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Dev
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te
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tes
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ip
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li
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lt
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e
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ro
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s th
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te
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th
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ly
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Ja
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in
d
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te p
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fo
r
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s 1
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rs.
K
ey
w
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s
:
B
ip
lo
t
C
o
r
r
elatio
n
Dim
en
s
io
n
ality
r
ed
u
ctio
n
Miss
in
g
v
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T
r
en
d
s
in
h
u
m
an
d
ev
elo
p
m
en
t
T
h
is i
s
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c
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ss
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rticle
u
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e
CC B
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SA
li
c
e
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se
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C
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s
p
o
nd
ing
A
uth
o
r
:
I
Ma
d
e
Su
m
er
tajay
a
Statis
t
ics an
d
Data
Scien
ce
St
u
d
y
Pro
g
r
am
,
Sch
o
o
l o
f
Data
Scien
ce
,
Ma
th
em
atics a
n
d
I
n
f
o
r
m
atics
I
PB
Un
iv
er
s
ity
Me
r
an
ti R
d
,
Dr
am
ag
a
Dis
tr
ict,
B
o
g
o
r
,
1
6
6
8
0
W
est J
av
a,
I
n
d
o
n
esia
E
m
ail: im
s
jay
a@
ap
p
s
.
ip
b
.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
On
e
o
f
th
e
m
o
s
t
u
s
ed
m
eth
o
d
s
f
o
r
d
im
en
s
io
n
ality
r
ed
u
ctio
n
is
p
r
in
cip
al
co
m
p
o
n
e
n
t
an
aly
s
is
(
PC
A)
.
T
h
is
m
eth
o
d
s
u
m
m
a
r
izes
m
an
y
v
ar
ia
b
les
in
to
a
f
ew
p
r
in
cip
al
co
m
p
o
n
en
ts
with
o
u
t
s
ig
n
if
ican
t
lo
s
s
o
f
in
f
o
r
m
atio
n
.
Ho
wev
er
,
PC
A
h
as
lim
itatio
n
s
wh
en
d
ea
lin
g
with
d
ata
th
at
ex
h
ib
its
co
r
r
elatio
n
s
ac
r
o
s
s
o
b
s
er
v
atio
n
s
(
r
o
ws)
[
1
]
,
[
2
]
.
T
o
ad
d
r
ess
th
is
lim
itatio
n
,
g
en
er
alize
d
p
r
in
cip
al
c
o
m
p
o
n
en
t
an
aly
s
is
(
GP
C
A)
,
also
k
n
o
wn
as
g
e
n
er
alize
d
lo
w
r
an
k
ap
p
r
o
x
im
atio
n
o
f
m
atr
ices
(
GL
R
AM
)
,
was
d
ev
elo
p
ed
.
GPC
A
is
ca
p
ab
le
o
f
s
im
u
ltan
eo
u
s
ly
r
ed
u
cin
g
t
h
e
d
im
en
s
io
n
s
o
f
b
o
th
co
r
r
e
lated
v
ar
iab
les
a
n
d
c
o
r
r
elate
d
o
b
s
er
v
atio
n
s
.
I
n
ad
d
itio
n
,
GPC
A
ca
n
r
ed
u
ce
t
h
e
d
ata
d
im
en
s
io
n
o
f
a
c
o
llectio
n
o
f
m
atr
ices
s
im
u
ltan
eo
u
s
ly
[
3
]
.
T
h
is
m
eth
o
d
was
f
ir
s
t
in
tr
o
d
u
ce
d
in
[
4
]
to
en
h
an
ce
th
e
ef
f
icien
cy
o
f
im
a
g
e
co
m
p
r
ess
io
n
an
d
h
as
b
ee
n
s
h
o
wn
to
p
r
o
d
u
ce
h
ig
h
er
v
is
u
al
q
u
ality
an
d
m
o
r
e
ef
f
icien
t c
o
m
p
u
tatio
n
tim
e
c
o
m
p
ar
ed
to
PC
A.
R
esear
ch
o
n
GPC
A
h
as
b
ee
n
ap
p
lied
ac
r
o
s
s
v
ar
io
u
s
f
ie
ld
s
,
ac
co
m
p
an
ied
b
y
d
ev
elo
p
m
en
ts
in
m
eth
o
d
o
l
o
g
ical
asp
ec
ts
.
Fo
r
ex
am
p
le,
GPC
A
h
as
b
ee
n
u
s
ed
to
i
d
en
tify
g
en
es
with
o
v
er
lap
p
in
g
p
atter
n
s
,
en
ab
lin
g
th
e
r
ec
o
g
n
itio
n
o
f
g
en
e
in
ter
ac
tio
n
s
an
d
f
u
n
ctio
n
s
.
I
n
th
is
co
n
tex
t,
GPC
A
h
as
p
r
o
v
e
n
ef
f
ec
tiv
e
in
co
m
p
r
ess
in
g
im
a
g
es
o
f
g
en
e
ex
p
r
ess
io
n
p
atter
n
s
[
5
]
.
T
h
is
ad
v
an
tag
e
was
f
u
r
t
h
er
e
x
am
i
n
ed
in
co
m
p
ar
ativ
e
s
tu
d
ies,
wh
ich
d
em
o
n
s
tr
ated
t
h
at
GPC
A
o
u
tp
er
f
o
r
m
s
o
th
e
r
d
im
en
s
io
n
ality
r
e
d
u
ctio
n
m
et
h
o
d
s
s
u
ch
as
PC
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dev
elo
p
men
t o
f g
e
n
era
liz
ed
p
r
in
cip
a
l c
o
mp
o
n
e
n
t a
n
a
lysi
s
u
s
in
g
mu
ltip
le
imp
u
ta
tio
n
…
(
F
a
h
r
eza
l Zu
b
ed
i)
455
an
d
m
u
ltil
in
ea
r
PC
A,
p
ar
ticu
lar
ly
in
p
atter
n
r
ec
o
g
n
iti
o
n
task
s
lik
e
im
ag
e
class
if
icatio
n
an
d
o
b
ject
id
en
tific
atio
n
[
6
]
.
I
n
o
th
er
wo
r
d
s
,
GPC
A
is
n
o
t
o
n
ly
ef
f
ec
tiv
e
in
p
r
ac
tice
b
u
t
also
s
u
p
p
o
r
ted
b
y
a
s
tr
o
n
g
an
d
m
ath
em
atica
lly
p
r
o
v
en
t
h
eo
r
etica
l
f
o
u
n
d
atio
n
.
T
o
ad
d
r
ess
n
ew
ch
allen
g
es
in
th
e
ap
p
licatio
n
o
f
GPC
A,
s
ev
er
al
f
u
r
t
h
er
d
ev
elo
p
m
en
ts
h
av
e
b
ee
n
ca
r
r
ied
o
u
t.
On
e
o
f
th
em
is
th
e
co
m
b
in
atio
n
o
f
G
PC
A
with
m
eth
o
d
s
s
u
ch
as
to
p
-
p
u
s
h
co
n
s
tr
ain
e
d
f
ea
tu
r
e
lear
n
in
g
(
T
FL)
to
i
m
p
r
o
v
e
th
e
ac
cu
r
ac
y
o
f
f
ac
e
im
ag
e
r
ec
o
g
n
itio
n
th
r
o
u
g
h
d
im
en
s
io
n
ality
r
ed
u
ct
io
n
[
7
]
.
An
o
t
h
er
d
ev
elo
p
m
en
t
is
r
an
d
o
m
ized
GPC
A,
wh
ich
aim
s
to
r
ed
u
ce
th
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
GPC
A
[
8
]
.
Ho
wev
er
,
m
o
s
t
d
e
v
elo
p
m
en
ts
o
f
GPC
A
h
av
e
co
n
tin
u
ed
to
f
o
cu
s
o
n
im
p
r
o
v
in
g
ac
cu
r
ac
y
an
d
co
m
p
u
tatio
n
al
ef
f
icien
c
y
,
with
o
u
t
ex
p
licitly
ad
d
r
ess
in
g
o
r
in
teg
r
atin
g
th
e
h
a
n
d
lin
g
o
f
m
is
s
in
g
v
alu
e
p
r
o
b
le
m
s
co
m
m
o
n
ly
f
o
u
n
d
in
e
m
p
ir
ical
d
a
ta.
T
h
e
m
ain
p
r
o
b
lem
in
th
is
s
tu
d
y
is
h
o
w
t
o
ef
f
ec
tiv
el
y
ap
p
ly
GPC
A
to
d
ata
co
n
tain
in
g
m
is
s
in
g
v
alu
es.
T
h
e
p
r
esen
ce
o
f
m
is
s
in
g
v
al
u
es
ca
n
r
ed
u
ce
an
aly
s
is
q
u
ality
,
b
o
t
h
in
ter
m
s
o
f
ac
cu
r
ac
y
an
d
in
ter
p
r
etab
ilit
y
[
9
]
,
[
1
0
]
.
C
o
n
v
en
tio
n
al
im
p
u
tatio
n
m
eth
o
d
s
,
s
u
ch
as
m
ea
n
o
r
m
ed
ian
im
p
u
tatio
n
,
ar
e
o
f
ten
u
s
ed
f
o
r
p
r
ac
ticality
b
u
t
h
a
v
e
f
u
n
d
am
en
tal
lim
itatio
n
s
.
Su
ch
m
eth
o
d
s
ten
d
to
u
n
d
er
esti
m
ate
v
a
r
ian
ce
an
d
alter
th
e
co
r
r
elatio
n
s
tr
u
ct
u
r
e
am
o
n
g
v
a
r
iab
les
[
1
1
]
.
As
a
r
esu
lt,
s
u
b
s
eq
u
en
t
a
n
aly
s
es,
s
u
ch
as
d
im
e
n
s
io
n
ality
r
ed
u
ctio
n
with
GPC
A,
m
ay
y
ield
r
ep
r
e
s
en
tatio
n
s
th
at
d
o
n
o
t
ad
e
q
u
a
tely
r
ef
lect
th
e
s
tr
u
ctu
r
e
o
f
th
e
o
r
ig
in
al
d
ata.
T
o
ad
d
r
ess
th
is
is
s
u
e,
v
ar
io
u
s
im
p
u
tatio
n
m
eth
o
d
s
h
av
e
b
ee
n
d
ev
elo
p
ed
,
o
n
e
o
f
wh
ich
is
th
e
m
u
ltip
le
im
p
u
tatio
n
g
en
etic
alg
o
r
ith
m
(
MI
GA)
.
