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
i
n
ee
ring
(
I
J
E
CE
)
Vo
l.
11
,
No
.
3
,
J
u
n
e
2021
,
p
p
.
2
1
0
9
~
2
1
1
9
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
1
1
i
3
.
p
p
2
1
0
9
-
2
1
1
9
2109
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
Clustering
using
k
e
rnel e
ntropy
pr
incipa
l co
m
po
nen
t
a
na
ly
sis
a
nd va
ria
ble kern
el esti
m
a
tor
L
o
ub
na
E
l F
a
t
t
a
hi
1
,
E
l H
a
s
s
a
n Sba
i
2
1
De
p
a
rt
m
e
n
t
o
f
P
h
y
sic
s,
M
o
u
lay
I
s
m
a
il
Un
iv
e
rsit
y
o
f
M
e
k
n
e
s
,
M
o
ro
c
c
o
2
Hig
h
S
c
h
o
o
l
o
f
T
e
c
h
n
o
l
o
g
y
,
M
o
u
lay
Is
m
a
il
Un
iv
e
rsit
y
o
f
M
e
k
n
e
s
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
9
,
2
0
1
9
R
ev
i
s
ed
Sep
2
6
,
2
0
2
0
A
cc
ep
ted
Oct
6
,
2
0
2
0
Clu
ste
rin
g
a
s
u
n
s
u
p
e
rv
ise
d
lea
rn
in
g
m
e
th
o
d
is
th
e
m
issio
n
o
f
d
iv
id
in
g
d
a
ta
o
b
jec
ts
in
t
o
c
lu
ste
rs
w
it
h
c
o
m
m
o
n
c
h
a
ra
c
teristics
.
In
th
e
p
re
se
n
t
p
a
p
e
r,
w
e
in
tro
d
u
c
e
a
n
e
n
h
a
n
c
e
d
tec
h
n
i
q
u
e
o
f
th
e
e
x
isti
n
g
EP
CA
d
a
ta
tran
s
f
o
r
m
a
ti
o
n
m
e
th
o
d
.
In
c
o
r
p
o
ra
ti
n
g
t
h
e
k
e
rn
e
l
f
u
n
c
ti
o
n
in
t
o
t
h
e
E
P
CA
,
th
e
in
p
u
t
sp
a
c
e
c
a
n
b
e
m
a
p
p
e
d
im
p
l
icitl
y
in
to
a
h
ig
h
-
d
im
e
n
sio
n
a
l
o
f
f
e
a
tu
re
sp
a
c
e
.
T
h
e
n
,
th
e
S
h
a
n
n
o
n
’s
e
n
tro
p
y
e
sti
m
a
ted
v
ia
th
e
in
e
rti
a
p
ro
v
i
d
e
d
b
y
th
e
c
o
n
t
rib
u
ti
o
n
o
f
e
v
e
r
y
m
a
p
p
e
d
o
b
jec
t
i
n
d
a
ta
is
th
e
k
e
y
m
e
a
su
re
to
d
e
term
in
e
th
e
o
p
t
im
a
l
e
x
trac
ted
fe
a
tu
re
s
sp
a
c
e
.
Ou
r
p
ro
p
o
se
d
m
e
th
o
d
p
e
r
f
o
rm
s
v
e
r
y
we
ll
th
e
c
lu
ste
rin
g
a
lg
o
rit
h
m
o
f
th
e
fa
st
s
e
a
rc
h
o
f
c
lu
ste
rs’
c
e
n
ters
b
a
se
d
o
n
th
e
lo
c
a
l
d
e
n
siti
e
s’
c
o
m
p
u
ti
n
g
.
Ex
p
e
rim
e
n
tal
re
su
lt
s
d
isc
lo
se
th
a
t
th
e
a
p
p
r
o
a
c
h
is
f
e
a
sib
le an
d
e
f
f
ici
e
n
t
o
n
th
e
p
e
rf
o
rm
a
n
c
e
q
u
e
ry
.
K
ey
w
o
r
d
s
:
C
lu
s
ter
i
n
g
Ker
n
el
en
tr
o
p
y
p
r
in
cip
al
co
m
p
o
n
e
n
t a
n
al
y
s
i
s
Ma
x
i
m
u
m
e
n
tr
o
p
y
p
r
in
cip
le
d
en
s
it
y
p
ea
k
Var
iab
le
k
er
n
el
est
i
m
ato
r
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
L
o
u
b
n
a
E
l Fatta
h
i
Dep
ar
t
m
en
t o
f
P
h
y
s
ics
Mo
u
la
y
I
s
m
ail
U
n
i
v
er
s
it
y
o
f
Me
k
n
e
s
K
m
5
,
R
u
e
d
'Ag
o
u
r
a
y
،
N6
,
Me
k
n
e
s
5
0
0
4
0
,
M
o
r
o
cc
o
E
m
ail: e
s
t
m
@
e
s
t
-
u
m
i.a
c.
m
a
1.
