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1136
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Prin
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b
g
1.
I
NT
RO
D
UCT
I
O
N
Prin
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co
m
p
o
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a
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s
is
(
PC
A)
is
a
wid
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s
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tech
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s
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n
ality
r
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d
u
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ata
ex
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[
1
]
.
I
t
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2
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Ma
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p
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in
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co
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p
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in
[
3
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[
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5
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lectio
n
alg
o
r
ith
m
s
,
th
e
c
o
n
v
er
s
io
n
is
h
ar
d
f
o
r
i
n
ter
p
r
etatio
n
as
th
e
d
ir
ec
t
lin
k
b
etwe
en
th
e
lin
ea
r
co
m
b
in
atio
n
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
an
d
th
e
o
r
ig
in
al
f
ea
tu
r
es
is
n
o
t
s
tr
aig
h
tf
o
r
war
d
[
1
]
.
T
h
er
ef
o
r
e,
PC
A
is
u
s
ed
as
a
d
im
en
s
io
n
ality
r
ed
u
ctio
n
tech
n
i
q
u
e
b
u
t
r
ar
el
y
as
a
m
eth
o
d
to
s
e
lect
co
n
c
r
ete
f
ea
tu
r
es.
R
eg
ar
d
less
o
f
th
is
,
th
e
ap
p
r
o
p
r
iate
s
elec
tio
n
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
is
a
k
ey
f
o
r
th
e
s
u
cc
ess
o
f
th
e
class
if
icatio
n
m
o
d
el.
T
h
er
ef
o
r
e,
r
esear
ch
er
s
aim
to
f
in
d
a
n
u
n
b
iased
an
d
s
t
r
aig
h
tf
o
r
wa
r
d
s
elec
tio
n
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
.
Fo
r
in
s
tan
ce
,
Gajjar
et
a
l.
[
6
]
p
r
o
p
o
s
es
a
n
o
v
el
m
eth
o
d
to
s
elec
t
n
o
n
-
ze
r
o
lo
a
d
in
g
s
in
s
p
ar
s
e
PC
A
in
s
tead
o
f
u
s
in
g
eig
en
v
alu
es
an
d
eig
en
v
ec
to
r
s
as
it is
in
th
e
s
tan
d
ar
d
PC
A
[
1
]
.
I
n
2
0
2
1
,
R
ah
o
m
a
et
a
l.
[
7
]
in
t
r
o
d
u
ce
d
a
n
o
v
el
m
eth
o
d
f
o
r
e
s
tim
atin
g
lo
ad
in
g
f
ac
to
r
s
in
PC
A
.
W
h
il
e
th
eir
alg
o
r
ith
m
s
h
ar
es
s
im
ilar
ities
with
th
e
ap
p
r
o
ac
h
p
r
o
p
o
s
ed
b
y
Gaja
ar
et
a
l.
[
6
]
p
ar
ticu
lar
ly
in
its
f
o
cu
s
o
n
lo
ad
in
g
f
ac
to
r
s
—
it
d
if
f
er
s
in
th
e
b
o
o
ts
tr
ap
tech
n
i
q
u
es
u
s
ed
to
ass
ess
th
e
d
is
tr
ib
u
tio
n
al
p
r
o
p
er
ties
o
f
th
e
elem
en
ts
with
in
th
e
lo
ad
in
g
v
ec
to
r
s
.
T
h
ese
elem
en
ts
ar
e
th
en
lev
er
ag
ed
to
co
n
s
tr
u
ct
a
s
p
ar
s
e
lo
ad
in
g
s
tr
u
ctu
r
e
f
o
r
PC
A.
B
ased
o
n
th
eir
f
in
d
i
n
g
s
,
R
ah
o
m
a
et
a
l.
[
7
]
p
r
o
p
o
s
ed
two
n
ew
PC
A
v
ar
ian
ts
:
B
o
o
ts
tr
ap
SP
C
A
an
d
Sp
ar
s
e
I
PC
A,
b
o
th
o
f
wh
ich
r
ely
o
n
b
o
o
ts
tr
ap
-
b
ased
r
esam
p
li
n
g
.
Alth
o
u
g
h
th
ese
m
eth
o
d
s
r
ep
r
esen
t
ad
v
an
ce
m
e
n
ts
in
PC
A,
n
o
n
e
o
f
th
em
p
r
o
v
id
e
a
n
au
to
m
ate
d
s
o
lu
tio
n
f
o
r
s
elec
tin
g
th
e
n
u
m
b
er
o
f
p
r
in
ci
p
al
co
m
p
o
n
en
ts
—
a
cr
itical
y
et
u
n
r
eso
lv
ed
is
s
u
e
in
m
a
n
y
a
p
p
licatio
n
s
.
T
h
is
r
esear
ch
ad
d
r
ess
es
th
at
g
ap
b
y
p
r
o
p
o
s
in
g
a
f
u
ll
y
a
u
to
m
atic
alg
o
r
ith
m
f
o
r
p
r
in
ci
p
al
co
m
p
o
n
en
t
s
elec
tio
n
.
Fo
r
in
s
tan
ce
,
Pach
ec
o
et
a
l.
[
8
]
o
u
tlin
es
a
m
u
lti
-
s
tep
v
ar
iab
l
e
s
elec
tio
n
p
r
o
ce
s
s
u
s
in
g
PC
A
b
u
t
ex
p
licitly
av
o
id
s
th
e
co
r
e
q
u
esti
o
n
o
f
d
eter
m
in
in
g
t
h
e
o
p
tim
al
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
.
An
im
p
o
r
tan
t
y
et
u
n
d
er
ex
p
lo
r
ed
r
esear
ch
d
i
r
ec
tio
n
in
v
o
lv
es
lev
er
ag
in
g
th
e
tex
tb
o
o
k
PC
A
ap
p
r
o
ac
h
f
o
r
au
to
m
atic
s
elec
tio
n
o
f
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
—
with
o
u
t
alter
in
g
th
e
co
r
e
PC
A
eq
u
atio
n
s
.
T
h
is
p
ap
er
f
o
c
u
s
es
o
n
ad
v
a
n
ci
n
g
th
is
lin
e
o
f
in
q
u
ir
y
an
d
c
o
n
tr
ib
u
tes
in
s
ev
er
al
k
e
y
way
s
.
First,
we
p
r
o
p
o
s
e
a
n
o
v
el
alg
o
r
ith
m
th
at
au
to
m
atica
lly
s
elec
ts
a
s
in
g
le
o
p
tim
al
co
m
b
in
atio
n
o
f
p
r
in
cip
al
co
m
p
o
n
e
n
ts
u
s
in
g
th
e
s
tan
d
ar
d
PC
A
f
r
am
ewo
r
k
[
1
]
.
Un
lik
e
o
t
h
er
m
eth
o
d
s
th
at
m
o
d
if
y
PC
A
co
m
p
u
tatio
n
s
o
r
r
ely
o
n
s
u
b
jectiv
e
ju
d
g
m
en
t,
o
u
r
ap
p
r
o
ac
h
ad
h
e
r
es
s
tr
ictly
to
th
e
tex
tb
o
o
k
m
eth
o
d
wh
ile
au
t
o
m
atin
g
t
h
e
c
o
m
p
o
n
en
t
s
elec
tio
n
p
r
o
ce
s
s
.
Seco
n
d
,
we
ex
p
a
n
d
o
n
p
r
ev
i
o
u
s
r
esear
ch
[
9
]
b
y
d
em
o
n
s
tr
atin
g
th
e
ef
f
ec
tiv
en
e
s
s
o
f
th
e
b
o
o
ts
tr
ap
p
r
o
ce
d
u
r
e
in
PC
A
b
ey
o
n
d
its
ap
p
licatio
n
in
lo
g
is
tic
r
eg
r
ess
io
n
.
W
h
ile
ea
r
lier
wo
r
k
s
h
o
we
d
th
at
b
o
o
ts
tr
ap
p
i
n
g
co
u
ld
g
u
id
e
c
o
m
p
o
n
en
t
s
elec
tio
n
f
o
r
lo
g
is
tic
m
o
d
els,
th
is
s
tu
d
y
ex
ten
d
s
th
o
s
e
f
in
d
in
g
s
to
s
u
p
p
o
r
t
v
ec
to
r
m
ac
h
in
es
(
SVM)
an
d
d
ec
is
io
n
tr
ee
class
if
ier
s
,
s
h
o
win
g
s
i
m
ilar
b
en
ef
its
in
class
if
icatio
n
p
er
f
o
r
m
a
n
ce
.
