s
F
u
r
n
a
c
e
1
5
0
7
6
8
7
2
0
0
6
9
9
6
9
0
2
1
4
2
7
0
1
7
8
5
4
7
3
3
4
5
1
0
0
0
2
9
6
4
8
21
10
15
10
13
13
10
6
1
2
3
2
3
2
2
6
2
3
5
2
0
0
4
.
2
.
T
he
re
s
ults o
f
t
he
co
m
pa
riso
n o
f
t
he
pro
po
s
ed
m
et
ho
ds
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
alg
o
r
ith
m
s
ev
alu
ated
an
d
co
m
p
ar
ed
b
ased
o
n
two
cr
iter
ia
,
t
r
ain
in
g
,
an
d
test
in
g
er
r
o
r
s
th
at
on
th
e
class
if
icatio
n
p
r
o
b
lem
s
it
m
ea
n
s
class
if
icatio
n
er
r
o
r
p
er
ce
n
tag
e.
T
h
e
er
r
o
r
f
u
n
ctio
n
f
o
r
Ma
ck
ey
-
Glass
d
ata
s
et
is
r
o
o
t
m
ea
n
s
q
u
ar
ed
er
r
o
r
(
R
MSE
)
an
d
f
o
r
g
as
f
u
r
n
ac
e
d
ataset
is
MSE
.
T
h
e
av
er
ag
e
r
esu
lts
af
ter
3
0
r
u
n
s
f
o
r
th
e
a
lg
o
r
ith
m
s
ar
e
s
h
o
wn
in
T
ab
le
2
.
T
h
e
r
esu
lts
s
h
o
w
th
e
s
u
p
er
io
r
ity
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
MK
-
I
T
L
B
O
alg
o
r
ith
m
p
er
f
o
r
m
s
b
etter
th
an
o
th
er
m
eth
o
d
s
.
W
e
u
s
ed
th
e
av
er
ag
e
r
an
k
in
g
test
to
f
in
d
th
e
b
est
alg
o
r
ith
m
.
T
h
ese
r
esu
lts
ar
e
f
o
u
n
d
u
s
in
g
th
e
R
ANK
f
u
n
ctio
n
in
Mic
r
o
s
o
f
t
E
x
ce
l,
an
d
th
e
av
er
ag
e
r
an
k
in
g
s
ar
e
s
h
o
wn
in
T
ab
le
3
.
T
h
e
r
esu
lts
s
h
o
w
th
at
MK
-
I
T
L
B
O
r
an
k
s
f
ir
s
t in
all
ca
s
es
f
o
r
tr
ain
in
g
er
r
o
r
s
an
d
test
in
g
er
r
o
r
s
.
T
ab
le
2
.
Av
e
r
ag
e
r
a
n
k
in
g
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
Tr
a
i
n
i
n
g
e
r
r
o
r
TLB
O
I
TLB
O
MK
-
I
TLB
O
A
l
g
o
r
i
t
h
m
2
.
7
5
0
0
2
.
1
6
6
7
1
.
0
8
3
3
R
a
n
k
Te
st
i
n
g
e
r
r
o
r
TLB
O
I
TLB
O
MK
-
I
TLB
O
A
l
g
o
r
i
t
h
m
2
.
9
1
6
7
2
.
0
0
0
0
1
.
0
8
3
3
R
a
n
k
T
ab
le
3
.
P
-
v
al
u
e
r
esu
lts
f
o
r
p
a
ir
wis
e
co
m
p
ar
in
g
of
MK
-
I
T
L
B
O
v
er
s
u
s
o
th
er
alg
o
r
ith
m
s
b
y
W
ilco
x
o
n
test
TLB
O
I
TLB
O
C
r
i
t
e
r
i
a
D
a
t
a
set
1.
I
r
i
s
Tr
a
i
n
i
n
g
e
r
r
o
r
Te
st
i
n
g
e
r
r
o
r
2
.
0
0
5
6
e
-
0
3
3
.
7
4
4
6
e
-
0
4
5
.
2
4
5
3
e
-
05
2
.
9
9
4
0
e
-
05
2.
D
i
a
b
e
t
e
s
Tr
a
i
n
i
n
g
e
r
r
o
r
Te
st
i
n
g
e
r
r
o
r
2
.
9
7
0
7
e
-
0
5
1
.
5
8
8
4
e
-
0
4
2
.
5
4
4
4
e
-
08
1
.
0
4
0
5
e
-
09
3.
Th
y
r
o
i
d
Tr
a
i
n
i
n
g
e
r
r
o
r
Te
st
i
n
g
e
r
r
o
r
2
.