I
NT
RO
D
UCT
I
O
N
C
lu
s
ter
i
n
g
th
e
d
ata
is
t
h
e
tas
k
o
f
d
is
co
v
er
in
g
n
at
u
r
al
g
r
o
u
p
i
n
g
s
i
n
d
ata,
n
a
m
ed
clu
s
ter
s
ac
co
r
d
in
g
to
th
eir
s
i
m
ilar
it
y
.
Ob
j
ec
ts
ar
e
s
i
m
ilar
in
s
id
e
t
h
e
s
a
m
e
cl
u
s
ter
w
h
er
ea
s
d
is
s
i
m
ilar
co
m
p
ar
ed
to
o
b
j
ec
ts
d
escen
d
in
g
f
r
o
m
o
th
er
cl
u
s
ter
s
.
C
l
u
s
ter
in
g
,
as
a
cla
s
s
o
f
u
n
s
u
p
er
v
is
ed
c
lass
if
ica
tio
n
m
et
h
o
d
,
h
as
b
ee
n
w
id
el
y
ap
p
lied
in
d
if
f
er
en
t
d
o
m
ai
n
s
,
m
ac
h
i
n
e
lear
n
i
n
g
,
i
m
a
g
e
s
e
g
m
e
n
tat
io
n
,
p
atter
n
r
ec
o
g
n
it
i
o
n
,
tex
t
m
i
n
i
n
g
an
d
m
an
y
o
th
er
d
o
m
ai
n
s
[
1
-
3
]
.
Gr
ea
t
n
u
m
b
er
o
f
clu
s
ter
in
g
alg
o
r
ith
m
s
l
ie
in
liter
at
u
r
e,
th
e
f
a
m
o
u
s
K
-
m
ea
n
clu
s
ter
i
n
g
[
4
]
,
h
ier
ar
ch
ical
clu
s
ter
in
g
[
5
]
,
k
-
m
ed
o
id
s
[
6
]
,
an
d
m
ea
n
s
h
i
f
t
[
7
]
h
av
e
b
ee
n
co
n
s
id
er
ed
in
v
ar
io
u
s
p
r
o
b
lem
s
.
Desp
ite
o
f
th
e
e
x
te
n
s
i
v
e
s
t
u
d
i
es
in
t
h
e
p
ast
o
n
clu
s
ter
i
n
g
,
a
cr
itical
is
s
u
e
r
e
m
ai
n
s
lar
g
el
y
u
n
s
o
lv
ed
:
h
o
w
to
au
to
m
atica
ll
y
d
eter
m
i
n
e
t
h
e
n
u
m
b
er
o
f
cl
u
s
ter
s
.
M
o
s
t
o
f
t
h
e
m
as
s
u
m
ed
t
h
at
t
h
e
n
u
m
b
er
o
f
cl
u
s
ter
s
eith
er
h
a
s
b
ee
n
m
a
n
u
al
l
y
s
et
o
r
is
k
n
o
w
n
i
n
ad
v
a
n
ce
[
4
,
8
]
.
R
ec
en
tl
y
,
g
r
ea
t
atten
tio
n
h
as
b
ee
n
ac
co
r
d
ed
to
tack
le
w
it
h
t
h
i
s
is
s
u
e.
C
l
u
s
ter
i
n
g
b
y
d
en
s
it
y
p
ea
k
s
s
elec
tio
n
cr
iter
io
n
[9
-
11]
is
a
tech
n
iq
u
e
th
at
te
n
d
s
to
f
in
d
in
t
u
iti
v
el
y
th
e
n
u
m
b
er
o
f
cl
u
s
ter
s
in
d
ep
en
d
e
n
tl
y
o
f
t
h
eir
s
h
ap
e
an
d
th
e
d
i
m
en
s
io
n
o
f
t
h
e
s
p
ac
e
co
n
tain
i
n
g
th
e
m
,
s
o
th
at
to
av
o
id
th
e
i
n
h
er
en
t
s
h
o
r
tco
m
in
g
s
o
f
p
r
o
v
id
i
n
g
t
h
e
n
u
m
b
er
o
f
cl
u
s
ter
s
as
an
in
p
u
t
p
ar
a
m
eter
lik
e
i
n
th
e
K
-
m
ea
n
s
.
T
h
e
ap
p
r
o
ac
h
p
r
o
p
o
s
ed
b
y
R
o
d
r
ig
u
ez
an
d
L
aio
[
1
0
]
r
elies
as
a
f
ir
s
t
s
tep
o
n
t
h
e
f
a
s
t
s
ea
r
ch
o
f
t
h
e
d
en
s
it
y
p
ea
k
s
r
ef
er
r
in
g
t
h
e
cl
u
s
ter
ce
n
ter
s
ch
ar
ac
ter
ized
b
y
h
av
i
n
g
a
h
i
g
h
er
lo
ca
l
d
en
s
it
y
co
m
p
ar
ed
to
th
eir
n
ei
g
h
b
o
r
h
o
o
d
an
d
r
elativ
el
y
lar
g
e
d
is
ta
n
ce
r
eg
ar
d
to
p
o
in
ts
h
av
in
g
h
i
g
h
er
d
en
s
ities
.