T
h
ir
d
,
th
is
wo
r
k
co
n
tr
ib
u
tes
to
th
e
b
r
o
ad
e
r
ex
p
lo
r
atio
n
o
f
b
o
o
ts
tr
ap
m
eth
o
d
s
in
m
ac
h
in
e
lea
r
n
in
g
,
o
u
ts
id
e
th
eir
tr
ad
itio
n
al
s
tatis
tical
ap
p
licati
o
n
s
.
Ou
r
p
r
e
v
io
u
s
r
esear
ch
estab
lis
h
ed
th
e
b
o
o
ts
tr
ap
as
a
v
iab
le
alter
n
ativ
e
to
cr
o
s
s
-
v
alid
atio
n
in
clas
s
if
icatio
n
p
r
o
b
lem
s
[
1
0
]
.
T
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
a
n
ew
ap
p
licatio
n
o
f
b
o
o
ts
tr
ap
p
in
g
:
aid
in
g
th
e
au
to
m
atic
s
elec
tio
n
o
f
th
e
n
u
m
b
e
r
o
f
p
r
i
n
cip
al
co
m
p
o
n
e
n
ts
[
1
1
]
,
[
1
2
]
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
l
o
g
y
o
f
f
er
s
s
ev
er
al
a
d
v
an
tag
es:
it
i
s
s
im
p
le
to
im
p
lem
en
t,
co
m
p
u
tatio
n
a
lly
ef
f
icien
t,
a
n
d
ea
s
y
to
in
ter
p
r
et,
m
ak
i
n
g
it
p
r
ac
tical
f
o
r
r
ea
l
-
wo
r
ld
d
at
a
an
aly
s
is
an
d
m
ac
h
in
e
lear
n
in
g
task
s
.
Nex
t
s
ec
t
io
n
d
escr
ib
es
th
e
alg
o
r
ith
m
p
r
o
p
o
s
ed
,
wh
ile
s
ec
tio
n
3
ela
b
o
r
ates o
u
r
f
i
n
d
in
g
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
I
n
th
is
s
ec
tio
n
,
we
p
r
esen
t
b
o
th
th
e
class
ical
PC
A
alg
o
r
ith
m
,
as d
escr
ib
ed
in
s
tan
d
ar
d
tex
tb
o
o
k
s
[
1
3
]
,
an
d
o
u
r
p
r
o
p
o
s
ed
al
g
o
r
ith
m
.
W
e
u
s
e
th
e
class
ical
m
eth
o
d
as
a
b
aselin
e
to
h
ig
h
lig
h
t
its
lim
itatio
n
s
an
d
t
o
co
m
p
ar
e
its
p
er
f
o
r
m
an
ce
ag
ai
n
s
t
o
u
r
au
to
m
ated
ap
p
r
o
ac
h
.
T
h
e
class
ical
PC
A
p
r
o
ce
d
u
r
e
is
im
p
lem
en
ted
in
Py
th
o
n
3
.
6
u
s
in
g
b
u
ilt
-
in
f
u
n
ctio
n
s
.
Fo
llo
win
g
th
e
class
ical
s
tep
s
o
u
tlin
ed
in
[
1
0
]
,
[
1
3
]
,
we
ap
p
ly
PC
A
b
u
t
ad
ap
t
th
e
class
if
icatio
n
s
tag
e
b
y
u
s
in
g
d
ec
is
io
n
tr
ee
class
if
ier
s
an
d
SVMs
in
s
tead
o
f
lo
g
i
s
tic
r
eg
r
ess
io
n
.
All
m
o
d
el
p
ar
a
m
ete
r
s
ar
e
k
ep
t
at
th
eir
d
ef
au
lt
v
alu
es
in
Py
th
o
n
,
with
th
e
SVM
u
s
in
g
C
=1
an
d
an
R
B
F
k
er
n
el.
T
h
e
class
ical
PC
A
p
r
o
ce
d
u
r
e
in
clu
d
es th
e
f
o
llo
win
g
s
tep
s
[
1
]
,
[
1
3
]
:
-
Data
s
tan
d
ar
d
izatio
n
: Stan
d
ar
d
ize
th
e
in
p
u
t d
ata
[
1
4
]
a
n
d
tr
a
n
s
f
o
r
m
th
em
in
to
p
r
in
cip
al
co
m
p
o
n
e
n
ts
-
Var
ian
ce
a
n
aly
s
is
:
An
aly
ze
eig
en
v
alu
es
[
1
5
]
an
d
eig
e
n
v
ec
to
r
s
[
1
6
]
to
d
ete
r
m
in
e
th
e
p
r
o
p
o
r
tio
n
o
f
v
ar
ian
ce
ea
c
h
p
r
in
cip
al
co
m
p
o
n
en
t
e
x
p
lain
s
.
C
alcu
late
t
h
e
cu
m
u
lativ
e
v
ar
ian
ce
ex
p
lain
e
d
b
y
th
e
f
ir
s
t
n
co
m
p
o
n
en
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
14
,
No
.
3
,
Dec
em
b
er
20
25
:
1
1
3
6
-
1
1
4
5
1138
-
C
o
m
p
o
n
en
t
s
elec
tio
n
:
Select
th
e
s
u
b
s
et
o
f
c
o
m
p
o
n
en
ts
th
a
t
ex
p
lain
s
th
e
h
ig
h
est
cu
m
u
lativ
e
v
ar
ian
c
e
[
1
7
]
.
T
h
is
m
et
h
o
d
d
if
f
e
r
s
f
r
o
m
o
th
er
ap
p
r
o
ac
h
es
th
at
u
s
e
cr
iter
ia
s
u
ch
as
A
I
C
o
r
B
I
C
f
o
r
co
m
p
o
n
en
t
s
elec
tio
n
[
1
8
]
.
-
Mo
d
el
t
r
ain
in
g
a
n
d
e
v
al
u
atio
n
:
Use
th
e
s
elec
ted
co
m
p
o
n
e
n
ts
to
tr
ain
an
d
test
class
if
ic
atio
n
m
o
d
els
(
d
ec
is
io
n
tr
ee
s
an
d
SVMs).
I
t
is
im
p
o
r
tan
t
to
n
o
te
th
at,
in
th
is
clas
s
ical
ap
p
r
o
ac
h
,
th
e
s
elec
ted
co
m
p
o
n
en
ts
ar
e
alwa
y
s
th
e
f
ir
s
t
n
co
m
p
o
n
en
ts
in
o
r
d
er
o
f
th
eir
i
n
d
ex
.
T
h
is
is
b
ased
s
o
lely
o
n
th
e
d
ec
r
ea
s
in
g
p
r
o
p
o
r
tio
n
o
f
v
ar
ian
ce
ex
p
lain
e
d
b
y
ea
ch
s
u
cc
ess
iv
e
co
m
p
o
n
en
t.
T
h
e
co
m
p
o
n
e
n
t
s
elec
tio
n
p
r
o
ce
s
s
is
in
d
ep
en
d
en
t
o
f
th
e
cl
ass
if
icatio
n
m
o
d
el
u
s
ed
.
Alth
o
u
g
h
th
e
class
ical
PC
A
a
lg
o
r
ith
m
[
1
9
]
is
s
im
p
le
an
d
wid
ely
ap
p
lied
,
it
o
f
ten
p
r
esen
t
s
a
cr
itical
lim
itatio
n
:
m
u
ltip
le
v
alid
co
m
b
in
atio
n
s
o
f
co
m
p
o
n
e
n
ts
m
ay
ex
p
lain
s
im
ilar
am
o
u
n
ts
o
f
v
ar
ian
ce
[
2
0
]
.
T
h
e
class
ical
m
eth
o
d
d
o
es
n
o
t
p
r
o
v
id
e
au
to
m
ate
d
m
ea
n
s
to
r
eso
l
v
e
th
is
am
b
ig
u
ity
.
R
esear
ch
er
s
ar
e
lef
t
to
s
elec
t
a
co
m
b
in
atio
n
m
an
u
ally
,
r
ely
in
g
o
n
p
r
io
r
d
o
m
ain
k
n
o
wled
g
e
,
liter
atu
r
e
g
u
id
elin
es,
o
r
ad
h
o
c
h
e
u
r
is
tics
[
1
]
.
I
n
m
an
y
ca
s
es,
h
o
wev
er
,
s
u
ch
k
n
o
wled
g
e
o
r
r
u
les
ar
e
n
o
t
av
ailab
le,
an
d
th
e
lack
o
f
a
clea
r
cr
iter
io
n
ca
n
in
tr
o
d
u
ce
s
u
b
jectiv
ity
o
r
b
ias in
to
th
e
an
al
y
s
is
[
2
1
]
,
[
2
2
]
.
