I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
1
0
,
No
.
2
,
A
p
r
il
2
0
2
0
,
p
p
.
1
4
0
6
~1
4
2
1
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
1
0
i
2
.
p
p
1
4
0
6
-
1
4
2
1
1406
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m/in
d
ex
.
p
h
p
/I
JE
C
E
Project
io
n
pursui
t
Ra
ndo
m
Forest
u
sing
discri
m
ina
n
t
feat
ure
a
na
ly
sis
m
o
de
l
f
o
r churn
ers pre
dic
tion
i
n
t
eleco
m
in
dustry
Asi
a
M
a
hd
i N
a
s
er
Alzuba
idi
1
,
E
m
a
n Sa
lih
Al
-
Sh
a
m
er
y
2
1
De
p
a
rtme
n
t
o
f
Co
m
p
u
ter S
c
ien
c
e
,
Un
iv
e
rsity
o
f
Ka
rb
a
la,
Ira
q
2
De
p
a
rtme
n
t
o
f
S
o
f
twa
re
En
g
in
e
e
rin
g
,
Un
iv
e
rsity
o
f
Ba
b
y
lo
n
,
Ira
q
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Sep
6
,
2
0
1
9
R
ev
i
s
ed
Oct
1
1
,
2
0
1
9
A
cc
ep
ted
Oct
2
0
,
2
0
1
9
A
m
a
jo
r
a
n
d
d
e
m
a
n
d
issu
e
in
th
e
t
e
lec
o
m
m
u
n
ica
ti
o
n
s
i
n
d
u
stry
is
th
e
p
re
d
icti
o
n
o
f
c
h
u
rn
c
u
sto
m
e
rs.
Ch
u
r
n
d
e
sc
rib
e
s
th
e
c
u
st
o
m
e
r
w
h
o
a
tt
rit
e
s
f
ro
m
th
e
c
u
rre
n
t
p
ro
v
id
e
r
t
o
c
o
m
p
e
ti
to
rs
se
a
rc
h
in
g
f
o
r
b
e
tt
e
r
se
rv
ice
o
ff
e
rs.
Co
m
p
a
n
ies
f
ro
m
th
e
T
e
lco
se
c
to
r
f
re
q
u
e
n
tl
y
h
a
v
e
c
u
sto
m
e
r
re
latio
n
sh
i
p
m
a
n
a
g
e
m
e
n
t
o
f
f
ic
e
s
it
is
th
e
m
a
in
o
b
jec
ti
v
e
in
h
o
w
to
w
in
b
a
c
k
d
e
f
e
c
ti
n
g
c
li
e
n
ts
b
e
c
a
u
se
p
re
se
rv
e
lo
n
g
-
term
c
u
sto
m
e
rs
c
a
n
b
e
m
u
c
h
m
o
re
b
e
n
e
f
icia
l
th
a
n
g
a
in
n
e
w
l
y
re
c
ru
it
e
d
c
u
sto
m
e
rs.
Re
se
a
rc
h
e
rs
a
n
d
p
r
a
c
ti
ti
o
n
e
rs
a
re
p
a
y
in
g
g
re
a
t
a
t
ten
ti
o
n
to
d
e
v
e
lo
p
in
g
a
ro
b
u
st
c
u
st
o
m
e
r
c
h
u
rn
p
re
d
icti
o
n
m
o
d
e
l,
e
sp
e
c
iall
y
in
th
e
tele
c
o
m
m
u
n
ica
ti
o
n
b
u
sin
e
ss
b
y
p
ro
p
o
se
d
n
u
m
e
ro
u
s
m
a
c
h
in
e
lea
rn
in
g
a
p
p
ro
a
c
h
e
s.
M
a
n
y
a
p
p
ro
a
c
h
e
s
o
f
Clas
sif
ica
ti
o
n
a
re
e
sta
b
li
sh
e
d
,
b
u
t
t
h
e
m
o
st
e
ffe
c
ti
v
e
in
re
c
e
n
t
ti
m
e
s
is a t
re
e
-
b
a
se
d
m
e
th
o
d
.
T
h
e
m
a
in
c
o
n
tri
b
u
ti
o
n
o
f
th
is
re
se
a
rc
h
is
to
p
re
d
ict
c
h
u
rn
e
rs/
n
o
n
-
c
h
u
r
n
e
rs
i
n
t
h
e
T
e
lec
o
m
se
c
to
r
b
a
se
d
o
n
p
ro
jec
t
p
u
rsu
it
Ra
n
d
o
m
F
o
re
st
(P
P
F
o
re
st)
t
h
a
t
u
se
s
d
isc
rim
in
a
n
t
f
e
a
tu
re
a
n
a
ly
sis
a
s
a
n
o
v
e
lt
y
e
x
t
e
n
sio
n
o
f
t
h
e
c
o
n
v
e
n
ti
o
n
a
l
R
a
n
d
o
m
F
o
re
st
f
o
r
lea
rn
in
g
o
b
li
q
u
e
P
r
o
jec
t
P
u
rsu
it
tree
(
P
P
t
re
e
).
T
h
e
p
r
o
p
o
se
d
m
e
th
o
d
o
lo
g
y
lev
e
ra
g
e
s
th
e
a
d
v
a
n
tag
e
o
f
tw
o
d
isc
rim
in
a
n
t
a
n
a
ly
sis
m
e
th
o
d
s
t
o
c
a
lcu
late
th
e
p
r
o
jec
t
in
d
e
x
u
se
d
in
th
e
c
o
n
stru
c
ti
o
n
o
f
P
P
tree
.
T
h
e
f
irst
m
e
th
o
d
u
se
d
S
u
p
p
o
rt
V
e
c
to
r
M
a
c
h
in
e
s
(S
V
M
)
w
h
il
e
,
t
h
e
se
c
o
n
d
m
e
th
o
d
u
se
d
L
in
e
a
r
Disc
rim
in
a
n
t
A
n
a
ly
sis
(L
D
A
)
to
a
c
h
iev
e
li
n
e
a
r
sp
li
tt
in
g
o
f
v
a
riab
les
d
u
ri
n
g
o
b
li
q
u
e
P
P
tree
c
o
n
stru
c
ti
o
n
to
p
r
o
d
u
c
e
in
d
iv
id
u
a
l
c
las
sif
iers
th
a
t
a
re
ro
b
u
st a
n
d
m
o
re
d
iv
e
rse
th
a
n
c
las
sic
a
l
Ra
n
d
o
m
F
o
re
st.
It
i
s
f
o
u
n
d
th
a
t
t
h
e
p
r
o
p
o
se
d
m
e
t
h
o
d
s
e
n
jo
y
th
e
b
e
st
p
e
rf
o
rm
a
n
c
e
m
e
a
su
re
m
e
n
ts
e
.
g
.
A
c
c
u
ra
c
y
,
h
it
ra
te,
ROC
c
u
rv
e
,
L
i
f
t
,
H
-
m
e
a
su
re
,
A
UC.
M
o
re
o
v
e
r,
P
P
F
o
re
st
b
a
se
d
o
n
L
D
A
d
e
li
v
e
r
s
e
ff
e
c
ti
v
e
e
v
a
lu
a
to
r
s
in
t
h
e
p
re
d
icti
o
n
m
o
d
e
l.
K
ey
w
o
r
d
s
:
C
h
u
r
n
p
r
ed
ictio
n
Dec
is
io
n
cla
s
s
i
f
icatio
n
tr
ee
s
d
is
cr
i
m
i
n
an
t r
an
d
o
m
f
o
r
est
L
i
n
ea
r
d
is
cr
i
m
i
n
a
n
t a
n
a
l
y
s
is
o
b
liq
u
e
tr
ee
P
r
o
j
ec
t p
u
r
s
u
it in
d
ex
Su
p
p
o
r
t v
ec
to
r
m
ac
h
i
n
e
s
Co
p
y
rig
h
t
©
2
0
2
0
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Asi
a
Ma
h
d
i N
a
s
er
Alzu
b
aid
i
,
Dep
ar
t
m
en
t o
f
C
o
m
p
u
ter
Scie
n
ce
,
Un
i
v
er
s
it
y
o
f
Kar
b
ala,
Kar
b
ala,
I
r
aq
.
E
m
ail:
as
ia.
m
@
u
o
k
er
b
ala.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
T
elec
o
m
in
d
u
s
tr
y
i
s
a
h
i
g
h
l
y
tec
h
n
o
lo
g
ical
s
ec
to
r
th
at
h
as d
ev
elo
p
ed
tr
e
m
e
n
d
o
u
s
l
y
o
v
er
th
e
p
ast
t
w
o
d
ec
ad
es
as
a
r
esu
lt
o
f
t
h
e
e
m
er
g
e
n
ce
an
d
co
m
m
er
cial
s
u
cc
es
s
o
f
b
o
th
m
o
b
ile
te
lec
o
m
m
u
n
icatio
n
a
n
d
th
e
in
ter
n
et
[
1
]
.
C
u
s
to
m
er
ch
u
r
n
o
r
cu
s
to
m
er
attr
itio
n
is
a
g
r
ea
t
ch
allen
g
e
f
o
r
m
a
n
y
t
e
leco
m
co
m
p
an
ie
s
.
I
t
h
ap
p
en
s
w
h
en
a
c
u
s
to
m
er
e
n
d
s
h
is
s
u
b
s
cr
ip
tio
n
a
n
d
s
w
itc
h
to
an
o
t
h
er
co
m
p
etito
r
.
T
h
er
e
ar
e
m
a
n
y
f
ac
to
r
s
af
f
ec
t
th
e
c
u
s
to
m
er
’
s
d
ec
is
io
n
to
ch
an
g
e
to
an
o
th
er
co
m
p
etit
o
r
.
I
n
g
en
er
al,
s
u
c
h
f
ac
to
r
s
r
el
ated
to
th
e
h
ig
h
co
s
t,
b
ad
cu
s
to
m
er
s
er
v
ice
-
r
elate
d
w
o
r
k
,
f
r
au
d
a
n
d
p
r
iv
ac
y
co
n
c
er
n
s
[2
,
3]
.
C
u
s
to
m
er
ch
u
r
n
c
au
s
e
s
s
er
io
u
s
p
r
o
f
it
lo
s
s
w
h
e
n
e
x
ce
ed
s
ce
r
tai
n
li
m
its
.
O
n
t
h
e
o
t
h
er
h
a
n
d
,
co
m
p
a
n
ies
r
ea
lize
t
h
at
at
tr
ac
tin
g
n
e
w
cu
s
to
m
er
s
is
m
u
c
h
m
o
r
e
e
x
p
en
s
iv
e
t
h
an
p
r
eser
v
i
n
g
e
x
is
t
in
g
o
n
es.
T
h
e
in
it
ial
an
d
f
o
r
e
m
o
s
t
s
tep
in
cu
r
tail
in
g
o
u
tb
o
u
n
d
ch
u
r
n
a
n
d
estab
lis
h
in
g
lo
y
alt
y
o
f
t
h
e
p
r
ev
aili
n
g
c
u
s
to
m
er
s
is
to
u
n
d
er
s
tan
d
t
h
e
r
ea
s
o
n
s
f
o
r
ch
u
r
n
i
n
g
.
I
n
t
h
is
s
it
u
atio
n
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
P
r
o
jectio
n
p
u
r
s
u
it R
a
n
d
o
m
F
o
r
est u
s
in
g
d
is
crimin
a
n
t fe
a
tu
r
e
a
n
a
lysi
s
mo
d
el
.
.
.
(
A
.
Ma
h
d
i
N
a
s
er
)
1407
th
e
c
h
u
r
n
p
r
o
p
h
ec
y
i
s
a
u
s
e
f
u
l
an
d
h
elp
f
u
l
to
o
l
to
f
o
r
ec
ast
cu
s
to
m
er
at
c
h
u
r
n
r
is
k
.
T
h
e
o
n
l
y
r
e
m
ed
y
to
o
v
er
co
m
e
ch
u
r
n
b
u
s
in
e
s
s
h
az
ar
d
s
an
d
to
r
etain
in
t
h
e
co
m
p
a
n
y
[
4
]
.
C
u
s
to
m
er
C
h
u
r
n
P
r
ed
ictio
n
(
C
C
P
)
h
as
b
ee
n
r
aised
as
a
k
e
y
is
s
u
e
in
m
a
n
y
f
ield
s
s
u
ch
a
s
T
elec
o
m
p
r
o
v
id
er
s
,
cr
ed
it
ca
r
d
s
,
in
ter
n
e
t
s
er
v
ice
p
r
o
v
id
er
s
,
elec
tr
o
n
ic
co
m
m
er
ce
,
r
etail
m
ar
k
eti
n
g
,
n
e
w
s
p
ap
er
p
u
b
lis
h
in
g
co
m
p
a
n
ies,
b
an
k
i
n
g
a
n
d
f
i
n
an
cial
s
er
v
ices
[
5
]
.
C
C
P
in
T
elec
o
m
m
u
n
ica
tio
n
co
m
p
a
n
ies
h
as
b
ec
o
m
e
an
in
cr
ea
s
i
n
g
l
y
p
o
p
u
lar
r
esear
ch
i
s
s
u
e
in
r
ec
en
t y
ea
r
s
an
d
t
h
er
ef
o
r
e,
T
elec
o
m
p
r
o
v
id
er
s
u
s
i
n
g
w
id
el
y
s
tr
ate
g
ies
to
id
en
ti
f
y
t
h
e
p
o
ten
t
ial
ch
u
r
n
cu
s
to
m
er
s
b
ased
o
n
th
eir
h
i
s
to
r
ical
in
f
o
r
m
atio
n
,
p
r
io
r
b
eh
av
io
r
s
an
d
o
f
f
er
in
g
s
o
m
e
s
er
v
ices
to
p
er
s
u
ad
e
th
e
m
to
s
ta
y
.
O
n
o
th
er
h
an
d
,
L
o
n
g
-
ter
m
s
c
u
s
to
m
er
s
ar
e
m
o
r
e
p
r
o
f
it
ab
le
f
o
r
th
e
s
er
v
ice
p
r
o
v
id
er
s
,
s
in
ce
th
e
y
ar
e
m
o
r
e
d
ep
en
d
en
c
y
to
b
u
y
ad
d
itio
n
al
p
r
o
d
u
cts
an
d
s
p
r
ea
d
th
e
cu
s
to
m
er
'
s
s
ati
s
f
ac
tio
n
i
n
th
eir
cir
cle,
th
u
s
p
r
o
ce
d
u
r
e
w
i
l
l in
d
ir
ec
tl
y
attr
ac
t
m
o
r
e
an
d
m
o
r
e
cu
s
to
m
er
s
[
6
]
.
Sto
ck
h
o
ld
er
s
f
o
r
ce
d
to
s
ea
r
ch
f
o
r
alt
er
n
at
iv
e
ap
p
r
o
ac
h
es
f
o
r
u
s
i
n
g
m
ac
h
in
e
lear
n
i
n
g
tec
h
n
iq
u
es
a
n
d
s
tatis
t
ical
to
o
ls
to
r
ec
o
g
n
ize
t
h
e
ca
u
s
e
o
f
c
h
u
r
n
i
n
ad
v
a
n
ce
an
d
to
y
ield
i
n
s
ta
n
ta
n
eo
u
s
e
f
f
o
r
ts
in
r
e
s
p
o
n
s
e.
T
h
is
is
p
o
s
s
ib
le
if
t
h
e
h
i
s
to
r
ical
d
ata
o
f
th
e
p
o
ten
tial
cu
s
t
o
m
er
s
an
al
y
ze
d
s
y
s
te
m
ati
ca
ll
y
[
7
]
.
Fo
r
tu
n
a
tel
y
,
t
elec
o
m
s
ec
to
r
s
p
r
o
d
u
ce
an
d
p
r
eser
v
e
a
lar
g
e
v
o
l
u
m
e
o
f
d
ata,
th
e
y
i
n
cl
u
d
e
n
o
n
-
r
elatio
n
al
d
ata
i.e
.
b
illi
n
g
in
f
o
r
m
atio
n
,
d
e
m
o
g
r
ap
h
ic,
cu
s
to
m
er
ca
r
e,
cu
s
to
m
er
b
eh
av
io
r
,
an
d
r
elatio
n
al
d
ata
i.e
.
C
all
Deta
il
R
ec
o
r
d
s
d
ata
(
C
DR
)
a
n
d
n
et
w
o
r
k
d
ata.
