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s
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ar
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cities
to
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p
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s
[
1
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–
[
8
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an
d
m
a
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y
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s
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to
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s
[
9
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.
W
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I
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&
C
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g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
9
9
-
1
1
0
8
1100
Ma
in
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1
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1
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et
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1
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p
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Ab
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aljab
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co
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in
ed
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ese
ap
p
r
o
ac
h
es
p
r
im
ar
ily
em
p
lo
y
ed
PC
A/KNN
w
ith
E
u
clid
ea
n
d
is
tan
ce
an
d
d
id
n
o
t
ex
p
lo
r
e
th
e
ef
f
icien
c
y
o
f
o
th
er
d
is
tan
ce
s
s
u
ch
as
Ma
n
h
attan
,
Min
k
o
wsk
i
,
C
h
eb
y
s
h
ev
,
co
s
in
e
s
im
ilar
ity
,
h
a
m
m
in
g
,
J
ac
ca
r
d
s
im
ilar
ity
,
an
d
co
r
r
elatio
n
-
b
ased
d
is
tan
ce
s
.
E
ac
h
o
f
t
h
ese
m
etr
ics
h
as
its
s
tr
en
g
th
s
an
d
m
a
y
b
e
m
o
r
e
s
u
itab
le
f
o
r
s
p
ec
if
ic
d
ata
ty
p
es o
r
p
atter
n
s
with
in
I
o
T
n
etwo
r
k
s
.
Few
o
th
er
s
tu
d
ies
h
av
e
em
p
lo
y
ed
th
e
n
o
n
-
lin
ea
r
v
er
s
io
n
o
f
PC
A,
n
am
ely
k
er
n
el
PC
A
(
KPC
A)
,
to
im
p
r
o
v
e
I
DS
p
er
f
o
r
m
a
n
ce
in
I
o
T
en
v
ir
o
n
m
en
ts
.
Fo
r
ex
am
p
le,
th
e
s
tu
d
y
[
2
1
]
co
m
b
i
n
ed
KPC
A
f
o
r
f
ea
tu
r
e
ex
tr
ac
tio
n
an
d
C
NN
f
o
r
attac
k
r
ec
o
g
n
itio
n
a
n
d
class
if
icatio
n
,
d
em
o
n
s
tr
atin
g
th
e
ef
f
ec
tiv
en
ess
o
f
th
is
ap
p
r
o
ac
h
u
s
in
g
b
en
c
h
-
m
ar
k
d
atasets
.
Similar
ly
,
Yan
g
et
a
l.
[
2
2
]
p
r
o
p
o
s
ed
a
f
ea
tu
r
e
en
g
in
ee
r
in
g
m
o
d
el
in
co
r
p
o
r
atin
g
KPC
A,
an
d
t
h
e
wo
r
k
[
2
3
]
u
tili
ze
d
KPC
A
f
o
r
f
ea
tu
r
e
e
x
tr
ac
tio
n
f
r
o
m
b
io
m
etr
ic
d
ata
in
I
o
T
-
b
ased
s
m
ar
t
b
u
il
d
in
g
s
.
Ho
wev
er
,
m
o
s
t
KPC
A
im
p
lem
en
tatio
n
s
p
r
ed
o
m
in
an
tly
u
tili
ze
th
e
r
a
d
ial
b
asis
f
u
n
ctio
n
(
R
B
F)
k
er
n
el,
with
o
u
t
th
o
r
o
u
g
h
ly
ex
p
l
o
r
in
g
th
e
p
o
ten
tial
b
en
ef
its
o
f
o
th
er
k
e
r
n
el
f
u
n
ctio
n
s
s
u
c
h
a
s
p
o
ly
n
o
m
ial
an
d
s
ig
m
o
id
k
e
r
n
e
ls
.
T
h
is
p
ap
er
f
o
cu
s
es
o
n
s
ev
er
al
cr
itical
ar
ea
s
o
f
s
tu
d
y
.
First,
we
ex
am
in
e
h
o
w
v
a
r
io
u
s
d
is
tan
ce
m
etr
ics
im
p
ac
t
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
KNN
class
if
ier
an
d
PC
A
in
I
DS
f
o
r
I
o
T
s
ec
u
r
ity
.
N
ex
t,
we
p
r
o
v
id
e
a
co
m
p
ar
ativ
e
an
al
y
s
is
o
f
k
er
n
e
l
PC
A,
u
tili
z
in
g
d
if
f
er
en
t
k
e
r
n
el
f
u
n
ctio
n
s
,
ag
ain
s
t
tr
ad
itio
n
a
l
PC
A.
T
h
e
r
est
o
f
th
e
p
ap
e
r
is
ar
r
an
g
e
d
in
th
e
f
o
llo
win
g
m
an
n
e
r
:
Sectio
n
2
d
etails
th
e
p
r
o
p
o
s
ed
I
DS
f
r
a
m
ewo
r
k
.
Sectio
n
3
p
r
esen
ts
an
d
d
is
cu
s
s
es th
e
ex
p
er
im
en
tal
r
esu
lts
.