9
0
2
7
e
-
1
1
3
.
6
2
0
5
e
-
11
9
.
5
9
8
2
e
-
10
2
.
9
0
8
2
e
-
11
4.
C
a
n
c
e
r
Tr
a
i
n
i
n
g
e
r
r
o
r
Te
st
i
n
g
e
r
r
o
r
5
.
5
5
6
9
e
-
0
4
3
.
0
0
5
0
e
-
0
7
3
.
0
6
7
1
e
-
09
2
.
6
7
0
6
e
-
11
5.
C
a
r
d
Tr
a
i
n
i
n
g
e
r
r
o
r
Te
st
i
n
g
e
r
r
o
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I
n
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&
C
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p
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g
I
SS
N:
2
0
8
8
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Usi
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5283
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o
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atio
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wh
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th
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MK
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I
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lt
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s
ig
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ican
tly
b
etter
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an
o
th
er
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o
r
ith
m
s
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ca
lcu
lated
th
e
p
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v
alu
e
test
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o
r
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ata
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o
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ased
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ata.
T
h
e
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aller
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ab
ilit
y
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e
g
r
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r
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lity
o
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th
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h
e
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ca
lcu
lated
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r
MK
-
I
T
L
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co
m
p
ar
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to
o
th
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o
r
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m
s
ar
e
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h
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wn
in
T
ab
le
4
.
T
ab
le
5
co
m
p
ar
es o
u
r
p
r
o
p
o
s
ed
MK
-
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L
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O
alg
o
r
ith
m
an
d
o
th
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ap
p
r
o
ac
h
es
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o
r
class
if
icatio
n
p
r
o
b
lem
s
.
T
ab
le
4
.
C
o
m
p
a
r
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o
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o
f
MK
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I
T
L
B
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an
d
o
th
er
a
p
p
r
o
ac
h
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r
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if
icatio
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r
o
b
lem
s
D
a
t
a
s
e
t
MK
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I
TLB
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g
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s
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Mk
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-
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
5
2
7
7
-
5
2
8
5
5284
T
h
is
tab
le
s
h
o
ws
th
e
r
esu
lts
o
f
o
u
r
p
r
o
p
o
s
ed
m
eth
o
d
with
s
o
m
e
d
ata
s
ets
th
at
h
av
e
b
ee
n
s
elec
ted
as
a
s
am
p
le
.
T
h
e
r
esu
lts
r
ep
r
esen
t
th
at
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
s
u
p
er
io
r
to
o
th
er
b
asic
n
eu
r
al
n
etwo
r
k
tr
ain
in
g
alg
o
r
ith
m
s
.
4
.
3
.
T
he
re
s
ults
co
m
pa
re
t
he
pro
po
s
ed
co
m
bin
ed
m
et
ho
d wit
h o
t
her
m
et
h
o
ds
a
v
a
ila
ble in t
he
lite
ra
t
ure
I
n
th
is
s
ec
tio
n
,
we
co
m
p
ar
e
th
e
to
p
alg
o
r
ith
m
am
o
n
g
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
s
with
o
th
er
m
eth
o
d
s
av
ailab
le
in
th
e
liter
atu
r
e
an
d
m
ak
e
all
co
m
p
ar
is
o
n
s
with
th
e
d
ataset
s
ets
in
tr
o
d
u
ce
d
in
th
is
p
ap
er
.
T
ab
le
5
co
m
p
ar
es
th
e
MK
_
I
T
L
B
O
m
eth
o
d
with
th
e
ap
p
r
o
ac
h
es
in
tr
o
d
u
ce
d
ab
o
v
e.
Field
s
with
a
s
y
m
b
o
l
-
in
d
icate
th
at
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
d
id
n
o
t
wo
r
k
o
n
th
at
d
ataset
o
r
th
at
th
e
r
esu
lts
ar
e
n
o
t
av
ailab
le.
I
n
th
is
tab
le
T
r
_
E
(
%)
m
ea
n
s
tr
ain
in
g
er
r
o
r
p
er
ce
n
tag
e
an
d
T
e_
E
(
%)
m
ea
n
s
test
in
g
er
r
o
r
p
er
ce
n
tag
e.
5.
C
O
N
C
L
U
SIO
N
T
h
is
ar
ticle
p
r
esen
ted
an
im
p
r
o
v
ed
teac
h
in
g
-
lear
n
in
g
b
ased
o
p
tim
izatio
n
alg
o
r
ith
m
f
o
r
n
eu
r
al
n
etwo
r
k
tr
ain
in
g
.