As
a
r
esu
lt,
th
e
cl
u
s
ter
ce
n
ter
s
ar
e
lo
ca
ted
in
g
e
n
er
al
at
t
h
e
u
p
p
er
r
ig
h
t
co
r
n
er
o
f
t
h
e
d
ec
is
io
n
g
r
ap
h
w
h
ic
h
is
th
e
p
lo
t
o
f
th
e
d
en
s
it
y
a
s
a
f
u
n
ct
io
n
o
f
t
h
e
d
is
ta
n
ce
o
f
ea
c
h
p
o
in
t.
T
h
er
ef
o
r
e,
o
n
ce
ce
n
ter
s
ar
e
d
eter
m
i
n
ed
all
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.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
1
0
9
-
2119
2110
r
e
m
ain
in
g
d
ata
p
o
in
ts
ar
e
as
s
i
g
n
ed
to
t
h
e
s
a
m
e
clu
s
ter
a
s
it
s
n
ea
r
est
n
eig
h
b
o
r
s
o
f
h
ig
h
er
d
en
s
it
y
s
o
as
to
f
o
r
m
f
i
n
al
clu
s
ter
s
.
As
a
f
u
r
th
er
w
o
r
k
,
t
h
e
R
o
d
r
ig
u
ez
an
d
L
aio
’
s
m
et
h
o
d
w
a
s
i
m
p
r
o
v
ed
b
y
W
a
n
g
a
n
d
Xu
[
1
1
]
th
r
o
u
g
h
s
u
b
s
t
itu
t
in
g
t
h
e
s
tep
f
u
n
ctio
n
b
y
t
h
e
P
ar
ze
n
es
ti
m
a
to
r
s
o
t
h
at
th
e
tr
u
n
ca
ted
d
en
s
it
y
b
ec
o
m
es
s
m
o
o
th
er
.
Her
e,
w
e
d
ev
elo
p
a
m
et
h
o
d
f
o
r
d
a
ta
tr
an
s
f
o
r
m
atio
n
an
d
r
ed
u
c
ti
o
n
b
ased
o
n
th
e
v
ar
iab
le
k
er
n
el
e
s
ti
m
ato
r
[
1
2
]
.
A
i
m
ed
at
th
e
p
r
o
b
lem
s
o
f
clu
s
ter
in
g
,
m
a
n
y
r
esear
c
h
er
s
ar
e
co
n
v
i
n
ce
d
th
at
th
e
d
i
m
en
s
io
n
alit
y
r
ed
u
ctio
n
i
s
an
i
m
p
o
r
ta
n
t
s
ta
g
e
t
h
at
m
u
s
t
b
e
ad
o
p
ted
in
d
ata
an
aly
s
is
b
ef
o
r
e
co
n
s
id
er
in
g
an
y
clas
s
i
f
icatio
n
s
tep
.
I
n
f
ac
t,
m
a
n
y
alg
o
r
ith
m
s
o
f
cl
u
s
ter
in
g
o
f
te
n
d
o
n
o
t
w
o
r
k
w
ell
i
n
h
i
g
h
d
i
m
en
s
io
n
,
s
o
,
to
i
m
p
r
o
v
e
th
e
ef
f
icie
n
c
y
,
a
d
ata
r
ed
u
ctio
n
i
s
n
ee
d
ed
[
1
]
.
I
n
th
is
s
e
n
s
e,
w
e
p
r
o
p
o
s
e
a
h
y
b
r
i
d
m
et
h
o
d
,
w
h
ic
h
co
m
b
i
n
es
th
e
en
tr
o
p
y
p
r
in
c
ip
al
co
m
p
o
n
e
n
t
a
n
al
y
s
is
(
E
P
C
A
)
[
1
3
,
1
4
]
an
d
th
e
d
ata
m
ap
p
in
g
.
T
h
e
co
r
e
elem
e
n
t
is
to
p
er
f
o
r
m
a
d
ata
m
ap
p
in
g
u
s
i
n
g
th
e
k
er
n
el
f
u
n
ctio
n
b
ef
o
r
e
im
p
le
m
en
t
in
g
th
e
E
P
C
A
.
Data
m
ap
p
i
n
g
co
n
s
is
t
s
o
f
tr
an
s
f
o
r
m
i
n
g
th
e
d
ata
in
to
a
h
i
g
h
-
d
i
m
e
n
s
io
n
al
f
ea
t
u
r
e
s
p
ac
e,
w
h
er
e
p
atter
n
s
b
ec
o
m
e
li
n
ea
r
a
n
d
t
h
e
n
o
n
l
in
ea
r
i
t
y
d
i
s
ap
p
ea
r
s
[
1
5
]
.
T
h
en
,
u
s
i
n
g
E
P
C
A
,
w
e
r
estrict
th
e
h
i
g
h
-
d
i
m
e
n
s
io
n
al
s
p
ac
e
to
a
s
u
b
s
p
ac
e
o
f
th
e
e
x
tr
ac
ted
f
e
atu
r
es.
I
n
m
a
n
y
ca
s
e
s
,
t
h
e
q
u
ali
t
y
o
f
clu
s
ter
in
g
i
s
ap
p
r
o
v
ed
b
y
a
l
o
w
s
i
m
ilar
it
y
o
f
th
e
in
ter
-
cl
u
s
ter
an
d
a
h
ig
h
s
i
m
ilar
it
y
o
f
th
e
i
n
tr
a
-
c
lu
s
ter
.