T
o
o
v
er
co
m
e
th
is
is
s
u
e,
we
p
r
o
p
o
s
e
a
n
o
v
el
m
eth
o
d
ca
lled
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
[
9
]
,
wh
ic
h
au
to
m
ates
th
e
s
elec
tio
n
o
f
th
e
o
p
tim
al
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
with
in
a
s
tan
d
ar
d
PC
A
f
r
am
ewo
r
k
.
T
h
is
m
eth
o
d
ex
ten
d
s
o
u
r
p
r
e
v
io
u
s
wo
r
k
th
at
ap
p
lied
b
o
o
ts
tr
ap
-
b
ased
co
m
p
o
n
e
n
t
s
elec
ti
o
n
in
th
e
co
n
tex
t
o
f
lo
g
is
tic
r
eg
r
ess
io
n
.
I
n
th
is
s
tu
d
y
,
we
d
em
o
n
s
tr
ate
its
ap
p
licab
ilit
y
to
d
ec
is
io
n
tr
ee
class
if
ier
s
an
d
SVM
.
W
e
r
ef
er
to
th
e
two
im
p
lem
en
tatio
n
s
as:
−
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
-
DT
: u
s
in
g
d
ec
is
io
n
tr
ee
class
if
ier
s
−
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
-
SVM:
u
s
in
g
SVM
h
e
alg
o
r
ith
m
u
tili
ze
s
ex
is
tin
g
Py
th
o
n
f
u
n
cti
o
n
s
,
in
clu
d
in
g
SVC
(
)
,
Dec
is
io
n
T
r
ee
C
lass
if
ie
r
(
)
,
PC
A(
)
f
r
o
m
s
k
lear
n
.
d
ec
o
m
p
o
s
itio
n
,
an
d
Pip
elin
e
f
r
o
m
s
k
lear
n
,
to
i
n
co
r
p
o
r
ate
ANOV
A
f
ea
tu
r
e
s
elec
tio
n
.
Ad
d
itio
n
ally
,
we
d
ev
el
o
p
ed
a
cu
s
to
m
s
cr
ip
t
to
im
p
lem
en
t
th
e
te
n
f
o
ld
b
o
o
ts
tr
ap
p
r
o
ce
d
u
r
e,
o
r
ig
in
ally
in
tr
o
d
u
ce
d
in
o
u
r
p
r
io
r
s
tu
d
y
[
1
0
]
.
W
h
ile
ea
r
lier
b
o
o
ts
tr
ap
s
tu
d
ies
[
1
1
]
,
[
1
2
]
f
o
cu
s
e
d
o
n
its
u
s
e
as
a
r
esam
p
lin
g
tech
n
i
q
u
e
in
s
tatis
tical
an
aly
s
is
,
th
ey
d
id
n
o
t
ex
p
lo
r
e
its
p
o
ten
tial
b
e
n
ef
its
in
m
ac
h
in
e
lear
n
i
n
g
.
Ou
r
p
r
e
v
io
u
s
wo
r
k
[
1
0
]
ad
d
r
ess
ed
th
is
g
ap
b
y
d
em
o
n
s
tr
atin
g
h
o
w
th
e
b
o
o
ts
tr
ap
ca
n
b
e
ad
a
p
ted
to
class
if
icatio
n
task
s
.
W
e
n
o
w
f
u
r
th
er
e
x
ten
d
th
is
b
y
i
n
teg
r
ati
n
g
b
o
o
ts
tr
ap
in
t
o
PC
A
f
o
r
a
u
to
m
ated
co
m
p
o
n
en
t
s
elec
tio
n
.
T
h
e
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
alg
o
r
ith
m
p
r
o
ce
ed
s
th
r
o
u
g
h
th
e
f
o
llo
win
g
s
tep
s
:
a)
Stan
d
ar
d
izatio
n
: Stan
d
ar
d
ize
t
h
e
in
p
u
t
d
ata
(
as in
th
e
class
ical
ap
p
r
o
ac
h
)
.
b)
PC
A
t
r
an
s
f
o
r
m
atio
n
: A
p
p
ly
P
C
A
to
th
e
s
tan
d
ar
d
ized
d
ata.
c)
No
r
m
aliza
tio
n
:
No
r
m
alize
th
e
r
esu
ltin
g
p
r
in
cip
al
co
m
p
o
n
en
ts
to
th
e
[
0
,
1
]
r
an
g
e
to
elim
in
ate
n
eg
ativ
e
v
alu
es.
d)
ANOVA
r
an
k
in
g
:
Per
f
o
r
m
ANOV
A
to
r
an
k
th
e
p
r
in
cip
al
co
m
p
o
n
en
ts
b
y
im
p
o
r
tan
c
e.
Un
lik
e
th
e
class
ical
m
eth
o
d
,
co
m
p
o
n
en
ts
ar
e
s
elec
ted
b
ased
o
n
ANOV
A
r
an
k
in
g
r
ath
er
th
an
in
d
ex
o
r
d
er
,
a
n
d
th
e
r
an
k
in
g
r
em
ain
s
in
d
e
p
en
d
e
n
t
o
f
th
e
class
if
icatio
n
m
o
d
el.
e)
Per
ce
n
tile
Gr
o
u
p
in
g
:
Div
id
e
th
e
co
m
p
o
n
en
ts
in
to
p
er
ce
n
tiles
(
1
0
%,
2
0
%,
.
.
.
,
1
0
0
%),
wh
er
e
ea
c
h
p
er
ce
n
tile c
o
n
tain
s
th
e
t
o
p
n
c
o
m
p
o
n
en
ts
b
ased
o
n
ANOV
A
r
an
k
in
g
s
.
f)
B
o
o
ts
tr
ap
p
ed
r
esam
p
lin
g
:
Fo
r
ea
ch
p
er
ce
n
tile,
s
p
lit
th
e
d
ata
in
to
tr
ain
in
g
an
d
test
in
g
s
ets
u
s
in
g
a
7
0
/3
0
r
atio
,
r
ep
ea
ted
v
ia
th
e
ten
f
o
ld
b
o
o
ts
tr
ap
[
1
0
]
.
g)
Mo
d
el
t
r
ain
in
g
an
d
e
v
alu
atio
n
:
Fo
r
ea
ch
p
er
ce
n
tile
g
r
o
u
p
,
tr
ain
an
d
ev
alu
ate
ten
m
o
d
els
(
b
o
th
SVM
an
d
d
ec
is
io
n
tr
ee
class
if
ier
s
)
.
C
a
l
cu
late
th
e
av
er
ag
e
ac
cu
r
ac
y
an
d
class
if
icatio
n
s
co
r
es
ac
r
o
s
s
b
o
o
ts
tr
ap
s
am
p
les.
h)
C
o
m
p
o
n
en
t
s
elec
tio
n
:
I
d
e
n
tif
y
th
e
p
er
ce
n
tile
(
i.e
.
,
co
m
p
o
n
en
t
co
m
b
i
n
atio
n
)
th
at
y
ield
s
th
e
h
ig
h
est
class
if
icatio
n
p
er
f
o
r
m
an
ce
.
T
h
is
d
ef
in
es th
e
o
p
tim
al
n
u
m
b
er
o
f
co
m
p
o
n
e
n
ts
f
o
r
ea
c
h
m
o
d
el.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
co
n
d
u
ct
th
e
ex
p
er
im
e
n
ts
,
we
u
s
e
th
r
ee
p
u
b
li
cly
av
ailab
l
e
d
atasets
[
2
3
]
-
[
2
5
]
.
W
e
d
ef
in
e
X
an
d
Y
v
ar
iab
les,
wh
er
e
Y
is
a
tar
g
et
v
ar
iab
le
th
at
r
e
p
r
esen
ts
ca
teg
o
r
ies.
As
PC
A
i
s
co
n
d
u
cted
o
n
ly
o
n
in
d
ep
e
n
d
en
t
v
ar
iab
les,
th
e
tar
g
et
v
ar
ia
b
le
Y
is
ex
clu
d
ed
f
r
o
m
th
e
e
x
p
er
i
m
en
ts
.
All
r
esu
lts
p
r
esen
ted
i
n
s
ec
t
io
n
3
r
elate
to
th
e
co
n
n
ec
tio
n
am
o
n
g
th
e
X
v
ar
iab
les
as
ea
ch
p
r
in
cip
al
co
m
p
o
n
e
n
t
f
o
r
m
s
a
lin
ea
r
c
o
m
b
in
atio
n
o
f
f
ea
tu
r
e
s
th
at
co
n
tain
s
as
m
u
ch
in
f
o
r
m
atio
n
ab
o
u
t
th
e
d
ata
as
p
o
s
s
ib
le.
T
h
e
aim
is
to
f
in
d
th
e
m
o
s
t
in
f
o
r
m
ativ
e
s
et
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
b
y
d
is
co
v
er
in
g
th
e
s
et
o
f
p
r
in
cip
a
l
co
m
p
o
n
en
ts
with
th
e
h
ig
h
est
v
ar
ian
ce
[
1
6
]
.