W
e
u
s
ed
two
m
eth
o
d
s
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
b
asic
alg
o
r
ith
m
.
First,
to
m
ak
e
a
m
o
r
e
ef
f
ec
tiv
e
s
ea
r
ch
s
p
ac
e
f
o
r
th
e
in
itial
po
p
u
latio
n
o
f
th
e
alg
o
r
ith
m
,
in
s
tead
o
f
r
an
d
o
m
ly
s
elec
tin
g
th
e
p
o
p
u
latio
n
we
u
s
ed
r
esu
lt
o
f
clu
s
ter
in
g
with
th
e
m
o
d
if
ied
k
-
m
ea
n
alg
o
r
ith
m
,
an
d
s
ec
o
n
d
,
we
h
av
e
im
p
r
o
v
ed
th
e
teac
h
in
g
-
lear
n
in
g
o
p
tim
izatio
n
alg
o
r
ith
m
to
cr
ea
te
a
b
alan
ce
b
etwe
en
ex
p
lo
itatio
n
an
d
ex
p
lo
r
atio
n
.
W
e
h
av
e
ap
p
lied
o
u
r
m
eth
o
d
to
class
if
icatio
n
an
d
tim
e
s
er
ies
p
r
ed
ictio
n
p
r
o
b
lem
s
.
T
h
e
r
esu
lts
in
s
ec
tio
n
4
s
h
o
w
th
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
as
m
en
tio
n
ed
,
th
is
v
er
s
io
n
h
as
a
p
o
wer
f
u
l
tr
ain
in
g
alg
o
r
ith
m
ag
ain
s
t
p
r
em
atu
r
e
co
n
v
er
g
en
ce
th
at
also
b
alan
ce
s
ex
p
lo
itatio
n
an
d
ex
p
lo
r
atio
n
.
I
n
ad
d
itio
n
,
it
is
co
m
b
in
ed
with
th
e
Mk
-
m
ea
n
alg
o
r
ith
m
,
wh
ich
ex
am
in
es
th
e
s
ea
r
ch
s
p
ac
e
m
o
r
e
ef
f
ec
tiv
ely
.
W
e
also
co
n
f
ir
m
ed
th
ese
r
esu
lts
with
s
tatis
tical
test
s
,
an
d
th
en
co
m
p
ar
ed
th
is
alg
o
r
ith
m
with
o
th
er
m
eth
o
d
s
o
f
liter
atu
r
e,
an
d
b
ased
o
n
d
if
f
er
en
t
ev
alu
atio
n
s
it
was
co
n
clu
d
ed
th
at
th
is
alg
o
r
ith
m
h
as
a
b
etter
ab
ilit
y
th
an
o
th
er
alg
o
r
ith
m
s
r
eg
ar
d
in
g
class
if
icatio
n
an
d
tim
e
s
er
ies
p
r
ed
ictio
n
er
r
o
r
s
.
T
h
e
r
esu
lts
m
o
tiv
ate
u
s
to
f
in
d
ap
p
r
o
ac
h
to
ch
an
g
e
o
u
r
m
eth
o
d
t
o
th
e
f
u
tu
r
e
wo
r
k
s
.
T
h
is
d
ev
elo
p
m
en
t c
o
u
ld
b
e
in
th
e
u
s
e
o
f
ch
ao
tic
m
ap
p
in
g
in
th
e
m
eth
o
d
.
R
E
FE
R
E
N
C
E
S
[1
]
N.
Zh
a
n
g
,
"
A
n
o
n
li
n
e
g
ra
d
ien
t
m
e
th
o
d
with
m
o
m
e
n
t
u
m
f
o
r
tw
o
-
lay
e
r
fe
e
d
f
o
rwa
rd
n
e
u
ra
l
n
e
tw
o
rk
s,"
A
p
p
l
ied
M
a
t
h
e
ma
ti
c
s
Co
m
p
u
t
a
ti
o
n
,
v
o
l.
2
1
2
,
n
o
.
2
,
p
p
.
4
8
8
-
4
9
8
,
2
0
0
9
,
d
o
i:
1
0
.
1
0
1
6
/
j.
a
m
c
.
2
0
0
9
.
0
2
.
0
3
8
.
[2
]
M
.
G
o
ri
a
n
d
A.
Tes
i,
"
On
t
h
e
p
ro
b
lem
o
f
l
o
c
a
l
m
in
ima
in
b
a
c
k
p
ro
p
a
g
a
ti
o
n
,
"
i
n
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Pa
tt
e
rn
An
a
lys
is
a
n
d
M
a
c
h
i
n
e
In
tell
ig
e
n
c
e
,
v
o
l
.