I
n
tr
o
d
u
ce
d
in
[
1
2
]
,
MI
GA
co
m
b
in
es
m
u
ltip
le
im
p
u
tatio
n
p
r
i
n
cip
les
with
g
en
etic
alg
o
r
ith
m
s
(
GA)
to
o
p
tim
ally
esti
m
ate
th
e
m
is
s
in
g
v
alu
es.
T
h
is
m
eth
o
d
is
d
esig
n
ed
to
p
r
es
er
v
e
th
e
s
tatis
tica
l
s
tr
u
ctu
r
e
o
f
d
ata,
s
u
ch
as m
ea
n
,
s
k
ewn
ess
,
an
d
co
v
ar
ian
c
e
m
atr
ices,
wh
ich
ar
e
o
f
ten
d
is
t
o
r
ted
b
y
c
o
n
v
e
n
tio
n
al
im
p
u
tatio
n
m
et
h
o
d
s
.
M
I
GA
h
as
b
ee
n
s
h
o
wn
t
o
o
u
tp
er
f
o
r
m
o
th
er
alg
o
r
ith
m
s
s
u
ch
as
ex
p
ec
tatio
n
m
ax
im
izatio
n
(
E
M)
,
a
u
x
iliar
y
r
eg
r
ess
io
n
s
,
an
d
k
-
n
ea
r
est
n
eig
h
b
o
r
s
im
p
u
tatio
n
(K
-
NN
I
)
.
Ho
wev
e
r
,
wh
e
n
GPC
A
is
ap
p
lied
af
ter
MI
GA
(
n
o
n
-
i
n
teg
r
ated
)
,
th
e
d
im
en
s
io
n
ality
r
ed
u
ctio
n
p
r
o
ce
s
s
f
o
llo
ws th
e
im
p
u
ted
d
ata
th
at
r
em
ain
f
ix
ed
,
r
at
h
er
t
h
an
d
ata
th
at
a
d
ap
t
d
y
n
a
m
ically
to
th
e
r
ed
u
ctio
n
m
o
d
el.
T
h
is
co
n
d
itio
n
m
ay
lea
d
to
a
lar
g
er
n
u
m
b
er
o
f
r
etain
e
d
d
im
en
s
io
n
s
an
d
a
d
ec
r
ea
s
e
i
n
th
e
to
tal
ex
p
lain
ed
v
ar
ia
n
ce
.
T
h
er
ef
o
r
e,
th
is
s
tu
d
y
p
r
o
p
o
s
es
a
n
ew
m
eth
o
d
ca
lle
d
th
e
in
teg
r
ated
GPC
A
-
MI
GA,
wh
ich
is
d
esig
n
ed
to
p
er
f
o
r
m
d
im
en
s
io
n
ality
r
ed
u
ctio
n
o
n
d
ata
c
o
n
tain
in
g
m
is
s
in
g
v
alu
es
ef
f
icien
tly
.
I
n
t
h
is
m
eth
o
d
,
th
e
c
o
v
ar
ia
n
ce
s
tr
u
ctu
r
e
g
en
er
ated
b
y
GPC
A
i
s
d
ir
ec
tly
u
tili
ze
d
to
u
p
d
ate
th
e
M
I
GA
im
p
u
tati
o
n
p
r
o
ce
s
s
in
th
e
s
u
b
s
eq
u
en
t
iter
atio
n
,
th
er
eb
y
ac
h
iev
in
g
a
b
alan
ce
b
etwe
en
im
p
u
tatio
n
ac
c
u
r
ac
y
a
n
d
r
e
d
u
c
tio
n
s
tab
ilit
y
.
T
h
e
em
p
i
r
ical
is
s
u
e
ad
d
r
ess
ed
in
th
is
s
tu
d
y
is
h
o
w
t
o
an
a
ly
ze
an
d
v
is
u
alize
th
e
tr
en
d
s
o
f
h
u
m
an
d
ev
elo
p
m
e
n
t
at
th
e
d
is
tr
ict/city
lev
el
in
I
n
d
o
n
esia
d
u
r
in
g
t
h
e
2
0
1
9
to
2
0
2
2
p
er
io
d
.
D
u
r
i
n
g
th
is
p
er
io
d
,
th
e
g
r
o
wth
r
ate
o
f
I
n
d
o
n
esia’
s
h
u
m
an
d
e
v
elo
p
m
e
n
t
in
d
ex
(
HDI
)
ten
d
e
d
to
s
lo
w
d
o
w
n
.
Ad
d
itio
n
ally
,
d
is
p
ar
ities
in
h
u
m
an
d
e
v
elo
p
m
e
n
t
ac
h
iev
e
m
en
ts
am
o
n
g
d
is
tr
ict/city
in
I
n
d
o
n
esia
p
er
s
is
t
[
1
3
]
–
[
1
6
]
.
T
h
is
s
i
tu
atio
n
in
d
icate
s
th
e
n
ee
d
f
o
r
a
m
o
r
e
in
-
d
e
p
th
an
d
co
m
p
r
e
h
en
s
iv
e
an
aly
s
is
o
f
th
e
d
y
n
am
ics
o
f
h
u
m
an
d
ev
elo
p
m
e
n
t
at
th
e
d
is
tr
ict/city
lev
el.
Ho
wev
er
,
h
u
m
an
d
e
v
elo
p
m
e
n
t
in
d
icato
r
d
ata
is
ch
ar
ac
ter
ized
b
y
h
i
g
h
d
im
en
s
io
n
ality
,
with
co
r
r
elatio
n
s
b
o
th
am
o
n
g
in
d
i
ca
to
r
s
an
d
am
o
n
g
d
is
tr
ict/city
,
an
d
co
n
tain
m
is
s
in
g
v
alu
es,
wh
ich
c
o
m
p
licate
d
ir
ec
t
an
aly
s
is
an
d
v
is
u
aliza
tio
n
.
T
o
ad
d
r
ess
is
s
u
es
in
em
p
i
r
ical
d
ata,
th
e
in
teg
r
ated
GPC
A
-
MI
GA
is
ap
p
lied
to
s
im
u
ltan
eo
u
s
ly
r
ed
u
ce
th
e
d
im
en
s
io
n
s
o
f
d
is
tr
ict/city
an
d
v
ar
iab
les,
ev
en
wh
en
th
e
d
a
ta
co
n
tain
s
m
is
s
in
g
v
alu
es.
T
h
e
r
ed
u
ce
d
d
ata
a
r
e
th
en
v
is
u
alize
d
u
s
in
g
th
e
b
i
p
lo
t
ap
p
r
o
ac
h
,
wh
ic
h
en
a
b
les
y
ea
r
ly
m
ap
p
in
g
o
f
d
is
tr
ict/city
p
o
s
itio
n
s
an
d
th
ei
r
ass
o
ciate
d
in
d
icato
r
s
th
r
o
u
g
h
a
v
ar
iety
o
f
in
f
o
r
m
ativ
e
v
is
u
al
d
is
p
lay
s
.
B
ased
o
n
th
e
d
escr
ip
tio
n
ab
o
v
e,
th
is
s
tu
d
y
h
as
two
m
ain
o
b
jectiv
es:
i
)
to
e
v
alu
ate
th
e
p
er
f
o
r
m
a
n
c
e
o
f
t
h
e
in
teg
r
ated
GPC
A
-
MI
GA
an
d
ii
)
to
an
al
y
ze
tr
en
d
s
in
h
u
m
an
d
ev
el
o
p
m
en
t
at
th
e
d
is
tr
ict/city
lev
el
in
I
n
d
o
n
esia
f
r
o
m
2019
t
o
2
0
2
2
.
2.
M
E
T
H
O
D
2
.
1
.
Da
t
a
T
h
is
s
tu
d
y
u
tili
ze
d
b
o
th
s
im
u
lated
an
d
em
p
ir
ical
d
ata.
T
h
e
s
im
u
lated
d
ata
c
o
n
s
is
ts
o
f
f
o
u
r
m
atr
ices
(
∈
ℝ
500
×
100
,
=
1
,
2
,
3
,
4
)
,
ea
ch
o
r
g
an
ized
in
to
2
5
o
b
s
er
v
atio
n
clu
s
ter
s
an
d
5
v
ar
iab
le
clu
s
ter
s
.
Ob
s
er
v
atio
n
s
an
d
v
ar
iab
les
with
in
th
e
s
am
e
clu
s
ter
a
r
e
co
r
r
elate
d
,
wh
ile
th
o
s
e
ac
r
o
s
s
clu
s
ter
s
ar
e
u
n
co
r
r
elate
d
.
T
h
e
f
o
u
r
s
im
u
l
ated
m
atr
ices
ar
e
co
n
s
tr
u
cte
d
to
b
e
m
u
tu
ally
c
o
r
r
elate
d
.
T
h
e
p
r
o
ce
s
s
o
f
d
ata
g
en
er
atio
n
is
d
escr
ib
e
d
as f
o
ll
o
ws
:
i)
Gen
er
ate
a
s
y
m
m
etr
ic
an
d
p
o
s
itiv
e
d
ef
in
ite
co
v
ar
ian
ce
m
at
r
ix
∈
ℝ
20
×
20
wh
er
e
all
d
iag
o
n
al
elem
e
n
ts
ar
e
1
an
d
all
o
f
f
-
d
iag
o
n
al
ele
m
en
ts
ar
e
0
.
8
.
ii)
Ap
p
ly
c
h
o
lesk
y
d
ec
o
m
p
o
s
itio
n
to
a
m
atr
ix
to
d
er
iv
e
a
m
at
r
ix
an
d
its
tr
an
s
p
o
s
e
m
atr
ix
[
1
7
]
.
iii)
Gen
er
ate
a
m
atr
ix
∈
ℝ
500
×
20
u
s
in
g
a
p
ar
titi
o
n
ap
p
r
o
ac
h
.
E
v
e
r
y
d
iv
is
io
n
m
atr
ix
is
p
r
o
d
u
ce
d
f
r
o
m
m
u
ltiv
ar
iate
n
o
r
m
al
(
MV
N
)
d
is
tr
ib
u
tio
n
,
a
d
is
tin
ct
m
ea
n
v
ec
to
r
f
o
r
ea
ch
co
lu
m
n
,
a
n
d
th
e
co
v
ar
ian
c
e
m
atr
ix
(
d
iag
o
n
al)
.
iv
)
T
r
an
s
f
o
r
m
ev
e
r
y
d
iv
is
io
n
m
atr
ix
f
r
o
m
m
atr
ix
ℝ
500
×
20
to
m
atr
i
x
∈
ℝ
500
×
20
em
p
lo
y
in
g
th
e
o
u
tco
m
e
o
f
C
h
o
lesk
y
d
ec
o
m
p
o
s
itio
n
v
ia:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
5
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
454
-
4
6
8
456
Su
b
m
atr
ix
1
=
20
×
20
×
20
×
20
×
20
×
20
⋮
Su
b
m
atr
ix
2
5
=
20
×
20
×
20
×
20
×
20
×
20
v)
R
ep
ea
t
s
tep
s
3
-
4
f
o
u
r
tim
es,
th
en
co
n
ca
te
n
atin
g
th
e
r
esu
lts
h
o
r
izo
n
tally
,
f
o
r
m
in
g
f
i
v
e
clu
s
ter
s
o
f
v
ar
iab
les.