T
o
th
is
e
n
d
,
w
e
i
n
te
g
r
ate
a
n
a
u
to
m
a
tic
m
et
h
o
d
f
o
r
clu
s
ter
ce
n
tr
o
id
s
elec
tio
n
b
ased
o
n
th
e
v
alid
it
y
i
n
d
ex
al
g
o
r
ith
m
u
s
i
n
g
t
h
e
c
o
n
ce
p
t
o
f
en
tr
o
p
y
in
tr
o
d
u
ce
d
b
y
J
a
y
e
n
s
E
d
w
in
i
n
[
1
6
]
an
d
co
m
p
u
ti
n
g
t
h
e
i
n
ter
-
c
lu
s
ter
a
n
d
in
tr
a
-
clu
s
ter
s
i
m
ilar
ities
[
1
7
]
.
T
h
e
p
r
esen
t
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
.
Sectio
n
2
p
r
esen
ts
a
b
r
ief
r
ev
ie
w
o
f
P
C
A
as
a
lin
ea
r
d
ata
tr
an
s
f
o
r
m
atio
n
.
W
e
m
o
v
e
to
co
n
s
id
er
th
e
k
er
n
e
l
en
tr
o
p
y
p
r
in
cip
al
co
m
p
o
n
en
t
a
n
al
y
s
i
s
(
KE
P
C
A
)
f
o
r
d
i
m
en
s
io
n
al
it
y
r
ed
u
ctio
n
.
I
n
s
ec
tio
n
3
,
w
e
p
r
esen
t
t
h
e
cl
u
s
t
er
in
g
b
y
th
e
f
ast
s
ea
r
ch
o
f
ce
n
ter
s
r
el
y
i
n
g
o
n
t
h
e
esti
m
atio
n
o
f
t
h
e
p
r
o
b
ab
ilit
y
d
en
s
it
y
f
u
n
ctio
n
(
P
DF)
as
w
e
ll
as
th
e
au
to
m
atic
cr
iter
io
n
f
o
r
th
e
s
elec
tio
n
o
f
clu
s
ter
ce
n
ter
s
u
s
i
n
g
v
al
id
it
y
in
d
ex
al
g
o
r
ith
m
.
Sect
io
n
4
,
is
d
ed
icate
d
to
t
h
e
v
alid
ati
o
n
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
n
b
o
th
s
y
n
t
h
etic
an
d
r
ea
l d
atasets
in
cl
u
d
i
n
g
a
co
m
p
ar
is
o
n
t
o
o
th
er
clu
s
ter
in
g
al
g
o
r
ith
m
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Dim
e
ns
io
na
lity
re
du
ct
io
n
C
lu
s
ter
i
n
g
al
g
o
r
it
h
m
s
ar
e
f
a
cin
g
p
r
o
b
lem
s
o
f
d
i
m
e
n
s
io
n
alit
y
e
s
p
ec
iall
y
w
h
e
n
t
h
e
d
i
m
e
n
s
io
n
in
cr
ea
s
es
i
m
p
o
r
tan
tl
y
.
T
h
er
ef
o
r
e,
in
s
o
m
e
ca
s
es,
t
h
e
y
lo
s
e
th
eir
e
f
f
icien
c
y
,
li
k
e
w
i
s
e,
th
eir
p
r
o
d
u
ctiv
i
t
y
esp
ec
iall
y
w
h
e
n
d
ata
p
r
esen
t
s
p
ar
s
en
ess
.
As
a
s
o
lu
tio
n
,
w
e
c
o
n
s
id
er
t
h
e
r
ed
u
ctio
n
o
f
t
h
e
d
im
en
s
io
n
a
lit
y
a
s
a
n
ef
f
icien
t
p
r
ep
r
o
ce
s
s
in
g
.
Du
e
t
o
th
is
ef
f
ec
t,
m
a
n
y
r
esear
c
h
es
h
av
e
b
ee
n
d
o
n
e
to
g
et
r
id
o
f
th
is
co
m
p
licatio
n
[
1
8
-
21]
.
T
h
u
s
,
w
e
estab
lis
h
a
n
o
n
li
n
ea
r
m
et
h
o
d
n
a
m
ed
KE
P
C
A
,
w
h
ic
h
i
m
p
r
o
v
e
s
th
e
e
x
is
ted
li
n
ea
r
E
P
C
A
m
et
h
o
d
[
1
3
]
.
T
h
e
p
u
r
p
o
s
e
is
to
d
is
ca
r
d
th
e
r
ed
u
n
d
an
t
an
d
ir
r
elev
an
t
i
n
f
o
r
m
atio
n
a
n
d
g
e
t
o
n
l
y
t
h
e
v
al
u
ab
le
o
n
e.