T
h
er
ef
o
r
e,
th
e
class
ical
ap
p
r
o
ac
h
p
r
o
d
u
ce
s
a
ta
b
le,
wh
e
r
e
th
e
p
er
ce
n
tag
e
o
f
v
a
r
ian
ce
ex
p
lain
e
d
o
f
ea
c
h
p
r
in
cip
al
co
m
p
o
n
en
t
is
ca
lcu
l
ated
(
%
o
f
v
ar
ex
p
lain
e
d
)
.
T
h
e
m
o
s
t
in
f
o
r
m
ativ
e
s
et
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
co
n
s
is
ts
o
f
th
e
f
ir
s
t
p
r
in
cip
al
co
m
p
o
n
en
ts
,
wh
i
ch
c
o
n
tr
ib
u
te
th
e
m
o
s
t
to
th
e
to
tal
v
ar
ia
n
ce
ex
p
lain
e
d
.
T
h
is
cr
iter
io
n
is
r
ef
er
r
e
d
to
as
‘
cu
m
u
lativ
e
p
er
ce
n
ta
g
e
ex
p
lain
e
d
’
.
Ho
wev
er
,
wh
en
th
e
to
tal
v
ar
ian
ce
ex
p
lain
e
d
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Th
e
b
o
o
ts
tr
a
p
p
r
o
ce
d
u
r
e
fo
r
s
elec
tin
g
th
e
n
u
m
b
er o
f p
r
in
cip
a
l c
o
mp
o
n
e
n
ts
in
P
C
A
(
B
o
r
is
la
va
To
leva
)
1139
two
o
r
m
o
r
e
s
ets
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
is
s
im
ilar
,
s
elec
t
in
g
th
e
co
r
r
ec
t
n
u
m
b
er
o
f
p
r
i
n
cip
al
co
m
p
o
n
e
n
ts
m
ay
n
o
t
b
e
s
tr
aig
h
tf
o
r
wa
r
d
.
On
th
e
o
th
er
h
an
d
,
t
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
i
n
th
is
p
a
p
er
elim
in
ates
th
e
in
v
o
lv
em
e
n
t
o
f
t
h
e
r
esear
ch
e
r
as
it
p
r
o
v
id
es
a
n
au
to
m
atic
s
elec
tio
n
o
f
th
e
n
u
m
b
er
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
r
eg
ar
d
less
o
f
t
h
e
to
tal
v
ar
ian
c
e
ex
p
lain
ed
.
T
h
e
r
esu
lts
f
r
o
m
th
e
two
ap
p
r
o
ac
h
es
a
r
e
s
u
m
m
ar
ized
b
y
d
ataset
in
th
e
n
ex
t su
b
s
ec
tio
n
s
.
3
.
1
.
T
he
E
D
da
t
a
s
et
[
2
3
]
T
ab
le
1
co
n
tain
s
th
e
o
u
tp
u
t
f
r
o
m
th
e
class
ical
ap
p
r
o
ac
h
t
h
at
ca
lcu
lates
th
e
co
n
tr
ib
u
tio
n
o
f
ea
ch
p
r
in
cip
al
co
m
p
o
n
e
n
t to
th
e
v
a
r
ia
n
ce
ex
p
lain
ed
a
n
d
th
e
cu
m
u
lativ
e
p
er
ce
n
tag
e
ex
p
lain
ed
f
o
r
th
e
f
ir
s
t n
n
u
m
b
e
r
o
f
p
r
i
n
c
i
p
a
l
c
o
m
p
o
n
e
n
t
s
.
T
h
e
p
e
r
c
e
n
t
a
g
e
o
f
v
a
r
i
a
n
c
e
e
x
p
l
a
i
n
e
d
i
s
c
a
l
c
u
l
a
t
e
d
b
y
e
i
g
e
n
v
a
l
u
e
s
a
n
d
e
i
g
e
n
v
e
c
t
o
r
s
[
1
6
]
.
T
ab
le
1
.
Prin
cip
al
c
o
m
p
o
n
en
ts
n
u
m
b
e
r
ac
co
r
d
in
g
t
o
th
e
class
ical
ap
p
r
o
ac
h
%
o
f
v
a
r
e
x
p
l
a
i
n
e
d
v
a
r
e
x
p
l
a
i
n
e
d
,
c
u
m
u
l
a
t
i
v
e
l
y
%
P
C
1
5
7
.
5
%
P
C
1
+
P
C
2
9
7
.
4
%
P
C
2
3
9
.
9
%
P
C
1
+
P
C
2
+
P
C
3
9
9
.
9
%
P
C
3
2
.
5
%
P
C
1
+
P
C
2
+
P
C
3
+
P
C
4
1
0
0
%
P
C
4
0%
P
C
1
+
P
C
2
+
P
C
3
+
P
C
4
+
P
C
5
1
0
0
%
P
C
5
0%
S
o
u
r
c
e
:
a
u
t
h
o
r
’
s rese
a
r
c
h
T
ab
le
1
s
h
o
ws
th
at
t
h
e
f
ir
s
t
p
r
in
cip
al
co
m
p
o
n
e
n
t
co
n
tr
i
b
u
te
s
th
e
m
o
s
t
to
th
e
d
ata
v
a
r
ian
c
e
(
5
7
.
9
%),
f
o
llo
wed
b
y
th
e
s
ec
o
n
d
(
3
9
.
9
%)
an
d
th
e
th
ir
d
.
T
h
e
f
ir
s
t
two
p
r
in
cip
al
co
m
p
o
n
en
ts
to
g
eth
e
r
ac
co
u
n
t
f
o
r
9
7
.
4
%
o
f
th
e
v
a
r
ian
ce
in
d
ata,
wh
i
le
th
e
f
i
r
s
t
th
r
ee
–
9
9
.
9
%.
T
h
e
co
n
tr
i
b
u
tio
n
o
f
th
e
f
o
u
r
th
an
d
f
if
th
p
r
in
cip
al
co
m
p
o
n
en
t
is
to
o
s
m
all
to
b
e
co
n
s
id
er
ed
.
I
n
th
is
ca
s
e,
th
e
b
o
o
k
r
u
le
[
1
6
]
a
d
v
is
es
to
s
elec
t
th
e
co
m
b
in
atio
n
th
at
r
esu
lts
in
th
e
h
ig
h
est
cu
m
u
lativ
e
v
ar
ian
ce
e
x
p
lain
ed
.
T
h
is
wo
u
ld
b
e
th
e
f
ir
s
t
th
r
ee
p
r
i
n
cip
al
co
m
p
o
n
en
ts
.
W
h
en
we
u
s
e
th
e
f
ir
s
t
th
r
ee
p
r
in
cip
al
co
m
p
o
n
en
ts
to
r
u
n
th
e
SVMs
wi
th
R
B
F
k
er
n
el,
t
h
e
m
o
d
el
ac
h
iev
es
9
6
.
9
%
ac
cu
r
ac
y
.
T
h
e
d
ec
is
io
n
tr
ee
class
if
ier
ac
h
iev
es
9
8
.
2
%.
Ho
wev
er
,
th
e
aim
o
f
th
e
PC
A
is
to
p
er
f
o
r
m
d
im
e
n
s
io
n
ality
r
ed
u
ctio
n
[
1
6
]
.
Giv
en
th
at
th
e
f
ir
s
t
two
p
r
in
cip
al
co
m
p
o
n
en
ts
ac
co
u
n
t
f
o
r
9
7
.
4
%
o
f
th
e
v
ar
iab
ilit
y
in
d
ata
an
d
th
e
v
er
y
s
m
all
co
n
tr
ib
u
tio
n
o
f
th
e
th
ir
d
p
r
in
cip
al
co
m
p
o
n
en
t,
an
o
th
er
r
esear
ch
er
m
a
y
s
elec
t
th
e
f
ir
s
t
two
p
r
in
cip
al
c
o
m
p
o
n
en
ts
.
I
n
t
h
i
s
ca
s
e,
a
s
m
aller
n
u
m
b
e
r
o
f
p
r
in
cip
al
c
o
m
p
o
n
en
ts
wo
u
l
d
b
e
s
elec
ted
,
wh
ile
th
e
v
ar
ia
n
ce
e
x
p
lain
ed
wo
u
ld
b
e
h
ig
h
en
o
u
g
h
.
T
h
e
ex
am
p
le
o
f
th
e
e
d
d
a
taset
d
em
o
n
s
tr
ates
th
at
in
s
o
m
e
ca
s
es
m
o
r
e
t
h
an
o
n
e
p
r
in
cip
al
co
m
p
o
n
e
n
t
co
m
b
in
atio
n
is
p
o
s
s
ib
le.