Var
iab
les
with
in
th
e
s
am
e
clu
s
ter
ar
e
c
o
r
r
elate
d
,
b
u
t
th
o
s
e
b
etwe
en
clu
s
ter
s
ar
e
n
o
t
co
r
r
elate
d
.
T
h
e
m
atr
ix
1
∈
ℝ
500
×
100
will b
e
f
o
r
m
e
d
.
v
i)
R
ep
ea
t
s
tep
s
3
-
5
th
r
ee
tim
es
to
g
en
er
ate
1
,
2
,
an
d
3
.
Un
d
er
th
e
co
n
d
itio
n
o
f
co
r
r
elate
d
m
atr
ices
1
,
2
,
3
an
d
4
,
as
d
etailed
b
el
o
w,
ea
ch
s
u
b
s
eq
u
en
t
m
atr
ix
+
1
is
o
b
tain
ed
b
y
ad
d
in
g
to
th
e
p
r
ec
ed
in
g
m
atr
ix
,
f
o
r
=1
,
2
,
3
.
T
h
e
s
im
u
lated
d
ata
wer
e
r
an
d
o
m
ly
r
em
o
v
ed
u
n
d
er
th
e
m
is
s
in
g
co
m
p
letely
at
r
an
d
o
m
(
MCA
R
)
m
ec
h
an
is
m
with
m
is
s
in
g
v
alu
e
p
er
ce
n
tag
es
o
f
5
,
1
0
,
1
5
,
an
d
2
0
%
in
ea
ch
s
im
u
lated
d
ata,
wh
ile
en
s
u
r
in
g
th
at
n
o
r
o
w
o
r
co
lu
m
n
h
ad
all
its
en
tr
ies m
is
s
in
g
.
T
h
is
s
im
u
latio
n
an
aly
s
is
aim
s
to
ev
alu
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
in
teg
r
ated
GPC
A
-
MI
GA
in
r
ed
u
cin
g
th
e
d
im
en
s
io
n
ality
o
f
d
ata
co
n
tain
in
g
m
is
s
in
g
v
alu
e
s
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
is
m
eth
o
d
was
co
m
p
ar
e
d
with
th
at
o
f
MI
GA+
GPC
A
(
n
o
n
-
in
teg
r
ate
d
)
,
m
ea
n
im
p
u
tatio
n
+G
PC
A,
an
d
m
ed
ian
im
p
u
tatio
n
+G
PC
A.
Fu
r
th
er
m
o
r
e,
th
e
r
esu
lts
o
f
th
e
s
e
f
o
u
r
a
p
p
r
o
ac
h
es
wer
e
co
m
p
ar
ed
with
GPC
A
ap
p
lied
to
co
m
p
lete
d
ata,
wh
ich
s
er
v
es
as
th
e
b
aselin
e
r
ep
r
esen
tin
g
th
e
id
ea
l
c
o
n
d
itio
n
with
o
u
t
an
y
in
f
o
r
m
atio
n
lo
s
s
.
T
h
e
o
v
er
a
ll
wo
r
k
f
lo
w
o
f
th
e
s
im
u
lati
o
n
an
aly
tical
p
r
o
ce
d
u
r
e
is
s
y
s
tem
atica
lly
an
d
s
tr
u
ctu
r
ally
d
esig
n
ed
,
as illu
s
tr
ated
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Flo
wch
ar
t
o
f
th
e
s
im
u
latio
n
d
ata
an
al
y
s
is
T
h
is
s
tu
d
y
em
p
lo
y
ed
em
p
ir
ic
al
d
ata
co
n
s
is
tin
g
o
f
in
d
icato
r
s
r
elate
d
to
th
e
d
im
en
s
io
n
s
o
f
h
u
m
an
d
ev
elo
p
m
e
n
t
at
th
e
d
is
tr
ict/cit
y
lev
el
in
I
n
d
o
n
esia
f
o
r
t
h
e
p
e
r
io
d
2
0
1
9
to
2
0
2
2
.
T
h
ese
d
ata
wer
e
s
o
u
r
ce
d
f
r
o
m
Statis
t
ics
I
n
d
o
n
esia
(
B
PS
)
p
u
b
licatio
n
s
,
wh
ich
ar
e
av
ailab
le
o
n
th
e
o
f
f
icial
web
s
ites
o
f
ea
ch
d
is
tr
ict/city
.
T
h
e
d
ata
co
n
s
is
ts
o
f
2
0
in
d
icat
o
r
s
co
v
e
r
in
g
a
t
o
tal
o
f
5
1
4
d
is
tr
ict
/city
in
I
n
d
o
n
esia
.
T
h
ese
in
d
icato
r
s
co
m
p
r
eh
e
n
s
iv
ely
r
ep
r
esen
t
th
e
th
r
ee
d
im
en
s
io
n
s
o
f
h
u
m
a
n
d
ev
elo
p
m
e
n
t,
n
am
ely
l
o
n
g
li
f
e
an
d
h
ea
lth
y
life
,
k
n
o
wled
g
e
,
a
n
d
a
d
ec
en
t
s
tan
d
ar
d
o
f
liv
in
g
.
T
h
e
l
o
n
g
l
if
e
an
d
h
ea
lth
l
if
e
d
im
en
s
io
n
in
clu
d
es
in
d
icato
r
s
s
u
ch
as
th
e
p
e
r
ce
n
tag
e
o
f
h
o
u
s
eh
o
l
d
s
with
clea
n
d
r
i
n
k
in
g
wate
r
s
o
u
r
ce
s
(X
1
)
,
th
e
p
er
ce
n
tag
e
o
f
h
o
u
s
eh
o
l
d
s
with
ac
ce
s
s
to
ad
eq
u
ate
d
r
in
k
in
g
wate
r
(X
2
),
th
e
p
er
ce
n
tag
e
o
f
h
o
u
s
eh
o
ld
s
th
at
d
o
n
o
t
h
av
e
d
ef
ec
atio
n
f
ac
ilit
ies
(X
3
)
,
an
d
m
o
r
b
id
ity
(X
4
)
.
T
h
e
k
n
o
wled
g
e
d
im
e
n
s
io
n
in
clu
d
es
in
d
icato
r
s
s
u
ch
as
s
ch
o
o
l
en
r
o
llm
en
t
r
ates
f
o
r
th
e
ag
e
g
r
o
u
p
s
7
-
1
2
y
ea
r
s
(X
5
),
13
-
1
5
y
ea
r
s
(X
6
),
16
-
1
8
y
ea
r
s
(X
7
),
g
r
o
s
s
p
ar
ticip
atio
n
r
at
es
at
th
e
elem
en
tar
y
(X
8
),
ju
n
io
r
h
ig
h
(X
9
)
,
an
d
s
en
io
r
h
ig
h
s
ch
o
o
l
lev
els
(
X
10
)
an
d
n
et
p
a
r
ticip
atio
n
r
ates
at
elem
en
tar
y
(X
11
),
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dev
elo
p
men
t o
f g
e
n
era
liz
ed
p
r
in
cip
a
l c
o
mp
o
n
e
n
t a
n
a
lysi
s
u
s
in
g
mu
ltip
le
imp
u
ta
tio
n
…
(
F
a
h
r
eza
l Zu
b
ed
i)
457
ju
n
io
r
h
ig
h
(X
12
),
an
d
s
en
io
r
h
ig
h
s
ch
o
o
l
lev
els
(X
13
)
.
T
h
e
d
ec
en
t
s
tan
d
ar
d
o
f
l
iv
in
g
d
im
en
s
io
n
in
clu
d
es
in
d
icato
r
s
s
u
ch
as
th
e
p
er
ce
n
tag
e
o
f
f
o
r
m
al
wo
r
k
er
s
(X
14
),
th
e
p
er
ce
n
tag
e
o
f
p
o
o
r
p
eo
p
le
(X
15
),
t
h
e
o
p
e
n
u
n
em
p
lo
y
m
en
t
r
ate
(X
16
)
,
th
e
av
er
ag
e
wa
g
es
o
f
wo
r
k
er
s
an
d
em
p
lo
y
ee
s
p
er
m
o
n
th
(X
17
),
th
e
g
r
o
s
s
r
eg
io
n
al
d
o
m
esti
c
p
r
o
d
u
ct
p
er
ca
p
ita
b
ased
o
n
cu
r
r
en
t
p
r
ices
(X
18
),
th
e
p
er
ce
n
tag
e
o
f
in
f
o
r
m
al
wo
r
k
er
s
(X
19
),
an
d
th
e
Gin
i r
atio
(X
20
)
[
1
3
]
–
[
1
6
]
.
T
h
e
f
lo
wch
ar
t o
f
th
e
em
p
ir
ical
d
ata
an
aly
s
is
is
p
r
esen
ted
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
th
e
em
p
ir
ical
d
ata
an
aly
s
is
2
.
2
.
G
ener
a
lized
princip
a
l c
o
m
po
nent
a
na
ly
s
is
GPC
A
is
a
d
im
en
s
io
n
ality
r
ed
u
ctio
n
m
et
h
o
d
th
at
s
im
u
ltan
eo
u
s
ly
m
in
im
izes
th
e
n
u
m
b
er
o
f
d
im
en
s
io
n
s
o
f
b
o
th
o
b
s
er
v
ati
o
n
s
an
d
v
ar
iab
les.
T
o
ac
h
iev
e
th
is
,
GPC
A
is
ap
p
lied
to
a
s
et
o
f
d
ata
m
atr
ices
{
}
=
1
∈
ℝ
,
with
th
e
aim
o
f
o
b
tain
in
g
a
lo
w
-
d
im
en
s
io
n
al
r
ep
r
esen
ta
tio
n
{
}
=
1
∈
ℝ
,
wh
ich
is
ex
p
r
ess
ed
as
(
1
)
[
1
8
]
.