Usi
n
g
t
h
e
m
a
x
i
m
u
m
e
n
tr
o
p
y
p
r
in
cip
le
[
1
6
]
,
w
e
ca
n
ea
s
il
y
d
eter
m
in
e
t
h
e
r
ed
u
ce
d
d
im
en
s
io
n
o
f
d
ata
in
k
er
n
el
s
p
ac
e.
2
.
1
.
1
.
P
rincipa
l
co
m
po
ne
nt
a
na
ly
s
is
P
r
in
cip
al
co
m
p
o
n
en
t
a
n
al
y
s
is
(
P
C
A
)
i
s
v
er
y
f
a
m
o
u
s
a
s
a
tec
h
n
iq
u
e
o
f
m
u
lti
v
ar
iate
s
tatis
ti
cs.
D
u
e
to
th
e
f
ac
t
o
f
an
al
y
zi
n
g
d
ata
i
n
ter
m
o
f
f
ea
t
u
r
e
e
x
tr
ac
tio
n
a
n
d
d
i
m
e
n
s
io
n
alit
y
r
ed
u
ctio
n
,
P
C
A
is
ad
o
p
ted
b
y
al
m
o
s
t
all
d
is
cip
li
n
es.
T
h
e
u
lt
i
m
ate
o
b
j
ec
tiv
e
o
f
P
C
A
i
s
to
s
elec
t
v
ar
iab
les
f
r
o
m
i
n
p
u
t
d
ata
tab
le
w
h
ic
h
h
a
v
e
h
ig
h
er
s
tati
s
tical
i
n
f
o
r
m
atio
n
th
en
s
q
u
ee
ze
o
u
t
t
h
is
i
n
f
o
r
m
a
tio
n
as
a
s
et
o
f
n
e
w
o
r
th
o
g
o
n
al
v
ar
iab
les
ca
lled
p
r
in
cip
al
co
m
p
o
n
e
n
t
b
ased
o
n
m
at
h
e
m
atic
n
o
tio
n
s
:
ei
g
e
n
v
alu
es,
ei
g
en
v
ec
to
r
s
,
m
ea
n
an
d
s
ta
n
d
ar
d
d
ev
iatio
n
[
1
4
,
2
0
]
.
2
.
1
.
2
.
Sh
a
nn
o
n e
ntr
o
py
C
lau
d
e
Sh
an
n
o
n
es
ta
b
lis
h
ed
th
e
en
t
r
o
p
y
c
o
n
ce
p
t
in
in
f
o
r
m
atio
n
th
eo
r
y
.
H
e
in
tr
o
d
u
ce
d
th
e
te
r
m
–
(
(
)
)
as
a
m
ea
s
u
r
em
en
t
o
f
th
e
in
f
o
r
m
atio
n
c
ar
r
i
ed
b
y
th
e
r
e
ali
za
tio
n
k
n
o
w
in
g
th
e
p
r
o
b
a
b
il
ity
o
f
d
is
t
r
i
b
u
ti
o
n
o
f
th
e
d
is
cr
ete
v
ar
i
ab
le
[
2
2
]
.
R
el
atin
g
t
o
a
d
is
cr
et
e
v
a
r
i
ab
le
,
th
e
en
t
r
o
p
y
m
ea
s
u
r
es
th
e
u
n
ce
r
t
ain
ty
.
T
h
e
Sh
an
n
o
n
en
t
r
o
p
y
r
el
ate
d
t
o
is
o
b
t
ain
e
d
ca
lc
u
latin
g
th
e
f
o
ll
o
w
in
g
f
o
r
m
u
la
(
1
)
:
(
)
=
∑
(
)
(
)
=
1
(
1
)
w
h
er
e
=
{
1
,
2
,
…
,
}
.
T
h
u
s
,
b
y
co
m
b
in
in
g
t
h
e
Sh
an
n
o
n
en
t
r
o
p
y
an
d
th
e
PC
A
it g
iv
es th
e
E
P
C
A
,
w
h
er
e
th
e
co
r
e
el
em
en
t
is
m
ax
i
m
u
m
en
tr
o
p
y
p
r
in
ci
p
l
e
(
M
E
P)
[
1
7
]
s
o
as
t
o
d
et
er
m
in
e
th
e
o
p
tim
al
d
im
en
s
io
n
o
f
th
e
p
r
in
ci
p
a
l su
b
s
p
ac
e
k
e
e
p
in
g
th
e
m
ax
i
m
u
m
in
f
o
r
m
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
C
lu
s
ter
in
g
u
s
in
g
ke
r
n
el
en
tr
o
p
y
p
r
in
cip
a
l c
o
mp
o
n
en
t
a
n
a
lysi
s
…
(
Lo
u
b
n
a
E
l F
a
tta
h
i
)
2111
2
.
1
.
3
.
K
er
nel
ent
ro
py
princip
a
l c
o
m
po
ne
nt
a
na
ly
s
is
Ou
r
p
r
o
p
o
s
e
d
a
p
p
r
o
a
ch
,
K
E
PC
A
,
is
a
n
o
n
lin
ea
r
v
e
r
s
i
o
n
o
f
E
P
C
A
[
2
3
]
.
T
h
e
b
asic
as
p
ec
t
o
f
k
er
n
el
E
P
C
A
m
eth
o
d
is
t
o
m
ap
in
p
u
t
d
a
ta
=
1
,
…
,
s
u
ch
th
at
=
1
,
.