Mo
r
eo
v
er
,
n
o
t
all
t
h
e
f
ea
t
u
r
es
o
f
th
e
t
elec
o
m
d
atab
ase
u
s
ed
b
y
all
th
e
p
r
ed
ictio
n
m
et
h
o
d
s
o
n
l
y
t
h
e
r
elev
a
n
t
f
ea
t
u
r
es t
h
at
r
ea
ll
y
co
n
tr
ib
u
te
to
t
h
e
C
C
P
u
s
ed
in
d
ata
m
in
in
g
(
DM
)
tech
n
iq
u
es
[
8
]
.
T
h
e
s
tatis
tical
lear
n
i
n
g
m
o
d
el
d
is
co
v
er
s
m
et
h
o
d
s
o
f
ap
p
r
o
x
i
m
a
t
in
g
f
u
n
ctio
n
al
d
ep
en
d
en
c
y
f
r
o
m
a
g
i
v
en
ass
o
r
t
m
en
t
o
f
d
ata.
I
t
co
v
er
s
s
i
g
n
i
f
ica
n
t
is
s
u
es
i
n
class
ical
s
tati
s
tic
s
s
u
c
h
as
d
i
s
cr
i
m
i
n
an
t
an
al
y
s
is
,
r
eg
r
ess
io
n
m
et
h
o
d
s
,
an
d
th
e
d
e
n
s
it
y
es
ti
m
a
tio
n
p
r
o
b
le
m
[
9
]
.
Statis
tical
lear
n
i
n
g
i
s
a
k
i
n
d
o
f
s
t
atis
tical
i
n
f
er
en
ce
,
also
ca
lled
i
n
d
u
cti
v
e
s
tatis
tics
.
R
ec
en
tl
y
,
s
tati
s
tical
lear
n
i
n
g
m
et
h
o
d
s
s
u
ch
as
Su
p
p
o
r
t
Vec
t
o
r
Ma
ch
in
e
s
(
SVM)
an
d
L
i
n
ea
r
Dis
cr
i
m
i
n
a
n
t
An
al
y
s
i
s
(
L
D
A
)
h
a
v
e
an
i
m
p
o
r
tan
t
r
o
le
in
d
es
cr
ib
i
n
g
t
h
e
d
if
f
er
en
ce
s
b
et
w
ee
n
a
r
ef
er
en
ce
co
llectio
n
o
f
p
atter
n
s
a
n
d
th
e
p
o
p
u
latio
n
u
n
d
er
e
x
p
lo
r
atio
n
[
1
0
]
.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
o
f
t
h
i
s
r
esear
ch
is
to
d
ev
elo
p
a
n
ew
e
n
s
e
m
b
le
lear
n
i
n
g
m
et
h
o
d
f
o
r
ch
u
r
n
p
r
ed
ictio
n
m
et
h
o
d
b
ased
o
n
R
an
d
o
m
Fo
r
est
co
n
s
tr
u
cted
b
u
t
w
it
h
o
b
liq
u
e
tr
ee
s
p
r
in
c
ip
al
u
s
in
g
an
o
p
ti
m
al
an
d
lin
ea
r
ass
o
ciatio
n
o
f
r
an
d
o
m
l
y
ch
o
s
en
p
r
ed
icto
r
s
,
w
h
ic
h
in
cr
ea
s
es
th
e
p
r
ed
ictiv
e
p
er
f
o
r
m
a
n
ce
w
h
e
n
t
h
e
cu
to
f
f
h
y
p
er
p
lan
e
b
et
w
ee
n
class
e
s
is
in
a
lin
ea
r
co
llectio
n
o
f
v
ar
ia
b
les.
T
h
e
s
u
g
g
esti
o
n
m
et
h
o
d
ca
lled
a
P
r
o
j
ec
tio
n
P
u
r
s
u
it
R
a
n
d
o
m
Fo
r
est
(
P
P
Fo
r
est).
Mo
r
eo
v
er
,
u
s
in
g
a
v
i
s
u
a
li
za
tio
n
to
o
l
o
f
C
o
n
s
tr
u
c
ted
P
P
F
o
r
est
an
d
co
m
p
ar
e
th
o
s
e
w
it
h
t
h
e
R
a
n
d
o
m
Fo
r
est
g
r
ap
h
in
o
r
d
er
to
u
n
d
er
s
ta
n
d
h
o
w
t
h
e
P
P
Fo
r
est m
o
d
el
s
u
m
m
ar
izes d
atasets
.
T
h
e
m
ai
n
d
i
ff
er
e
n
ce
w
it
h
th
e
k
n
o
w
n
R
an
d
o
m
Fo
r
est
ap
p
r
o
ac
h
is
t
h
at
t
h
e
o
b
liq
u
e
p
ar
titi
o
n
s
o
f
v
ar
iab
les
n
o
t
s
elec
ted
r
a
n
d
o
m
l
y
.
Ne
v
er
t
h
eles
s
,
t
h
e
li
n
ea
r
as
s
o
ciatio
n
i
n
ea
c
h
tr
ee
co
n
s
tr
u
ct
io
n
i
s
ca
lc
u
lated
b
y
i
m
p
r
o
v
i
n
g
a
p
r
o
j
ec
tio
n
p
u
r
s
u
it
in
d
e
x
d
ep
en
d
o
n
a
lin
ea
r
d
is
cr
i
m
i
n
an
t
a
n
al
y
s
i
s
(
L
D
A
)
o
r
Su
p
p
o
r
t
Vec
to
r
Ma
ch
in
e
(
SVM)
to
d
is
co
v
er
t
h
e
p
r
o
j
ec
tio
n
d
ata
o
f
t
h
e
v
ar
iab
les
t
h
at
b
e
s
t
s
p
lits
t
h
e
cla
s
s
e
s
ta
k
en
i
n
to
ac
c
o
u
n
t
th
e
co
r
r
elatio
n
b
et
w
ee
n
th
e
tar
g
et
v
ar
iab
le
a
n
d
o
th
er
d
ataset
v
ar
iab
les.
P
P
Fo
r
est
o
u
tp
er
f
o
r
m
s
a
tr
ad
iti
o
n
al
R
a
n
d
o
m
Fo
r
est
w
h
e
n
s
ep
ar
atio
n
s
b
et
w
ee
n
g
r
o
u
p
s
o
cc
u
r
in
L
i
n
ea
r
co
m
b
in
a
ti
o
n
s
o
f
v
ar
iab
les.
T
h
e
P
P
Fo
r
est
u
s
es
th
e
P
r
o
j
ec
t
P
u
r
s
u
it
tr
ee
(
PP
tr
ee
)
as
an
o
b
liq
u
e
m
o
d
el
f
o
r
class
i
fi
ca
tio
n
p
r
o
b
lem
w
h
er
e
th
e
r
esp
o
n
s
e
v
ar
iab
le
is
ca
teg
o
r
ical
an
d
th
e
m
et
h
o
d
is
d
efin
e
to
u
s
e
th
e
q
u
an
ti
tati
v
e
f
ea
tu
r
e,
w
h
ich
b
u
i
lt
t
h
e
tr
ee
f
r
o
m
th
e
a
v
ailab
le
v
ar
i
ab
les
to
en
h
an
ce
its
p
er
f
o
r
m
a
n
ce
in
m
u
lti
-
cla
s
s
p
r
o
b
le
m
s
an
d
in
t
h
e
p
r
ese
n
ce
o
f
n
o
n
li
n
ea
r
s
ep
ar
atio
n
s
[
1
1
]
.
T
w
o
p
r
o
j
ec
t p
u
r
s
u
it in
d
e
x
es,
L
D
A
a
n
d
SVM
u
s
ed
i
n
t
h
is
r
esea
r
ch
,
P
P
tr
ee
as b
ased
o
n
o
p
ti
m
ized
t
h
e
p
r
o
j
ec
tio
n
p
u
r
s
u
it
in
d
e
x
to
f
i
n
d
lo
w
-
d
i
m
en
s
i
o
n
al
p
r
o
j
ec
tio
n
s
th
at
s
ep
ar
ate
c
lass
es
o
f
t
h
e
g
r
o
u
p
.
A
t
ea
c
h
n
o
d
e,
th
e
P
P
tr
ee
u
s
e
s
th
e
b
e
s
t
p
r
o
j
ec
tio
n
to
s
ep
ar
ate
t
w
o
g
r
o
u
p
s
o
f
clas
s
es
u
s
i
n
g
L
D
A
o
r
SVM
p
r
o
j
ec
tio
n
p
u
r
s
u
it
in
d
ices
w
it
h
clas
s
in
f
o
r
m
atio
n
.
O
n
e
class
ass
i
g
n
ed
to
o
n
l
y
o
n
e
f
i
n
al
n
o
d
e
w
it
h
th
e
co
n
d
itio
n
th
at
t
h
e
d
ep
th
o
f
th
e
o
b
liq
u
e
P
P
tr
ee
ca
n
n
o
t
b
e
g
r
ea
ter
th
a
n
th
e
n
u
m
b
e
r
o
f
class
es.
T
h
er
ef
o
r
e,
th
e
P
P
tr
ee
co
n
s
tr
u
ct
s
a
s
i
m
p
l
e
b
u
t
m
o
r
e
u
n
d
er
s
tan
d
ab
le
tr
e
e
f
o
r
cl
as
s
i
fi
ca
tio
n
.
T
h
e
p
r
o
j
e
ctio
n
co
ef
f
icie
n
t
s
o
f
ea
ch
n
o
d
e
r
ep
r
esen
t
th
e
i
m
p
o
r
tan
ce
o
f
th
e
v
ar
iab
les
to
t
h
e
class
s
ep
ar
atio
n
o
f
ea
ch
n
o
d
e.
T
o
en
h
an
ce
th
e
p
er
f
o
r
m
an
ce
ac
cu
r
ac
y
o
f
t
h
e
en
s
e
m
b
le
P
P
Fo
r
est
m
eth
o
d
an
d
to
im
p
r
o
v
e
th
e
g
e
n
er
aliz
atio
n
o
f
th
is
m
o
d
el,
a
n
o
v
el
w
ea
k
tr
ee
r
e
m
o
v
er
u
s
ed
to
ig
n
o
r
e
th
e
tr
ee
s
w
it
h
lo
w
er
o
u
t
o
f
a
b
ag
a
n
d
tu
n
e
t
h
e
P
P
t
r
ee
in
o
r
d
er
t
o
en
h
a
n
ce
th
e
p
er
f
o
r
m
a
n
ce
ac
cu
r
ac
y
o
f
t
h
e
P
P
Fo
r
est in
g
en
er
a
l.
C
h
i
-
s
q
u
ar
e
m
eth
o
d
u
s
ed
f
o
r
f
ea
t
u
r
e
s
elec
tio
n
to
p
r
o
v
e
if
r
u
n
n
i
n
g
t
h
e
P
P
Fo
r
est
alg
o
r
ith
m
w
it
h
a
r
elativ
el
y
s
m
all
s
ize
o
f
t
h
e
d
atas
et
co
u
ld
i
m
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
P
P
Fo
r
est
[
1
2
]
.
A
f
ter
an
al
y
s
i
s
t
h
e
o
u
tco
m
e
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
b
ased
o
n
class
i
f
icatio
n
p
er
f
o
r
m
a
n
ce
m
e
tr
ics
r
eg
ar
d
in
g
d
i
f
f
er
e
n
t
T
elec
o
m
d
atasets
in
th
e
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
a
n
d
attr
ib
u
tes,
i
t
h
as
b
ee
n
s
h
o
w
n
t
h
at
t
h
e
p
r
o
p
o
s
ed
en
s
e
m
b
le
m
e
th
o
d
u
s
in
g
P
P
F
o
r
est
w
it
h
L
D
A
I
n
d
ice
h
as
r
o
b
u
s
t
r
esu
lt
s
o
f
o
v
er
all
ch
u
r
n
er
s
p
r
ed
ictio
n
s
y
s
te
m
.
Far
f
r
o
m
co
m
p
lex
i
t
y
co
m
p
u
ta
tio
n
al
i
n
t
h
e
ter
m
s
o
f
ti
m
e
a
n
d
s
av
i
n
g
co
m
p
le
x
ities
,
t
h
er
e
ar
e
n
o
d
if
f
er
en
ce
s
in
c
h
u
r
n
cla
s
s
if
icatio
n
o
u
tp
u
t
o
f
w
i
th
er
u
s
i
n
g
f
ea
tu
r
e
s
e
lectio
n
m
et
h
o
d
o
r
n
o
t.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
s
u
g
g
e
s
ted
p
ap
er
p
r
e
p
ar
ed
in
s
ec
tio
n
s
as
ill
u
s
tr
ate
i
n
f
o
llo
w
s
:
Sect
io
n
1
,
p
r
esen
t
t
h
e
i
n
tr
o
d
u
ctio
n
an
d
p
r
ev
io
u
s
s
tu
d
ie
s
ab
o
u
t
c
u
s
to
m
er
ch
u
r
n
p
r
ed
ictio
n
i
n
th
e
T
elco
s
ec
to
r
.
Me
th
o
d
o
lo
g
y
,
m
o
d
el
b
u
ild
i
n
g
,
d
ata
p
r
ep
r
o
ce
s
s
in
g
,
ch
i
-
s
q
u
ar
e
test
,
ex
ec
u
ted
m
et
h
o
d
s
ar
e
d
escr
ib
ed
in
S
ec
tio
n
2
.
Sectio
n
3
,
i
llu
s
tr
ated
th
e
ex
p
er
im
e
n
tal
i
m
p
le
m
e
n
t
atio
n
an
d
o
u
tco
m
es
o
f
ch
u
r
n
s
y
s
te
m
ar
e
d
is
cu
s
s
ed
.
P
P
Fo
r
est g
r
ap
h
an
d
h
u
b
er
p
lo
t
o
f
p
p
tr
ee
v
is
u
alize
in
s
ec
t
io
n
s
4
an
d
5
.
C
o
n
clu
s
io
n
s
ar
e
co
n
s
id
er
ed
in
S
ec
tio
n
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
2
,
A
p
r
il 2
0
2
0
:
1
4
0
6
-
1421
1408
C
h
u
r
n
er
s
an
d
n
on
-
c
h
u
r
n
er
s
cl
ass
i
f
icatio
n
r
eg
ar
d
as
p
r
ed
o
m
i
n
an
t
tr
o
u
b
le
f
o
r
t
elec
o
m
p
r
o
v
i
d
er
s
an
d
is
d
ef
in
ed
as th
e
m
i
s
s
i
n
g
o
f
cu
s
t
o
m
er
s
b
ec
au
s
e
th
e
y
lea
v
e
f
o
r
co
m
p
eti
to
r
s
.
B
ein
g
ab
le
to
clas
s
if
y
c
u
s
to
m
er
ch
u
r
n
in
ad
v
an
ce
,
p
r
o
v
id
es
th
e
T
elc
o
co
m
p
an
y
a
n
ap
p
r
ec
iated
in
s
ig
h
t
to
r
etain
its
cu
s
to
m
er
b
as
e.
W
id
e
r
an
g
es
o
f
ch
u
r
n
clas
s
i
f
icatio
n
m
et
h
o
d
s
h
av
e
i
n
v
e
s
ti
g
ated
in
r
ec
e
n
t
y
ea
r
s
.
Mo
s
t
i
n
n
o
v
ati
v
e
m
o
d
els
m
a
k
e
u
s
e
o
f
s
tate
-
of
-
th
e
-
a
rt
m
ac
h
i
n
e
lear
n
i
n
g
clas
s
if
ier
s
a
n
d
id
en
ti
f
ied
t
h
at
th
e
o
r
ig
in
s
o
f
c
u
s
to
m
er
ch
u
r
n
r
elat
ed
to
th
e
q
u
alit
y
o
f
s
er
v
ices,
d
e
m
o
g
r
ap
h
ic
f
ac
to
r
s
,
cu
s
to
m
er
s
atis
f
ac
tio
n
/d
is
s
ati
s
f
ac
tio
n
,
an
d
ec
o
n
o
m
ic
v
alu
e
f
ac
to
r
s
.
T
ab
le
1
.
T
h
e
L
iter
at
u
r
e
R
e
v
ie
w
o
f
r
ec
en
t
r
esear
c
h
r
elate
d
to
t
h
e
s
u
g
g
e
s
ted
C
C
P
m
o
d
el
b
ased
o
n
E
n
s
e
m
b
le
P
P
Fo
r
est
alg
o
r
ith
m
.
T
ab
le
1
.