=
(
1
)
W
h
er
e
∈
ℝ
r
ep
r
esen
ts
th
e
f
in
al
r
ed
u
ce
d
f
o
r
m
f
o
r
th
e
o
b
s
e
r
v
atio
n
s
d
im
en
s
io
n
,
wh
ile
∈
ℝ
r
ep
r
esen
ts
th
e
f
in
al
r
ed
u
ce
d
f
o
r
m
f
o
r
th
e
v
ar
iab
le
d
im
en
s
io
n
.
C
o
n
v
er
s
ely
,
to
ap
p
r
o
x
i
m
ate
a
s
et
o
f
d
ata
m
atr
ices
,
th
e
(
2
)
is
u
s
ed
.
̂
≈
(
2
)
T
h
e
o
p
t
i
m
a
l
a
n
d
m
a
t
r
i
c
e
s
a
r
e
o
b
t
a
i
n
e
d
t
h
r
o
u
g
h
a
n
i
t
e
r
a
t
i
v
e
p
r
o
c
e
d
u
r
e
u
n
t
i
l
a
c
o
n
v
e
r
g
e
n
c
e
c
r
i
t
e
r
i
o
n
b
a
s
e
d
o
n
r
o
o
t
m
e
a
n
s
q
u
a
r
e
e
r
r
o
r
(
R
M
S
E
)
i
s
m
e
t
.
O
n
c
e
c
o
n
v
e
r
g
e
n
c
e
i
s
r
e
a
c
h
e
d
,
t
h
e
l
o
w
-
d
i
m
e
n
s
i
o
n
a
l
r
e
p
r
e
s
e
n
t
a
t
i
o
n
a
n
d
t
h
e
a
p
p
r
o
x
i
m
a
t
e
d
o
r
i
g
i
n
a
l
d
a
t
a
m
a
t
r
i
c
e
s
a
r
e
c
o
m
p
u
t
e
d
u
s
i
n
g
t
h
e
f
i
n
a
l
a
n
d
m
a
t
r
i
c
e
s
[
1
9
]
.
T
h
e
d
e
t
a
i
l
e
d
s
t
e
p
s
o
f
t
h
e
G
P
C
A
a
r
e
p
r
e
s
e
n
t
e
d
i
n
A
l
g
o
r
i
t
h
m
1
,
s
p
e
c
i
f
i
c
a
l
l
y
i
n
s
t
e
p
s
1
1
t
o
2
3
o
f
t
h
e
i
n
t
e
g
r
a
t
e
d
G
P
C
A
–
M
I
G
A
a
l
g
o
r
i
t
h
m
[
2
0
]
.
GPC
A
also
f
ac
ilit
ates
an
aly
s
is
o
f
th
e
p
o
s
itio
n
s
o
f
o
b
s
er
v
atio
n
s
an
d
v
a
r
iab
les
u
s
in
g
th
e
b
ip
lo
t
co
n
ce
p
t,
a
two
-
d
im
e
n
s
io
n
al
v
is
u
aliza
tio
n
th
at
s
im
p
lifie
s
th
e
in
ter
p
r
etatio
n
o
f
m
u
ltiv
ar
iate
r
elatio
n
s
h
ip
s
.
R
eg
io
n
s
(
d
is
tr
ict/city
)
alig
n
e
d
with
in
d
icato
r
v
ec
to
r
s
a
r
e
in
t
er
p
r
eted
as
h
av
i
n
g
ab
o
v
e
-
av
er
ag
e
v
alu
es,
th
o
s
e
in
th
e
o
p
p
o
s
ite
d
ir
ec
tio
n
as
b
elo
w
-
av
er
ag
e,
an
d
th
o
s
e
n
ea
r
th
e
ce
n
ter
as
clo
s
e
t
o
th
e
av
er
a
g
e
[
2
1
]
–
[
2
3
]
.
Af
te
r
p
er
f
o
r
m
in
g
th
e
GPC
A,
th
e
p
r
in
cip
al
co
m
p
o
n
e
n
t
s
co
r
es
f
o
r
o
b
s
er
v
atio
n
s
an
d
v
ar
iab
les
ar
e
ca
lcu
lated
as
f
o
llo
ws:
̂
=
.
T
h
e
p
o
s
itio
n
s
o
f
o
b
s
er
v
atio
n
s
an
d
v
ar
ia
b
les
ar
e
p
lo
tted
u
s
in
g
p
r
in
cip
al
co
m
p
o
n
e
n
t
s
co
r
es
as
s
h
o
wn
in
(
3
)
an
d
(
4
)
.
=
(
3
)
=
(
)
=
(
)
(
4
)
W
h
er
e
=
0
.
5
,
co
n
tain
s
o
b
s
er
v
atio
n
co
o
r
d
in
ates
,
a
n
d
co
n
tain
s
v
ar
i
ab
le
co
o
r
d
in
ates
[
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
5
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
454
-
4
6
8
458
2
.
3
.
M
ultiple
im
pu
t
a
t
io
n g
e
net
ic
a
lg
o
rit
hm
T
h
e
MI
GA
was
d
ev
elo
p
ed
t
o
ad
d
r
ess
th
e
p
r
o
b
lem
o
f
m
is
s
in
g
v
alu
es
in
m
u
ltiv
ar
ia
te
d
ata
b
y
in
teg
r
atin
g
im
p
u
tatio
n
tech
n
iq
u
es
with
GA
as
an
o
p
tim
izati
o
n
m
eth
o
d
[
2
4
]
,
[
2
5
]
.
T
h
e
b
asic
id
ea
is
to
im
p
u
te
m
is
s
in
g
v
alu
es
b
y
g
en
er
atin
g
ca
n
d
id
ate
im
p
u
tatio
n
s
th
at
n
o
t
o
n
ly
a
p
p
r
o
x
im
ate
th
e
o
r
i
g
in
al
d
ata
b
u
t
also
p
r
eser
v
e
th
e
ess
en
tial
s
tatis
t
ic
al
p
r
o
p
e
r
ties
o
f
m
u
ltiv
ar
iate
d
ata,
s
u
ch
as
m
ea
n
s
,
co
v
ar
ian
ce
s
,
an
d
s
k
ewn
ess
.
T
h
e
co
r
e
in
s
ig
h
t
o
f
MI
GA
is
th
at
GA
,
with
th
eir
ev
o
lu
tio
n
ar
y
n
atu
r
e,
ca
n
b
e
em
p
l
o
y
e
d
to
ex
p
lo
r
e
a
wid
e
s
o
lu
tio
n
s
p
ac
e
f
o
r
im
p
u
tatio
n
s
,
en
s
u
r
in
g
th
at
m
is
s
in
g
d
ata
im
p
u
tatio
n
is
n
o
t
m
er
ely
th
e
ac
t
o
f
f
illi
n
g
em
p
t
y
en
tr
ies
b
u
t
a
p
r
o
ce
s
s
o
f
m
ain
tain
in
g
th
e
d
is
tr
ib
u
tio
n
al
ch
ar
ac
ter
is
tics
an
d
in
ter
-
v
a
r
iab
le
r
elatio
n
s
h
ip
s
n
ec
ess
ar
y
f
o
r
v
alid
an
d
r
eliab
l
e
s
tatis
tical
an
aly
s
is
.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
o
f
MI
GA
lies
i
n
th
e
f
o
r
m
u
latio
n
o
f
a
m
u
ltio
b
jectiv
e
f
itn
ess
f
u
n
cti
o
n
b
ased
o
n
th
e
Min
k
o
wsk
i
d
is
tan
ce
,
wh
ich
s
im
u
ltan
eo
u
s
ly
p
r
eser
v
es
m
ea
n
s
,
co
v
ar
ian
ce
s
,
an
d
s
k
ewn
ess
.
T
h
e
f
itn
ess
f
u
n
ctio
n
is
d
ef
in
ed
as
(
5
)
.
∶
=
(
(
(
̃
,
̃
)
+
(
̃
,
)
+
(
,
)
)
(
5
)
W
h
er
e
(
̃
,
̃
)
r
ep
r
esen
ts
th
e
d
is
tan
c
e
b
etwe
en
th
e
r
elativ
e
m
ea
n
s
o
f
th
e
co
m
p
lete
d
ata
an
d
th
e
im
p
u
ted
d
ata,
wh
ile
(
̃
,
)
r
ep
r
esen
ts
th
e
d
is
tan
ce
b
etwe
en
th
e
r
elativ
e
co
v
ar
ian
ce
m
atr
ix
(
̃
)
an
d
th
e
i
d
en
t
ity
m
atr
ix
(
)
,
th
u
s
en
s
u
r
in
g
th
at
th
e
co
v
ar
ian
ce
an
d
co
r
r
elatio
n
s
tr
u
ctu
r
es
ar
e
p
r
eser
v
e
d
.
Similar
ly
,
(
,
)
r
ep
r
esen
ts
th
e
d
is
tan
ce
b
etwe
e
n
th
e
s
k
ewn
ess
v
ec
to
r
s
o
f
t
h
e
co
m
p
lete
d
ata
an
d
th
e
im
p
u
ted
d
ata
[
1
2
]
,
[
2
6
]
.
2
.
4
.
T
he
inte
g
ra
t
ed
G
P
CA
-
M
I
G
A
a
lg
o
rit
hm
T
h
e
i
n
teg
r
ated
GPC
A
-
MI
GA
alg
o
r
ith
m
im
p
u
tes
m
is
s
in
g
v
alu
es
an
d
r
e
d
u
ce
s
d
ata
d
im
en
s
io
n
ality
with
in
a
u
n
if
ied
iter
ativ
e
f
r
a
m
ewo
r
k
.
I
n
ea
ch
iter
atio
n
,
M
I
GA
im
p
u
tes
m
is
s
in
g
v
alu
es
t
h
r
o
u
g
h
e
v
o
lu
tio
n
ar
y
o
p
er
atio
n
s
in
clu
d
i
n
g
s
elec
tio
n
,
cr
o
s
s
o
v
er
,
an
d
m
u
tatio
n
,
f
o
llo
wed
b
y
GPC
A,
wh
ich
p
er
f
o
r
m
s
d
ata
d
im
en
s
io
n
ality
r
e
d
u
ctio
n
.
T
h
e
ap
p
r
o
x
im
ate
o
r
ig
in
al
d
ata
o
b
tain
ed
f
r
o
m
GPC
A
co
n
tain
s
elem
en
ts
in
th
e
p
o
s
itio
n
s
o
f
p
r
ev
i
o
u
s
ly
m
is
s
in
g
v
al
u
es.
T
h
ese
elem
e
n
ts
s
er
v
e
as
th
e
b
asis
f
o
r
MI
GA
to
u
p
d
ate
th
e
i
m
p
u
ted
m
is
s
in
g
v
alu
es
in
th
e
n
ex
t
ite
r
atio
n
.