.
,
in
t
o
k
e
r
n
el
s
p
a
ce
th
r
o
u
g
h
th
e
k
e
r
n
e
l
fu
n
ctio
n
.
T
h
en
,
k
er
n
el
m
atr
ix
i
s
g
iv
en
b
y
Φ
:
ℜ
→
ℱ
w
h
er
e
=
Φ
(
)
,
is
Φ
=
[
(
1
)
,
…
,
(
)
]
.
A
s
s
o
o
n
as
d
a
ta
m
ap
p
in
g
is
d
o
n
e
,
E
PC
A
is
im
p
lem
en
ted
in
.
T
h
e
p
o
s
i
tiv
e
s
em
i
-
d
ef
in
it
e
k
e
r
n
el
f
u
n
ctio
n
p
r
o
v
i
d
es
d
at
a
m
ap
p
in
g
,
=
×
→
w
h
ich
p
r
o
d
u
c
e
s
an
in
n
er
p
r
o
d
u
ct
in
th
e
Hil
b
e
r
t
s
p
ac
e
:
(
,
′
)
=
〈
(
)
,
(
′
)
,
〉
(
2
)
w
h
er
e
ev
e
r
y
s
in
g
le
el
em
en
t
(
,
′
)
,
o
f
th
e
(
,
)
k
er
n
el
m
atr
ix
,
is
e
q
u
iv
alen
t
t
o
(
,
′
)
.
T
h
u
s
,
th
e
in
n
er
p
r
o
d
u
c
t
is
=
Φ
×
Φ
.
T
o
elu
ci
d
ate
m
o
r
e
ex
p
li
cit
ly
h
o
w
w
e
p
r
o
ce
ed
in
im
p
lem
en
tin
g
th
e
E
P
C
A
,
l
et
1
,
…
,
b
e
th
e
m
ap
p
e
d
d
a
ta
co
n
t
ain
e
d
in
d
ef
in
e
d
b
y
f
ea
tu
r
es
1
,
…
,
an
d
i
s
th
e
s
u
b
s
p
a
ce
w
ith
=
1
,
…
,
.
T
h
e
av
e
r
ag
e
in
f
o
r
m
atio
n
s
u
p
p
lie
d
b
y
th
e
co
n
tr
i
b
u
ti
o
n
o
f
ea
c
h
m
ap
p
e
d
el
em
en
t
to
th
e
co
n
s
tr
u
ct
io
n
o
f
th
e
s
u
b
s
p
a
ce
o
f
p
r
o
jec
ti
o
n
is
t
h
e
ex
p
lain
e
d
in
e
r
tia
,
w
h
er
ea
s
t
h
e
av
e
r
ag
e
in
f
o
r
m
atio
n
g
iv
en
b
y
th
e
c
o
n
tr
ib
u
t
io
n
o
f
ev
er
y
m
ap
p
e
d
in
d
iv
id
u
al
t
o
th
e
lo
s
s
o
f
in
e
r
ti
a
is
th
e
r
es
id
u
al
in
e
r
t
ia
.
B
o
th
co
n
t
r
i
b
u
ti
o
n
s
to
th
e
ex
p
la
in
ed
in
er
t
ia
(
E
I
C
)
an
d
t
o
th
e
r
esi
d
u
al
in
er
tia
(
R
I
C
)
o
f
e
ac
h
s
in
g
le
in
d
iv
i
d
u
al
all
o
v
er
th
e
s
u
b
s
p
a
ce
o
f
f
e
atu
r
es
ar
e
s
u
c
ce
s
s
iv
ely
g
iv
en
as
a
p
r
o
b
a
b
il
ity
d
is
tr
i
b
u
t
io
n
in
(
3
)
an
d
(
4
)
[
2
3
]
.
1
(
)
=
(
,
)
(
3
)
2
(
)
=
(
,
)
(
4
)
w
ith
∑
(
,
)
=
1
=
1
,
an
d
∑
(
,
)
=
1
=
1
.
T
h
u
s
,
th
e
Sh
an
n
o
n
en
t
r
o
p
y
p
r
o
v
i
d
ed
b
y
t
h
ese
d
is
t
r
i
b
u
ti
o
n
s
r
es
p
ec
tiv
ely
is
g
i
v
en
as
in
(
5
)
an
d
(
6
)
:
1
(
1
)
=
∑
1
(
)
1
(
)
=
1
(5
)
2
(
2
)
=
∑
2
(
)
2
(
)
=
1
(6
)
T
h
e
v
a
r
i
ati
o
n
o
f
th
e
q
u
an
t
iti
es
in
(
5
)
an
d
(
6
)
is
an
t
ag
o
n
i
s
t.
A
cc
o
r
d
in
g
t
o
th
e
m
ax
i
m
u
m
en
tr
o
p
y
p
r
in
ci
p
l
e,
th
e
m
ax
i
m
ized
s
u
m
o
f
th
e
b
o
th
en
tr
o
p
ies
o
f
th
e
p
r
o
b
a
b
i
lity
d
is
tr
ib
u
t
io
n
s
co
r
r
es
p
o
n
d
s
to
th
e
m
in
i
m
u
m
d
im
en
s
io
n
o
f
th
e
s
u
b
s
p
ac
e
o
f
f
e
atu
r
es
.