T
h
e
l
iter
atu
r
e
r
ev
ie
w
N
o.
A
u
t
h
o
r
s
T
i
t
l
e
Jo
u
r
n
a
l
Y
e
a
r
O
b
j
e
c
t
i
v
e
T
e
c
h
n
i
q
u
e
s
D
a
t
a
se
t
P
e
r
f
o
r
man
c
e
M
e
t
r
i
c
s
a
n
d
O
u
t
c
o
me
s
1
L
e
e
,
Y
o
o
n
D
o
n
g
C
o
o
k
,
D
i
a
n
n
e
P
a
r
k
,
Ji
-
w
o
n
L
e
e
,
Eu
n
-
K
y
u
n
g
[
1
3
]
P
P
t
r
e
e
:
P
r
o
j
e
c
t
i
o
n
p
u
r
s
u
i
t
c
l
a
ssi
f
i
c
a
t
i
o
n
t
r
e
e
El
e
c
t
r
o
n
i
c
Jo
u
r
n
a
l
o
f
S
t
a
t
i
st
i
c
s
2
0
1
3
P
r
o
p
o
se
d
n
e
w
c
l
a
ssi
f
i
c
a
t
i
o
n
t
r
e
e
,
t
h
e
p
r
o
j
e
c
t
i
o
n
p
u
r
s
u
i
t
c
l
a
ssi
f
i
c
a
t
i
o
n
t
r
e
e
(
P
P
t
r
e
e
)
.
C
o
mb
i
n
e
s t
r
e
e
-
st
r
u
c
t
u
r
e
d
me
t
h
o
d
s w
i
t
h
p
r
o
j
e
c
t
i
o
n
p
u
r
s
u
i
t
d
i
me
n
s
i
o
n
r
e
d
u
c
t
i
o
n
.
T
h
e
P
P
t
r
e
e
u
se
s
L
D
A
,
L
r
o
r
P
D
A
a
s i
n
d
i
c
e
s
.
I
r
i
s d
a
t
a
P
r
o
j
e
c
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
s
c
a
n
b
e
u
se
d
t
o
e
x
t
r
a
c
t
t
h
e
v
a
r
i
a
b
l
e
i
m
p
o
r
t
a
n
c
e
.
T
h
i
s i
n
f
o
r
mat
i
o
n
i
s
v
e
r
y
h
e
l
p
f
u
l
i
n
c
l
a
ssi
f
i
c
a
t
i
o
n
p
r
o
b
l
e
ms
.
2
A
b
b
a
si
me
h
e
t
a
k
a
n
d
T
a
r
o
k
h
[
1
4
]
A
c
o
mp
a
r
a
t
i
v
e
a
sse
ssm
e
n
t
o
f
t
h
e
p
e
r
f
o
r
man
c
e
o
f
e
n
se
mb
l
e
l
e
a
r
n
i
n
g
i
n
c
u
s
t
o
me
r
c
h
u
r
n
p
r
e
d
i
c
t
i
o
n
.
I
n
t
.
A
r
a
b
J.
I
n
f
.
T
e
c
h
n
o
l
.
2
0
1
4
P
e
r
f
o
r
me
d
a
c
o
mp
a
r
a
t
i
v
e
a
sse
ssm
e
n
t
o
f
t
h
e
p
e
r
f
o
r
man
c
e
o
f
f
o
u
r
p
o
p
u
l
a
r
e
n
se
mb
l
e
me
t
h
o
d
s.
A
l
so
,
i
t
i
n
v
e
st
i
g
a
t
e
d
t
h
e
e
f
f
e
c
t
i
v
e
n
e
ss o
f
t
w
o
d
i
f
f
e
r
e
n
t
sam
p
l
i
n
g
t
e
c
h
n
i
q
u
e
s,
i
.
e
.
,
o
v
e
r
samp
l
i
n
g
a
s
a
r
e
p
r
e
se
n
t
a
t
i
v
e
o
f
b
a
s
i
c
s
a
m
p
l
i
n
g
t
e
c
h
n
i
q
u
e
s
a
n
d
t
h
e
S
y
n
t
h
e
t
i
c
M
i
n
o
r
i
t
y
O
v
e
r
samp
l
i
n
g
T
e
c
h
n
i
q
u
e
.
B
a
g
g
i
n
g
,
B
o
o
st
i
n
g
,
S
t
a
c
k
i
n
g
,
a
n
d
V
o
t
i
n
g
b
a
se
d
o
n
f
o
u
r
k
n
o
w
n
b
a
se
l
e
a
r
n
e
r
s,
i
.
e
.
,
C
4
.
5
D
e
c
i
si
o
n
T
r
e
e
(
D
T
)
,
A
r
t
i
f
i
c
i
a
l
N
e
u
r
a
l
N
e
t
w
o
r
k
(
A
N
N
)
,
S
u
p
p
o
r
t
V
e
c
t
o
r
M
a
c
h
i
n
e
(
S
V
M
)
a
n
d
R
e
d
u
c
e
d
I
n
c
r
e
me
n
t
a
l
P
r
u
n
i
n
g
t
o
P
r
o
d
u
c
e
Er
r
o
r
R
e
d
u
c
t
i
o
n
(
R
I
P
P
ER
)
.
L
a
r
o
se
A
U
C
,
se
n
si
t
i
v
i
t
y
,
a
n
d
s
p
e
c
i
f
i
c
i
t
y
.
C
o
n
c
l
u
d
e
t
h
a
t
B
o
o
st
i
n
g
R
I
P
P
ER
a
n
d
B
o
o
st
i
n
g
C
4
.
5
a
r
e
t
h
e
t
w
o
b
e
st
me
t
h
o
d
s
a
n
d
t
h
e
se
r
e
su
l
t
s i
n
d
i
c
a
t
e
t
h
a
t
e
n
se
mb
l
e
me
t
h
o
d
s
c
a
n
b
e
t
h
e
b
e
st
c
a
n
d
i
d
a
t
e
f
o
r
t
h
e
C
C
P
m
o
d
e
l
.
3
I
d
r
i
s a
n
d
K
h
a
n
[
1
5
]
En
se
mb
l
e
B
a
se
d
Ef
f
i
c
i
e
n
t
C
h
u
r
n
P
r
e
d
i
c
t
i
o
n
M
o
d
e
l
f
o
r
T
e
l
e
c
o
m
P
r
o
c
.
-
1
2
t
h
I
n
t
.
C
o
n
f
.
F
r
o
n
t
.
I
n
f
.
T
e
c
h
n
o
l
.
F
I
T
2
0
1
4
2
0
1
4
E
x
p
l
o
i
t
s
t
h
e
d
i
s
c
r
i
mi
n
a
t
i
v
e
f
e
a
t
u
r
e
se
l
e
c
t
i
o
n
c
a
p
a
b
i
l
i
t
i
e
s o
f
mi
n
i
m
u
m
r
e
d
u
n
d
a
n
c
y
a
n
d
max
i
mu
m re
l
e
v
a
n
c
e
i
n
t
h
e
f
i
r
st
s
t
e
p
,
l
e
a
d
i
n
g
t
o
a
n
e
n
h
a
n
c
e
d
f
e
a
t
u
r
e
-
l
a
b
e
l
a
sso
c
i
a
t
i
o
n
a
n
d
r
e
d
u
c
e
d
f
e
a
t
u
r
e
se
t
.
D
i
v
e
r
se
En
se
mb
l
e
i
s
c
o
n
st
r
u
c
t
e
d
u
si
n
g
maj
o
r
i
t
y
v
o
t
i
n
g
t
h
e
n
f
e
a
t
u
r
e
se
l
e
c
t
i
o
n
u
se
d
a
s
t
h
e
se
c
o
n
d
s
t
e
p
.
F
i
n
a
l
d
e
c
i
si
o
n
m
a
d
e
u
si
n
g
En
se
mb
l
i
n
g
o
f
R
a
n
d
o
m
F
o
r
e
st
,
R
o
t
a
t
i
o
n
F
o
r
e
st
,
a
n
d
K
N
N
.
O
r
a
n
g
e
T
e
l
e
c
o
m,
C
e
l
l
2
c
e
l
l
A
U
C
,
S
e
n
si
t
i
v
i
t
y
,
S
p
e
c
i
f
i
c
i
t
y
.
Q
-
S
t
a
t
i
st
i
c
s
,
T
h
e
p
r
o
p
o
se
d
E
n
se
mb
l
e
a
p
p
r
o
a
c
h
h
a
s
t
h
e
b
e
st
p
e
r
f
o
r
man
c
e
.
4
N
a
t
a
l
i
a
d
a
S
i
l
v
a
[
1
6
]
B
a
g
g
e
d
p
r
o
j
e
c
t
i
o
n
me
t
h
o
d
s fo
r
su
p
e
r
v
i
se
d
c
l
a
ssi
f
i
c
a
t
i
o
n
i
n
b
i
g
d
a
t
a
I
o
w
a
S
t
a
t
e
U
n
i
v
e
r
si
t
y
,
D
i
g
i
t
a
l
R
e
p
o
si
t
o
r
y
2
0
1
7
D
e
v
e
l
o
p
s n
e
w
c
l
a
ssi
f
i
c
a
t
i
o
n
me
t
h
o
d
s,
a
n
d
v
i
s
u
a
l
t
o
o
l
s fo
r
r
a
n
d
o
m
f
o
r
e
st
b
u
i
l
t
o
n
t
r
e
e
s
u
si
n
g
l
i
n
e
a
r
c
o
mb
i
n
a
t
i
o
n
s o
f
v
a
r
i
a
b
l
e
s
.
P
r
o
c
e
ss o
f
b
a
g
g
i
n
g
a
n
d
c
o
mb
i
n
i
n
g
r
e
su
l
t
s fr
o
m
d
i
f
f
e
r
e
n
t
P
P
t
r
e
e
.
A
u
st
r
a
l
i
a
n
c
r
a
b
d
a
t
a
se
t
T
h
e
a
l
g
o
r
i
t
h
m
i
mp
l
e
me
n
t
e
d
i
n
t
h
e
R
p
a
c
k
a
g
e
a
n
d
d
e
si
g
n
a
sm
a
l
l
w
e
b
a
p
p
.
5
N
a
t
a
l
i
a
d
a
S
i
l
v
a
,
C
o
o
k
a
n
d
L
e
e
[
1
7
]
A
P
r
o
j
e
c
t
i
o
n
P
u
r
su
i
t
F
o
r
e
st
A
l
g
o
r
i
t
h
m
f
o
r
S
u
p
e
r
v
i
se
d
C
l
a
ssi
f
i
c
a
t
i
o
n
,
a
r
X
i
v
:
1
8
0
7
.
0
7
2
0
7
v
2
[
st
a
t
.
M
L
]
2
5
Ju
l
2
0
1
8
2
0
1
8
N
e
w
e
n
se
mb
l
e
l
e
a
r
n
i
n
g
me
t
h
o
d
f
o
r
c
l
a
ssi
f
i
c
a
t
i
o
n
p
r
o
b
l
e
ms c
a
l
l
e
d
p
r
o
j
e
c
t
i
o
n
p
u
r
s
u
i
t
r
a
n
d
o
m fo
r
e
st
(
P
P
F
)
.
P
P
t
r
e
e
s
a
r
e
c
o
n
st
r
u
c
t
e
d
b
y
sp
l
i
t
t
i
n
g
o
n
l
i
n
e
a
r
c
o
mb
i
n
a
t
i
o
n
s o
f
r
a
n
d
o
ml
y
c
h
o
se
n
v
a
r
i
a
b
l
e
s.
P
r
o
j
e
c
t
i
o
n
p
u
r
s
u
i
t
i
s
u
se
d
t
o
c
h
o
o
se
a
p
r
o
j
e
c
t
i
o
n
o
f
t
h
e
v
a
r
i
a
b
l
e
s t
h
a
t
b
e
st
se
p
a
r
a
t
e
s t
h
e
c
l
a
sse
s.
C
r
a
b
,
f
i
sh
c
a
t
c
h
,
l
e
u
k
e
mi
a
,
l
y
mp
h
o
ma,
o
l
i
v
e
,
a
n
d
w
i
n
e
.
P
e
r
f
o
r
man
c
e
c
o
mp
a
r
i
so
n
g
r
a
p
h
i
c
a
l
l
y
b
e
t
w
e
e
n
R
F
,
P
P
t
r
e
e
,
P
P
F
o
r
e
st
a
n
d
C
A
R
T
o
n
u
se
d
d
a
t
a
se
t
s
a
n
d
f
o
u
n
d
t
h
a
t
P
P
F
p
e
r
f
o
r
ms
b
e
st
a
s
c
o
m
p
a
r
e
d
t
o
o
t
h
e
r
me
t
h
o
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
P
r
o
jectio
n
p
u
r
s
u
it R
a
n
d
o
m
F
o
r
est u
s
in
g
d
is
crimin
a
n
t fe
a
tu
r
e
a
n
a
lysi
s
mo
d
el
.
.
.
(
A
.
Ma
h
d
i
N
a
s
er
)
1409
T
ab
le
1
.
T
h
e
l
iter
atu
r
e
r
ev
ie
w
(
co
n
tin
u
e
)
N
o
.
A
u
t
h
o
r
s
T
i
t
l
e
Jo
u
r
n
a
l
Y
e
a
r
O
b
j
e
c
t
i
v
e
T
e
c
h
n
i
q
u
e
s
D
a
t
a
se
t
P
e
r
f
o
r
man
c
e
M
e
t
r
i
c
s
a
n
d
O
u
t
c
o
me
s
6
A
h
mad
,
Jafar,
a
n
d
.
A
l
j
o
u
maa
[
1
8
]
C
u
s
t
o
me
r
c
h
u
r
n
p
r
e
d
i
c
t
i
o
n
i
n
t
e
l
e
c
o
m
u
si
n
g
mac
h
i
n
e
l
e
a
r
n
i
n
g
i
n
b
i
g
d
a
t
a
p
l
a
t
f
o
r
m
Jo
u
r
n
a
l
o
f
B
i
g
D
a
t
a
2
0
1
9
D
e
v
e
l
o
p
a
c
h
u
r
n
p
r
e
d
i
c
t
i
o
n
mo
d
e
l
t
h
a
t
a
ssi
s
t
s t
e
l
e
c
o
m
o
p
e
r
a
t
o
r
s t
o
p
r
e
d
i
c
t
c
u
s
t
o
me
r
s c
h
u
r
n
i
n
b
i
g
d
a
t
a
b
y
e
x
t
r
a
c
t
i
n
g
S
N
A
f
e
a
t
u
r
e
s b
a
se
d
o
n
c
l
o
u
d
c
o
mp
u
t
i
n
g
.
T
h
e
mo
d
e
l
i
s p
r
e
p
a
r
e
d
a
n
d
t
e
st
e
d
t
h
r
o
u
g
h
t
h
e
S
p
a
r
k
e
n
v
i
r
o
n
me
n
t
u
si
n
g
c
l
o
u
d
c
o
m
p
u
t
i
n
g
.
T
h
e
mo
d
e
l
u
se
d
D
e
c
i
si
o
n
T
r
e
e
,
R
a
n
d
o
m
F
o
r
e
st
,
G
r
a
d
i
e
n
t
B
o
o
st
e
d
M
a
c
h
i
n
e
T
r
e
e
“
G
B
M
”
a
n
d
Ex
t
r
e
me
G
r
a
d
i
e
n
t
B
o
o
st
i
n
g
“
X
G
B
O
O
S
T
”
.
S
y
r
i
a
T
e
l
,
M
T
N
t
e
l
e
c
o
m
c
o
mp
a
n
i
es
A
U
C
,
t
h
e
b
e
st
r
e
su
l
t
s w
e
r
e
o
b
t
a
i
n
e
d
b
y
a
p
p
l
y
i
n
g
t
h
e
X
G
B
O
O
S
T
a
l
g
o
r
i
t
h
m.