GPC
A
th
en
r
ef
in
es
th
e
lo
w
-
d
im
en
s
io
n
al
r
ep
r
esen
tati
o
n
u
s
in
g
th
e
latest
im
p
u
tatio
n
r
esu
lts
f
r
o
m
M
I
GA.
T
h
e
iter
ativ
e
p
r
o
ce
s
s
ter
m
in
ates
wh
en
th
e
r
elativ
e
ch
an
g
e
o
f
all
im
p
u
te
d
m
is
s
in
g
en
tr
ies
b
etwe
en
two
co
n
s
ec
u
tiv
e
iter
atio
n
s
is
les
s
th
an
o
r
eq
u
al
to
0
.
0
0
1
.
T
h
e
d
etailed
s
tep
s
o
f
th
e
in
teg
r
ated
GPC
A
-
MI
GA
alg
o
r
ith
m
ar
e
p
r
esen
ted
in
Alg
o
r
ith
m
1
.
Alg
o
r
ith
m
1
.
T
he
in
te
g
r
ated
G
PC
A
-
MI
GA
I
n
p
u
t
:
1
,
2
,
3
,
4
,
1
=
2
=
5
,
3
=
10
,
=
100
Ou
tp
u
t
:
1
,
2
,
3
,
4
,
̂
1
,
̂
2
,
̂
3
,
̂
4
,
,
,
R
MSE
,
f
itn
ess
v
alu
es
1.
C
r
ea
te
m
atr
ices
1
,
2
,
3
an
d
4
wh
ich
co
n
s
is
t
o
f
co
m
p
lete
o
b
s
er
v
a
tio
n
s
(
r
o
ws)
f
r
o
m
m
atr
ices
1
,
2
,
3
,
4
.
2.
C
o
m
p
u
t
e
t
h
e
c
o
l
u
m
n
-
w
i
s
e
m
e
a
n
,
s
k
e
w
n
e
s
s
,
a
n
d
t
h
e
c
o
v
a
r
i
a
n
c
e
m
a
t
r
i
x
f
o
r
e
a
c
h
o
f
1
,
2
,
3
,
a
n
d
4
.
3.
C
r
ea
te
m
atr
ices
1
,
2
,
3
an
d
4
co
n
s
is
ti
n
g
o
f
o
b
s
er
v
atio
n
s
(
r
o
ws)
f
r
o
m
1
,
2
,
3
,
4
with
at
least
o
n
e
m
is
s
in
g
elem
en
t.
4.
C
r
ea
te
v
ec
to
r
in
d
ices
o
f
1
,
2
,
3
an
d
4
with
in
m
atr
ices
1
,
2
,
3
,
4
.
5.
G
e
n
e
r
a
t
e
a
n
i
n
i
t
i
a
l
p
o
p
u
l
a
t
i
o
n
c
o
n
t
a
i
n
i
n
g
i
n
d
i
v
i
d
u
a
l
s
b
a
s
e
d
o
n
t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
o
f
v
a
r
i
a
b
l
e
s
f
o
r
e
a
c
h
m
a
t
r
i
x
.
6.
C
o
m
p
u
te
f
itn
ess
v
alu
es f
o
r
all
in
d
iv
id
u
als in
th
e
p
o
p
u
latio
n
.
7.
Select
in
d
iv
id
u
als f
r
o
m
t
h
e
p
o
p
u
latio
n
with
th
e
s
m
allest f
itn
ess
v
alu
es.
8.
Per
f
o
r
m
m
u
tatio
n
o
n
th
e
s
elec
ted
1
in
d
iv
id
u
als an
d
th
e
n
r
ep
ea
t it
3
tim
es p
er
in
d
iv
id
u
al
.
9.
Per
f
o
r
m
cr
o
s
s
o
v
er
o
n
th
e
s
elec
ted
1
in
d
iv
i
d
u
als
an
d
th
en
r
ep
ea
t
it
f
o
r
th
e
2
−
1
r
em
ain
in
g
in
d
iv
id
u
als.
10.
R
ec
alcu
late
th
e
f
itn
ess
v
alu
es
o
f
in
d
i
v
id
u
als
af
ter
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
.
T
h
e
in
d
iv
i
d
u
al
with
th
e
s
m
allest f
itn
es
s
v
alu
e
is
u
s
ed
as th
e
im
p
u
tatio
n
f
o
r
m
is
s
in
g
v
alu
es.
11.
Stan
d
ar
d
ize
d
ata
m
atr
ices
1
,
2
,
3
,
4
to
f
o
r
m
1
,
2
,
…
,
.
12.
I
n
itialize
m
atr
ix
as a
n
id
en
tity
m
atr
ix
0
=
(
,
0
)
.
13.
=
0
,
R
M
SE
(
)
=
∞
14.
C
o
m
p
u
te
m
atr
ix
u
s
in
g
th
e
f
o
r
m
u
la:
=
∑
=
1
.
15.
Dete
r
m
in
e
th
e
eig
en
v
ec
to
r
s
{
}
=
1
f
r
o
m
th
at
co
r
r
esp
o
n
d
to
a
cu
m
u
lativ
e
v
ar
ian
ce
p
r
o
p
o
r
tio
n
(
≤
9
0
%),
r
esu
ltin
g
i
n
=
[
1
,
…
,
]
.
16.
C
o
m
p
u
te
m
atr
ix
u
s
in
g
th
e
f
o
r
m
u
la
=
∑
=
1
.
17.
Dete
r
m
in
e
th
e
eig
en
v
ec
to
r
s
{
β
j
}
j
=
1
v
f
r
o
m
th
at
co
r
r
esp
o
n
d
to
a
cu
m
u
lativ
e
v
ar
ian
c
e
p
r
o
p
o
r
tio
n
(
≤
9
0
%),
r
esu
ltin
g
i
n
=
[
1
,
…
,
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dev
elo
p
men
t o
f g
e
n
era
liz
ed
p
r
in
cip
a
l c
o
mp
o
n
e
n
t a
n
a
lysi
s
u
s
in
g
mu
ltip
le
imp
u
ta
tio
n
…
(
F
a
h
r
eza
l Zu
b
ed
i)
459
18.
C
o
m
p
u
te
R
MSE
as
(
)
=
√
1
∑
|
|
−
=
1
|
|
2
.
19.
R
ep
ea
t step
s
1
3
-
1
7
u
n
til
(
−
1
)
−
(
)
≤
0
,
001
.
20.
Der
iv
e
th
e
m
atr
ices
an
d
f
r
o
m
co
n
clu
d
i
n
g
iter
atio
n
.
21.
C
r
ea
te
th
e
r
ed
u
ce
d
-
d
im
en
s
io
n
al
d
ata
m
atr
ix
u
s
in
g
=
,
f
o
r
ea
ch
f
r
o
m
to
.
22.
Ap
p
r
o
x
im
ate
t
h
e
o
r
i
g
in
al
d
ata
m
atr
ix
as
̂
=
,
f
o
r
ea
ch
f
r
o
m
to
.
23.
C
o
n
v
er
t th
e
s
ca
le
o
f
t
h
e
d
ata
m
atr
ix
̂
to
th
e
o
r
ig
in
al
s
ca
le
̂
.
24.
Sav
e
th
e
im
p
u
ted
d
ata
v
alu
es f
r
o
m
th
e
f
ir
s
t iter
atio
n
o
f
t
h
e
in
teg
r
ated
GPC
A
-
MI
GA.
25.
C
alcu
late
th
e
r
elativ
e
ch
an
g
e
f
o
r
ea
ch
m
is
s
in
g
v
al
u
e
p
o
i
n
t.
26.
R
ep
ea
t
s
tep
s
6
to
2
5
u
s
in
g
th
e
u
p
d
ated
in
d
i
v
id
u
als.
I
f
th
e
d
i
f
f
er
en
ce
in
r
elativ
e
ch
a
n
g
e
b
et
wee
n
th
e
cu
r
r
en
t
a
n
d
p
r
ev
io
u
s
iter
atio
n
s
o
f
all
im
p
u
te
d
m
is
s
in
g
v
alu
es
is
≤
1
.
10
−
3
,
th
en
th
e
iter
ativ
e
p
r
o
ce
s
s
s
to
p
s
.
27.
Ob
tain
th
e
d
i
m
en
s
io
n
ally
r
ed
u
ce
d
d
ata
f
r
o
m
th
e
in
teg
r
ate
d
GPC
A
–
MI
GA
an
d
th
e
ap
p
r
o
x
im
ate
d
o
r
ig
in
al
d
ata
.
T
h
e
ex
p
lan
atio
n
o
f
th
e
in
teg
r
a
ted
GPC
A
-
MI
GA
alg
o
r
ith
m
is
f
o
llo
wed
b
y
a
p
er
f
o
r
m
an
ce
ev
alu
atio
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icien
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ata
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r
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lts
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m
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r
m
ain
ap
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ex
am
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ed
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s
u
m
m
ar
ized
in
T
a
b
le
1
[
2
7
]
,
[
2
8
]
.
T
ab
le
1
.
C
o
m
p
a
r
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aly
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is
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tatio
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GPC
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m
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M
I
G
A
+
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‒
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e
m
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mp
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p
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ss t
o
r
e
mai
n
f
a
s
t
a
n
d
s
t
a
b
l
e
.
‒
M
e
a
n
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ma
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l
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s.
‒
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e
m
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h
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d
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s
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s
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‒
M
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n
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t
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t
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a
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m
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ss t
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mai
n
f
a
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t
a
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l
e
.
‒
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me
d
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m G
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a
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.
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m
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s
.
‒
M
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m
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.
As
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Pro
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(
d
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p
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s
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es
[
2
9
]
.
T
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im
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s
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co
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.
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[
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3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
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3
.
1
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Sim
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ts
b
etwe
en
s
u
cc
ess
iv
e
iter
atio
n
s
b
ec
am
e
n
eg
lig
ib
le.
Acc
o
r
d
in
g
to
th
e
s
im
u
latio
n
r
esu
lts
,
c
o
n
v
er
g
en
ce
was a
ch
iev
ed
at
th
e
423
rd
iter
atio
n
at
a
5
%
lev
el
o
f
m
is
s
in
g
d
ata,
at
th
e
4
5
8
t
h
iter
atio
n
at
a
1
0
%
lev
el,
at
th
e
4
8
6
th
iter
atio
n
at
a
1
5
% lev
el,
an
d
at
th
e
5
2
7
th
iter
atio
n
at
a
2
0
% lev
el.