I
n
t
h
e
ca
s
e
o
f
t
h
e
e
d
d
ataset
s
elec
tin
g
two
o
r
th
r
ee
p
r
in
cip
al
co
m
p
o
n
e
n
ts
wo
u
ld
n
o
t
af
f
e
ct
th
e
o
u
tco
m
e
o
f
th
e
m
o
d
el
s
ig
n
if
ican
tly
d
u
e
to
its
s
m
al
l
n
u
m
b
er
o
f
co
m
p
o
n
e
n
ts
.
Ho
wev
er
,
th
e
is
s
u
e
o
f
h
o
w
m
an
y
p
r
in
cip
al
co
m
p
o
n
e
n
ts
to
s
elec
t
an
d
av
o
id
th
e
m
an
u
al
s
elec
tio
n
is
v
er
y
i
m
p
o
r
tan
t in
d
ataset
with
m
an
y
p
r
in
cip
al
co
m
p
o
n
en
ts
.
T
o
ac
h
iev
e
an
au
t
o
m
atic
s
elec
tio
n
o
f
th
e
n
u
m
b
er
o
f
p
r
in
ci
p
a
l
co
m
p
o
n
e
n
ts
,
we
p
r
o
p
o
s
e
th
e
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
clas
s
if
icat
io
n
.
I
n
th
is
alg
o
r
ith
m
,
th
e
im
p
o
r
tan
ce
o
f
th
e
p
r
in
cip
al
c
o
m
p
o
n
en
ts
is
f
ir
s
t
ca
lcu
l
ated
u
s
in
g
ANOV
A.
S
i
m
ilar
ly
,
to
th
e
class
ical
alg
o
r
ith
m
,
th
eir
im
p
o
r
tan
ce
d
o
es
n
o
t
ch
an
g
e
with
th
e
class
if
icatio
n
m
o
d
el
u
s
ed
.
T
ab
le
2
s
u
m
m
ar
izes th
e
im
p
o
r
tan
c
e
o
f
th
e
p
r
in
cip
al
c
o
m
p
o
n
en
ts
in
th
e
ed
d
ataset.
T
ab
le
2
.
I
m
p
o
r
ta
n
ce
o
f
th
e
p
r
i
n
cip
al
co
m
p
o
n
en
ts
ac
co
r
d
in
g
to
th
e
n
ew
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
PC
I
mp
o
r
t
a
n
c
e
P
C
1
1
7
.
1
6
7
7
P
C
2
8
.
7
0
9
8
8
P
C
3
3
5
5
0
.
9
2
P
C
4
4
1
.
9
0
3
8
P
C
5
8
.
9
5
7
8
9
S
o
u
r
c
e
:
a
u
t
h
o
r
’
s c
a
l
c
u
l
a
t
i
o
n
s
Acc
o
r
d
in
g
t
o
T
ab
le
2
,
th
e
m
o
s
t
im
p
o
r
tan
t
p
r
in
ci
p
al
co
m
p
o
n
en
ts
ar
e
th
e
th
ir
d
o
n
e,
th
e
f
o
u
r
th
an
d
th
e
f
ir
s
t
o
n
e.
A
n
im
p
o
tan
t
h
ig
h
li
g
h
t
is
th
at
th
is
o
u
tco
m
e
is
d
if
f
er
en
t
f
r
o
m
th
e
class
ical
ap
p
r
o
ac
h
.
T
h
e
class
ical
ap
p
r
o
ac
h
id
e
n
tifie
s
th
e
f
ir
s
t
n
m
o
s
t
im
p
o
r
tan
ce
p
r
in
cip
al
c
o
m
p
o
n
e
n
ts
,
wh
er
e
th
e
f
ir
s
t
alw
ay
s
co
n
tr
i
b
u
tes
th
e
m
o
s
t,
an
d
th
e
s
ec
o
n
d
is
s
ec
o
n
d
in
o
r
d
er
.
H
o
wev
er
,
t
h
e
n
ewl
y
p
r
o
p
o
s
ed
a
p
p
r
o
a
ch
o
b
s
er
v
es
th
e
im
p
o
r
tan
ce
o
f
ea
ch
p
r
in
cip
al
co
m
p
o
n
en
t
s
ep
ar
ately
an
d
t
h
eir
im
p
o
r
tan
ce
d
o
es
n
o
t
d
ep
e
n
d
o
n
th
eir
p
lace
in
th
e
d
ataset.
T
h
e
im
p
o
r
tan
ce
o
f
ea
ch
p
r
in
cip
al
co
m
p
o
n
en
t
r
em
ai
n
s
th
e
s
am
e
r
eg
ar
d
less
o
f
th
e
class
if
i
ca
tio
n
m
o
d
el
u
s
ed
.
T
ab
le
3
s
h
o
ws
h
o
w
m
an
y
p
r
i
n
cip
al
co
m
p
o
n
e
n
ts
ar
e
s
elec
ted
u
s
in
g
th
e
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
class
if
icatio
n
alg
o
r
ith
m
wh
e
n
th
e
SVM
an
d
th
e
d
ec
is
io
n
tr
ee
class
if
ier
ar
e
f
itted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
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7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
14
,
No
.
3
,
Dec
em
b
er
20
25
:
1
1
3
6
-
1
1
4
5
1140
T
ab
le
3
.
Nu
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
s
elec
ted
u
s
in
g
th
e
ANOVA
-
bo
o
ts
tr
ap
p
ed
class
if
icatio
n
in
SVM
an
d
DT
P
e
r
c
e
n
t
i
l
e
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u
mb
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o
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1
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5
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5
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9
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4
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1
9
6
.
5
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9
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4
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3
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1
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9
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3
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9
8
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2
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4
0
%
2
9
8
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3
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2
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9
8
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3
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9
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%
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7
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5
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3
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5
9
9
.
2
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9
7
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5
%
8
0
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4
9
9
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2
%
9
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6
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4
.
5
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9
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S
o
u
r
c
e
:
a
u
t
h
o
r
’
s c
a
l
c
u
l
a
t
i
o
n
I
n
th
e
ca
s
e
o
f
th
e
d
ec
is
io
n
tr
ee
class
if
ier
,
th
e
th
r
ee
m
o
s
t
i
m
p
o
r
tan
t
p
r
in
ci
p
al
co
m
p
o
n
en
ts
th
at
ar
e
s
elec
ted
ar
e
th
e
f
o
u
r
th
,
th
ir
d
a
n
d
f
ir
s
t
(
T
ab
le
3
)
.
Usi
n
g
th
is
co
m
b
in
atio
n
,
th
e
d
ec
is
io
n
th
r
ee
class
if
ier
ac
h
iev
es
th
e
h
ig
h
est
ac
cu
r
ac
y
o
f
9
9
.
2
%,
wh
ile
r
etain
in
g
th
e
s
m
allest
p
o
s
s
ib
le
co
m
b
in
atio
n
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
(
p
er
f
o
r
m
in
g
d
i
m
en
s
io
n
ality
r
e
d
u
ctio
n
)
.
Alth
o
u
g
h
th
e
ac
c
u
r
a
cy
o
f
9
9
.
2
%
ca
n
also
b
e
ac
h
iev
ed
b
y
ad
d
in
g
th
e
f
if
th
p
r
in
cip
al
co
m
p
o
n
en
t
(
as
it
is
th
e
f
o
u
r
th
m
o
s
t
im
p
o
r
t
an
t)
,
th
is
co
m
b
in
atio
n
wo
u
ld
u
s
e
m
o
r
e
p
r
i
n
cip
al
co
m
p
o
n
en
ts
th
an
o
p
tim
al
f
o
r
d
im
en
s
io
n
ality
r
ed
u
ctio
n
.
T
h
er
ef
o
r
e,
s
elec
tin
g
th
e
f
o
u
r
th
,
th
ir
d
a
n
d
f
ir
s
t
p
r
in
cip
al
c
o
m
p
o
n
en
ts
a
r
e
t
h
e
b
est
co
m
b
in
atio
n
f
o
r
ac
h
i
ev
in
g
t
h
e
h
ig
h
est
ac
cu
r
ac
y
in
th
e
d
ec
is
io
n
tr
ee
class
if
ier
.
Usi
n
g
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
th
e
ca
s
e
f
o
r
th
e
SVM
is
d
if
f
er
en
t.
T
a
b
le
3
s
h
o
ws
th
at
th
e
h
ig
h
est
ac
cu
r
ac
y
(
9
8
.