7
S
e
l
v
a
r
a
j
a
n
d
S
r
u
t
h
i
[
1
9
]
A
n
Ef
f
e
c
t
i
v
e
C
l
a
ssi
f
i
e
r
f
o
r
P
r
e
d
i
c
t
i
n
g
C
h
u
r
n
i
n
T
e
l
e
c
o
mm
u
n
i
c
a
t
i
o
n
Jo
u
r
n
a
l
o
f
A
d
v
a
n
c
e
d
R
e
se
a
r
c
h
i
n
D
y
n
a
mi
c
a
l
a
n
d
C
o
n
t
r
o
l
S
y
st
e
ms
1
1
(
0
1
-
sp
e
c
i
a
l
i
ssu
e
)
:
2
2
1
2
0
1
9
T
h
e
su
g
g
e
st
e
d
mo
d
e
l
a
i
ms
t
o
f
i
n
d
t
h
e
f
e
a
t
u
r
e
s t
h
a
t
h
i
g
h
l
y
i
n
f
l
u
e
n
c
e
o
f
c
u
s
t
o
me
r
c
h
u
r
n
o
p
e
r
a
t
i
o
n
.
M
a
c
h
i
n
e
-
l
e
a
r
n
i
n
g
a
l
g
o
r
i
t
h
ms l
i
k
e
K
N
N
,
R
a
n
d
o
m F
o
r
e
st
a
n
d
X
G
B
o
o
st
.
I
B
M
W
a
t
so
n
F
-
S
c
o
r
e
,
A
c
c
u
r
a
c
y
.
F
i
b
e
r
O
p
t
i
c
c
u
s
t
o
me
r
s
w
i
t
h
g
r
e
a
t
e
r
mo
n
t
h
l
y
c
h
a
r
g
e
s
a
t
t
r
i
b
u
t
e
s
h
a
v
e
h
i
g
h
e
r
i
n
f
l
u
e
n
c
e
f
o
r
c
h
u
r
n
.
X
G
b
o
o
st
c
l
a
ss
i
f
i
e
r
p
e
r
f
o
r
ms
o
u
t
p
e
r
f
o
r
m t
h
e
o
t
h
e
r
me
t
h
o
d
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
o
b
j
ec
tiv
e
o
f
t
h
e
s
u
g
g
ested
s
ch
e
m
e
co
n
s
i
s
ts
o
f
b
u
ild
in
g
a
class
i
f
icat
io
n
m
o
d
el
f
o
r
in
d
ic
atin
g
ea
c
h
in
d
iv
id
u
al
clien
t
to
b
e
a
p
o
te
n
tial
ch
u
r
n
er
o
r
n
o
n
-
c
h
u
r
n
er
in
T
elec
o
m
d
atasets
.
T
h
is
p
r
o
ce
d
u
r
e
w
ill
ass
i
s
t
cu
s
to
m
er
r
elatio
n
s
h
ip
m
an
a
g
e
m
en
t
(
C
R
M)
,
b
y
ad
o
p
tin
g
t
h
e
cr
u
cial
r
eten
tio
n
p
o
licies
th
at
ar
e
lik
el
y
to
attr
ac
t
cu
s
to
m
er
s
a
n
d
attr
ac
t
w
h
o
h
av
e
th
e
m
o
s
t
ten
d
e
n
c
y
to
c
h
u
r
n
er
an
d
p
u
r
s
u
i
t
th
e
m
to
r
e
m
ai
n
.
T
h
e
in
p
u
t
f
o
r
s
u
g
g
e
s
ti
n
g
cu
s
to
m
er
ch
u
r
n
p
r
ed
ictio
n
(
C
C
P
)
m
o
d
el
in
cl
u
d
es
in
f
o
r
m
a
tio
n
f
r
o
m
p
as
t
ca
lls
f
o
r
ea
ch
m
o
b
il
e
s
u
b
s
cr
ib
er
,
to
g
eth
er
w
it
h
all
th
e
in
d
iv
id
u
a
l
an
d
b
u
s
i
n
ess
i
n
f
o
r
m
atio
n
p
r
eser
v
ed
b
y
th
e
t
elec
o
m
s
er
v
ice
p
r
o
v
id
er
.
Af
ter
t
h
e
p
r
ed
ictio
n
m
o
d
el
e
n
t
ir
el
y
tr
ai
n
ed
w
it
h
t
h
e
tr
ai
n
i
n
g
d
ataset.
T
h
en
,
t
h
e
m
o
d
el
m
u
s
t
b
e
ab
le
to
p
r
ed
ict
ch
u
r
n
er
s
f
r
o
m
t
h
e
te
s
t
d
ataset
.
T
h
e
r
ec
o
m
m
e
n
d
ed
m
et
h
o
d
o
lo
g
y
f
o
r
c
h
u
r
n
er
s
p
r
ed
ictio
n
h
as
b
ee
n
d
en
o
ted
as
a
s
ch
e
m
atic
d
iag
r
a
m
as
m
e
n
t
io
n
ed
in
Fig
u
r
e1
an
d
t
h
e
d
et
ailed
ex
p
lan
at
io
n
o
f
th
e
s
tep
s
f
o
llo
w
ed
in
g
i
v
e
n
s
u
b
s
ec
tio
n
s
.
Fig
u
r
e1
.
C
u
s
to
m
er
c
h
u
r
n
p
r
ed
ictio
n
u
s
i
n
g
E
n
s
e
m
b
le
P
P
Fo
r
e
s
t
m
o
d
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
2
,
A
p
r
il 2
0
2
0
:
1
4
0
6
-
1421
1410
2
.
1
.
Da
t
a
s
et
s
T
h
e
p
r
ac
tical
p
ar
t
o
f
th
e
r
es
ea
r
ch
is
r
u
n
n
in
g
o
n
d
i
f
f
er
e
n
t
T
elec
o
m
d
ataset
s
p
r
o
v
id
ed
b
y
v
ar
io
u
s
w
ir
ele
s
s
T
elco
o
p
er
ato
r
s
ar
o
u
n
d
th
e
w
o
r
ld
.
T
ab
le
2
s
u
m
m
ar
izes
th
e
m
ai
n
c
h
ar
ac
ter
is
tic
s
o
f
t
h
ese
d
ataset
s
i.e
.
n
a
m
e,
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
,
n
u
m
b
er
o
f
attr
ib
u
tes a
n
d
C
h
u
r
n
R
ates a
n
d
m
i
s
s
i
n
g
v
al
u
e
p
e
r
ce
n
tag
e.
T
ab
le
2
.
Su
m
m
ar
ize
So
m
e
o
f
R
esear
ch
Da
taset
s
D
a
t
a
se
t
s
#
O
b
se
r
v
a
t
i
o
n
s
#
F
e
a
t
u
r
e
s
T
a
r
g
e
t
C
h
u
r
n
V
a
r
i
a
b
l
e
M
i
ss
i
n
g
V
a
l
u
e
R
a
t
e
N
o
n
-
c
h
u
r
n
C
h
u
r
n
C
h
u
r
n
R
a
t
e
L
a
r
o
se
T
e
l
c
o
5
0
0
0
21
0
.
8
5
9
0
.
1
4
5
7
.
0
7
0
.
0
0
0
T
e
l
e
c
o
m1
Te
l
c
o
1
2
4
9
9
20
0
.
6
0
7
0
.
3
9
3
2
.
5
4
0
.
4
4
1
W
A
_
F
n
_
u
se
_
T
e
l
c
o
7
0
3
2
21
0
.
7
3
5
0
.
2
6
5
3
.
7
7
0
.
0
0
7
S
o
u
t
h
A
si
a
n
T
e
l
c
o
2
0
0
0
14
0
.
5
0
0
0
.
5
0
0
1
.
0
0
1
.
6
1
8
C
e
l
l
2
c
e
l
l
Te
l
c
o
7
1
0
0
0
78
0
.
7
1
0
0
.
2
9
0
3
.
4
5
0
.
6
4
7
T
e
l
c
o
m2
T
e
l
c
o
5
0
0
0
0
1
6
3
0
.
4
9
4
0
.
5
0
6
1
.
9
8
0
.
0
0
0
As
ca
n
b
e
s
ee
n
f
r
o
m
t
h
e
tab
le,
th
e
s
m
alle
s
t
d
ata
s
et
co
n
tain
s
2
0
0
0
o
b
s
er
v
atio
n
s
,
an
d
t
h
e
lar
g
est
u
p
to
7
1
0
0
0
o
b
s
er
v
atio
n
s
.
T
o
im
p
l
e
m
en
t
C
C
P
m
e
th
o
d
o
lo
g
y
t
h
i
s
ch
ar
ac
ter
is
tic
allo
w
s
u
s
to
s
p
lit
ea
ch
d
ataset
r
an
d
o
m
l
y
in
to
0
.
8
tr
ain
i
n
g
s
et
an
d
0
.
2
test
s
et.
T
h
e
d
atasets
also
d
if
f
er
s
u
b
s
tan
t
iall
y
r
e
g
ar
d
in
g
t
h
e
n
u
m
b
er
o
f
attr
ib
u
tes,
i
n
a
r
a
n
g
e
f
r
o
m
1
4
u
p
to
1
6
3
.
Ho
w
ev
er
,
m
o
r
e
attr
ib
u
tes
d
o
n
o
t
g
u
ar
an
tee
a
b
etter
c
lass
i
f
icatio
n
m
o
d
el
it
m
ea
n
s
h
ea
v
il
y
i
n
cr
ea
s
es
i
n
th
e
co
m
p
u
tatio
n
al
co
m
p
le
x
it
y
r
eq
u
ir
ed
to
r
u
n
t
h
e
e
m
p
ir
ical
co
d
es
o
f
r
esear
ch
.
T
h
e
f
in
al
p
er
f
o
r
m
an
ce
o
f
a
cl
ass
i
f
ier
m
a
in
l
y
d
ep
en
d
s
o
n
th
e
f
ea
t
u
r
e
en
g
in
ee
r
i
n
g
o
f
t
h
e
at
tr
ib
u
tes,
an
d
n
o
t
o
n
th
e
n
u
m
b
er
o
f
attr
ib
u
tes
av
aila
b
le.
Mo
s
t
o
f
th
e
d
ata,
h
o
w
e
v
er
,
ar
e
co
llected
o
v
er
a
p
er
io
d
o
f
t
h
r
ee
to
s
ix
m
o
n
t
h
s
,
w
it
h
a
c
h
u
r
n
f
lag
in
d
icati
n
g
w
h
et
h
er
a
cu
s
to
m
er
c
h
u
r
n
ed
in
th
e
m
o
n
th
a
f
ter
t
h
e
m
o
n
t
h
f
o
llo
w
i
n
g
t
h
e
p
er
io
d
w
h
e
n
th
e
d
ata
w
as
co
llected
.
T
h
e
tab
le
also
in
d
icate
s
th
e
class
d
is
tr
ib
u
tio
n
,
w
h
ic
h
is
f
o
r
all
d
atasets
h
ea
v
il
y
s
k
e
w
ed
.
T
h
e
p
e
r
ce
n
tag
e
o
f
ch
u
r
n
er
s
t
y
p
ical
l
y
lies
w
it
h
i
n
a
r
an
g
e
o
f
1
%
to
5
%
o
f
th
e
en
tire
cu
s
to
m
er
b
ase,
d
ep
en
d
in
g
o
n
th
e
len
g
t
h
o
f
t
h
e
p
er
io
d
in
w
h
ic
h
ch
u
r
n
i
s
m
ea
s
u
r
ed
.
T
h
e
tab
le
also
s
h
o
w
s
t
h
e
m
is
s
i
n
g
v
al
u
e
r
ate,
th
e
p
r
esen
ce
o
f
t
h
e
a
m
b
ig
u
it
y
o
f
th
ese
v
al
u
e
s
h
as
a
s
i
g
n
if
i
ca
n
t
in
f
l
u
e
n
ce
o
n
t
h
e
lo
w
p
r
e
d
ictiv
e
ac
cu
r
ac
y
o
f
th
e
C
C
P
m
o
d
el.
2
.
2
.
Da
t
a
s
et
s
pre
-
pro
ce
s
s
ing
P
r
ep
r
o
ce
s
s
in
g
is
a
d
ata
m
in
in
g
ap
p
r
o
ac
h
in
v
o
lv
ed
co
n
v
er
ti
n
g
r
a
w
d
ata
in
to
a
co
m
p
r
eh
en
s
ib
le
f
o
r
m
at.
T
h
e
ac
tu
al
in
f
o
r
m
atio
n
i
n
th
e
w
o
r
ld
o
f
ten
i
n
co
m
p
lete,
i
n
co
n
s
is
te
n
t
m
is
s
in
g
in
ce
r
tai
n
b
eh
av
io
r
s
an
d
p
atter
n
s
an
d
m
a
y
h
a
v
e
m
a
n
y
m
i
s
tak
e
s
.
P
r
e
-
p
r
o
ce
s
s
in
g
is
p
r
o
v
ed
f
o
r
s
o
lv
in
g
t
h
ese
p
r
o
b
le
m
s
.
Mo
s
t
o
f
t
h
e
t
elec
o
m
d
atasets
co
m
e
w
it
h
h
ig
h
m
is
s
i
n
g
v
al
u
es.
I
n
s
tead
o
f
r
e
m
o
v
i
n
g
v
ar
iab
les
an
d
o
b
s
er
v
atio
n
s
th
a
t
h
av
e
h
i
g
h
m
is
s
i
n
g
v
al
u
e
s
,
a
n
o
th
er
ap
p
r
o
ac
h
is
to
f
ill
u
p
i
n
m
i
s
s
i
n
g
v
al
u
e
v
ar
ia
b
les.
A
d
iv
er
s
i
t
y
ap
p
r
o
ac
h
ca
n
b
e
u
s
ed
i
n
m
is
s
i
n
g
f
ea
t
u
r
es
i
m
p
u
tat
io
n
t
h
at
r
an
g
e
s
f
r
o
m
e
x
tr
e
m
el
y
s
i
m
p
le
to
r
el
ativ
el
y
co
m
p
le
x
.
T
h
is
p
ap
er
u
s
ed
th
e
m
a
in
m
et
h
o
d
f
o
r
ex
p
lo
r
in
g
a
n
d
f
il
l
w
it
h
m
i
s
s
i
n
g
v
al
u
es
ca
lled
P
r
ed
ictiv
e
Me
an
Ma
tc
h
i
n
g
(
P
MM
)
[
2
0
]
.
P
MM
tech
n
iq
u
e
is
w
id
el
y
u
s
ed
as
an
o
u
ts
tan
d
i
n
g
m
et
h
o
d
f
o
r
v
ar
iab
les
im
p
u
t
atio
n
an
d
h
as
an
attr
ac
ti
v
e
w
a
y
to
d
o
m
u
ltip
le
i
m
p
u
ta
tio
n
s
esp
ec
iall
y
f
o
r
f
ill
i
n
g
u
p
th
e
q
u
a
n
titat
i
v
e
v
ar
iab
les
th
at
ar
e
s
u
f
f
er
i
n
g
f
r
o
m
ir
r
eg
u
lar
d
is
tr
ib
u
tio
n
[
2
1
]
.
P
MM
ca
n
b
e
ap
p
lied
in
t
w
o
s
t
ep
s
.
First,
t
h
e
ap
p
r
o
x
i
m
ati
n
g
m
ea
n
f
u
n
ctio
n
is
p
r
ed
ictin
g
.
S
ec
o
n
d
,
th
e
d
ata
w
i
th
m
is
s
i
n
g
v
al
u
e
i
m
p
u
ted
b
y
f
i
n
d
in
g
t
h
e
s
i
m
ilar
f
i
e
ld
s
i
n
th
e
d
ataset,
th
i
s
d
o
n
e
b
y
m
ea
n
s
o
f
a
n
ea
r
e
s
t
-
n
ei
g
h
b
o
r
tech
n
iq
u
e
t
h
en
,
t
h
e
o
b
s
er
v
ed
o
u
tco
m
e
v
al
u
e
o
f
t
h
e
n
ea
r
est
n
e
ig
h
b
o
r
ca
n
b
e
u
s
ed
f
o
r
i
m
p
u
ta
t
io
n
.
2
.
3
.
F
e
a
t
ures
s
elec
t
io
n ba
s
ed
o
n
c
hi
-
s
qu
a
re
t
est
T
h
e
m
o
s
t
i
m
p
o
r
tan
t
s
tep
in
d
a
ta
p
r
e
-
p
r
o
ce
s
s
in
g
i
s
to
id
en
ti
f
y
attr
ib
u
te
s
t
h
at
ar
e
ce
r
tai
n
l
y
r
elev
an
t
to
th
e
tar
g
et
v
ar
iab
le.
Ho
w
e
v
er
,
n
o
t
all
at
tr
ib
u
tes
ar
e
w
ell
co
n
tr
ib
u
ted
to
t
h
e
cla
s
s
i
f
ier
lear
n
er
m
o
d
el.