Du
r
in
g
ea
ch
iter
atio
n
,
th
e
MI
GA
g
en
er
ated
s
ev
er
al
im
p
u
tatio
n
ca
n
d
id
ates
an
d
ev
alu
ated
t
h
em
u
s
in
g
th
e
f
itn
ess
f
u
n
ctio
n
.
T
h
e
ca
n
d
id
ate
with
th
e
s
m
allest
f
itn
ess
v
alu
e
was
s
elec
ted
as
th
e
o
p
tim
al
im
p
u
tatio
n
r
esu
lt
an
d
in
te
g
r
ated
in
t
o
th
e
GPC
A
p
r
o
ce
s
s
f
o
r
d
im
en
s
io
n
ality
r
ed
u
ctio
n
.
T
h
e
co
n
s
is
ten
t
d
ec
r
ea
s
e
in
f
itn
ess
v
alu
es
with
in
cr
ea
s
in
g
iter
atio
n
s
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
,
in
d
icate
s
a
g
r
ad
u
al
im
p
r
o
v
em
e
n
t
in
th
e
d
im
en
s
io
n
ality
r
e
d
u
ctio
n
p
r
o
c
ess
.
Fig
u
r
e
3
(
a
)
p
r
esen
ts
th
e
r
esu
lts
f
o
r
m
is
s
in
g
v
alu
e
p
er
ce
n
tag
es
o
f
5
%
,
a
n
d
1
0
%
as p
r
esen
ted
in
Fig
u
r
e
3
(
b
)
o
n
ly
,
as th
eir
co
n
v
e
r
g
en
ce
p
atter
n
s
r
ef
lect
s
im
ilar
ten
d
en
cies a
t o
th
er
m
is
s
in
g
v
alu
e
lev
els.
(
a)
(
b
)
Fig
u
r
e
3
.
Fit
n
ess
v
alu
es a
t d
if
f
er
en
t p
er
ce
n
tag
es o
f
m
is
s
in
g
v
alu
es
of
(
a)
5
% a
n
d
(
b
)
1
0
%
T
h
e
s
im
u
lated
d
ata
u
s
ed
in
th
is
s
tu
d
y
h
ad
an
u
n
d
e
r
ly
in
g
s
tr
u
ctu
r
e
o
f
2
5
×
5
,
co
m
p
r
is
in
g
2
5
clu
s
ter
s
o
f
o
b
s
er
v
atio
n
s
an
d
5
clu
s
ter
s
o
f
v
ar
iab
les.
T
h
is
co
n
f
ig
u
r
atio
n
was
u
s
ed
as
a
r
ef
er
en
ce
to
as
s
ess
h
o
w
ef
f
ec
tiv
e
ea
ch
ap
p
r
o
ac
h
was
in
p
er
f
o
r
m
in
g
d
im
e
n
s
io
n
ality
r
ed
u
ctio
n
o
n
d
atasets
co
n
tain
in
g
m
is
s
in
g
v
alu
es.
T
h
e
in
teg
r
ated
GPC
A
-
MI
GA
d
em
o
n
s
tr
ated
th
e
m
o
s
t
co
n
s
is
ten
t
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
t
o
th
e
o
th
er
m
eth
o
d
s
.
At
m
is
s
in
g
v
alu
e
p
e
r
ce
n
tag
es
o
f
5
an
d
1
0
%
,
th
e
i
n
teg
r
ated
GPC
A
-
MI
GA
p
r
eser
v
ed
th
e
o
r
ig
in
al
s
tr
u
ctu
r
e
b
y
p
r
o
d
u
cin
g
d
im
en
s
io
n
s
o
f
2
5
×
5
ac
r
o
s
s
all
r
ep
licatio
n
s
,
i
n
d
i
ca
tin
g
its
ab
ilit
y
t
o
r
e
d
u
ce
d
i
m
en
s
io
n
ality
s
tab
ly
ev
en
in
th
e
p
r
esen
ce
o
f
m
is
s
in
g
v
alu
es.
As
th
e
p
er
ce
n
tag
e
o
f
m
is
s
in
g
v
alu
es
in
cr
ea
s
ed
,
th
e
in
teg
r
ate
d
GPC
A
-
MI
GA
p
r
o
d
u
ce
d
lar
g
er
r
ed
u
ce
d
d
im
e
n
s
io
n
s
,
y
et
it
r
em
ain
ed
m
o
r
e
ef
f
icien
t
th
an
th
e
o
th
er
m
eth
o
d
s
.
I
n
co
n
tr
ast,
th
e
o
th
er
m
eth
o
d
s
ten
d
ed
to
g
en
er
ate
lar
g
er
d
i
m
en
s
io
n
s
ev
en
at
r
elativ
ely
lo
w
p
er
ce
n
tag
es
o
f
m
is
s
in
g
v
alu
es.
As
s
h
o
wn
in
T
ab
le
2
,
th
e
2
v
al
u
es
f
r
o
m
th
e
P
r
o
c
r
u
s
tes
an
aly
s
is
b
etwe
en
th
e
o
r
ig
in
al
d
ata
an
d
th
e
ap
p
r
o
x
im
ated
o
r
i
g
in
al
d
ata
o
b
tain
ed
f
r
o
m
GPC
A
r
an
g
e
f
r
o
m
0
.
9
9
1
to
0
.
9
9
3
,
in
d
icatin
g
th
at
GPC
A
ca
n
ap
p
r
o
x
im
ate
th
e
o
r
ig
i
n
al
d
ata
f
r
o
m
its
lo
w
-
d
im
e
n
s
io
n
al
r
e
p
r
esen
tatio
n
with
a
v
e
r
y
s
m
al
l
er
r
o
r
lev
el.
I
n
th
e
d
ata
co
n
tain
in
g
m
is
s
in
g
v
alu
e
s
,
th
e
in
teg
r
ated
GPC
A
-
MI
GA
p
r
o
d
u
ce
d
th
e
h
ig
h
est
an
d
m
o
s
t
s
tab
le
2
v
alu
es
ac
r
o
s
s
all
lev
els
o
f
m
is
s
in
g
n
ess
co
m
p
ar
ed
to
o
t
h
er
m
eth
o
d
s
.
T
h
is
in
d
icate
s
th
e
ab
ilit
y
o
f
th
e
m
eth
o
d
to
ap
p
r
o
x
im
ate
th
e
o
r
i
g
in
al
d
at
a
f
r
o
m
its
lo
w
-
d
im
en
s
io
n
al
r
ep
r
esen
tatio
n
with
a
v
er
y
s
m
all
er
r
o
r
lev
el.
I
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dev
elo
p
men
t o
f g
e
n
era
liz
ed
p
r
in
cip
a
l c
o
mp
o
n
e
n
t a
n
a
lysi
s
u
s
in
g
mu
ltip
le
imp
u
ta
tio
n
…
(
F
a
h
r
eza
l Zu
b
ed
i)
461
ad
d
itio
n
,
th
e
2
v
alu
es
o
f
th
e
in
teg
r
ated
GPC
A
-
MI
GA
wer
e
clo
s
er
to
th
o
s
e
o
f
GPC
A
o
n
co
m
p
lete
d
ata
co
m
p
ar
ed
to
o
th
er
m
eth
o
d
s
.
I
n
o
th
e
r
wo
r
d
s
,
th
e
d
im
en
s
io
n
a
lity
r
ed
u
ctio
n
r
esu
lts
o
b
tain
ed
f
r
o
m
t
h
e
in
teg
r
ate
d
GPC
A
-
MI
GA
f
o
r
d
ata
co
n
tain
in
g
m
is
s
in
g
v
alu
es
s
till
r
ef
le
ct
th
e
s
am
e
s
tr
u
ctu
r
e
an
d
r
elatio
n
s
h
ip
p
atter
n
s
as
th
e
d
ata
b
ef
o
r
e
th
e
m
is
s
in
g
v
alu
es o
cc
u
r
r
e
d
.
T
ab
le
2
.
T
h
e
2
v
alu
e
s
f
r
o
m
th
e
P
r
o
cr
u
s
tes an
aly
s
is
o
f
d
if
f
er
e
n
t m
eth
o
d
s
at
v
ar
i
o
u
s
lev
els o
f
m
is
s
in
g
v
alu
e
D
a
t
a
p
a
i
r
s
P
e
r
c
e
n
t
a
g
e
o
f
mi
ssi
n
g
v
a
l
u
e
s
(
%)
G
P
C
A
I
n
t
e
g
r
a
t
e
d
G
P
C
A
-
M
I
G
A
M
e
a
n
i
mp
u
t
a
t
i
o
n
+
G
P
C
A
M
e
d
i
a
n
i
mp
u
t
a
t
i
o
n
+
G
P
C
A
M
I
G
A
+
G
P
C
A
1
a
n
d
̂
1
0
0
.
9
9
1
-
-
-
-
5
-
0
.
9
7
4
0
.
6
5
5
0
.
6
3
3
0
.
7
2
4
10
-
0
.
9
6
2
0
.
6
2
8
0
.
6
1
2
0
.
7
0
6
15
-
0
.
9
6
0
0
.
6
0
3
0
.
5
8
3
0
.
6
7
1
20
-
0
.
9
4
4
0
.
5
6
2
0
.
5
3
2
0
.
6
4
6
2
a
n
d
̂
2
0
0
.
9
9
3
-
-
-
-
5
-
0
.
9
7
6
0
.
6
5
1
0
.
6
3
0
0
.
7
2
1
10
-
0
.
9
6
1
0
.
6
2
5
0
.
6
1
0
0
.
7
0
3
15
-
0
.
9
5
4
0
.
6
0
5
0
.
5
8
7
0
.
6
7
4
20
-
0
.
9
4
1
0
.
5
6
5
0
.
5
3
1
0
.
6
4
1
3
a
n
d
̂
3
0
0
.
9
9
2
-
-
-
-
5
-
0
.
9
7
3
0
.
6
4
7
0
.
6
2
7
0
.
7
2
5
10
-
0
.
9
5
9
0
.
6
2
1
0
.
6
0
7
0
.
6
9
8
15
-
0
.
9
5
7
0
.
6
0
9
0
.
5
8
1
0
.
6
6
9
20
-
0
.
9
4
6
0
.
5
5
7
0
.
5
3
6
0
.
6
4
1
4
a
n
d
̂
4
0
0
.
9
9
1
-
-
-
-
5
-
0
.
9
7
1
0
.
6
4
9
0
.
6
2
6
0
.
7
2
2
10
-
0
.
9
6
3
0
.
6
2
3
0
.
6
0
9
0
.
6
9
6
15
-
0
.
9
5
8
0
.
6
0
2
0
.