Fin
ally
,
Sectio
n
4
s
u
m
m
a
r
izes th
e
k
ey
f
in
d
in
g
s
.
2.
M
E
T
H
O
D
T
h
e
p
r
o
p
o
s
ed
I
DS,
as
d
ep
icte
d
in
Fig
u
r
e
1
,
co
n
s
is
ts
o
f
two
m
ain
p
h
ases
:
th
e
tr
ain
in
g
p
h
a
s
e
an
d
t
h
e
test
in
g
p
h
ase.
I
n
th
e
in
itial
p
h
ase,
d
ata
is
co
llected
f
r
o
m
th
r
ee
d
ev
ices,
f
o
llo
wed
b
y
d
ata
p
r
e
p
r
o
ce
s
s
in
g
p
r
o
ce
d
u
r
e,
wh
ich
in
v
o
l
v
es
clea
n
in
g
th
e
d
ata
an
d
r
ep
lacin
g
m
is
s
in
g
v
alu
es.
Su
b
s
eq
u
en
tly
,
th
e
p
r
o
ce
s
s
ed
d
at
a
u
n
d
er
g
o
es
s
ca
lin
g
m
eth
o
d
s
,
in
clu
d
in
g
s
tan
d
a
r
d
,
m
i
n
-
m
ax
,
an
d
R
o
b
u
s
tScaler
s
,
d
is
cu
s
s
ed
ex
ten
s
iv
ely
in
Sectio
n
2
.
2
to
en
s
u
r
e
th
at
a
ll
f
ea
tu
r
es
ar
e
co
m
p
ar
a
b
ly
s
ca
led
,
p
r
ev
en
tin
g
a
n
y
in
d
iv
i
d
u
al
f
ea
t
u
r
e
f
r
o
m
d
o
m
in
atin
g
s
o
lely
b
ased
o
n
its
m
ag
n
itu
d
e
.
Fig
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
I
DS m
o
d
el
Evaluation Warning : The document was created with Spire.PDF for Python.
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n
t J E
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&
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o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
E
n
h
a
n
cin
g
in
tern
et
o
f th
in
g
s
a
tta
ck
d
etec
tio
n
u
s
in
g
p
r
in
cip
a
l c
o
mp
o
n
e
n
t…
(
Zya
d
E
lkh
a
d
i
r
)
1101
Fo
llo
win
g
s
ca
lin
g
,
p
r
in
cip
al
co
m
p
o
n
en
t
PC
A
o
r
k
er
n
el
K
PC
A
is
ap
p
lied
to
th
e
r
esu
lti
n
g
d
ata
to
ex
tr
ac
t
th
e
a
x
es
(
PC
s
)
o
f
th
e
r
ed
u
ce
d
s
p
ac
e
an
d
g
e
n
er
ate
t
r
ain
in
g
d
ata
with
r
e
d
u
ce
d
f
ea
tu
r
es,
m
o
r
e
d
etails
ab
o
u
t
PC
A
an
d
KPC
A
ar
e
g
i
v
en
in
s
u
b
s
ec
tio
n
2
.
3
.
I
n
th
e
class
if
icatio
n
o
r
test
in
g
p
h
ase,
d
ata
is
c
o
llected
f
r
o
m
th
e
s
am
e
d
ev
ices,
an
d
id
en
tical
p
r
e
p
r
o
ce
s
s
in
g
a
n
d
s
ca
lin
g
tech
n
i
q
u
es
ar
e
ap
p
lied
as
in
th
e
tr
ai
n
in
g
p
h
ase.
T
h
e
r
esu
ltin
g
d
ata
is
th
en
p
r
o
jecte
d
o
n
to
th
e
r
ed
u
ce
d
s
p
ac
e
u
s
in
g
th
e
PC
s
.
Fin
ally
,
t
h
e
o
b
tain
ed
test
in
g
d
ata
is
co
m
p
ar
e
d
to
th
e
tr
ain
i
n
g
d
ata
i
n
th
e
s
am
e
r
ed
u
ce
d
s
p
ac
e
u
s
in
g
th
e
KNN
alg
o
r
ith
m
to
class
if
y
n
o
r
m
al
an
d
m
alicio
u
s
d
ata.
Su
b
s
ec
tio
n
2
.
4
.
g
iv
es a
n
o
v
er
v
iew
ab
o
u
t
KNN
an
d
th
e
em
p
l
o
y
ed
d
is
tan
ce
s
.
2
.
1
.
Da
t
a
s
et
T
h
e
d
ataset
u
tili
ze
d
in
th
is
s
t
u
d
y
was
s
o
u
r
ce
d
f
r
o
m
[
2
4
]
,
k
n
o
wn
as
th
e
I
o
T
-
2
3
d
ataset,
it
co
n
tain
s
r
ea
l
an
d
lab
eled
in
s
tan
ce
s
o
f
I
o
T
m
alwa
r
e
in
f
ec
tio
n
s
alo
n
g
s
id
e
n
o
r
m
al
tr
af
f
ic.
T
h
e
2
3
ca
p
tu
r
es
a
r
e
co
n
s
tr
u
ctin
g
th
e
d
ataset
an
d
o
r
g
an
ized
as
3
n
o
r
m
al
ca
p
tu
r
es
an
d
2
0
m
alicio
u
s
ca
p
tu
r
es.