D
u
e
to
th
e
w
id
e
-
s
ca
le
d
atasets
i
n
t
elec
o
m
p
r
o
v
id
er
s
er
v
ice
s
,
th
e
f
ea
t
u
r
e
s
elec
tio
n
p
r
o
ce
s
s
b
ec
a
m
e
e
s
s
e
n
tial
to
i
m
p
r
o
v
e
th
e
p
er
f
o
r
m
an
ce
a
n
d
m
ak
e
t
h
e
C
C
P
m
o
d
el
ea
s
ier
to
in
ter
p
r
et,
d
ec
r
ea
s
e
o
v
er
f
itti
n
g
,
eli
m
i
n
ati
n
g
v
ar
iab
les
th
at
ar
e
r
ed
u
n
d
an
t
an
d
d
o
n
o
t
p
r
o
v
id
e
an
y
i
n
f
o
r
m
atio
n
o
r
co
n
tr
ib
u
tio
n
in
t
h
e
o
u
tp
u
t
o
f
t
h
e
m
o
d
el.
Mo
r
eo
v
er
,
it
r
ed
u
ce
s
th
e
s
ize
o
f
t
h
e
p
r
ed
ictio
n
p
r
o
b
lem
an
d
en
ab
le
s
class
if
icatio
n
alg
o
r
it
h
m
s
as
p
o
s
s
ib
l
e
to
y
ield
o
u
tco
m
e
s
in
a
f
aster
m
a
n
n
er
[
2
2
]
.
T
h
e
C
h
i
-
Sq
u
ar
e
test
is
a
n
o
n
p
ar
a
m
e
t
r
ic
s
tatis
tical
an
al
y
s
is
m
e
th
o
d
co
m
m
o
n
l
y
u
s
ed
to
d
eter
m
in
e
th
e
s
i
g
n
if
ica
n
t
r
e
latio
n
s
h
ip
b
et
w
ee
n
d
ataset
f
ea
tu
r
es
[
2
3
]
.
T
h
e
m
eth
o
d
o
l
o
g
y
o
f
m
ea
s
u
r
in
g
th
e
in
d
ep
en
d
e
n
ce
b
et
w
ee
n
q
u
alitativ
e
s
tati
s
tic
v
a
lu
e
s
b
ased
o
n
th
e
C
h
i
-
Sq
u
ar
e
test
d
ep
icted
in
th
e
f
o
llo
w
in
g
alg
o
r
ith
m
s
tep
s
.
C
h
i
-
s
q
u
ar
e
in
d
e
p
en
d
e
n
t te
s
t p
s
eu
d
o
co
d
e
:
1.
State
t
h
e
h
y
p
o
th
e
s
es
:
T
h
e
s
tatis
tical
test
f
o
r
i
n
d
ep
en
d
en
ce
ca
n
b
e
ap
p
lied
to
ca
teg
o
r
ical
v
ar
iab
les.
T
h
e
n
u
ll
h
y
p
o
th
e
s
is
s
tates
w
i
t
h
er
th
e
v
ar
iab
les
ar
e
in
d
ep
en
d
en
t.
T
h
e
alter
n
ativ
e
h
y
p
o
th
e
s
is
s
ta
tes
w
it
h
er
th
e
v
ar
iab
les ar
e
d
ep
en
d
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
P
r
o
jectio
n
p
u
r
s
u
it R
a
n
d
o
m
F
o
r
est u
s
in
g
d
is
crimin
a
n
t fe
a
tu
r
e
a
n
a
lysi
s
mo
d
el
.
.
.
(
A
.
Ma
h
d
i
N
a
s
er
)
1411
2.
Fo
r
m
u
la
te
an
al
y
s
is
p
la
n
:
T
h
e
an
al
y
s
i
s
s
tr
ate
g
y
d
escr
ib
es
h
o
w
to
u
s
e
s
a
m
p
le
s
o
f
d
ata
to
ac
ce
p
t
o
r
r
e
j
ec
t
th
e
n
u
ll
h
y
p
o
t
h
esi
s
.
3.
An
al
y
ze
s
a
m
p
le
d
ata
:
Us
in
g
d
ata
s
a
m
p
le,
f
i
n
d
th
e
d
e
g
r
ee
s
o
f
f
r
ee
d
o
m
,
e
x
p
ec
ted
f
r
eq
u
e
n
ci
es,
test
s
tatis
tic,
an
d
th
e
P
-
v
alu
e
a
s
s
o
ciate
d
w
it
h
th
e
s
tatis
tic
test
.
a.
T
h
e
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
(
DF)
ar
e
co
m
p
u
ted
an
d
eq
u
al
to
E
q
u
atio
n
1.
DF
=
(
r
−
1
)
∗
(
c
−
1
)
(
1
)
w
h
er
e
r
is
th
e
n
u
m
b
er
o
f
lev
e
l
s
f
o
r
o
n
e
ca
teg
o
r
ical
v
ar
iab
le,
an
d
c
is
th
e
n
u
m
b
er
o
f
lev
e
ls
f
o
r
th
e
o
th
er
ca
teg
o
r
ical
v
ar
iab
le.
b.
T
h
e
ex
p
ec
ted
f
r
eq
u
en
c
y
co
u
n
t
ca
n
b
e
co
m
p
u
ted
s
ep
ar
atel
y
f
o
r
ea
ch
lev
el
o
f
o
n
e
ca
teg
o
r
ic
al
v
ar
iab
le
at
ea
ch
lev
el
o
f
th
e
o
t
h
er
ca
teg
o
r
ical
v
ar
iab
le
as in
E
q
u
a
tio
n
2
.
E
r
,
c
=
nr
∗
nc
n
(
2
)
T
h
e
C
h
i
-
Sq
u
ar
e
r
an
d
o
m
te
s
t o
f
th
e
v
ar
iab
le
(
Χ
2
)
d
ef
in
ed
b
y
t
h
e
f
o
llo
w
i
n
g
E
q
u
atio
n
3
.
X
2
=
∑
[
(
O
r
,
c
−
E
r
,
c
)
2
/
E
r
,
c
]
(
3
)
w
h
er
e
Or
,
c
is
t
h
e
o
b
s
er
v
ed
f
r
e
q
u
en
c
y
co
u
n
t
at
le
v
el
r
o
f
v
ar
i
ab
le
A
a
n
d
lev
e
l
c
o
f
v
ar
iab
le
B
,
an
d
E
r
,
c
is
th
e
e
x
p
ec
ted
f
r
eq
u
e
n
c
y
co
u
n
t a
t le
v
e
l
r
o
f
v
ar
iab
le
A
an
d
l
ev
el
c
o
f
v
ar
iab
le
B
.
c.
T
h
e
P
-
v
alu
e
is
t
h
e
p
r
o
b
ab
ilit
y
o
f
o
b
s
er
v
i
n
g
a
s
tati
s
tic
s
a
m
p
le
as
ex
tr
e
m
e
as
t
h
e
test
s
tatis
tic.
Si
n
c
e
th
e
s
tatis
t
ic
test
is
a
C
h
i
-
Sq
u
ar
e,
th
e
d
is
tr
ib
u
tio
n
ca
lc
u
lato
r
to
ass
es
s
t
h
e
li
k
eli
h
o
o
d
r
elate
d
to
th
e
s
tat
is
tic
test
.
4.
I
n
ter
p
r
et
r
esu
lts
:
I
f
th
e
o
u
tp
u
t
s
a
m
p
les
ar
e
i
m
p
r
o
b
ab
le
m
ea
n
s
g
iv
e
n
t
h
e
n
u
ll
h
y
p
o
th
e
s
is
,
t
h
e
p
r
o
ce
d
u
r
e
r
e
j
ec
ts
th
e
n
u
ll
h
y
p
o
t
h
esi
s
.
T
y
p
icall
y
,
th
is
i
n
v
o
lv
e
s
co
m
p
ar
in
g
th
e
P
-
v
a
lu
e
to
t
h
e
co
n
s
eq
u
en
ce
le
v
e
l,
an
d
r
ej
ec
tin
g
th
e
n
u
ll
h
y
p
o
th
e
s
is
w
h
e
n
t
h
e
P
-
v
al
u
e
is
s
m
aller
t
h
a
n
t
h
e
s
i
g
n
i
f
ica
n
ce
le
v
el
[
2
4
]
.
T
ab
le
3
s
h
o
w
r
ep
r
ese
n
t
s
th
e
T
elec
o
m
d
ataset
s
af
ter
i
m
p
u
tatio
n
o
f
th
e
m
i
s
s
i
n
g
v
al
u
es
a
n
d
Featu
r
e
Selec
tio
n
.
T
ab
le
3
.
T
elec
o
m
d
atasets
a
f
te
r
ap
p
ly
P
P
M
an
d
ch
i
-
s
q
u
ar
e
D
a
t
a
se
t
s
O
r
i
g
i
n
a
l
D
a
t
a
se
t
s
D
a
t
a
se
t
s
/
c
h
i
-
s
q
u
a
r
e
t
e
st
#
O
b
se
r
v
a
t
i
o
n
s
#
F
e
a
t
u
r
e
s
#
O
b
se
r
v
a
t
i
o
n
s
#
F
e
a
t
u
r
e
s
L
a
r
o
se
Te
l
c
o
5
0
0
0
21
5
0
0
0
7
T
e
l
e
c
o
m1
1
2
4
9
9
20
1
2
4
9
9
18
C
e
l
l
2
c
e
l
l
Te
l
c
o
7
1
0
0
0
78
71
44
W
A
F
n
u
se
T
e
l
c
o
7
0
3
2
20
7
0
3
2
12
T
e
l
c
o
m2
T
e
l
c
o
5
0
0
0
0
1
6
3
5
0
0
0
0
1
3
6
S
o
u
t
h
A
si
a
n
T
e
l
c
o
2
0
0
0
14
2
0
0
0
10
2
.
4
.
P
r
o
j
ec
t
pu
rsu
it
ra
nd
o
m
f
o
re
s
t
(
P
P
F
o
re
s
t
)
A
R
a
n
d
o
m
Fo
r
est
is
a
n
E
n
s
e
m
b
le
-
lear
n
i
n
g
m
o
d
el
b
u
ilt
o
n
b
ag
g
i
n
g
m
u
ltip
le
o
b
liq
u
e
tr
ee
s
th
at
r
ep
r
esen
t
in
d
ep
en
d
en
t
d
ec
is
io
n
tr
ee
s
w
i
t
h
f
ea
t
u
r
e
s
elec
tio
n
a
n
d
g
en
er
a
te
th
e
r
esu
lt
o
f
clas
s
i
f
icatio
n
b
y
f
ee
d
in
g
t
h
e
in
p
u
t
to
th
ese
i
n
ter
n
al
tr
ee
s
a
n
d
co
llectin
g
th
e
ir
o
u
tco
m
e
s
b
ased
o
n
v
o
ti
n
g
tec
h
n
iq
u
e
[
1
6
]
.
Mo
s
t
o
f
th
e
a
v
ailab
le
tr
ad
itio
n
al
R
a
n
d
o
m
f
o
r
est
s
ar
e
v
u
l
n
er
ab
le
to
o
v
er
f
itti
n
g
i
n
s
o
m
e
T
elec
o
m
d
atasets
a
n
d
d
o
n
o
t
h
an
d
le
h
u
g
e
n
u
m
b
er
s
o
f
r
ed
u
n
d
an
t
f
ea
tu
r
es.
I
t
is
m
o
r
e
ef
f
i
cien
t
to
ch
o
o
s
e
a
r
an
d
o
m
d
ec
is
io
n
b
o
u
n
d
ar
y
t
h
an
u
s
i
n
g
th
e
a
v
ailab
le
tec
h
n
iq
u
es,
th
u
s
m
ak
i
n
g
lar
g
er
en
s
e
m
b
le
m
et
h
o
d
s
ar
e
m
o
r
e
ac
h
ie
v
ab
le.
A
lt
h
o
u
g
h
t
h
is
m
a
y
s
ee
m
to
b
e
a
b
en
ef
it
it
h
a
s
t
h
e
co
n
s
eq
u
en
ce
o
f
s
h
i
f
ti
n
g
t
h
e
co
m
p
u
tatio
n
co
m
p
lex
it
y
f
r
o
m
tr
ain
in
g
ti
m
e
to
ass
es
s
m
en
t
ti
m
e,
w
h
ich
is
ac
t
u
all
y
a
d
is
ad
v
an
ta
g
e
f
o
r
m
o
s
t
m
ac
h
in
e
lear
n
i
n
g
i
m
p
le
m
e
n
tat
io
n
[
2
5
]
.
T
h
e
m
o
s
t
av
ailab
le
r
an
d
o
m
f
o
r
est
ar
e
s
e
p
ar
ate
f
ea
tu
r
es
s
p
ac
e
b
y
h
y
p
e
r
p
lan
es
t
h
at
a
r
e
o
r
th
o
g
o
n
al
to
s
in
g
le
f
ea
t
u
r
e
ax
e
s
w
h
e
n
t
h
e
d
ata
ar
e
co
lli
n
ea
r
w
it
h
co
r
r
elate
d
f
ea
t
u
r
es,
h
y
p
er
p
la
n
es th
at
ar
e
o
b
liq
u
e
to
t
h
e
a
x
is
d
o
th
e
b
etter
clas
s
s
ep
ar
atio
n
.
T
r
ee
s
th
at
u
s
e
li
n
ea
r
co
m
b
in
a
tio
n
s
o
f
v
ar
iab
le
s
in
a
n
o
d
e
s
p
lit
ti
n
g
p
r
o
ce
d
u
r
e
th
at
in
cl
u
d
ed
in
th
e
r
an
d
o
m
co
ef
f
ic
ien
t
g
en
er
at
io
n
k
n
o
w
n
i
n
t
h
e
liter
atu
r
e
as
o
b
liq
u
e
tr
ee
s
[
2
6
]
.
P
P
Fo
r
est
in
v
o
l
v
es
s
tr
u
ct
u
r
ed
tr
ee
ap
p
r
o
ac
h
es
w
ith
p
r
o
j
ec
tio
n
p
u
r
s
u
it
i
n
d
ices,
f
o
r
d
i
m
en
s
io
n
alit
y
r
ed
u
ctio
n
,
th
e
y
d
ef
i
n
ed
h
y
p
e
r
p
lan
es
th
at
ar
e
o
b
liq
u
e
to
t
h
e
f
ea
t
u
r
e
ax
es
in
th
e
d
ec
is
i
o
n
tr
ee
th
at
tr
ain
ed
in
d
ep
en
d
en
tl
y
a
n
d
h
as
i
ts
u
n
iq
u
e
s
tr
u
ct
u
r
e
an
d
p
r
o
p
er
ties
.
I
n
o
th
er
w
o
r
d
s
,
P
P
tr
ee
o
p
ti
m
izes
a
p
r
o
j
ec
tio
n
p
u
r
s
u
i
t
in
d
ex
to
o
b
tain
a
lo
w
-
d
i
m
e
n
s
io
n
al
p
r
o
j
ec
tio
n
to
s
ep
ar
ate
class
es
an
d
it
s
clas
s
i
f
icati
o
n
p
r
o
b
lem
s
w
h
er
e
th
e
r
esp
o
n
s
e
v
ar
iab
le
is
ca
teg
o
r
ical
an
d
th
e
m
et
h
o
d
is
d
esc
r
ib
ed
t
o
u
s
e
q
u
an
titati
v
e
f
ea
t
u
r
e
v
ar
iab
les
[
1
3
]
.
A
t e
ac
h
s
p
lit,
a
r
an
d
o
m
s
a
m
p
l
e
o
f
p
r
ed
icto
r
s
ar
e
s
elec
ted
an
d
th
en
an
o
p
ti
m
al
p
r
o
j
ec
tio
n
p
u
r
s
u
it r
an
d
o
m
f
o
r
es
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
2
,
A
p
r
il 2
0
2
0
:
1
4
0
6
-
1421
1412
class
i
fi
ca
tio
n
ad
ap
ts
r
an
d
o
m
v
ar
iab
les
to
u
tili
ze
an
o
p
ti
m
al
li
n
ea
r
ass
o
ciatio
n
b
et
w
ee
n
v
ar
ia
b
l
es
in
s
tead
o
f
o
n
l
y
o
n
e
v
ar
iab
le
f
o
r
ea
ch
s
p
lit
i
n
t
h
e
co
n
s
tr
u
ctio
n
o
f
th
e
tr
ee
to
b
u
ild
th
e
P
P
tr
ee
,
th
is
o
r
d
er
m
ay
lead
to
a
d
iv
er
s
it
y
o
f
d
ec
is
io
n
tr
ac
k
s
to
ac
h
iev
e
th
e
f
i
n
al
f
o
r
est
p
r
ed
ictio
n
,
it
is
d
esire
d
to
u
n
d
er
s
tan
d
a
n
d
co
m
p
ar
e
all
d
ec
is
io
n
tr
ee
tr
ac
k
s
i
n
th
e
co
n
tex
t o
f
all
tr
ee
s
s
tr
u
ct
u
r
e
[
1
7
]
.