5
8
8
0
.
6
6
6
20
-
0
.
9
4
0
0
.
5
5
5
0
.
5
3
5
0
.
6
4
3
B
ased
o
n
T
ab
le
3
,
GPC
A
ap
p
lied
co
m
p
lete
d
ata
an
d
y
ield
e
d
an
a
v
er
ag
e
R
MSE
o
f
1
.
9
0
8
,
in
d
icatin
g
a
v
er
y
lo
w
esti
m
atio
n
er
r
o
r
.
All
ap
p
r
o
ac
h
es
ex
h
ib
ited
an
in
cr
ea
s
e
in
R
MSE
as
th
e
p
er
ce
n
tag
e
o
f
m
is
s
in
g
v
alu
es
in
cr
ea
s
ed
.
I
n
th
e
5
%
m
is
s
in
g
v
alu
e
s
ce
n
ar
io
,
th
e
in
teg
r
ated
GPC
A
-
MI
GA
ac
h
iev
ed
th
e
lo
west
av
er
ag
e
R
MSE
o
f
2
.
0
8
,
f
o
llo
wed
b
y
MI
GA+
GPC
A
with
2
.
2
7
,
wh
i
le
m
ea
n
im
p
u
tatio
n
+G
PC
A
with
2
.
4
2
an
d
m
e
d
ian
im
p
u
tatio
n
+G
PC
A
with
2
.
5
4
r
esu
lted
in
lar
g
er
esti
m
atio
n
er
r
o
r
s
.
T
h
is
p
atter
n
was
co
n
s
is
ten
t
at
th
e
1
0
,
1
5
,
an
d
2
0
%
m
is
s
in
g
v
alu
e
lev
els,
with
th
e
in
teg
r
ated
GP
C
A
-
MI
GA
co
n
s
is
ten
tly
o
u
tp
er
f
o
r
m
in
g
th
e
o
th
er
ap
p
r
o
ac
h
es,
an
d
its
av
er
a
g
e
R
MSE
r
em
ain
in
g
clo
s
e
to
t
h
at
o
f
GPC
A
in
ev
er
y
s
ce
n
ar
io
.
GPC
A
y
i
el
d
e
d
a
v
er
y
s
m
al
l
s
ta
n
d
a
r
d
d
ev
iati
o
n
o
f
0
.
0
6
i
n
t
h
e
co
m
p
let
e
d
at
a,
d
em
o
n
s
t
r
ati
n
g
s
tab
ilit
y
i
n
p
r
ese
r
v
i
n
g
th
e
o
r
ig
in
al
d
a
ta
s
t
r
u
ct
u
r
e
t
h
r
o
u
g
h
d
im
en
s
io
n
alit
y
r
e
d
u
cti
o
n
.
I
n
t
h
e
d
ata
w
it
h
5
%
m
is
s
i
n
g
v
al
u
es
,
th
e
i
n
t
eg
r
a
te
d
GPC
A
-
MI
GA
r
ec
o
r
d
ed
a
s
ta
n
d
a
r
d
d
e
v
i
ati
o
n
o
f
0
.
1
7
,
w
h
ic
h
was
m
o
r
e
s
ta
b
le
t
h
a
n
MI
GA
+G
PC
A
,
m
e
a
n
i
m
p
u
ta
ti
o
n
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PC
A
,
a
n
d
m
e
d
ia
n
i
m
p
u
t
ati
o
n
+G
PC
A
.
T
h
is
p
att
er
n
r
e
m
ai
n
e
d
c
o
n
s
is
t
en
t
at
a
h
ig
h
e
r
p
e
r
ce
n
ta
g
e
o
f
m
is
s
i
n
g
v
a
lu
es.
T
h
e
s
ta
n
d
a
r
d
d
ev
iat
io
n
v
al
u
es
f
o
r
e
ac
h
m
et
h
o
d
a
r
e
p
r
es
en
te
d
i
n
T
a
b
le
3
.
Ov
e
r
a
ll
,
t
h
es
e
f
in
d
i
n
g
s
c
o
n
f
i
r
m
t
h
at
t
h
e
i
n
t
e
g
r
ate
d
G
PC
A
-
MI
GA
is
m
o
r
e
ac
c
u
r
ate
a
n
d
m
o
r
e
r
o
b
u
s
t in
r
e
d
u
c
in
g
th
e
d
i
m
e
n
s
i
o
n
al
it
y
o
f
d
at
a
co
n
ta
in
in
g
m
is
s
i
n
g
v
al
u
es
.
T
o
co
m
p
le
m
e
n
t
t
h
e
d
es
cr
ip
ti
v
e
i
n
te
r
p
r
et
ati
o
n
o
f
t
h
e
av
er
ag
e
R
MS
E
an
d
its
s
ta
n
d
a
r
d
d
e
v
i
ati
o
n
,
s
ta
tis
ti
ca
l
a
n
a
ly
s
is
(
a
n
al
y
s
is
o
f
v
ar
ian
ce
(
ANOV
A)
an
d
T
u
c
k
e
y
t
est
)
was
ca
r
r
ie
d
o
u
t
.
T
ab
le
3
.
Av
e
r
ag
e
R
MSE
(
s
tan
d
ar
d
d
e
v
iatio
n
)
o
f
d
i
f
f
er
en
t
m
eth
o
d
s
at
v
ar
io
u
s
lev
els o
f
m
is
s
in
g
v
alu
es
M
e
t
h
o
d
s
P
e
r
c
e
n
t
a
g
e
o
f
mi
ss
i
n
g
v
a
l
u
e
s
0%
5%
1
0
%
1
5
%
2
0
%
G
P
C
A
1
.
9
1
(
0
.
0
6
)
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-
-
-
I
n
t
e
g
r
a
t
e
d
G
P
C
A
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M
I
G
A
-
2
.
0
8
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0
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1
7
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2
.
5
7
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0
.
2
7
)
3
.
0
1
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0
.
2
1
)
4
.
2
8
(
0
.
2
9
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M
e
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n
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m
p
u
t
a
t
i
o
n
+
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P
C
A
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2
.
4
2
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0
.
2
4
)
2
.
6
9
(
0
.
3
1
)
3
.
3
2
(
0
.
3
3
)
4
.
4
7
(
0
.
3
9
)
M
e
d
i
a
n
i
m
p
u
t
a
t
i
o
n
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P
C
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2
.
5
4
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2
6
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2
.
7
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0
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3
2
)
3
.
4
6
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0
.
3
3
)
4
.
6
1
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0
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4
0
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M
I
G
A
+
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P
C
A
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2
.
2
7
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0
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2
6
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2
.
6
6
(
0
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3
2
)
3
.
2
0
(
0
.
3
2
)
4
.
4
2
(
0
.
3
4
)
ANOV
A
wa
s
u
s
ed
to
s
ta
tis
tic
ally
ev
alu
ate
th
e
m
eth
o
d
s
.
T
h
is
test
aim
ed
to
d
eter
m
in
e
th
e
ef
f
ec
ts
o
f
th
e
m
eth
o
d
,
t
h
e
p
er
ce
n
tag
e
o
f
m
is
s
in
g
v
alu
es,
an
d
th
eir
in
te
r
ac
tio
n
o
n
t
h
e
R
MSE
v
alu
es.
B
ased
o
n
T
a
b
le
4
,
all
f
ac
to
r
s
h
av
e
p
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v
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es
<0
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0
5
,
in
d
icatin
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s
ig
n
if
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t
d
if
f
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s
in
R
MSE
v
al
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o
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g
m
eth
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a
m
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en
tag
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an
d
in
th
eir
i
n
ter
ac
tio
n
.
Sin
ce
th
e
ANOV
A
r
esu
lts
s
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s
ig
n
i
f
ican
t
d
if
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ce
s
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T
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tify
wh
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r
o
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p
s
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if
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e
r
ed
s
ig
n
if
ica
n
tly
f
r
o
m
ea
ch
o
th
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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9
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t J Ar
tif
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tell
,
Vo
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1
5
,
No
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1
,
Feb
r
u
ar
y
2
0
2
6
:
454
-
4
6
8
462
B
ased
o
n
th
e
r
esu
lts
o
f
t
h
e
T
u
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test
,
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e
in
teg
r
ated
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o
u
tp
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o
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m
e
d
th
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r
m
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m
p
u
tes
all
p
o
s
s
ib
le
p
air
wi
s
e
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m
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ar
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o
n
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o
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th
e
m
eth
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p
s
.
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h
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s
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d
y
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s
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ly
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m
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a
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o
n
s
in
v
o
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g
th
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m
eth
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aselin
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ased
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n
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le
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th
e
in
teg
r
ated
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A
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MI
GA
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as
th
e
s
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alle
s
t
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ea
n
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er
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ce
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m
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ar
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d
is
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ted
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ig
n
if
ican
ce
lev
el,
in
d
icatin
g
th
at
its
p
er
f
o
r
m
an
ce
is
th
e
clo
s
est
to
GPC
A.
I
n
co
n
t
r
ast,
th
e
o
th
er
m
eth
o
d
s
s
h
o
w
m
u
ch
lar
g
er
m
ea
n
d
if
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e
r
en
ce
s
,
in
d
icatin
g
a
s
ig
n
if
ican
t in
cr
ea
s
e
in
R
MSE
v
alu
es c
o
m
p
ar
e
d
to
GPC
A.
T
ab
le
4
.
R
esu
lts
o
f
ANOV
A
o
n
th
e
ef
f
ec
ts
o
f
m
eth
o
d
s
an
d
p
er
ce
n
tag
es o
f
m
is
s
in
g
v
al
u
es o
n
R
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S
o
u
r
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a
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1
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P
e
r
c
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n
t
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ss
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5
3
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5
7
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4
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6
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1
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M
e
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6
2
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T
ab
le
5
.
R
esu
lts
o
f
th
e
T
u
k
ey
test
co
m
p
ar
in
g
a
v
er
ag
e
R
MSE
d
if
f
er
en
ce
s
am
o
n
g
m
eth
o
d
s
C
o
m
p
a
r
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so
n
M
e
a
n
d
i
f
f
e
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c
e
A
d
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st
e
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p
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0
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P
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P
C
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4
2
6
3
0
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0
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.
2
.
Appl
ica
t
io
n t
o
re
a
l da
t
a
T
h
e
p
er
ce
n
tag
e
o
f
m
is
s
in
g
v
alu
es
in
ea
ch
d
ata
is
5
%.