(
∗
)
=
(
1
(
1
)
+
2
(
2
)
(
7
)
∗
is
th
e
o
p
tim
al
d
im
en
s
io
n
o
f
th
e
f
e
atu
r
e
s
u
b
s
p
ac
e.
2
.
2
.
Clus
t
er
ing
by
dens
it
y
pea
k
s
elec
t
io
n
R
ec
en
t
r
ese
ar
ch
es
g
iv
e
b
ig
in
t
er
est
to
th
e
clu
s
t
er
in
g
b
y
th
e
f
ast
s
ea
r
ch
o
f
clu
s
te
r
ce
n
t
r
o
i
d
s
b
ase
d
o
n
th
e
n
o
n
p
ar
am
etr
ic
esti
m
atio
n
o
f
th
e
PDF.
T
h
e
ex
ten
d
e
d
v
e
r
s
io
n
o
f
R
o
d
r
ig
u
ez
an
d
L
ai
o
’
s
m
eth
o
d
[
1
0
]
g
iv
en
b
y
W
an
g
an
d
Xu
[
1
1
]
is
s
u
m
m
ar
ize
d
h
er
e
th
r
o
u
g
h
th
e
Par
ze
n
esti
m
ato
r
r
a
th
e
r
th
an
th
e
s
te
p
f
u
n
ctio
n
.
T
h
e
m
ain
asp
ec
t
o
f
th
e
m
eth
o
d
is
th
e
m
ea
s
u
r
em
en
t
o
f
th
e
c
o
u
p
l
e
(
d
en
s
ity
,
d
is
t
an
ce
)
v
alu
es
ch
a
r
ac
t
er
i
zin
g
e
ac
h
d
at
a
p
o
in
t.
2
.
2
.
1
.
Densi
t
y
esti
m
a
t
io
n a
nd
dis
t
a
nce
R
ely
in
g
o
n
R
o
d
r
ig
u
ez
an
d
L
a
io
’
s
c
lu
s
te
r
in
g
m
eth
o
d
[
1
0
]
,
w
e
r
esu
m
e
h
er
e
th
e
c
o
m
p
u
tat
io
n
o
f
th
e
d
en
s
ity
an
d
d
is
tan
ce
v
alu
es
.
T
h
e
m
ain
r
o
le
is
t
o
i
d
en
tif
y
th
e
clu
s
te
r
ce
n
t
r
o
i
d
s
b
ase
d
o
n
th
e
tw
o
ass
u
m
p
tio
n
s
:
th
e
f
ir
s
t
o
n
e
est
ab
lis
h
es
th
e
f
a
ct
th
at
ea
ch
clu
s
t
er
ce
n
t
er
is
e
n
clo
s
ed
b
y
elem
en
ts
,
w
h
ich
h
av
e
l
o
c
al
d
en
s
it
ies
lo
w
er
th
an
th
e
ce
n
te
r
d
en
s
ity
.
T
h
e
S
ec
o
n
d
o
n
e
est
ee
m
s
th
at
ea
ch
clu
s
t
er
c
en
te
r
is
f
ar
en
o
u
g
h
f
r
o
m
all
o
th
e
r
p
o
in
ts
w
ith
h
ig
h
er
d
en
s
ity
.
Fo
r
a
g
iv
en
d
at
a
p
o
in
t
,
th
e
l
o
c
al
d
en
s
ity
an
d
th
e
d
is
ta
n
ce
a
r
e
d
ef
in
e
d
r
es
p
e
ctiv
e
ly
as
(
8
)
an
d
(9
)
:
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.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
1
0
9
-
2119
2112
=
∑
(
(
,
)
<
)
=
1
,
(8
)
̂
(
)
=
:
̂
(
)
<
̂
(
)
(
,
)
.
(9
)
w
h
er
e
(
)
is
th
e
s
te
p
f
u
n
cti
o
n
o
f
th
e
s
et
;
(
,
)
is
th
e
E
u
cli
d
i
an
d
is
tan
ce
b
e
tw
ee
n
tw
o
d
if
f
e
r
en
t
d
ata
p
o
in
ts
;
an
d
is
th
e
cu
t
-
o
f
f
d
is
ta
n
ce
d
ef
in
e
d
in
ad
v
an
ce
.
A
n
aly
zin
g
d
ef
in
iti
o
n
(
8
)
,
w
e
co
u
l
d
u
n
d
e
r
s
tan
d
th
a
t
is
s
im
p
ly
th
e
c
o
u
n
t
o
f
p
o
in
ts
t
h
at
a
r
e
cl
o
s
er
th
an
to
th
e
ℎ
d
a
ta
p
o
in
t,
w
h
er
ea
s
in
(
9
)
,
th
e
m
ea
s
u
r
em
en
t
is
d
et
e
r
m
in
ed
as
th
e
m
in
im
u
m
d
is
t
an
ce
a
m
o
n
g
d
is
t
an
ce
s
c
o
m
p
u
ted
b
etw
ee
n
th
e
ℎ
d
ata
p
o
in
t
an
d
al
l
o
th
e
r
p
o
in
ts
h
av
in
g
h
ig
h
er
d
en
s
it
y
.