On
e
i
m
p
o
r
tan
t
d
is
tin
g
u
is
h
i
n
g
o
f
P
P
tr
ee
is
th
at
i
t
d
ea
ls
w
i
th
t
h
e
v
ar
iab
le
s
al
w
a
y
s
a
s
a
t
w
o
-
c
lass
s
y
s
te
m
w
h
e
n
th
e
cla
s
s
e
s
ar
e
m
o
r
e
th
a
n
t
w
o
th
e
m
ea
n
s
o
f
ea
c
h
clas
s
is
d
eter
m
i
n
ed
an
d
u
s
ed
to
m
ak
e
a
r
ed
u
ctio
n
to
t
w
o
g
r
o
u
p
s
o
n
l
y
b
y
u
s
i
n
g
t
h
e
d
is
ta
n
ce
s
b
et
w
ee
n
t
h
e
m
ea
n
s
o
f
cla
s
s
es.
Fo
r
ex
a
m
p
le,
i
f
w
e
h
a
v
e
f
iv
e
clas
s
es
a
n
d
t
h
eir
m
ea
n
s
o
f
th
e
p
r
o
j
ec
te
d
v
ar
iab
l
es
in
ea
ch
class
ar
e
2
.
1
,
2
.
3
,
2
.
5
,
3
.
5
,
an
d
3
.
7
,
th
e
class
es w
it
h
m
ea
n
2
.
1
,
2
.
3
,
an
d
2
.
5
ar
e
s
et
to
th
e
f
ir
s
t
g
r
o
u
p
an
d
th
e
cla
s
s
e
s
w
it
h
m
ea
n
3
.
5
an
d
3
.
7
ar
e
s
et
to
th
e
s
ec
o
n
d
g
r
o
u
p
.
A
ls
o
,
i
n
ea
c
h
n
o
d
e
o
f
th
e
P
P
tr
ee
,
th
e
p
r
o
j
ec
tio
n
co
ef
f
icie
n
ts
d
en
o
te
t
h
e
v
ar
iab
le
i
m
p
o
r
tan
ce
f
o
r
th
e
clas
s
s
p
litt
i
n
g
.
T
h
is
in
f
o
r
m
atio
n
is
v
er
y
s
u
p
p
o
r
tiv
e
to
s
elec
t
i
m
p
o
r
tan
t
v
ar
i
ab
les
b
y
P
P
tr
ee
.
P
P
Fo
r
est
o
u
tp
er
f
o
r
m
a
tr
ad
itio
n
al
r
an
d
o
m
f
o
r
est
w
h
e
n
s
p
litt
i
n
g
h
y
p
er
p
lan
e
b
et
w
ee
n
cla
s
s
e
s
o
cc
u
r
s
in
a
li
n
ea
r
an
d
r
an
d
o
m
l
y
co
m
b
i
n
atio
n
o
f
p
r
ed
icto
r
s
f
o
r
s
ep
ar
atin
g
t
h
e
cl
ass
es t
h
at
co
m
p
u
ted
b
y
s
ea
r
ch
es f
o
r
a
lo
w
d
i
m
e
n
s
io
n
al
p
r
o
j
e
ctio
n
p
u
r
s
u
it i
n
d
e
x
s
u
c
h
as
L
in
ea
r
Dis
cr
i
m
i
n
an
t
An
al
y
s
i
s
(
L
D
A
)
,
P
en
alize
d
L
i
n
ea
r
Dis
cr
i
m
i
n
a
n
t
(
P
DA
)
,
GI
NI
,
E
NT
R
OP
Y
an
d
Su
p
p
o
r
t Fac
to
r
Ma
ch
in
e
(
SV
M)
[
2
7
]
.
I
n
th
e
f
ir
s
t
s
tep
o
f
th
e
o
p
ti
m
iz
atio
n
p
r
o
b
lem
an
d
b
ased
o
n
th
e
class
in
f
o
r
m
atio
n
,
a
p
r
o
j
ec
ti
o
n
p
u
r
s
u
it
in
d
ex
is
u
s
ed
to
f
i
n
d
an
o
p
t
im
al
o
n
e
-
d
i
m
e
n
s
io
n
al
h
y
p
er
p
lan
e
f
o
r
s
ep
ar
atin
g
all
d
ata
an
d
p
r
o
j
ec
t
th
e
tr
ain
i
n
g
d
ata
in
to
th
e
p
r
o
j
ec
tio
n
lin
e.
T
h
en
,
u
s
i
n
g
t
h
e
p
r
o
j
ec
ted
d
ata
to
r
ed
ef
in
e
th
e
o
p
ti
m
izatio
n
m
eth
o
d
in
a
t
w
o
-
clas
s
p
r
o
b
lem
b
y
co
m
p
ar
in
g
t
h
e
m
e
an
o
f
clas
s
es,
a
n
d
as
s
ig
n
a
n
e
w
lab
el
to
ea
ch
o
b
s
e
r
v
atio
n
.
T
h
e
n
e
x
t
s
tep
is
to
f
i
n
d
an
o
p
t
i
m
al
o
n
e
-
d
i
m
e
n
s
io
n
al
p
r
o
j
ec
tio
n
to
s
ep
ar
ate
th
e
t
w
o
class
es
o
f
t
h
e
clas
s
i
f
icatio
n
p
r
o
b
lem
.
R
ep
ea
t
all
th
e
s
tep
s
u
n
til
ea
c
h
g
r
o
u
p
h
a
s
o
n
l
y
o
n
e
clas
s
f
r
o
m
t
h
e
o
r
ig
i
n
al
class
e
s
.
B
ased
o
n
th
e
s
e
s
tep
s
th
e
tr
ee
g
r
o
w
s
a
n
d
t
h
e
m
a
x
i
m
u
m
d
ep
t
h
o
f
ea
ch
tr
ee
in
th
e
f
o
r
est d
eter
m
i
n
ed
[
1
6
]
.
P
r
o
j
ec
tio
n
P
u
r
s
u
it R
a
n
d
o
m
Fo
r
est
P
s
eu
d
o
co
d
e:
1.
L
et
d
n
=
{(
x
i,
y
i)
}i=
1
N
,
b
e
th
e
tr
ain
in
g
d
ataset
w
h
er
e
x
i
is
a
p
-
d
i
m
e
n
s
io
n
al
v
ec
to
r
o
f
ex
p
la
n
ato
r
y
v
ar
iab
le
s
an
d
y
i
r
ep
r
esen
ts
cla
s
s
i
n
f
o
r
m
atio
n
w
it
h
i =
1
,
.
.
.
N.
2.
B
o
o
ts
tr
ap
s
am
p
le
s
:
s
a
m
p
le
s
o
f
s
ize
n
r
an
d
o
m
l
y
ta
k
i
n
g
f
r
o
m
t
h
e
o
r
ig
i
n
al
d
atase
t
w
it
h
r
ep
lac
e
m
en
t to
cr
ea
te
k
n
u
m
b
er
o
f
e
n
s
e
m
b
le
tr
ee
s
t
o
u
s
e
as
th
e
tr
ai
n
in
g
d
ataset
an
d
th
e
r
e
m
ai
n
i
n
g
s
a
m
p
le
s
r
eser
v
ed
as
a
test
d
ataset
f
o
r
ev
al
u
ati
n
g
o
f
th
e
p
r
o
p
o
s
ed
ch
u
r
n
p
r
ed
ictio
n
m
o
d
el.
3.
Gr
o
w
t
h
e
o
b
liq
u
e
tr
ee
(
P
P
tr
ee
)
:
f
o
r
ea
ch
b
o
o
ts
tr
ap
s
a
m
p
le
b
u
ild
t
h
e
o
b
liq
u
e
tr
ee
s
tr
u
ct
u
r
e
w
it
h
o
u
t
p
r
u
n
in
g
as d
etailed
b
elo
w
:
a.
Op
ti
m
ize
a
p
r
o
j
ec
tio
n
p
u
r
s
u
it
in
d
ex
to
ca
lc
u
late
an
o
p
ti
m
u
m
o
n
e
-
d
i
m
e
n
s
io
n
al
p
r
o
j
ec
tio
n
p
lan
e
α
u
s
i
n
g
L
D
A
o
r
SVM
f
o
r
s
p
litt
in
g
all
class
es i
n
t
h
e
cu
r
r
en
t b
o
o
ts
tr
ap
s
a
m
p
l
es a
n
d
y
ield
a
p
r
o
j
ec
te
d
d
ata
z
=α
x
.
b.
On
th
e
p
r
o
j
ec
ted
d
ata
z,
r
ep
e
ated
d
ec
r
ea
s
e
th
e
n
u
m
b
er
o
f
g
r
o
u
p
s
u
n
til
p
r
o
d
u
ce
t
w
o
clas
s
es
o
n
l
y
,
b
y
co
m
p
ar
i
n
g
t
h
e
m
ea
n
s
o
f
d
ata,
an
d
ass
i
g
n
a
n
e
w
lab
el
G1
o
r
G2
to
ea
ch
class
.
c.
On
th
e
p
r
o
j
ec
ted
d
ata
z
,
r
e
d
o
P
r
o
j
ec
t
p
u
r
s
u
it
w
it
h
th
e
s
e
n
e
w
class
lab
els
(
G1
,
G2
)
an
d
f
in
d
in
g
t
h
e
o
n
e
-
d
i
m
en
s
io
n
al
p
r
o
j
ec
tio
n
p
ath
α
*
a
n
d
ass
ig
n
a
n
e
w
g
r
o
u
p
la
b
el
G1
*
o
r
G2
*
to
ea
c
h
g
r
o
u
p
w
h
ic
h
ca
n
co
n
tain
m
o
r
e
th
a
n
o
n
e
o
r
ig
i
n
al
class
.
d.
Dete
r
m
i
n
e
t
h
e
d
ec
is
io
n
r
u
les
c
w
h
ic
h
is
t
h
e
b
est
s
ep
ar
at
io
n
o
f
G1
*
a
n
d
G2
*
a
n
d
k
ee
p
b
o
th
α
an
d
c
to
p
r
o
v
id
in
g
t
h
e
d
ec
is
io
n
b
o
u
n
d
ar
y
f
o
r
th
e
n
o
d
e.
e.
Sp
lit
d
ata
in
to
t
w
o
s
et
s
i
n
e
ac
h
n
o
d
e
i
n
t
h
e
tr
ee
t
h
e
n
,
u
s
in
g
t
h
e
n
e
w
g
r
o
u
p
lab
els
G
1
*
an
d
G2
*
.
I
f
α
∗
TM
1
<c
th
en
allo
ca
te
G1
*
to
th
e
lef
t
n
o
d
e
else
allo
ca
te
G
2
*
to
th
e
r
i
g
h
t n
o
d
e,
w
h
er
e
M
1
is
th
e
m
ea
n
o
f
G1
*
.
f.
Fo
r
ea
ch
g
r
o
u
p
,
s
to
p
if
th
er
e
is
o
n
l
y
o
n
e
c
lass
e
ls
e
r
ep
ea
t
s
t
h
e
p
r
o
ce
d
u
r
e,
th
e
s
p
litt
in
g
s
tep
iter
ated
u
n
ti
l
th
e
last
t
w
o
cla
s
s
es
s
ep
ar
ated
.
g.
On
e
clas
s
ass
ig
n
ed
o
n
l
y
to
o
n
e
f
in
a
l n
o
d
e;
th
e
d
ep
th
o
f
t
h
e
t
r
ee
is
at
m
o
s
t t
h
e
n
u
m
b
er
o
f
cl
ass
es.
4.
R
ep
ea
t step
3
f
o
r
k
=
1
…,
B
w
h
er
e
B
co
u
n
t th
e
tr
ee
i
n
t
h
e
f
o
r
est.
5.
P
r
o
d
u
ce
s
th
e
en
s
e
m
b
le
o
b
liq
u
e
tr
ee
s
,
b
ased
o
n
th
e
m
aj
o
r
ity
v
o
te
m
ec
h
an
i
s
m
to
p
r
ed
ict
th
e
class
f
o
r
tr
ain
i
n
g
d
ata.
6.
P
r
ed
ict
th
e
class
es o
f
ea
c
h
ca
s
e
n
o
t in
cl
u
d
ed
i
n
t
h
e
b
o
o
ts
tr
ap
s
a
m
p
le
an
d
co
m
p
u
te
m
is
s
-
c
la
s
s
i
f
icatio
n
er
r
o
r
an
d
s
y
s
te
m
ac
cu
r
ac
y
.
7.
T
h
e
p
r
o
j
ec
tio
n
co
ef
f
icien
t
s
u
s
ed
to
o
b
tain
th
e
d
i
m
en
s
io
n
r
ed
u
ctio
n
at
ea
c
h
n
o
d
e
u
s
ed
to
m
ea
s
u
r
e
th
e
v
ar
iab
le
i
m
p
o
r
tan
ce
.
8.
W
ea
k
tr
ee
r
em
o
v
er
(
clas
s
i
f
ier
)
:
T
o
en
h
an
ce
th
e
p
er
f
o
r
m
a
n
c
e
ac
cu
r
ac
y
o
f
th
e
P
P
Fo
r
est
alg
o
r
ith
m
an
d
to
i
m
p
r
o
v
e
t
h
e
g
e
n
er
aliza
tio
n
o
f
m
o
d
el,
b
atter
tr
ee
s
w
i
th
h
i
g
h
p
er
f
o
r
m
an
ce
s
elec
ted
b
ased
o
n
th
e
lo
w
er
o
u
t
o
f
b
ag
er
r
o
r
f
o
r
class
if
icatio
n
(
OOB
er
r
o
r
)
th
at
u
s
e
to
t
u
n
e
th
e
m
o
d
el
a
n
d
av
o
id
t
h
e
tr
ee
s
w
it
h
t
h
e
w
o
r
s
t
o
u
tco
m
e.
9.
D
eter
m
i
n
e
t
h
e
m
aj
o
r
ity
v
o
ti
n
g
tech
n
iq
u
e,
a
n
d
ev
al
u
ate
t
h
e
s
y
s
te
m
b
ased
o
n
th
e
s
elec
tio
n
o
f
g
o
o
d
o
b
liq
u
e
tr
ee
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
P
r
o
jectio
n
p
u
r
s
u
it R
a
n
d
o
m
F
o
r
est u
s
in
g
d
is
crimin
a
n
t fe
a
tu
r
e
a
n
a
lysi
s
mo
d
el
.
.
.
(
A
.
Ma
h
d
i
N
a
s
er
)
1413
2
.
5
.
Dis
cr
i
m
i
na
nt
f
un
ct
io
n a
na
ly
s
is
(
DF
A)
T
h
is
s
ec
tio
n
in
tr
o
d
u
ce
s
an
d
d
is
cu
s
s
es
s
o
m
e
asp
ec
ts
o
f
s
t
atis
tical
l
ea
r
n
i
n
g
p
h
ilo
s
o
p
h
y
co
n
ce
r
n
to
d
is
cr
i
m
i
n
an
t
SVM
a
n
d
L
D
A
.
I
t
is
a
s
tatis
tical
p
r
o
ce
d
u
r
e
u
s
e
d
to
s
o
lv
e
p
r
o
b
lem
s
as
s
o
ciate
d
w
it
h
t
h
e
s
tati
s
tical
s
ep
ar
atio
n
a
m
o
n
g
d
is
t
in
ct
c
lass
es
w
i
th
t
h
e
as
s
u
m
p
tio
n
th
at
t
h
e
s
a
m
p
le
i
s
n
o
r
m
a
ll
y
d
is
tr
ib
u
ted
f
o
r
th
e
attr
ib
u
te
s
a
lo
n
g
w
it
h
h
o
m
o
g
e
n
eo
u
s
v
ar
ia
n
ce
-
co
v
ar
ian
ce
m
atr
ices
[
2
8
]
.