E
v
er
y
ca
p
tu
r
e
f
r
o
m
co
r
r
u
p
te
d
d
e
v
ices
is
lab
eled
with
a
co
r
r
esp
o
n
d
in
g
m
alwa
r
e
s
am
p
le
ex
ec
u
te
d
.
Du
e
to
t
h
e
v
ast
s
ize
o
f
th
e
d
ataset,
a
d
ec
is
io
n
was
m
ad
e
to
r
etain
a
s
m
all
p
ar
t
o
f
co
n
n
ec
tio
n
s
f
r
o
m
ea
ch
in
d
i
v
id
u
al
d
ataset
an
d
s
u
b
s
eq
u
en
tly
m
er
g
e
th
em
i
n
to
a
n
o
v
el
d
ataset.
T
h
is
m
a
n
ip
u
latio
n
was
u
n
d
er
tak
e
n
t
o
en
s
u
r
e
th
at
o
u
r
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
co
u
l
d
ef
f
icien
tly
m
a
n
ag
e
th
e
w
o
r
k
lo
ad
o
f
th
e
n
o
v
el
d
ataset
an
d
s
im
u
ltan
eo
u
s
ly
ex
tr
ac
tin
g
th
e
m
o
s
t o
f
attac
k
t
y
p
es p
r
esen
t w
ith
in
th
e
i
n
itial I
o
T
-
2
3
d
ataset.
I
n
itially
,
th
e
Py
th
o
n
lib
r
ar
y
Pan
d
as
was
em
p
lo
y
e
d
to
in
d
iv
i
d
u
ally
lo
a
d
all
2
3
d
atasets
f
r
o
m
th
e
I
o
T
-
23
d
ataset
in
to
d
ata
f
r
am
es.
A
co
n
d
itio
n
was
ap
p
lied
t
o
s
k
ip
th
e
f
ir
s
t
1
0
r
o
ws
an
d
r
ea
d
th
e
s
u
b
s
eq
u
en
t
o
n
e
h
u
n
d
r
ed
th
o
u
s
an
d
r
o
ws.
Su
b
s
eq
u
en
tly
,
th
ese
2
3
d
ata
f
r
a
m
es
wer
e
co
n
s
o
lid
ated
in
to
a
s
in
g
le
d
ata
f
r
am
e.
Miss
in
g
v
alu
es
wer
e
r
ep
lace
d
with
0
.
Fin
ally
,
t
h
e
co
m
b
in
ed
d
ataset
was
g
en
er
ated
an
d
s
av
ed
as
th
e
“io
t2
3
co
m
b
in
ed
.
csv
”
f
ile.
T
h
e
r
esu
ltin
g
“io
t
2
3
co
m
b
in
ed
.
cs
v
”
f
ile
co
m
p
r
is
es
a
to
tal
o
f
1
,
4
4
4
,
6
7
4
r
ec
o
r
d
s
.
I
t
en
co
m
p
ass
es 1
0
ty
p
es o
f
attac
k
s
.
2
.
2
.
Sca
lin
g
t
ec
hn
iqu
es
I
n
th
e
d
o
m
ain
o
f
d
ata
p
r
e
p
r
o
ce
s
s
in
g
f
o
r
m
ac
h
in
e
lear
n
in
g
,
s
ca
lin
g
tech
n
iq
u
es
a
r
e
i
n
s
tr
u
m
en
tal
in
en
h
an
cin
g
th
e
r
o
b
u
s
tn
ess
an
d
ef
f
icac
y
o
f
p
r
ed
ictiv
e
m
o
d
els.
T
h
r
ee
co
m
m
o
n
ly
u
tili
ze
d
s
ca
ler
s
ar
e
Stan
d
ar
d
Scaler
,
Min
Ma
x
Scal
er
,
an
d
R
o
b
u
s
tScaler
.
Stan
d
a
r
d
Scaler
:
t
h
is
s
ca
ler
s
tan
d
ar
d
i
ze
s
th
e
f
ea
tu
r
es
b
y
s
u
b
tr
ac
tin
g
th
e
m
ea
n
(
µ)
an
d
d
iv
id
in
g
b
y
th
e
s
tan
d
a
r
d
d
e
v
iatio
n
(
σ
)
.
S
ta
n
d
a
r
d
iz
ed
F
ea
tu
r
e
=
F
ea
tu
r
e
−
I
t
is
p
ar
ticu
lar
ly
ef
f
ec
tiv
e
w
h
en
f
ea
tu
r
es
ex
h
ib
it
d
if
f
er
en
t
s
ca
les,
en
s
u
r
in
g
th
at
ea
ch
f
ea
tu
r
e
co
n
tr
ib
u
tes
eq
u
ally
to
th
e
m
o
d
el.