2
%)
f
o
r
th
e
SV
M
m
o
d
el
ca
n
b
e
ac
h
iev
ed
u
s
i
n
g
o
n
ly
2
p
r
in
cip
al
co
m
p
o
n
e
n
ts
,
th
ese
b
ein
g
th
e
th
ir
d
an
d
th
e
f
o
u
r
th
(
T
a
b
le
2
)
.
T
h
e
th
ir
d
an
d
th
e
f
o
u
r
th
p
r
in
cip
al
co
m
p
o
n
en
ts
ar
e
th
e
b
est
s
elec
tio
n
f
o
r
th
e
SVM
f
o
r
th
r
ee
r
ea
s
o
n
s
.
First,
th
ey
ar
e
th
e
m
o
s
t
im
p
o
r
tan
t
o
n
es
ac
co
r
d
in
g
to
T
ab
le
2
.
Seco
n
d
,
th
ey
p
r
o
d
u
ce
th
e
h
ig
h
es
t a
cc
u
r
ac
y
f
o
r
th
e
S
VM
.
T
h
ir
d
,
th
e
SVM
ac
cu
r
ac
y
u
s
in
g
th
e
two
an
d
th
r
ee
m
o
s
t im
p
o
r
tan
t p
r
in
cip
al
co
m
p
o
n
en
ts
is
s
im
ilar
.
T
h
er
e
f
o
r
e,
th
e
th
ir
d
m
o
s
t
im
p
o
r
tan
t
p
r
in
cip
al
co
m
p
o
n
en
ts
d
o
es
n
o
t
ad
d
ad
d
itio
n
al
in
f
o
r
m
atio
n
to
th
e
m
o
d
el.
T
h
is
r
esu
lt d
if
f
er
s
f
r
o
m
th
e
class
ical
ap
p
r
o
ac
h
.
I
n
th
e
class
ical
ap
p
r
o
ac
h
t
h
e
n
u
m
b
er
o
f
p
r
i
n
cip
al
co
m
p
o
n
e
n
ts
s
elec
ted
is
th
e
s
am
e
r
eg
ar
d
less
o
f
th
e
class
if
icatio
n
m
o
d
el
u
s
ed
.
Ho
wev
er
,
o
u
r
ap
p
r
o
ac
h
s
elec
ts
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
c
o
m
p
o
n
en
ts
th
at
wo
u
ld
p
r
o
d
u
ce
th
e
b
est
a
cc
u
r
ac
y
g
iv
e
n
t
h
e
class
if
icatio
n
m
o
d
el
u
s
ed
.
Ou
r
alg
o
r
ith
m
ca
n
b
e
u
s
ed
to
s
elec
t
th
e
co
m
b
in
atio
n
o
f
p
r
in
cip
al
co
m
p
o
n
e
n
ts
th
at
wo
u
ld
im
p
r
o
v
e
th
e
m
o
d
el’
s
p
er
f
o
r
m
an
ce
.
Fo
r
in
s
tan
ce
,
t
h
e
class
ical
ap
p
r
o
ac
h
r
esu
lted
in
9
6
.
9
%
ac
cu
r
ac
y
f
r
o
m
th
e
SVM
u
s
in
g
th
e
f
ir
s
t
3
p
r
in
cip
al
c
o
m
p
o
n
en
ts
.
T
h
e
ANOV
A
-
b
o
o
ts
tr
ap
p
ed
-
P
C
A
S
VM
ac
h
iev
ed
9
8
.
2
%
ac
c
u
r
ac
y
u
s
in
g
o
n
l
y
t
h
e
f
ir
s
t
two
m
o
s
t
im
p
o
r
tan
t
p
r
in
cip
al
co
m
p
o
n
en
ts
.
T
h
e
alg
o
r
ith
m
we
p
r
o
p
o
s
e
im
p
r
o
v
e
d
th
e
ac
cu
r
ac
y
r
esu
lt
in
g
f
r
o
m
t
h
e
class
ical
PC
A
SVM
b
y
1
.
3
%
an
d
it
p
er
f
o
r
m
ed
d
im
e
n
s
io
n
ality
r
ed
u
ctio
n
b
etter
as
it
u
s
es
o
n
l
y
2
p
r
i
n
cip
al
c
o
m
p
o
n
en
ts
.
T
h
er
ef
o
r
e,
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
ca
n
b
e
u
s
ed
n
o
t
o
n
ly
to
au
to
m
atica
lly
s
elec
t
th
e
n
u
m
b
er
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
,
b
u
t
it
also
im
p
r
o
v
es
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
m
o
d
el
an
d
p
e
r
f
o
r
m
d
im
en
s
io
n
ality
r
ed
u
ctio
n
b
etter
.
Similar
ca
s
e
is
o
b
s
er
v
ed
with
th
e
d
ec
i
s
io
n
tr
ee
class
if
ier
,
wh
er
e
th
e
class
ical
PC
A
ap
p
r
o
ac
h
r
esu
lted
in
9
8
.
2
%
ac
cu
r
ac
y
u
s
in
g
th
r
ee
p
r
in
ci
p
al
co
m
p
o
n
en
ts
,
w
h
ile
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
ac
h
iev
e
d
9
9
.
2
%
ac
cu
r
ac
y
u
s
in
g
3
p
r
in
c
ip
al
co
m
p
o
n
en
ts
(
T
ab
le
3
)
.
I
n
th
e
ex
am
p
le
o
f
t
h
e
d
ec
is
io
n
tr
ee
class
if
ier
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
p
r
o
v
id
es
an
au
to
m
atic
s
elec
tio
n
o
f
th
r
ee
p
r
in
cip
al
co
m
p
o
n
en
ts
,
elim
in
atin
g
th
e
ch
o
ice
b
etwe
en
th
e
f
ir
s
t
two
an
d
th
r
ee
p
r
in
cip
al
co
m
p
o
n
e
n
ts
th
at
is
o
f
f
er
ed
b
y
th
e
class
ical
ap
p
r
o
ac
h
.
Als
o
,
th
e
n
ec
ess
ar
y
p
r
in
cip
al
co
m
p
o
n
e
n
ts
ar
e
au
to
m
atica
lly
s
elec
ted
u
s
in
g
th
e
ANOVA
-
b
o
o
ts
tr
ap
p
ed
-
PC
A
alg
o
r
ith
m
.
3
.
2
.
T
he
f
o
o
d da
t
a
s
et
[
2
4
]
Similar
r
esu
lts
ca
n
b
e
o
b
s
er
v
ed
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th
e
f
o
o
d
d
ataset.
T
ab
le
4
s
u
m
m
ar
izes
th
e
co
n
tr
i
b
u
ti
o
n
o
f
ea
c
h
p
r
in
cip
al
c
o
m
p
o
n
en
t
t
o
th
e
to
t
al
v
ar
iab
ilit
y
o
f
d
ata
an
d
th
e
c
u
m
u
lativ
e
c
o
n
tr
ib
u
ti
o
n
ac
c
o
r
d
in
g
to
th
e
class
ical
ap
p
r
o
ac
h
.
T
ab
le
4
.
C
lass
ical
ap
p
r
o
ac
h
in
th
e
f
o
o
d
d
ataset
PC
%
o
f
v
a
r
e
x
p
l
a
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d
V
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l
a
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n
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d
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c
u
m
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l
a
t
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v
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%
P
C
1
4
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P
C
1
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C
2
6
3
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C
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2
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P
C
1
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P
C
2
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P
C
3
7
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C
3
1
6
%
P
C
1
+
P
C
2
+
P
C
3
+
P
C
4
9
3
%
P
C
4
1
4
%
P
C
1
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P
C
2
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P
C
3
+
P
C
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P
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1
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P
C
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S
o
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c
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:
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t
h
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s c
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s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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o
m
m
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ec
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n
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I
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N:
2252
-
8
7
7
6
Th
e
b
o
o
ts
tr
a
p
p
r
o
ce
d
u
r
e
fo
r
s
elec
tin
g
th
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n
u
m
b
er o
f p
r
in
cip
a
l c
o
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o
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(
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To
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1141
T
h
e
o
u
tp
u
t
in
T
a
b
le
4
d
o
es
n
o
t
ch
an
g
e
with
th
e
class
if
icati
o
n
m
o
d
el
u
s
ed
.
T
h
e
n
u
m
b
er
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
s
elec
ted
b
ased
o
n
T
ab
le
4
is
th
e
o
n
e
to
b
e
u
s
ed
in
all
clas
s
if
icatio
n
m
o
d
els.
T
ab
le
4
s
h
o
ws
th
at
th
e
f
ir
s
t
f
o
u
r
p
r
in
cip
al
co
m
p
o
n
en
ts
h
av
e
a
s
ig
n
if
ican
t
co
n
tr
ib
u
tio
n
to
th
e
v
ar
iab
ilit
y
o
f
d
ata
ac
co
u
n
tin
g
f
o
r
9
3
%
o
f
to
tal
v
ar
ian
ce
in
d
ata.