T
h
e
lin
ea
r
m
o
d
el
s
ar
e
ea
s
y
to
u
n
d
er
s
ta
n
d
w
h
er
e
th
e
f
i
n
al
o
u
t
p
u
t
is
a
w
e
ig
h
ted
s
u
m
o
f
t
h
e
i
n
p
u
t
at
tr
ib
u
tes
‘
xi
’
.
T
h
e
m
a
g
n
itu
d
e
o
f
t
h
e
w
ei
g
h
t
‘
wi
’
s
h
o
w
s
t
h
e
i
m
p
o
r
tan
ce
o
f
in
p
u
t
a
n
d
its
s
ig
n
i
n
d
icate
s
i
f
th
e
ef
f
ec
t
i
s
p
o
s
itiv
e
o
r
n
e
g
ati
v
e.
Mo
s
t
f
u
n
ctio
n
s
ar
e
ad
d
itiv
e
in
th
at
t
h
e
o
u
tp
u
t
i
s
th
e
s
u
m
o
f
t
h
e
ef
f
ec
ts
o
f
s
e
v
e
r
al
attr
ib
u
tes
w
h
er
e
t
h
e
w
ei
g
h
t
s
m
a
y
b
e
en
f
o
r
ci
n
g
o
r
in
h
ib
iti
n
g
[
2
9
]
.
2
.
5
.
1
.
L
inea
r
di
s
cr
i
m
i
na
nt
a
na
ly
s
is
(
L
DA)
T
h
is
p
ap
er
in
tr
o
d
u
ce
s
th
e
o
b
l
iq
u
e
tr
ee
alg
o
r
ith
m
f
o
r
ch
u
r
n
er
class
if
ica
tio
n
t
h
at
ca
n
s
i
m
u
ltan
eo
u
s
l
y
s
h
r
i
n
k
t
h
e
tr
ee
s
ize,
s
o
l
v
e
th
e
p
r
o
b
lem
o
f
t
h
e
cu
r
s
e
o
f
d
i
m
e
n
s
i
o
n
alit
y
,
e
n
h
a
n
ce
clas
s
clas
s
i
f
ic
atio
n
,
an
d
i
m
p
r
o
v
ed
tr
ee
d
ata
an
d
s
tr
u
ct
u
r
e
v
i
s
u
a
liz
atio
n
.
T
h
is
ca
n
b
e
ac
h
iev
ed
b
y
p
r
ed
ictin
g
a
li
n
ea
r
d
is
cr
i
m
in
a
n
t
m
o
d
el
to
th
e
d
ata
in
ea
ch
n
o
d
e
o
n
th
e
tr
ee
u
s
in
g
th
e
d
is
cr
i
m
i
n
an
t
f
u
n
ctio
n
.
L
DA
i
s
a
k
in
d
o
f
Di
s
cr
i
m
i
n
a
n
t
Fu
n
ct
io
n
An
al
y
s
i
s
(
L
D
A
)
th
at
d
is
co
v
er
ies
li
n
ea
r
f
u
n
ct
io
n
s
o
f
th
e
as
s
o
ciate
d
v
ar
iab
les
th
at
lead
to
m
a
x
i
m
u
m
d
is
cr
i
m
in
a
tio
n
b
et
w
ee
n
th
e
g
r
o
u
p
ce
n
tr
o
id
s
[
3
0
]
.
L
D
A
is
a
s
i
m
p
le
an
d
m
a
th
e
m
atica
ll
y
r
o
b
u
s
t
tech
n
iq
u
e
f
r
eq
u
en
tl
y
u
s
ed
in
p
atter
n
r
ec
o
g
n
itio
n
ap
p
licati
o
n
s
as
a
d
im
e
n
s
io
n
r
ed
u
ctio
n
tech
n
iq
u
e,
o
b
j
ec
t
class
if
ic
atio
n
in
to
m
u
tu
al
l
y
ex
clu
s
i
v
e
a
n
d
ex
h
au
s
ti
v
e
g
r
o
u
p
s
a
n
d
m
a
x
i
m
ize
s
t
h
e
i
n
ter
-
clas
s
s
ca
tter
,
m
i
n
i
m
ize
s
t
h
e
in
tr
a
-
clas
s
s
ca
tter
co
n
cu
r
r
en
tl
y
a
n
d
d
is
co
v
er
ies a
p
p
r
o
p
r
iate
p
r
o
j
ec
t
p
u
r
s
u
it d
ir
ec
tio
n
s
f
o
r
class
i
f
icatio
n
p
r
o
b
le
m
[
3
1
]
.
T
h
r
ee
s
tep
s
n
ee
d
ed
to
p
e
r
f
o
r
m
t
h
e
L
D
A
ca
lcu
la
tio
n
.
T
h
e
f
i
r
s
t
s
ta
g
e
is
to
f
in
d
t
h
e
d
is
ta
n
ce
b
et
w
ee
n
th
e
m
ea
n
v
a
lu
e
s
o
f
d
i
f
f
er
en
t
cl
ass
es
w
h
ic
h
ar
e
ca
l
led
th
e
b
e
t
w
ee
n
-
clas
s
v
ar
ia
n
ce
(
SB
)
,
w
h
i
l
e
th
e
s
ec
o
n
d
s
tag
e
in
v
o
l
v
ed
th
e
ca
lcu
latio
n
o
f
th
e
d
is
tan
ce
b
et
w
ee
n
t
h
e
m
ea
n
an
d
th
e
s
am
p
le
s
o
f
ea
ch
class
w
h
ich
is
lik
el
y
k
n
o
w
n
as
w
it
h
in
-
cla
s
s
v
ar
ian
ce
(
SW
)
.
T
h
e
th
ir
d
o
n
e
is
to
cr
ea
te
th
e
lo
w
er
-
d
i
m
e
n
s
io
n
a
l
s
p
ac
e
w
h
ic
h
m
a
x
i
m
ize
s
th
e
b
et
w
ee
n
-
clas
s
v
ar
ian
c
e
an
d
m
i
n
i
m
izes
t
h
e
w
i
th
i
n
-
clas
s
v
ar
ian
ce
[
3
2
]
.
T
o
ac
h
iev
e
th
e
m
ai
n
g
o
al
o
f
th
es
e
s
tep
s
,
L
D
A
attr
ac
ti
v
e
p
r
o
ce
d
u
r
e
th
at
m
a
k
es
cla
s
s
a
s
s
i
g
n
m
en
ts
b
y
f
o
r
m
a
ti
v
e
t
h
e
li
n
ea
r
tr
an
s
f
o
r
m
atio
n
o
f
th
e
d
ata
in
f
ea
t
u
r
e
s
p
ac
e
th
at
m
ax
i
m
izes
t
h
e
r
atio
o
f
th
e
b
etw
ee
n
-
clas
s
v
ar
ian
ce
to
m
in
i
m
ize
th
e
w
ith
in
-
cla
s
s
v
ar
ian
ce
.
I
n
th
e
t
w
o
-
clas
s
v
ar
i
ab
le,
th
e
m
a
x
i
m
u
m
cla
s
s
s
p
lit
t
in
g
o
cc
u
r
s
w
h
e
n
th
e
v
ec
to
r
o
f
q
u
an
tit
ies,
‘
w
’
,
an
d
in
ter
ce
p
t
w
it
h
‘
y
’
v
ec
to
r
b
,
u
s
ed
to
ex
p
r
ess
t
h
e
lin
ea
r
tr
an
s
f
o
r
m
at
io
n
a
s
i
n
E
q
u
at
io
n
4
.
T
h
e
class
e
s
ar
e
w
ell
-
s
ep
ar
atio
n
,
w
h
ic
h
i
m
p
lie
s
t
h
at
af
ter
t
h
e
o
r
ig
i
n
al
d
ata
ar
e
p
r
o
j
e
cted
th
e
d
is
ta
n
ce
b
et
w
ee
n
t
h
e
t
w
o
m
ea
n
s
i
s
lar
g
e,
an
d
th
e
d
is
ta
n
ce
o
f
i
n
s
ta
n
ce
s
a
r
o
u
n
d
ea
ch
m
ea
n
i
s
s
m
all
[
3
3
]
.
=
Σ
−
1
(
−
)
=
−
0
.
5
∗
(
+
)
)
Σ
−
1
(
−
)
+
l
og
(
)
(
4
)
w
h
er
e
Σ
-
1
is
a
v
ar
ia
n
ce
-
co
v
a
r
ian
ce
Ma
tr
ix
,
an
d
µ
r
ep
r
esen
ts
t
h
e
m
ea
n
v
ec
to
r
o
f
class
k
.
k
is
t
h
e
p
r
io
r
p
r
o
b
a
b
ilit
y
o
f
th
e
k
t
h
clas
s
.
T
o
f
in
d
th
e
b
et
w
ee
n
-
cla
s
s
e
s
v
ar
ian
ce
(
SB
)
,
th
e
s
ep
ar
atio
n
d
is
tan
ce
b
et
w
ee
n
d
if
f
er
e
n
t c
las
s
es t
h
at
d
en
o
ted
b
y
(
−
)
w
i
ll c
a
lcu
la
te
as in
E
q
u
ati
o
n
5
.
(
−
)
2
=
(
−
)
(
−
)
(
5
)
w
h
er
e
=
(
−
)
(
−
)
r
ep
r
esen
t
th
e
s
ep
ar
ati
o
n
d
is
tan
ce
b
et
w
ee
n
th
e
m
ea
n
o
f
th
e
i
th
cla
s
s
an
d
th
e
en
tire
m
ea
n
μ
.
T
h
en
,
th
e
to
tal
b
etw
ee
n
-
clas
s
m
atr
i
x
is
ca
lcu
lated
b
y
ad
d
in
g
all
th
e
b
etw
ee
n
-
clas
s
m
atr
ice
s
o
f
all
class
e
s
SB
i.
T
h
e
to
tal
w
i
th
i
n
-
c
lass
m
atr
ice
s
(
S
w
)
ar
e
ca
lcu
lated
as i
n
E
q
u
atio
n
6
.
S
w
=
∑
S
k
N
k
=
1
S
k
=
∑
(
x
ki
−
x
̅
k
)
(
x
ki
−
x
̅
k
)
T
N
k
i
=
1
(
6
)
I
n
th
e
ab
o
v
e
eq
u
atio
n
s
,
x
k
i
a
n
d
̅
d
en
o
te
t
h
e
it
h
tr
ai
n
i
n
g
s
a
m
p
le
o
f
cla
s
s
k
a
n
d
t
h
e
co
r
r
esp
o
n
d
in
g
class
m
ea
n
s
,
r
esp
ec
ti
v
el
y
.
Af
ter
f
i
n
d
in
g
t
h
e
b
et
w
ee
n
-
clas
s
v
ar
ian
ce
(
SB
)
an
d
w
it
h
i
n
-
cl
ass
v
ar
ian
ce
(
SW
)
,
th
e
in
d
e
x
m
a
tr
ix
(
W
ld
a)
o
f
th
e
L
D
A
tec
h
n
iq
u
e
ca
n
b
e
ca
lc
u
l
ated
as in
eq
u
atio
n
7
.
=
|
|
|
|
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
2
,
A
p
r
il 2
0
2
0
:
1
4
0
6
-
1421
1414
T
h
e
s
o
lu
tio
n
o
f
t
h
i
s
eq
u
atio
n
ca
n
b
e
ca
lcu
lated
b
y
f
i
n
d
in
g
t
h
e
ei
g
en
v
ec
to
r
s
a
n
d
t
h
e
ei
g
en
v
alu
e
s
o
f
=
−
1
.
T
h
e
eig
en
v
a
lu
e
s
ar
e
s
ca
lar
v
alu
e
s
th
at
p
r
o
v
id
e
in
f
o
r
m
ati
o
n
ab
o
u
t
th
e
L
D
A
s
p
ac
e
w
h
ile
th
e
eig
e
n
v
ec
to
r
s
r
ep
r
esen
t
th
e
d
ir
ec
tio
n
s
o
f
th
e
n
e
w
s
p
ac
e
[
3
4
]
.
T
h
e
r
o
b
u
s
tn
e
s
s
o
f
th
e
ei
g
en
v
ec
to
r
s
r
ef
lect
s
th
e
ab
ilit
y
to
d
is
cr
i
m
in
a
n
t
b
et
w
ee
n
d
if
f
er
en
t
cla
s
s
e
s
.
T
h
e
p
r
o
j
ec
tio
n
p
u
r
s
u
it
alg
o
r
it
h
m
s
ea
r
ch
es
f
o
r
a
lo
w
d
i
m
en
s
io
n
al
p
r
o
j
ec
tio
n
th
at
o
p
ti
m
izes
th
e
L
D
A
.
T
h
e
ei
g
en
v
ec
to
r
s
w
it
h
th
e
k
h
i
g
h
est
e
i
g
en
v
al
u
es
u
s
ed
to
co
n
s
tr
u
ct
t
h
e
lo
w
er
-
d
i
m
en
s
io
n
al
s
p
ac
e
o
f
L
D
A
w
h
ile
t
h
e
r
est
ar
e
n
eg
li
g
ib
le.
T
h
e
p
r
o
j
e
ctio
n
p
u
r
s
u
it
in
d
e
x
is
an
ess
en
tial
in
a
p
r
o
j
ec
tio
n
p
u
r
s
u
i
t
L
D
A
b
ec
au
s
e
it
lead
s
to
ac
h
iev
e
th
e
p
u
r
p
o
s
e
o
f
th
e
m
et
h
o
d
th
r
o
u
g
h
its
o
p
ti
m
izatio
n
.
T
h
e
b
asic
i
n
p
r
o
j
ec
tio
n
p
u
r
s
u
it
is
to
f
in
d
w
h
at
p
r
o
j
ec
tio
n
s
p
u
r
s
u
it
is
in
ter
esti
n
g
[
3
5
]
.
T
h
e
d
is
tin
ct
b
en
ef
it
o
f
th
e
p
r
o
j
ec
tio
n
p
u
r
s
u
it
w
a
y
o
v
er
m
e
th
o
d
s
ca
n
av
o
id
th
e
cu
r
s
e
o
f
d
i
m
en
s
io
n
al
it
y
b
y
f
o
cu
s
in
g
o
n
t
h
e
lo
w
d
i
m
e
n
s
io
n
al
p
r
o
j
ec
tio
n
s
an
d
ca
n
ig
n
o
r
e
th
e
r
ed
u
n
d
a
n
t f
ea
t
u
r
es.
2
.
5
.
2
.
Dis
cr
i
m
ina
nt
SVM
f
ra
m
ew
o
r
k
R
ec
en
t
l
y
,
m
a
n
y
r
esear
c
h
er
s
f
a
v
o
r
ed
u
s
in
g
SVM
as
a
s
u
p
er
v
is
ed
m
ac
h
i
n
e
lear
n
i
n
g
alg
o
r
it
h
m
.
I
t
h
as
b
ee
n
o
b
tain
ed
w
ell
r
ep
u
tat
io
n
i
n
t
h
e
d
ata
m
in
i
n
g
m
eth
o
d
o
lo
g
i
es
d
u
e
to
it
s
p
r
o
m
is
i
n
g
ex
p
er
i
m
en
tal
p
er
f
o
r
m
a
n
ce
,
r
ea
s
o
n
ab
le
m
e
m
o
r
y
,
an
d
ti
m
e
co
m
p
lex
it
y
w
it
h
its
s
tr
o
n
g
m
at
h
e
m
atic
al
b
asis
s
i
g
n
if
y
in
g
th
a
t
SVM
b
e
a
co
m
p
etiti
v
e
class
i
f
ier
[
3
6
]
.
SVM
r
eg
ar
d
ed
as
o
n
e
o
f
th
e
m
o
s
t
in
f
l
u
e
n
tial
m
ac
h
i
n
e
lear
n
in
g
alg
o
r
it
h
m
s
th
at
ca
n
b
e
ap
p
lied
in
lar
g
e
d
o
m
ain
s
o
f
r
ea
l
-
w
o
r
ld
ap
p
licatio
n
s
a
n
d
p
r
o
d
u
ce
m
a
n
y
b
e
n
ef
i
ts
o
v
er
tr
ad
itio
n
al
class
i
f
icatio
n
an
d
r
eg
r
e
s
s
io
n
t
ec
h
n
iq
u
es.