1
4
,
n
o
.
1
,
p
p
.
7
6
-
8
6
,
Ja
n
.
1
9
9
2
,
d
o
i:
1
0
.
1
1
0
9
/3
4
.
1
0
7
0
1
4
.
[3
]
O
.
Ara
n
a
n
d
E.
Al
p
a
y
d
ı
n
,
"
An
In
c
re
m
e
n
tal
Ne
u
ra
l
Ne
two
rk
Co
n
stru
c
t
io
n
Alg
o
r
it
h
m
fo
r
Train
in
g
M
u
lt
i
lay
e
r
P
e
rc
e
p
tro
n
s,
"
Arti
fi
c
ia
l
Ne
u
ra
l
N
e
two
rk
s
a
n
d
Ne
u
ra
l
In
f
o
rm
a
ti
o
n
Pro
c
e
ss
in
g
,
Ista
n
b
u
l,
T
u
rk
e
y
:
I
CAN
N/ICON
IP
2
0
0
3
.
[4
]
S
.
Ku
ll
u
k
,
L
.
Oz
b
a
k
ir
,
a
n
d
A
.
Ba
y
k
a
so
g
lu
,
"
Train
i
n
g
n
e
u
ra
l
n
e
two
rk
s
with
h
a
rm
o
n
y
se
a
rc
h
a
lg
o
r
it
h
m
s
f
o
r
c
las
sifica
ti
o
n
p
ro
b
lem
s,"
E
n
g
i
n
e
e
rin
g
A
p
p
l
ica
ti
o
n
s
o
f
Arti
fi
c
i
a
l
I
n
t
e
ll
ig
e
n
c
e
,
v
o
l.
2
5
,
n
o
.
1
.
p
p
.
1
1
-
1
9
,
F
e
b
.
2
0
1
2
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
n
g
a
p
p
a
i.
2
0
1
1
.
0
7
.
0
0
6
.
[5
]
N.
S
.
Ja
d
d
i,
S
.
Ab
d
u
ll
a
h
,
a
n
d
A.
R.
Ha
m
d
a
n
,
"
Op
t
imiz
a
ti
o
n
o
f
n
e
u
ra
l
n
e
tw
o
rk
m
o
d
e
l
u
si
n
g
m
o
d
ifi
e
d
b
a
t
-
i
n
sp
ire
d
,
"
Ap
p
li
e
d
S
o
ft
Co
mp
u
ti
n
g
,
v
o
l.
3
7
,
p
p
.
7
1
-
8
6
,
De
c
.
2
0
1
5
,
d
o
i
:
1
0
.
1
0
1
6
/j
.
a
so
c
.
2
0
1
5
.
0
8
.
0
0
2
.
[6
]
V.
G
.
G
u
d
ise
a
n
d
G
.
K.
Ve
n
a
y
a
g
a
m
o
o
rt
h
y
,
"
Co
m
p
a
riso
n
o
f
p
a
rti
c
le
sw
a
rm
o
p
ti
m
iza
ti
o
n
a
n
d
b
a
c
k
p
ro
p
a
g
a
ti
o
n
a
s
train
in
g
a
lg
o
r
it
h
m
s
fo
r
n
e
u
ra
l
n
e
two
rk
s,"
Pr
o
c
e
e
d
in
g
s
o
f
th
e
2
0
0
3
IEE
E
S
w
a
rm
In
telli
g
e
n
c
e
S
y
mp
o
siu
m
.
S
IS
'
0
3
(Ca
t.
N
o
.
0
3
EX
7
0
6
)
,
2
0
0
3
,
p
p
.
1
1
0
-
1
1
7
,
d
o
i:
1
0
.
1
1
0
9
/
S
IS
.
2
0
0
3
.
1
2
0
2
2
5
5
.
[7
]
K.
Krish
n
a
a
n
d
M
.
N.
M
u
r
ty
,
"
G
e
n
e
ti
c
K
-
m
e
a
n
s
a
lg
o
rit
h
m
,
"
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
y
ste
ms
,
M
a
n
,
a
n
d
Cy
b
e
rn
e
ti
c
s,
Pa
rt B
(Cy
b
e
rn
e
ti
c
s)
,
v
o
l.
2
9
,
n
o
.
3
,
p
p
.
4
3
3
-
4
3
9
,
Ju
n
.
1
9
9
9
,
d
o
i:
1
0
.