Ho
wev
er
,
if
th
e
f
ir
s
t
th
r
ee
p
r
in
cip
al
co
m
p
o
n
en
ts
ar
e
s
elec
te
d
,
th
en
o
n
ly
7
9
%
o
f
th
e
v
ar
iab
ilit
y
o
f
d
ata
wo
u
ld
b
e
ex
p
lain
ed
.
I
n
th
is
ca
s
e,
th
e
an
s
wer
is
s
tr
aig
h
tf
o
r
war
d
,
s
o
th
e
f
ir
s
t
f
o
u
r
p
r
in
cip
al
co
m
p
o
n
e
n
ts
s
h
o
u
ld
b
e
s
elec
ted
.
Selectin
g
th
e
f
ir
s
t th
r
ee
wo
u
ld
lead
to
a
s
ig
n
i
f
ican
t lo
s
s
o
f
im
p
o
r
tan
t
in
f
o
r
m
atio
n
.
T
ab
le
4
d
em
o
n
s
tr
ates
th
at
in
th
e
ca
s
e
o
f
th
e
f
o
o
d
d
ataset.
T
h
e
s
elec
tio
n
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
f
o
llo
win
g
t
h
e
class
ical
ap
p
r
o
a
c
h
is
o
b
v
io
u
s
.
Ho
wev
er
,
th
e
d
im
en
s
io
n
ality
r
e
d
u
ctio
n
is
n
o
t
ef
f
ec
tiv
e
as
o
n
ly
o
n
e
p
r
in
cip
al
c
o
m
p
o
n
en
t
s
h
o
u
ld
b
e
r
em
o
v
ed
f
r
o
m
th
e
class
if
icatio
n
m
o
d
el
ac
co
r
d
i
n
g
to
th
e
class
ical
ap
p
r
o
ac
h
.
T
h
er
ef
o
r
e,
in
c
o
m
p
l
ex
m
o
d
els
a
b
etter
s
et
o
f
p
r
in
c
ip
al
co
m
p
o
n
en
ts
m
ig
h
t
b
e
th
e
f
ir
s
t
th
r
ee
b
u
t
th
at
wo
u
ld
co
m
e
at
t
h
e
co
s
t
o
f
s
o
m
e
lo
s
s
in
d
ata
in
f
o
r
m
atio
n
.
T
h
er
ef
o
r
e
,
th
e
r
esear
ch
er
s
h
o
u
l
d
d
ec
id
e
wh
eth
er
to
u
s
e
th
e
f
ir
s
t th
r
ee
o
r
f
ir
s
t f
o
u
r
p
r
in
cip
al
co
m
p
o
n
e
n
ts
d
ep
en
d
i
n
g
o
n
th
e
p
u
r
p
o
s
e
o
f
th
eir
task
.
An
o
th
er
d
is
ad
v
an
tag
e
o
f
th
e
class
ical
ap
p
r
o
ac
h
is
th
at
th
e
r
esear
ch
er
d
o
es
n
o
t
k
n
o
w
wh
eth
er
a
s
tr
aig
h
tf
o
r
war
d
s
elec
tio
n
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
wo
u
l
d
b
e
p
o
s
s
ib
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atic
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ates
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S
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Acc
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5
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em
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T
ab
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.
R
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r
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m
th
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OVA
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e
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ile
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ts
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ith
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ased
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5
d
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ate
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T
ab
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3
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ile
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ased
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6
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T
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with
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p
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th
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
2
5
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8
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I
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&
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m
m
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T
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n
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l
,
Vo
l.
14
,
No
.
3
,
Dec
em
b
er
20
25
:
1
1
3
6
-
1
1
4
5
1142
b
est
ac
cu
r
ac
y
ac
co
r
d
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n
g
to
th
e
ANOVA
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b
o
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ts
tr
ap
p
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PC
A
ap
p
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r
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h
wh
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th
e
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p
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h
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s
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g
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th
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d
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at
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ata
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im
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p
r
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ap
p
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with
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r
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s
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s
e
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ich
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co
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ts
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r
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im
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n
d
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r
r
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Ho
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th
e
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r
ed
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n
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f
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th
e
p
r
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m
eth
o
d
o
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r
s
e
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th
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r
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ch
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h
is
ca
n
b
e
s
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n
in
T
a
b
le
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at
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m
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ar
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th
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class
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m
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ics
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(
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s
h
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at
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class
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e
im
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Ho
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t
th
e
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s
e
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th
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ANOVA
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o
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ts
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e
d
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it
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r
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1
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t
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9
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th
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s
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s
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to
th
e
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ap
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h
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h
e
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tr
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ier
in
b
o
th
ca
s
es
g
iv
es
s
im
ilar
m
ea
s
u
r
es
d
esp
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th
e
clas
s
im
b
alan
ce
.
T
ab
le
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.
C
lass
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m
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f
th
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(
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b
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ltin
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t
h
e
class
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3
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a
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l
8
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v
g
/
t
o
t
a
l
8
2
%
8
2
%
8
2
%
1
1
9
0
1
S
o
u
r
c
e
:
a
u
t
h
o
r
’
s c
a
l
c
u
l
a
t
i
o
n
s
I
n
th
e
ca
s
e
o
f
im
b
alan
ce
d
d
a
ta,
we
d
o
n
o
t
r
ec
o
m
m
en
d
u
s
in
g
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
with
SVM
.
Fu
r
th
er
r
esear
ch
s
h
o
u
ld
b
e
co
n
d
u
cted
t
o
ex
p
l
o
r
e
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
al
g
o
r
it
h
m
o
n
i
m
b
alan
ce
d
d
ata
an
d
o
t
h
er
class
if
icatio
n
m
o
d
els
th
at
ca
n
n
o
t
co
m
p
e
n
s
ate
f
o
r
im
b
alan
ce
d
class
es.
T
h
e
d
ec
is
io
n
tr
ee
class
if
ier
,
h
o
wev
er
,
is
a
p
p
r
o
p
r
iate
to
u
s
e
with
th
e
p
r
o
p
o
s
ed
ANOVA
-
b
o
o
ts
tr
ap
p
ed
-
P
C
A
in
im
b
alan
ce
d
d
atasets
.
3
.
3
.
T
he
f
ra
ud
da
t
a
s
et
[
2
5
]
T
h
e
Fra
u
d
d
ataset
h
as
5
p
r
in
c
ip
al
co
m
p
o
n
en
ts
.
I
ts
class
es
a
r
e
r
elativ
ely
b
alan
ce
d
as
was
in
th
e
E
d
d
ataset.
T
ab
le
8
s
h
o
ws
th
e
co
n
tr
ib
u
tio
n
o
f
ea
ch
p
r
in
cip
al
co
m
p
o
n
e
n
t
to
th
e
to
tal
v
ar
ian
ce
o
f
d
ata
ac
co
r
d
in
g
to
th
e
class
ical
ap
p
r
o
ac
h
.
T
h
e
f
i
r
s
t
th
r
ee
p
r
in
cip
al
co
m
p
o
n
en
t
s
ac
co
u
n
t
f
o
r
9
6
.
7
%
p
er
ce
n
t
o
f
th
e
v
ar
iab
ilit
y
o
f
d
ata.
T
h
ey
a
r
e
u
s
ed
to
f
it th
e
S
VM
an
d
DT
class
if
ier
s
.
T
h
e
class
ical
PC
A
r
esu
lts
in
9
6
.
7
%
ac
cu
r
a
cy
wh
e
n
th
e
d
ec
is
io
n
tr
ee
class
if
ier
is
f
itted
u
s
in
g
th
e
f
ir
s
t
th
r
ee
p
r
in
cip
al
co
m
p
o
n
en
ts
(
T
ab
le
8
)
an
d
in
7
5
.
8
%
wh
en
th
e
SVM
cla
s
s
if
ier
is
f
it
ted
with
th
e
s
am
e
p
r
in
cip
al
co
m
p
o
n
en
ts
lik
e
in
th
e
d
ec
is
i
o
n
tr
ee
class
if
ier
.
As
T
ab
le
9
s
h
o
ws
th
e
p
r
o
p
o
s
ed
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
SVM
an
d
DT
p
er
f
o
r
m
b
etter
th
an
th
e
class
ical
ap
p
r
o
ac
h
.
As
T
ab
le
9
s
h
o
ws
th
e
b
o
o
ts
tr
ap
p
ed
PC
A
d
ec
is
io
n
tr
ee
ac
h
iev
ed
9
8
.