T
h
e
tr
an
s
f
o
r
m
ed
d
ata
h
as
a
m
ea
n
o
f
ze
r
o
a
n
d
a
s
tan
d
ar
d
d
ev
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ased
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r
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s
t statis
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t u
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~
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d
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ter
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ak
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atasets
with
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o
r
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k
ewe
d
d
is
tr
ib
u
tio
n
s
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n
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m
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ar
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ler
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en
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te
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ir
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e
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ts
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m
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ac
h
s
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er
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n
iq
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es
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ter
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ai
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r
ity
o
f
th
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u
n
d
er
ly
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g
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n
f
o
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m
atio
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.
2
.
3
.
F
e
a
t
ure
ex
t
r
a
ct
io
n m
e
t
ho
ds
2
.
3
.
1
.
P
rincipa
l
c
o
m
po
nent
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na
ly
s
is
T
h
e
g
o
al
o
f
PC
A
is
to
d
ec
r
ea
s
e
d
im
en
s
io
n
ality
w
h
ile
p
r
eser
v
in
g
as
m
u
ch
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ar
ian
ce
as
p
o
s
s
ib
le.
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h
is
is
ac
h
iev
ed
b
y
f
o
cu
s
in
g
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n
t
h
e
lead
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g
p
r
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cip
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c
o
m
p
o
n
en
ts
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PC
s
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,
wh
ich
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e
ar
r
an
g
e
d
i
n
d
escen
d
in
g
o
r
d
er
o
f
th
eir
v
ar
ian
c
e
[
2
5
]
.
Ma
th
e
m
atica
lly
,
g
iv
en
a
tr
ai
n
in
g
s
et
o
f
M
v
ec
to
r
s
ea
ch
with
n
f
e
atu
r
es.
W
e
o
b
tain
′
(
′
<
<
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p
r
in
cip
al
co
m
p
o
n
en
ts
f
r
o
m
th
e
tr
ain
in
g
s
et
th
r
o
u
g
h
th
e
f
o
llo
win
g
s
tep
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
9
9
-
1
1
0
8
1102
−
C
alcu
late
th
e
ar
ith
m
etic
m
ea
n
o
f
th
is
s
et:
=
1
∑
(
=
1
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(
1
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−
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em
o
v
e
th
e
m
ea
n
f
r
o
m
to
o
b
tain
:
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−
(
2
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−
C
o
n
s
tr
u
ct
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e
co
v
ar
ia
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ce
m
atr
ix
,
wh
er
e:
×
=
1
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(
=
1
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=
(
3
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a
nd
×
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1
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(
4
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L
et
b
e
t
h
e
−
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eig
en
v
ec
to
r
o
f
co
r
r
esp
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d
in
g
to
th
e
ass
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ciate
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r
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a
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tr
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.
.
′
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s
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g
o
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th
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e
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r
s
,
s
u
ch
th
at:
=
(
5
)
T
h
e
f
ir
s
t
co
r
r
esp
o
n
d
i
n
g
to
t
h
e
lar
g
est eig
en
v
alu
es
ar
e
ter
m
e
d
p
r
in
cip
al
c
o
m
p
o
n
en
ts
(
PC
s
)
.
2
.
3
.
2
.
K
er
nel
p
rincipa
l
c
o
m
po
nent
a
na
ly
s
is
Ker
n
el
p
r
in
cip
al
c
o
m
p
o
n
en
t
an
aly
s
is
(
k
er
n
el
PC
A)
[
2
6
]
i
s
an
ex
ten
s
io
n
o
f
PC
A
th
at
u
s
es
k
er
n
el
m
eth
o
d
s
to
p
er
f
o
r
m
n
o
n
lin
ea
r
d
im
en
s
io
n
ality
r
ed
u
ctio
n
.
T
h
e
b
asic
id
ea
b
eh
in
d
k
er
n
el
P
C
A
is
to
im
p
licitl
y
m
ap
th
e
i
n
p
u
t
d
ata
in
to
a
h
ig
h
er
-
d
im
e
n
s
io
n
al
f
ea
tu
r
e
s
p
ac
e
,
wh
er
e
it
b
ec
o
m
es
lin
ea
r
l
y
s
ep
ar
ab
le,
a
n
d
t
h
en
p
er
f
o
r
m
PC
A
in
th
at
s
p
ac
e.
T
h
is
allo
ws
k
er
n
el
PC
A
to
ca
p
tu
r
e
n
o
n
lin
ea
r
r
elatio
n
s
h
i
p
s
b
etwe
en
th
e
o
r
ig
in
al
f
ea
tu
r
es
.
T
h
e
k
er
n
el
tr
ick
is
u
s
ed
to
co
m
p
u
te
th
e
d
o
t
p
r
o
d
u
ct
in
th
e
h
ig
h
er
-
d
im
en
s
io
n
al
f
ea
tu
r
e
s
p
ac
e
ef
f
icien
tly
with
o
u
t
ex
p
licitly
co
m
p
u
tin
g
th
e
tr
an
s
f
o
r
m
atio
n
.