1
1
0
9
/
3
4
7
7
.
7
6
4
8
7
9
.
[8
]
J.
M
a
c
Qu
e
e
n
,
"
S
o
m
e
m
e
th
o
d
s
fo
r
c
las
sifica
ti
o
n
a
n
d
a
n
a
ly
s
is
o
f
m
u
lt
iv
a
riate
o
b
se
rv
a
t
io
n
s,"
Pro
c
e
e
d
in
g
s
o
f
t
h
e
fi
ft
h
Ber
k
e
ley
s
y
mp
o
siu
m o
n
ma
th
e
ma
t
ica
l
sta
t
isti
c
s a
n
d
p
ro
b
a
b
il
it
y
,
v
o
l
.
1
,
n
o
.
1
4
,
p
p
.
2
8
1
-
2
9
7
,
J
u
n
.
1
9
6
7
.
[9
]
R.
V.
Ra
o
a
n
d
V.
J.
S
.
D.
P.
V
a
k
h
a
ria
,
"
Tea
c
h
in
g
-
lea
rn
i
n
g
-
b
a
se
d
o
p
ti
m
iza
ti
o
n
:
A
n
o
v
e
l
m
e
th
o
d
fo
r
c
o
n
stra
in
e
d
m
e
c
h
a
n
ica
l
d
e
sig
n
o
p
ti
m
iza
ti
o
n
p
ro
b
lem
s,"
Co
m
p
u
ter
-
Ai
d
e
d
De
si
g
n
,
v
o
l.
4
3
,
n
o
.
3
,
p
p
.
3
0
3
-
3
1
5
,
M
a
r
.
2
0
1
1
,
d
o
i:
1
0
.
1
0
1
6
/
j.
c
a
d
.
2
0
1
0
.
1
2
.
0
1
5
.
[1
0
]
C.
H.
L
ó
p
e
z
-
Ca
ra
b
a
ll
o
,
S
a
lfate
,
J.
A.
Laz
z
ú
s,
P
.
R
o
jas
,
M
.
Ri
v
e
ra
,
a
n
d
L.
P
a
lma
-
Ch
il
la
,
"
M
a
c
k
e
y
-
G
las
s
n
o
isy
c
h
a
o
ti
c
ti
m
e
se
ries
p
re
d
ictio
n
b
y
a
sw
a
r
m
-
o
p
ti
m
ize
d
n
e
u
ra
l
n
e
two
rk
,
"
J
o
u
rn
a
l
o
f
Ph
y
sic
s:
Co
n
fer
e
n
c
e
S
e
rie
s.
IOP
Pu
b
li
s
h
in
g
,
v
o
l.
7
2
0
,
n
o
.
1
,
p
p
.
1
2
0
0
2
-
1
2
0
1
1
,
M
a
y
2
0
1
6
,
d
o
i:
1
0
.
1
0
8
8
/
1
7
4
2
-
6
5
9
6
/
7
2
0
/1
/0
1
2
0
0
2
.
[1
1
]
K.
Du
n
n
,
"
T
h
e
g
a
s
f
u
rn
a
c
e
d
a
ta
s
e
t
fro
m
Bo
x
a
n
d
Je
n
k
i
n
s
Bo
o
k
o
n
Ti
m
e
S
e
ries
An
a
l
y
sis
,"
Op
e
n
M
V.n
e
t
Da
tas
e
ts
,
2
0
1
8
.
[On
li
n
e
].
Av
a
il
a
b
le:
h
t
tp
:/
/
o
p
e
n
m
v
.
n
e
t/
i
n
fo
/
g
a
s
-
fu
r
n
a
c
e
[1
2
]
C
.
Blak
e
,
"
UCI Re
p
o
sit
o
ry
o
f
M
a
c
h
in
e
Lea
rn
i
n
g
Da
tab
a
se
s,
"
U
n
iv
e
rsity
o
f
Ca
li
f
o
rn
ia at I
rv
i
n
e
,
1
9
9
8
.
[1
3
]
K.
Yu
,
X.
Wan
g
,
a
n
d
Z.
Wan
g
,
"
Co
n
stra
in
e
d
o
p
ti
m
iza
ti
o
n
b
a
se
d
o
n
imp
r
o
v
e
d
tea
c
h
in
g
-
lea
rn
i
n
g
-
b
a
se
d
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
,
"
I
n
fo
rm
a
ti
o
n
S
c
ien
c
e
s,
v
o
l
.
3
5
2
-
3
5
3
,
p
p
.
6
1
-
7
8
,
J
u
l.
2
0
1
6
,
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