1
%
ac
cu
r
ac
y
u
s
in
g
3
p
r
in
cip
al
co
m
p
o
n
en
ts
(
th
e
s
ec
o
n
d
,
th
ir
d
an
d
f
o
u
r
th
as
T
ab
le
1
0
s
h
o
ws),
wh
ich
is
1
.
4
%
p
.
p
.
h
ig
h
er
th
an
th
e
class
ical
Evaluation Warning : The document was created with Spire.PDF for Python.
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8
7
7
6
Th
e
b
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ts
tr
a
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r
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fo
r
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elec
tin
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1
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.
p
.
h
ig
h
er
th
an
th
e
class
ic
PC
A
S
VM
ap
p
r
o
ac
h
.
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h
e
class
if
icati
o
n
s
co
r
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ar
e
s
im
ilar
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o
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th
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o
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ed
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r
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th
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d
ata
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et.
W
h
en
class
es
ar
e
b
alan
ce
d
,
th
e
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
PC
A
class
if
icatio
n
ca
n
s
elec
t
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
e
n
ts
au
to
m
at
ically
an
d
in
m
an
y
ca
s
es
im
p
r
o
v
e
th
e
ac
c
u
r
ac
y
o
f
th
e
m
o
d
el.
As
T
ab
les
3,
6
,
an
d
9
d
em
o
n
s
tr
ate
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ca
n
also
b
e
u
s
ed
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
d
if
f
e
r
en
t
class
if
icatio
n
m
o
d
els
u
s
in
g
d
if
f
er
en
t
n
u
m
b
er
s
o
f
p
r
in
cip
al
c
o
m
p
o
n
e
n
ts
.
A
d
ec
is
io
n
n
o
t
o
n
ly
ab
o
u
t
th
e
n
u
m
b
e
r
o
f
p
r
in
cip
al
co
m
p
o
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e
n
ts
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t
a
ls
o
ab
o
u
t
wh
at
m
o
d
el
to
u
s
e
c
an
b
e
m
a
d
e.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ca
n
also
b
e
u
s
e
d
f
o
r
m
o
d
el
s
elec
tio
n
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
a
n
o
v
el
ap
p
r
o
ac
h
to
s
elec
tin
g
th
e
n
u
m
b
e
r
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
f
o
r
class
if
icatio
n
.
T
h
e
ANOV
A
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
c
lass
if
icat
i
o
n
alg
o
r
ith
m
p
r
o
v
id
es
a
f
ast
a
n
d
ef
f
ec
tiv
e
way
to
s
elec
t
th
e
n
u
m
b
er
o
f
p
r
in
cip
a
l
co
m
p
o
n
e
n
ts
an
d
im
p
r
o
v
e
th
e
ac
cu
r
ac
y
o
f
th
e
m
o
d
el.
I
t
c
an
also
b
e
u
s
ed
f
o
r
m
o
d
el
s
elec
tio
n
as
th
e
p
er
f
o
r
m
an
ce
o
f
s
ev
e
r
al
class
if
icatio
n
m
o
d
els
ca
n
b
e
co
m
p
ar
ed
.
B
ased
o
n
th
e
ac
cu
r
ac
y
an
d
n
u
m
b
er
o
f
p
r
in
cip
al
c
o
m
p
o
n
en
ts
s
elec
ted
,
o
n
e
class
if
icatio
n
m
o
d
el
ca
n
b
e
s
elec
ted
o
v
er
a
n
o
th
er
o
n
e.
Ho
wev
er
,
th
e
al
g
o
r
ith
m
p
er
f
o
r
m
s
well
o
n
ly
in
d
atasets
with
b
alan
ce
d
class
es.
I
n
ca
s
e
o
f
i
m
b
alan
ce
d
d
ata,
th
e
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
alg
o
r
ith
m
wo
r
k
s
well
with
th
e
d
ec
is
io
n
tr
ee
class
if
ier
.
T
h
e
d
ec
is
io
n
tr
ee
class
if
ier
h
an
d
les
th
e
im
b
alan
ce
in
class
e
s
,
th
er
ef
o
r
e
allo
win
g
th
e
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
alg
o
r
ith
m
to
b
e
co
m
p
etitiv
e
to
th
e
class
ical
PC
A
ap
p
r
o
ac
h
.
T
h
e
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
d
ec
is
io
n
tr
ee
class
if
ier
o
f
f
er
s
au
to
m
atic
s
elec
tio
n
o
f
p
r
in
ci
p
al
co
m
p
o
n
en
ts
,
u
n
lik
e
th
e
class
ical
ap
p
r
o
ac
h
.
Desp
ite
t
h
is
ad
v
an
tag
e,
th
e
d
ec
is
io
n
tr
ee
class
if
ier
is
n
o
t
ap
p
r
o
p
r
iate
in
all
ca
s
es,
s
o
th
e
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
d
ec
is
io
n
tr
ee
class
if
ier
ca
n
n
o
t
b
e
a
p
p
li
ed
in
all
ca
s
es
with
im
b
alan
c
ed
d
ata.
Ho
w
th
e
ANOVA
-
B
o
o
ts
tr
ap
p
ed
-
PC
A
C
las
s
if
icatio
n
ca
n
h
an
d
le
class
im
b
alan
ce
is
a
to
p
ic
o
f
f
u
r
th
er
r
esear
ch
.
T
ab
le
8
.
Prin
cip
al
c
o
m
p
o
n
en
ts
s
elec
ted
ac
co
r
d
in
g
to
th
e
clas
s
ical
ap
p
r
o
ac
h
PC
%
o
f
v
a
r
e
x
p
l
a
i
n
e
d
v
a
r
e
x
p
l
a
i
n
e
d
P
C
1
5
3
%
P
C
1
+
P
C
2
8
3
%
P
C
2
3
0
%
P
C
1
+
P
C
2
+
P
C
3
1
0
0
%
P
C
3
1
6
%
P
C
4
0%
P
C
5
0%
S
o
u
r
c
e
:
a
u
t
h
o
r
’
s c
a
l
c
u
l
a
t
i
o
n
s
T
ab
le
9
.
R
esu
lts
f
r
o
m
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
P
e
r
c
e
n
t
i
l
e
N
u
mb
e
r
o
f
f
e
a
t
u
r
e
s
A
c
c
u
r
a
c
y
o
f
D
T
A
c
c
u
r
a
c
y
o
f
S
V
M
1
0
%
0
.
4
8
3
.
9
2
%
7
6
.
7
8
%
2
0
%
0
.
8
8
3
.
9
2
%
7
6
.
7
8
%
3
0
%
1
.
2
8
3
.
9
2
%
7
6
.
7
8
%
4
0
%
1
.
6
9
7
.
9
5
%
7
6
.
8
5
%
5
0
%
2
9
7
.
9
5
%
7
6
.
8
5
%
6
0
%
2
.
4
9
7
.
9
5
%
7
6
.
8
5
%
7
0
%
2
.
8
9
8
.
1
4
%
7
5
.
9
8
%
8
0
%
3
.
2
9
8
.
1
4
%
7
5
.
9
8
%
9
0
%
3
.
6
9
8
.
1
4
%
7
5
.
9
8
%
1
0
0
%
4
9
8
.
4
5
%
7
5
.
8
5
%
S
o
u
r
c
e
:
a
u
t
h
o
r
’
s
c
a
l
c
u
l
a
t
i
o
n
s
T
ab
le
1
0
.
I
m
p
o
r
tan
ce
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
t
s
ac
co
r
d
in
g
t
o
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
PC
I
mp
o
r
t
a
n
c
e
P
C
1
1
.
0
6
3
5
6
P
C
2
5
6
0
.
4
7
8
P
C
3
1
2
6
.
3
8
2
P
C
4
3
.
5
8
5
0
4
S
o
u
r
c
e
:
a
u
t
h
o
r
’
s c
a
l
c
u
l
a
t
i
o
n
s
4.
CO
NCLU
SI
O
N
T
h
is
r
esear
ch
d
ev
elo
p
s
a
s
i
m
p
le
alg
o
r
ith
m
f
o
r
au
to
m
atic
d
etec
tio
n
o
f
th
e
n
u
m
b
er
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
ts
in
class
if
icatio
n
m
o
d
els.
T
h
e
ad
v
a
n
tag
es
o
f
th
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
in
cl
u
d
e
s
tr
aig
h
t
f
o
r
war
d
s
elec
tio
n
o
f
p
r
in
ci
p
al
co
m
p
o
n
en
ts
,
m
o
d
el
s
elec
tio
n
wh
en
n
e
ce
s
s
ar
y
a
n
d
im
p
r
o
v
ed
m
o
d
el
p
er
f
o
r
m
a
n
ce
.
Un
lik
e
th
e
class
ical
p
r
in
cip
al
co
m
p
o
n
en
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