Giv
en
a
k
er
n
el
f
u
n
ctio
n
(
,
)
,
wh
er
e
an
d
ar
e
in
p
u
t
d
ata
p
o
i
n
ts
,
th
e
k
er
n
el
PC
A
alg
o
r
ith
m
ca
n
b
e
s
u
m
m
ar
ized
as
(
6
)
-
(
1
1
)
:
−
C
o
m
p
u
te
th
e
k
e
r
n
el
m
atr
ix
K:
=
(
x
,
x
)
(
6
)
−
C
en
ter
th
e
k
er
n
el
m
at
r
ix
:
′
=
−
1
−
1
+
1
1
(
7
)
w
h
er
e
1
d
e
n
o
tes a
m
atr
ix
o
f
o
n
es.
−
C
o
m
p
u
te
th
e
eig
en
v
ec
to
r
s
an
d
eig
en
v
al
u
es
o
f
th
e
ce
n
ter
ed
k
er
n
el
m
atr
ix
′
:
′
=
(
8
)
Select
th
e
f
ir
s
t
n′
eig
en
v
ec
to
r
s
co
r
r
esp
o
n
d
in
g
to
th
e
lar
g
est eig
en
v
alu
es to
f
o
r
m
th
e
p
r
in
ci
p
al
co
m
p
o
n
en
ts
t
h
e
R
B
F k
er
n
el
is
d
ef
in
ed
as
(
9
)
:
(
,
)
=
e
xp
(
−
‖
−
‖
2
2
2
)
(
9
)
wh
er
e
is
th
e
k
er
n
el
b
an
d
wid
th
p
ar
am
eter
.
T
h
e
Po
ly
n
o
m
ial
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er
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el
is
d
ef
in
e
d
as
(
1
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:
(
,
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=
(
+
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(
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wh
er
e
is
th
e
d
eg
r
ee
o
f
th
e
p
o
ly
n
o
m
ial
an
d
is
a
co
n
s
tan
t te
r
m
.
T
h
e
s
ig
m
o
i
d
k
er
n
el
is
d
ef
in
ed
as
(
1
1
)
:
(
,
)
=
ta
n
h
(
+
)
(
1
1
)
wh
er
e
α
an
d
β ar
e
s
ca
lin
g
p
ar
a
m
eter
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:
2088
-
8
7
0
8
E
n
h
a
n
cin
g
in
tern
et
o
f th
in
g
s
a
tta
ck
d
etec
tio
n
u
s
in
g
p
r
in
cip
a
l c
o
mp
o
n
e
n
t…
(
Zya
d
E
lkh
a
d
i
r
)
1103
2
.
4
.
k
-
nea
re
s
t
neig
hb
o
rs
I
n
o
r
d
er
to
class
if
y
a
d
ata
p
o
i
n
t,
KNN
lo
o
k
s
at
th
e
m
ajo
r
it
y
class
o
f
its
k
-
n
ea
r
est
n
eig
h
b
o
r
s
in
th
e
f
ea
tu
r
e
s
p
ac
e.
Giv
en
a
d
ataset
(
1
,
1
)
,
(
2
,
2
)
…
(
,
)
wh
er
e
r
ep
r
esen
ts
th
e
f
e
atu
r
e
v
ec
to
r
an
d
is
th
e
co
r
r
esp
o
n
d
in
g
class
lab
el,
th
e
KNN
alg
o
r
ith
m
o
p
er
ates
as
:
i)
C
h
o
o
s
e
th
e
n
u
m
b
er
o
f
n
eig
h
b
o
r
s
;
ii)
C
o
m
p
u
te
th
e
d
is
tan
ce
b
etw
ee
n
th
e
tar
g
et
p
o
in
t
an
d
ea
ch
d
ata
p
o
in
t
in
th
e
tr
ain
in
g
s
et
;
i
ii)
Dete
r
m
in
e
th
e
clo
s
est
n
eig
h
b
o
r
s
b
ased
o
n
t
h
e
co
m
p
u
ted
d
is
tan
ce
s
;
an
d
iv
)
Fo
r
class
if
icatio
n
,
ass
ig
n
th
e
class
lab
el
b
y
m
ajo
r
ity
v
o
te
am
o
n
g
th
e
n
ei
g
h
b
o
r
s
.
Fo
r
r
eg
r
ess
io
n
,
p
r
ed
ic
t
th
e
ar
ith
m
etic
m
ea
n
o
f
th
e
n
eig
h
b
o
r
s
tar
g
et
v
alu
es.
Var
io
u
s
d
is
tan
ce
m
etr
ics
an
d
s
im
ilar
ity
m
ea
s
u
r
es
ar
e
u
s
ed
to
q
u
a
n
tify
t
h
e
d
is
s
im
ilar
ity
or
s
im
ilar
ity
b
etwe
en
d
ata
p
o
i
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ts
.
−
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n
h
attan
d
is
tan
ce
:
T
h
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Ma
n
h
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d
is
tan
ce
,
also
k
n
o
wn
a
s
T
ax
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r
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n
o
r
m
,
b
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p
o
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d
in
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n
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im
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s
p
ac
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is
g
iv
en
b
y
(
1
2
)
.