O
n
e
o
f
t
h
e
g
r
ea
tes
t
s
ig
n
i
f
ica
n
t
r
e
w
ar
d
s
is
t
h
e
s
o
lu
tio
n
o
f
p
r
o
b
le
m
s
r
elate
s
to
a
s
m
all
s
u
b
s
et
o
f
th
e
o
r
ig
i
n
al
d
ataset,
w
h
ic
h
m
a
k
e
SVM
a
s
p
o
w
er
f
u
l
c
o
m
p
u
tatio
n
,
r
o
b
u
s
t
m
at
h
e
m
a
tical
co
n
te
x
t
u
al,
b
etter
g
en
er
aliza
tio
n
s
k
ill co
r
r
esp
o
n
d
in
g
to
o
th
er
class
if
ica
tio
n
m
eth
o
d
s
[
3
7
]
.
On
e
r
e
m
ar
k
ab
le
c
h
ar
ac
ter
ize
o
f
SVM
an
d
o
t
h
er
k
er
n
el
-
b
ase
d
co
m
p
u
tatio
n
al
m
et
h
o
d
s
w
o
r
k
i
n
m
u
lti
-
d
i
m
en
s
io
n
al
w
it
h
o
u
t
s
ig
n
i
f
ica
n
t
co
m
p
u
ta
tio
n
co
s
t
an
d
f
ea
t
u
r
e
s
elec
tio
n
m
et
h
o
d
s
,
its
r
o
b
u
s
t
n
es
s
ag
ai
n
s
t
t
h
e
er
r
o
r
o
f
m
o
d
els
a
n
d
h
a
s
t
h
e
ab
il
it
y
to
lear
n
w
ell
w
i
th
o
n
l
y
a
v
er
y
s
m
a
l
l
n
u
m
b
er
o
f
f
ea
tu
r
es.
Ho
w
e
v
er
,
th
e
m
a
in
w
ea
k
n
e
s
s
o
f
SVM
t
h
at
ar
is
es
f
r
o
m
it
i
s
th
e
tr
ai
n
i
n
g
p
h
ase
is
co
m
p
u
tat
io
n
a
ll
y
e
x
p
e
n
s
i
v
e
d
u
e
to
a
g
o
o
d
esti
m
atio
n
o
f
it
is
co
n
s
tan
t
p
a
r
a
m
eter
s
s
u
ch
as
g
a
m
m
a,
s
i
g
m
a,
an
d
d
eg
r
ee
.
Mo
r
eo
v
er
,
it
is
h
i
g
h
l
y
r
elian
t
on
th
e
s
ize
o
f
th
e
o
r
ig
in
al
d
ataset
t
[
3
8
]
.
T
h
is
lin
ea
r
class
i
f
ier
is
also
k
n
o
w
n
as
an
o
p
ti
m
al
h
y
p
er
p
la
n
e,
t
h
e
f
ea
t
u
r
es
ar
e
n
o
r
m
all
y
n
o
r
m
alize
d
to
g
en
er
all
y
lie
b
et
w
e
en
-
1
an
d
1
s
o
th
at
th
e
s
a
m
p
les
ca
n
b
e
d
iv
id
ed
in
to
t
w
o
d
is
t
in
ct
cla
s
s
e
s
.
Dis
cr
i
m
i
n
an
t
f
u
n
ctio
n
s
ca
lcu
lated
b
y
SVM
ar
e
ef
f
icie
n
t
w
a
y
s
f
o
r
p
r
o
j
ec
tin
g
o
f
m
u
lti
-
d
i
m
en
s
io
n
al
d
ata
in
a
d
ir
ec
tio
n
p
er
p
en
d
icu
lar
to
th
e
d
is
cr
i
m
in
ati
n
g
h
y
p
er
p
lan
e.
T
h
en
,
th
e
p
r
o
j
ec
ted
d
ata
f
itted
to
esti
m
at
e
an
d
d
is
p
la
y
t
h
e
p
o
s
ter
io
r
p
r
o
b
ab
ilit
y
d
en
s
it
ies
an
d
en
h
a
n
ce
m
en
t
t
h
e
class
if
i
ca
tio
n
ac
cu
r
ac
y
o
f
d
is
cr
i
m
i
n
an
t f
u
n
ctio
n
[
3
9
]
.
T
h
e
b
asic id
ea
o
f
clas
s
if
icatio
n
i
s
to
tr
y
to
s
ep
ar
ate
d
if
f
er
en
t
s
a
m
p
les i
n
to
d
if
f
er
e
n
t
class
es,
f
o
r
b
in
ar
y
clas
s
i
f
icatio
n
t
h
e
p
r
ed
ictio
n
o
f
li
n
ea
r
h
y
p
e
r
p
lan
e
d
escr
ib
ed
as in
E
q
u
atio
n
8
.
f
(
x
)
=
w
T
.
x
+
b
=
0
)
(
8
)
w
h
er
e
w
a
n
d
b
ar
e
th
e
w
ei
g
h
t
v
ec
to
r
an
d
a
co
n
s
tan
t
r
esp
ec
t
iv
el
y
,
w
h
ic
h
h
a
v
e
esti
m
ated
f
r
o
m
t
h
e
d
ataset
in
n
-
d
i
m
e
n
s
io
n
s
p
ac
e,
.
is
th
e
i
n
te
r
n
al
p
r
o
d
u
ct
o
f
w
∈
R
n
an
d
x
∈
R
n
v
ec
to
r
s
[
4
0
]
.
T
h
e
d
ataset
ca
n
b
e
s
ep
ar
ated
g
eo
m
etr
icall
y
b
y
a
h
y
p
er
p
lan
e
.
I
t
s
h
o
u
ld
b
u
ild
tw
o
h
y
p
er
p
la
n
es
s
o
th
at
th
e
h
y
p
er
p
la
n
es
ar
e
as
f
ar
aw
a
y
as
p
o
s
s
ib
le,
an
d
n
o
s
a
m
p
les
s
h
o
u
ld
b
e
b
et
w
ee
n
th
ese
t
w
o
p
lan
e
s
th
i
s
ar
r
an
g
e
m
en
t
m
at
h
e
m
atica
ll
y
r
ep
r
esen
ted
b
y
E
q
u
atio
n
9
.
w
T
.
x
+
b
≥
+
1
w
T
.
x
+
b
≤
−
1
(
9
)
Fro
m
th
i
s
eq
u
atio
n
,
it
i
s
s
tr
aig
h
t
f
o
r
w
ar
d
to
co
n
f
ir
m
t
h
at
t
h
e
n
o
r
m
al
d
is
tan
ce
b
et
w
ee
n
t
h
ese
t
w
o
h
y
p
er
p
lan
es
(
d
)
is
th
e
r
ev
er
s
e
r
elatio
n
s
h
ip
to
t
h
e
n
o
r
m
|
|
w
|
|
v
ia
E
q
u
atio
n
1
0
.
d
=
2
‖
w
‖
(
1
0
)
T
h
e
h
y
p
er
p
lan
e
ca
n
m
at
h
e
m
a
t
icall
y
r
ep
r
esen
t b
y
u
s
in
g
(
11
)
.
f
(
x
)
=
s
gn
(
w
T
.
x
+
b
)
=
s
gn
(
(
∑
α
i
n
i
=
0
y
i
x
i
)
.
x
+
b
)
(
1
1
)
W
h
er
e:
s
ig
n
(
)
is
k
n
o
w
n
as
a
s
ig
n
f
u
n
ctio
n
,
α
i
ar
e
n
o
n
-
n
e
g
ati
v
e
L
a
g
r
an
g
e
co
ef
f
icie
n
t
s
ca
lcu
lated
b
y
r
eso
lv
in
g
a
q
u
ad
r
atic
o
p
tim
iza
tio
n
f
u
n
ct
io
n
b
ased
o
n
lin
ea
r
an
d
in
eq
u
i
t
y
co
n
s
tr
ai
n
ts
.
T
h
e
tr
ain
in
g
o
b
s
er
v
atio
n
s
‘
xi
’
w
it
h
n
o
n
-
ze
r
o
α
i
f
i
n
d
s
o
n
t
h
e
f
r
o
n
tier
o
f
th
e
m
ar
g
in
ca
lled
s
u
p
p
o
r
t
v
ec
to
r
s
(
SV)
.
T
h
e
tr
an
s
f
o
r
m
at
io
n
s
h
o
u
ld
b
e
ch
o
s
en
i
n
a
c
o
n
f
id
en
t
w
a
y
s
o
th
at
th
eir
d
o
t p
r
o
d
u
ct
lead
s
to
a
k
er
n
el
-
s
t
y
le
f
u
n
ct
io
n
[
4
1
]
.
T
h
e
k
er
n
el
f
u
n
ctio
n
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
P
r
o
jectio
n
p
u
r
s
u
it R
a
n
d
o
m
F
o
r
est u
s
in
g
d
is
crimin
a
n
t fe
a
tu
r
e
a
n
a
lysi
s
mo
d
el
.
.
.
(
A
.
Ma
h
d
i
N
a
s
er
)
1415
to
u
s
e
k
(
xi
,
xj
)
s
u
c
h
t
h
at
it
s
d
is
cr
etiza
t
io
n
Ki
j
=
k
(
xi
,
xj
)
is
a
p
o
s
itiv
e
ce
r
tai
n
m
atr
i
x
.
T
h
e
d
ec
is
io
n
p
r
ed
ictio
n
ca
n
th
e
n
r
ep
r
esen
t a
s
i
n
1
2
.
f
(
x
)
=
s
gn
(
∑
α
i
n
i
=
0
y
i
k
(
i
,
j
)
+
b
)
(
1
2
)
L
D
A
A
s
s
u
m
e
s
th
at
d
ata
ar
e
n
o
r
m
al
l
y
d
is
tr
ib
u
ted
,
all
class
es
id
en
ticall
y
Ga
u
s
s
ian
d
is
tr
ib
u
t
ed
,
in
ca
s
e,
th
e
clas
s
es
h
av
e
d
i
f
f
er
e
n
t
co
v
ar
i
an
ce
m
atr
ices
t
h
e
n
L
D
A
b
ec
o
m
es
q
u
ad
r
a
tic
an
d
n
o
t
lin
ea
r
d
is
cr
i
m
in
a
n
t
an
al
y
s
is
[
4
2
]
.
Ho
w
e
v
er
,
SV
M
ass
u
m
e
s
t
h
at
all
c
lass
e
s
ar
e
v
e
r
y
s
ep
ar
ab
le;
it
m
ak
e
s
u
s
e
o
f
a
s
lack
v
ar
iab
le
t
h
at
p
er
m
i
ts
a
ce
r
tain
a
m
o
u
n
t
o
f
o
v
er
lap
b
et
w
ee
n
t
h
e
class
es.
S
VM
is
a
p
r
ec
is
e
f
lex
ib
le
p
r
ed
ictio
n
m
et
h
o
d
th
at
m
ak
e
s
n
o
ex
p
ec
tat
io
n
s
ab
o
u
t
t
h
e
in
p
u
t
d
atasets
at
all.
T
h
e
f
l
ex
ib
ilit
y
,
o
n
th
e
o
t
h
er
h
an
d
,
was
f
r
eq
u
e
n
tl
y
g
i
v
e
n
it
m
o
r
e
d
if
f
icu
lt
to
u
n
d
er
s
tan
d
th
e
o
u
tco
m
es
f
r
o
m
an
SVM
class
i
f
ier
,
as
co
m
p
ar
ed
to
L
DA
.
Mo
r
eo
v
er
,
L
DA
m
ak
e
s
u
s
e
o
f
th
e
co
m
p
lete
i
n
p
u
t
d
ataset
to
ap
p
r
o
x
im
atio
n
co
v
ar
ian
ce
m
a
tr
ices
th
a
t
ar
e
s
o
m
e
w
h
at
p
r
o
n
e
to
o
u
tlier
s
.
W
h
i
le
SVM
o
p
ti
m
iza
tio
n
f
u
n
ctio
n
s
o
v
er
a
s
u
b
s
e
t
o
f
th
e
d
ata
t
h
at
lo
ca
te
o
n
th
e
s
ep
ar
atin
g
m
ar
g
i
n
[
4
3
]
.
3.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
R
o
b
u
s
t
p
r
ac
tical
s
etu
p
an
d
u
s
e
o
f
s
tatis
tical
test
s
an
d
ap
p
r
o
p
r
iate
p
er
f
o
r
m
a
n
ce
m
ea
s
u
r
es
ar
e
ess
en
tia
l
to
f
ig
u
r
i
n
g
a
co
r
r
ec
t
co
n
cl
u
s
i
o
n
.
T
h
e
t
elec
o
m
in
d
u
s
tr
y
r
e
f
lects
d
if
f
er
en
t
t
y
p
es
o
f
m
ea
s
u
r
e
m
e
n
ts
to
ass
es
s
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
ch
u
r
n
p
r
ed
ictio
n
m
o
d
el.
3
.
1
.
Acc
ura
cy
C
o
u
n
t
t
h
e
co
r
r
ec
t
p
r
ed
ictio
n
s
ac
co
m
p
lis
h
ed
b
y
t
h
e
p
r
ed
ictio
n
m
o
d
el
o
v
er
a
ll
k
in
d
s
o
f
p
r
ed
ictio
n
s
m
ad
e.
Ov
er
all,
h
o
w
o
f
ten
t
h
e
class
i
f
ier
m
o
d
el
is
co
r
r
ec
t
A
c
c
=
TP
+
TN
TP
+
TN
+
FP
+
FN
(
1
3
)
3
.
2
.
P
re
cisi
o
n (
Co
nfidence
)
T
h
e
n
u
m
b
er
o
f
p
o
s
iti
v
e
ca
s
e
s
t
h
at
co
r
r
ec
tl
y
r
ec
o
g
n
ized
.
Pr
e
c
ision
=
TP
TP
+
FP
(
1
4
)
3
.
3
.
Sens
it
iv
it
y
(
Rec
a
ll)
T
h
e
am
o
u
n
t o
f
ac
tu
al
p
o
s
iti
v
e
ca
s
es th
a
t c
o
r
r
ec
tl
y
r
ec
o
g
n
ize
d
.
Se
n
s
itivit
y
=
TP
TP
+
TN
+
FP
+
FN
(
1
5
)
3
.
4
.
Sp
ec
if
icit
y
T
h
e
am
o
u
n
t o
f
ac
tu
al
n
e
g
ati
v
e
ca
s
es th
at
co
r
r
ec
tl
y
r
ec
o
g
n
ize
d
.
Sp
e
c
ifi
c
ity
=
FP
FP
+
TN
(
1
6
)
3
.
5
.
P
re
v
a
lence
Ho
w
o
f
te
n
d
o
es th
e
p
o
s
iti
v
e
c
o
n
d
itio
n
o
cc
u
r
in
t
h
e
s
a
m
p
le
.
Pr
e
va
l
e
n
c
e
=
TP
+
FN
TP
+
TN
+
FP
+
FN
(
1
7
)
3
.
6
.
E
rr
o
r
r
a
t
e
(
E
R)
T
h
e
n
u
m
b
er
o
f
all
n
eg
ati
v
e
p
r
ed
ictio
n
s
d
iv
id
ed
b
y
th
e
to
tal
n
u
m
b
er
o
f
s
a
m
p
le
s
,
h
o
w
m
u
c
h
i
s
th
e
in
ac
c
u
r
ate
p
r
ed
ictio
n
o
r
m
i
s
class
if
ica
tio
n
o
n
t
h
e
p
r
ed
ictiv
e
m
eth
o
d
ER
=
FP
+
FN
TP
+
TN
+
FP
+
FN
(
1
8
)
3
.
7
.
F
-
Sco
r
e
P
r
ec
is
io
n
is
in
v
al
u
ab
le
f
o
r
ass
ess
i
n
g
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
d
ata
m
i
n
i
n
g
class
i
f
ier
s
,
b
u
t
it
s
u
r
el
y
leav
es
o
u
t
s
o
m
e
f
ac
ts
an
d
f
o
r
th
at
r
ea
s
o
n
w
ill
also
b
e
co
m
p
licate
d
.
T
h
e
R
ec
all
is
a
p
o
r
tio
n
o
f
th
e
tr
u
e
o
p
ti
m
i
s
tic
p
r
ed
ictio
n
s
to
to
tal
p
o
s
itiv
e
o
b
s
er
v
atio
n
s
in
th
e
d
ataset.
C
o
m
p
u
te
t
h
e
p
er
ce
n
t
o
f
ch
u
r
n
r
ate
th
at
ap
p
r
o
p
r
iatel
y
Evaluation Warning : The document was created with Spire.PDF for Python.