B
ased
o
n
th
e
s
im
u
latio
n
r
esu
lts
,
th
e
i
n
teg
r
ated
GPC
A
-
MI
GA
o
u
tp
er
f
o
r
m
ed
t
h
e
o
th
er
m
et
h
o
d
s
in
r
e
d
u
cin
g
th
e
d
im
en
s
io
n
ality
o
f
d
ata
co
n
tain
in
g
m
is
s
in
g
v
alu
es.
T
h
er
ef
o
r
e,
th
e
in
teg
r
at
ed
GPC
A
-
MI
GA
wa
s
s
u
b
s
eq
u
en
tly
ap
p
lied
to
th
e
em
p
ir
ica
l
d
ata.
I
n
th
is
ca
s
e,
th
e
in
teg
r
ated
GPC
A
-
MI
GA
s
to
p
p
ed
at
t
h
e
4
0
1
st
iter
atio
n
af
t
er
m
ee
tin
g
th
e
c
r
iter
ia.
B
ased
o
n
th
e
r
esu
lts
o
b
tain
ed
,
an
in
cr
ea
s
in
g
n
u
m
b
er
o
f
th
e
i
n
teg
r
ated
GPC
A
-
MI
GA
iter
at
io
n
s
lead
s
to
a
d
ec
r
ea
s
e
in
f
itn
ess
v
alu
e
s
.
T
h
is
in
d
icate
s
th
at
th
e
in
teg
r
ated
GPC
A
-
MI
GA
s
u
cc
ess
f
u
lly
o
p
tim
izes
th
e
s
o
lu
tio
n
s
p
r
o
g
r
ess
iv
ely
f
o
r
ea
ch
d
ataset.
T
h
e
R
MSE
v
alu
e
o
f
th
e
in
teg
r
ated
GPC
A
-
MI
GA,
wh
ich
is
4
.
1
2
8
an
d
clo
s
e
to
th
e
R
MSE
v
alu
e
o
f
GPC
A,
wh
ich
is
3
.
3
9
2
,
in
d
icate
s
th
at
b
o
th
m
eth
o
d
s
ca
n
p
r
o
d
u
c
e
lo
w
-
d
im
en
s
io
n
al
d
ata
with
n
e
ar
ly
eq
u
iv
ale
n
t e
r
r
o
r
lev
els.
T
h
is
s
u
g
g
ests
th
at
th
e
in
teg
r
ated
GPC
A
-
MI
GA
d
o
es
n
o
t
p
r
o
v
id
e
a
s
ig
n
if
ican
t
d
if
f
e
r
en
ce
in
esti
m
atin
g
th
e
o
r
i
g
in
al
d
ata
f
r
o
m
th
e
r
ed
u
ce
d
d
ata
co
m
p
ar
ed
to
GPC
A.
T
h
e
d
im
en
s
io
n
r
ed
u
ctio
n
p
r
o
ce
s
s
u
s
in
g
m
atr
ices
an
d
s
u
cc
ess
f
u
lly
r
etain
s
m
o
s
t
o
f
th
e
v
ar
iat
io
n
in
th
e
o
r
i
g
in
al
d
ata.
I
n
th
i
s
p
r
o
ce
s
s
,
d
ata
f
r
o
m
5
1
4
d
is
tr
ict
/city
wer
e
r
ed
u
ce
d
to
3
2
p
r
in
cip
al
co
m
p
o
n
en
ts
th
r
o
u
g
h
m
atr
ix
,
with
a
cu
m
u
lativ
e
v
ar
ian
ce
p
r
o
p
o
r
tio
n
o
f
8
8
.
1
1
%.
Me
an
wh
ile,
d
ata
f
r
o
m
2
0
in
d
icato
r
s
wer
e
r
ed
u
ce
d
t
o
6
p
r
i
n
cip
al
c
o
m
p
o
n
en
ts
th
r
o
u
g
h
m
atr
ix
,
with
a
cu
m
u
lativ
e
v
a
r
ian
ce
p
r
o
p
o
r
tio
n
o
f
8
8
.
3
1
%.
Fig
u
r
e
4
illu
s
tr
ated
t
h
e
v
is
u
al
o
f
th
e
m
atr
ix
s
tr
u
ctu
r
e
b
ef
o
r
e
(
Fig
u
r
e
4
(
a)
)
an
d
af
ter
(
Fig
u
r
e
4
(
b
)
)
d
im
en
s
io
n
ality
r
ed
u
ctio
n
.
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h
is
m
eth
o
d
ef
f
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tiv
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s
u
m
m
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izes
th
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ata
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im
en
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io
n
s
with
o
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t
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ig
n
if
ican
t
lo
s
s
o
f
th
e
to
tal
ex
p
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ed
v
ar
ia
n
ce
.
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h
e
R
2
v
alu
es
f
r
o
m
th
e
Pr
o
cr
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s
tes
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aly
s
is
f
o
r
th
e
in
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ated
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ar
e
0
.
8
8
9
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r
(
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d
̂
1
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,
0
.
8
8
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r
(
2
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d
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,
0
.
8
7
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r
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d
0
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8
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r
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d
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,
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em
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n
s
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atin
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th
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ap
p
r
o
x
im
ated
o
r
ig
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al
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ata
f
r
o
m
th
e
in
teg
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G
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clo
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ely
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e
o
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ig
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al
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ata.
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h
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R
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es
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e
f
r
o
m
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8
7
7
to
0
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8
9
6
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r
GPC
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m
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an
d
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A
f
o
r
ea
ch
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ata
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air
in
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icate
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at
b
o
th
m
eth
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d
s
ex
h
ib
it
s
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ilar
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er
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o
r
m
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ce
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p
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g
t
h
e
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ar
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ilit
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o
f
th
e
o
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ig
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al
d
at
a.
T
h
e
in
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r
ated
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A
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r
esu
lts
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e
th
en
v
is
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alize
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u
s
in
g
th
e
b
ip
lo
t
ap
p
r
o
ac
h
.
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s
h
o
wn
in
Fig
u
r
e
5
,
th
e
d
is
tr
ict
/city
ar
e
d
is
tr
ib
u
ted
in
to
f
o
u
r
q
u
a
d
r
an
ts
,
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ch
d
e
f
in
ed
b
y
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is
tin
ct
s
ets
o
f
in
d
icato
r
s
.
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h
e
d
is
tr
ict
/city
lo
ca
ted
in
q
u
ad
r
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n
t
1
ar
e
ass
o
ciate
d
with
in
d
icato
r
s
X
5
,
X
6
,
X
7
,
X
10
,
X
14
,
X
16
,
X
17
,
an
d
X
19
.
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h
o
s
e
i
n
q
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ad
r
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t
2
a
r
e
ass
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ciate
d
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in
d
icato
r
s
X
12
,
X
15
,
a
n
d
X
20
,
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ile
q
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ad
r
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t
3
ar
e
ass
o
ciate
d
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in
d
icato
r
s
X
3
,
X
4
,
an
d
X
11
.
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an
wh
ile,
d
is
tr
ict
/city
in
q
u
ad
r
an
t
4
ar
e
ass
o
ciate
d
wit
h
in
d
icato
r
s
X
1
,
X
2
,
X
8
,
X
9
,
X
10
,
X
13
,
an
d
X
18
.
T
h
e
to
tal
c
u
m
u
l
ativ
e
v
ar
ian
ce
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p
lain
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b
y
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ip
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t
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n
ts
to
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%,
in
d
icatin
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th
at
m
o
r
e
th
an
h
alf
o
f
th
e
d
ata’
s
in
f
o
r
m
atio
n
is
r
ep
r
esen
ted
b
y
th
e
ex
tr
ac
ted
co
m
p
o
n
en
ts
.
T
h
e
d
is
tr
ict
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o
s
itio
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clo
s
e
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o
n
e
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o
t
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o
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b
i
p
lo
t
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h
i
b
it
s
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ilar
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ar
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s
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ased
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th
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p
r
in
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p
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d
er
i
v
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f
r
o
m
t
h
e
in
teg
r
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-
MI
GA.
Fo
r
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am
p
le,
B
an
g
k
a,
B
a
n
g
k
a
T
en
g
a
h
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d
B
an
g
k
a
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im
u
r
e
x
h
ib
it si
m
ilar
ch
ar
ac
ter
is
tics
ac
r
o
s
s
th
e
d
im
en
s
io
n
s
o
f
h
u
m
an
d
ev
elo
p
m
en
t.
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l c
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n
t a
n
a
lysi
s
u
s
in
g
mu
ltip
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imp
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(
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(
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u
r
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4
.
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atr
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s
tr
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ct
u
r
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o
f
(
a)
b
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r
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d
im
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d
u
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d
(
b
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af
ter
d
im
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s
io
n
ality
r
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n
Fig
u
r
e
5
.
T
h
e
in
teg
r
ate
d
GPC
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-
MI
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r
esu
lts
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e
illu
s
tr
ate
d
in
a
b
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p
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er
iv
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d
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r
o
m
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2
0
1
9
d
at
a
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s
h
o
wn
in
Fig
u
r
e
6
,
th
e
d
is
tr
ict
/city
ar
e
d
is
tr
ib
u
ted
in
to
f
o
u
r
q
u
a
d
r
an
ts
,
ea
ch
d
e
f
in
ed
b
y
d
is
tin
ct
s
ets
o
f
in
d
icato
r
s
.
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h
e
d
is
tr
ict
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lo
ca
ted
in
q
u
ad
r
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t
1
ar
e
ass
o
ciate
d
wi
th
in
d
icato
r
s
X
5
,
X
6
,
X
8
,
X
9
,
X
13
,
X
14
,
X
16
,
X
18
,
a
n
d
X
19
.
T
h
o
s
e
in
q
u
ad
r
an
t
2
a
r
e
ass
o
ciate
d
with
i
n
d
icato
r
s
X
4
,
X
11
,
X
15
,
an
d
X
20
,
wh
ile
q
u
ad
r
a
n
t
3
ar
e
ass
o
ciate
d
with
in
d
icato
r
s
X
2
,
X
3
,
an
d
X
10
.
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an
wh
ile,
d
is
tr
ict
/city
in
q
u
ad
r
a
n
t
4
ar
e
ass
o
ciate
d
with
in
d
icato
r
s
X
1
,
X
7
,
an
d
X
17
.
T
h
e
to
tal
c
u
m
u
l
ativ
e
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ar
ian
ce
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p
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ed
b
y
th
e
b
ip
lo
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o
u
n
ts
t
o
5
0
.
9
4
%.
T
h
e
d
is
tr
ict
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u
ch
as
Ma
r
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s
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T
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r
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e
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en
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n
s
o
f
h
u
m
an
d
ev
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m
en
t.
I
I
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Evaluation Warning : The document was created with Spire.PDF for Python.