M
a
nha
tt
a
n
(
,
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=
∑
|
=
1
−
|
(
1
2
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−
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k
o
wsk
i
d
is
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ce
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Min
k
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wsk
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d
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o
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tio
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f
b
o
t
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E
u
clid
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M
inkows
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,
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C
h
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b
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also
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n
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b
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tw
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m
ax
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v
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p
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|
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(
1
4
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o
s
in
e
s
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ity
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C
o
s
in
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s
im
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m
ea
s
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r
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th
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o
s
in
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th
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o
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ze
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s
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d
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(
p
,
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(
=
1
2
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(
=
1
2
)
(
1
5
)
−
Ham
m
in
g
d
is
tan
ce
:
T
h
e
Ham
m
in
g
d
is
tan
ce
b
etwe
en
two
s
tr
in
g
s
o
f
e
q
u
al
len
g
t
h
is
d
ef
in
e
d
as
th
e
co
u
n
t
o
f
p
o
s
itio
n
s
wh
er
e
th
e
co
r
r
esp
o
n
d
in
g
s
y
m
b
o
ls
ar
e
d
if
f
e
r
en
t.
(
s
tr
in
g
1
,
s
tr
in
g
2
)
=
∑
(
=
1
(
s
tr
in
g
1
[
]
≠
s
tr
in
g
2
[
]
)
)
(
1
6
)
−
J
ac
ca
r
d
s
im
ilar
ity
:
J
ac
ca
r
d
s
im
ilar
ity
m
ea
s
u
r
es
th
e
r
atio
of
th
e
s
ize
of
th
e
in
ter
s
ec
tio
n
to
th
e
s
ize
of
th
e
u
n
io
n
of
two
s
ets
.
(
s
et
1
,
s
et
2
)
=
|
s
e
t
1
∩
s
e
t
2
|
|
s
e
t
1
∪
s
e
t
2
|
(
1
7
)
−
C
o
r
r
elatio
n
-
b
ased
d
is
tan
ce
s
:
C
o
r
r
elatio
n
-
b
ased
d
is
tan
ce
s
c
o
n
s
id
er
th
e
c
o
r
r
elatio
n
c
o
ef
f
ic
ien
t
b
etwe
en
two
v
ec
to
r
s
.
T
h
e
Pear
s
o
n
co
r
r
elati
o
n
co
ef
f
icien
t is co
m
m
o
n
ly
u
s
ed
(
1
8
)
.
C
o
r
r
ela
tio
n
(
p
,
q
)
=
∑
(
=
1
(
−
)
(
−
)
)
√
∑
(
=
1
(
−
)
2
)
⋅
√
∑
(
=
1
(
−
)
2
)
(
1
8
)
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
ac
cu
r
ac
y
of
an
I
DS
is
a
cr
itical
m
etr
ic
th
at
m
ea
s
u
r
es
it
s
ef
f
ec
tiv
en
ess
in
co
r
r
ec
tly
id
en
t
if
y
in
g
an
d
class
if
y
in
g
in
s
tan
ce
s
o
f
in
tr
u
s
io
n
o
r
ab
n
o
r
m
al
b
eh
av
io
r
with
in
a
n
etwo
r
k
.
T
h
e
ac
cu
r
ac
y
is
g
e
n
er
ally
ca
lcu
lated
as
th
e
r
atio
of
co
r
r
e
ctly
id
en
tifie
d
in
s
tan
ce
s
(
tr
u
e
p
o
s
itiv
es
an
d
tr
u
e
n
eg
ativ
es
)
t
o
th
e
to
tal
n
u
m
b
er
of
in
s
tan
ce
s
.
T
h
e
f
o
r
m
u
la
f
o
r
ac
c
u
r
ac
y
is
as
f
o
llo
ws:
A
cc
u
r
a
cy
=
Tr
u
e
P
o
s
itives
+
Tr
u
e
N
eg
a
tives
To
ta
l I
n
s
ta
n
ce
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
1
,
Feb
r
u
ar
y
20
25
:
1
0
9
9
-
1
1
0
8
1104
w
h
er
e:
−
T
r
u
e
p
o
s
itiv
es
(
T
P):
in
s
tan
ce
s
co
r
r
ec
tly
id
e
n
tifie
d
as in
tr
u
s
io
n
s
.
−
T
r
u
e
n
e
g
ativ
es
(
T
N)
:
in
s
tan
ce
s
co
r
r
ec
tly
id
en
tifie
d
as
n
o
r
m
a
l
.
−
T
o
tal
in
s
tan
ce
s
:
+
+
+
.
I
n
th
e
c
o
n
d
u
cted
ex
p
er
im
en
ts
,
we
r
an
d
o
m
ly
s
elec
ted
1
0
,
0
0
0
n
o
r
m
al
d
ata
a
n
d
1
,
0
0
0
m
ali
cio
u
s
d
ata
f
o
r
th
e
tr
ain
in
g
p
h
ase.
Fo
r
th
e
test
in
g
p
h
ase,
5
,
0
0
0
n
o
r
m
al
d
ata
an
d
1
,
0
0
0
m
alicio
u
s
d
ata
wer
e
s
elec
ted
.
T
h
is
s
elec
tio
n
p
r
o
ce
s
s
was r
ep
ea
ted
2
0
tim
es.
T
h
is
s
ettin
g
en
s
u
r
es
th
e
r
eliab
ilit
y
an
d
g
en
e
r
aliza
b
ilit
y
o
f
f
in
d
in
g
s
b
y
m
itig
atin
g
b
iases
in
tr
o
d
u
ce
d
b
y
a
s
in
g
le
r
an
d
o
m
s
p
lit
an
d
ass
es
s
in
g
v
ar
iab
ilit
y
ac
r
o
s
s
it
er
atio
n
s
.
B
y
m
im
ick
in
g
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
an
d
ass
es
s
in
g
s
y
s
tem
p
er
f
o
r
m
a
n
ce
ac
r
o
s
s
d
iv
er
s
e
d
ata
s
am
p
les,
i
t
en
ab
les
in
s
ig
h
ts
in
to
g
en
e
r
al
izatio
n
ca
p
ab
ilit
ies
an
d
s
tab
ilit
y
.
Fu
r
th
er
m
o
r
e,
s
tatis
tical
s
ig
n
if
ican
ce
ca
n
b
e
estab
lis
h
ed
,
f
ac
ilit
atin
g
ef
f
icien
t
r
eso
u
r
ce
u
tili
za
tio
n
d
esp
ite
m
u
ltip
le
r
ep
etitio
n
s
.
T
h
e
ex
p
e
r
im
en
ts
ar
e
d
iv
id
ed
in
two
p
ar
ts
,
th
e
f
ir
s
t
o
n
e
c
o
n
ce
r
n
s
PC
A/KNN
an
d
in
v
e
s
tig
ate
th
e
ef
f
icien
cy
o
f
o
th
er
d
is
tan
ce
s
s
u
ch
as
Ma
n
h
attan
d
is
tan
ce
,
Min
k
o
wsk
i
d
is
tan
ce
,
C
h
eb
y
s
h
ev
d
is
tan
ce
,
co
s
in
e
s
im
ilar
ity
,
Ham
m
in
g
d
is
tan
ce
,
J
ac
ca
r
d
s
im
ilar
ity
,
a
n
d
c
o
r
r
elatio
n
-
b
ased
d
is
tan
ce
s
.
W
e
ex
p
lo
r
ed
th
r
ee
d
if
f
er
en
t
s
ca
lin
g
tech
n
iq
u
es:
Stan
d
ar
d
Scaler
,
Min
Ma
x
Scal
er
,
an
d
R
o
b
u
s
tScaler
.
W
h
en
ass
es
s
in
g
th
e
KNN
d
is
tan
ce
s
u
s
in
g
Stan
d
a
r
d
Scaler
,
we
m
ain
tain
ed
a
co
n
s
is
ten
t
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
e
n
ts
at
“
3
”
as
s
h
o
wn
in
Fig
u
r
e
2
,
“
5
”
as
s
h
o
wn
in
F
ig
u
r
e
3
,
an
d
“
7
”
as
s
h
o
wn
in
Fig
u
r
e
4
,
wh
ile
s
y
s
tem
atica
lly
ad
ju
s
tin
g
th
e
v
alu
e
o
f
K.
I
n
an
o
th
er
ex
p
er
im
e
n
t
a
s
s
h
o
wn
in
Fig
u
r
e
5
,
we
k
ep
t
f
ix
ed
at
1
a
n
d
v
ar
ied
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
.
Acr
o
s
s
b
o
th
e
x
p
er
im
en
ts
in
v
o
l
v
in
g
Min
Ma
x
Scaler
an
d
R
o
b
u
s
tScaler
,
we
s
et
to
1
wh
ile
m
o
d
if
y
in
g
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
.
T
h
e
r
esu
lts
illu
s
tr
ated
b
y
Fig
u
r
e
6
a
n
d
Fi
g
u
r
e
7
co
n
s
is
ten
tly
in
d
icate
d
th
at
co
s
in
e
d
is
tan
ce
ex
h
ib
ited
s
lig
h
tly
b
etter
p
e
r
f
o
r
m
a
n
ce
co
m
p
ar
e
d
to
o
th
e
r
d
is
tan
ce
m
etr
ics.
Ho
wev
er
,
it
i
s
wo
r
th
n
o
tin
g
th
at
J
ac
ca
r
d
d
is
tan
ce
d
id
n
o
t
y
ie
ld
f
av
o
r
a
b
le
o
u
tc
o
m
es
in
an
y
o
f
th
e
in
v
esti
g
ated
s
ce
n
ar
io
s
.
T
h
e
r
o
b
u
s
tn
ess
o
f
co
s
in
e
d
is
tan
ce
to
n
o
is
e
a
n
d
o
u
tlier
s
c
o
n
tr
ib
u
tes
s
ig
n
if
ica
n
tly
to
th
e
o
b
tain
e
d
r
esu
lts
.
Un
lik
e
d
is
tan
ce
m
etr
i
cs
th
at
co
n
s
id
er
b
o
th
th
e
d
ir
e
ctio
n
an
d
m
ag
n
itu
d
e
o
f
v
ec
to
r
s
,
co
s
in
e
d
is
tan
ce
f
o
cu
s
es
s
o
lely
o
n
d
ir
ec
tio
n
al
s
im
ilar
ity
.
B
y
m
ea
s
u
r
in
g
th
e
co
s
in
e
o
f
t
h
e
an
g
le
b
etwe
en
two
v
ec
to
r
s
,
it
em
p
h
asizes
th
e
s
im
ilar
ity
in
th
eir
d
ir
ec
tio
n
s
r
ath
er
th
an
th
eir
m
ag
n
itu
d
es.
T
h
is
p
r
o
p
e
r
ty
en
ab
les
co
s
in
e
d
is
tan
ce
to
ef
f
ec
tiv
ely
ca
p
t
u
r
e
ess
en
tial
d
ir
ec
tio
n
al
p
atter
n
s
in
th
e
d
ata,
ev
en
in
th
e
p
r
esen
ce
o
f
n
o
is
e
o
r
o
u
tlier
s
.
W
h
en
v
ec
to
r
s
ex
h
ib
i
t
s
im
ilar
d
ir
ec
tio
n
s
,
co
s
in
e
s
i
m
ilar
ity
r
em
ain
s
h
ig
h
,
in
d
icatin
g
th
eir
s
im
ilar
ity
r
eg
ar
d
less
o
f
p
o
ten
tial d
if
f
e
r
e
n
ce
s
.
I
n
th
e
s
ec
o
n
d
p
ar
t
o
f
o
u
r
ex
p
er
im
en
ts
,
we
aim
ed
to
f
u
r
th
er
en
h
an
ce
t
h
e
ac
cu
r
ac
y
o
f
o
u
r
I
DS
b
y
em
p
lo
y
in
g
k
er
n
el
PC
A
wh
il
e
ex
p
lo
r
in
g
v
a
r
io
u
s
k
er
n
el
f
u
n
ctio
n
s
.
Sp
ec
if
ically
,
we
in
v
esti
g
ated
th
e
R
B
F,
p
o
ly
n
o
m
ial,
an
d
s
ig
m
o
id
f
u
n
ctio
n
s
,
co
m
p
a
r
in
g
t
h
eir
p
e
r
f
o
r
m
an
ce
a
g
ain
s
t
PC
A
with
b
o
th
E
u
clid
ea
n
an
d
co
s
in
e
d
is
tan
ce
m
et
r
ics.
T
h
e
co
n
s
id
er
e
d
v
alu
es
o
f
k
e
r
n
el
p
ar
am
eter
s
ar
e
g
iv
en
b
y
:
=
1
/
(
)
f
o
r
r
a
d
ial
b
asis
f
u
n
ctio
n
(
R
B
F)
.
=
3
is
th
e
d
e
g
r
ee
a
n
d
=
1
f
o
r
p
o
ly
n
o
m
ial
k
er
n
el.
α
a
n
d
β
ar
e
s
ca
lin
g
p
ar
am
eter
s
an
d
g
iv
en
b
y
=
1
/
(
)
a
n
d
=
1
f
o
r
s
ig
m
o
i
d
k
er
n
el.
Fig
u
r
e
2
.
K
v
s
Acc
u
r
ac
y
(
%)
f
o
r
3
PC
u
s
in
g
Stan
d
ar
d
Scaler
Fig
u
r
e
3.
K
vs
Acc
u
r
ac
y
(
%)
f
o
r
5
PC
u
s
in
g
Stan
d
ar
d
Scaler
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:
2088
-
8
7
0
8
E
n
h
a
n
cin
g
in
tern
et
o
f th
in
g
s
a
tta
ck
d
etec
tio
n
u
s
in
g
p
r
in
cip
a
l c
o
mp
o
n
e
n
t…
(
Zya
d
E
lkh
a
d
i
r
)
1105
Fig
u
r
e
4.
K
vs
Acc
u
r
ac
y
(
%)
f
o
r
7
PC
u
s
in
g
Stan
d
ar
d
Scaler
Fig
u
r
e
5
.
PC
v
s
Acc
u
r
ac
y
(
%)
f
o
r
K=
1
u
s
in
g
Stan
d
ar
d
Scaler
Fig
u
r
e
6
.
PC
v
s
Acc
u
r
ac
y
(
%)
f
o
r
K=
1
u
s
in
g
Min
Ma
x
Scaler
Fig
u
r
e
7.
PC
vs
Acc
u
r
ac
y
(
%)
f
o
r
K=
1
u
s
in
g
R
o
b
u
s
tScaler
Fig
u
r
e
s
8
an
d
9
illu
s
tr
ate
ex
p
e
r
im
en
ts
wh
er
e
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
ts
(
PC
s
)
was
s
et
to
3
an
d
5
r
esp
ec
tiv
ely
,
wh
ile
th
e
v
alu
e
o
f
K
i
n
th
e
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RE
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E
R
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NC
E
S
[
1
]
Z.
C
h
e
n
,
C
.
B
.
S
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p
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n
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.
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t
h
u
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o
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[
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3
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C
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5
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T.
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.
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h
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t
a
l
.
,
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I
o
T
f
o
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sm
a
r
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c
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s
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M
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Evaluation Warning : The document was created with Spire.PDF for Python.