Fin
ally
,
th
e
p
o
in
t,
w
h
ich
h
as
th
e
h
ig
h
est
d
en
s
ity
,
is
d
ef
in
e
d
t
o
be
(
,
)
.
No
n
eth
eless
,
th
e
ch
o
ic
e
o
f
is
n
o
t
a
lw
a
y
s
u
s
ef
u
l
b
ec
au
s
e
th
e
r
esu
lt
o
f
th
e
alg
o
r
ith
m
f
u
n
d
am
en
tally
d
e
p
en
d
s
o
n
it.
T
h
e
ca
u
s
e
is
t
h
at
d
esc
r
i
b
es
th
e
av
e
r
ag
e
n
u
m
b
er
o
f
n
eig
h
b
o
r
s
,
cl
o
s
e
to
1
%
an
d
2
%
o
f
th
e
w
h
o
le
n
u
m
b
er
o
f
d
ata
p
o
in
ts
.
C
o
n
s
eq
u
en
tly
,
th
e
ch
o
i
ce
o
f
is
u
n
s
y
s
te
m
atic
an
d
u
n
s
ta
b
le
w
h
en
th
e
s
iz
e
o
f
th
e
s
am
p
le
is
ch
an
g
in
g
.
T
o
g
et
r
i
d
o
f
th
e
b
a
d
ef
f
e
ct
o
f
,
w
e
o
p
t
u
s
in
g
th
e
P
a
r
z
en
esti
m
ato
r
an
d
th
e
v
ar
ia
b
l
e
k
er
n
el
es
tim
ato
r
in
lieu
o
f
th
e
s
tep
f
u
n
cti
o
n
th
at
h
as
g
o
o
d
ef
f
ec
t o
n
th
e
q
u
e
r
y
o
f
p
er
f
o
r
m
an
ce
[
1
0
]
.
C
o
n
ce
r
n
in
g
th
e
b
an
d
w
id
th
p
ar
am
eter
,
it
is
ef
f
icien
tly
c
o
m
p
u
ted
u
s
in
g
th
e
r
u
l
e
o
f
S
ilv
e
r
m
an
[
2
4
]
.
2
.
2
.
2
.
Va
ria
ble k
er
nel e
s
t
i
m
a
t
o
r
T
h
e
v
a
r
ia
b
l
e
k
e
r
n
el
esti
m
ato
r
(
VK
E
)
is
a
c
o
m
b
in
ati
o
n
o
f
P
a
r
ze
n
es
tim
ato
r
w
h
er
e
th
e
s
ca
l
e
o
f
th
e
b
u
m
p
s
p
l
ac
ed
o
n
th
e
d
at
a
p
o
in
ts
a
r
e
all
o
w
ed
t
o
v
ar
y
f
r
o
m
d
ata
p
o
in
t
t
o
an
o
th
e
r
[
2
5
,
26]
an
d
th
e
k
NN
esti
m
ato
r
.
T
h
e
es
tim
ato
r
o
f
Par
ze
n
-
R
o
s
e
n
b
lat
t
is
d
ef
in
e
d
as
in
(
10
:
̂
(
)
=
1
ℎ
∑
(
(
,
)
ℎ
)
=
1
(
1
0
)
w
h
er
e
is
th
e
k
er
n
el,
ℎ
is
th
e
s
m
o
o
th
in
g
p
a
r
am
eter
an
d
(
,
)
is
th
e
E
u
cli
d
e
an
d
is
t
an
ce
b
etw
ee
n
a
n
d
.
T
h
e
k
-
n
ea
r
es
t n
e
ig
h
b
o
r
s
(
k
NN
)
esti
m
ato
r
is
d
ef
in
ed
as
i
n
(
11
)
[
2
4
]
:
̂
(
)
=
(
⁄
)
(
(
)
)
=
⁄
(
)
(
1
1
)
w
h
er
e
is
a
p
o
s
i
tiv
e
in
teg
e
r
,
(
)
is
th
e
d
is
t
an
ce
f
r
o
m
to
th
e
ℎ
n
ea
r
e
s
t p
o
in
t
an
d
(
)
is
th
e
v
o
lu
m
e
o
f
a
s
p
h
e
r
e
o
f
r
ad
iu
s
(
)
an
d
is
th
e
v
o
lu
m
e
o
f
th
e
u
n
it
s
p
h
er
e
in
d
i
m
en
s
io
n
s
.
T
h
e
s
m
o
o
th
n
ess
d
e
g
r
ee
o
f
th
is
esti
m
ato
r
is
af
f
ec
te
d
b
y
th
e
p
a
r
am
eter
,
tak
en
t
o
b
e
v
e
r
y
s
m
aller
th
an
th
e
s
am
p
le
s
i
ze
.
T
h
e
V
K
E
is
c
o
n
s
t
r
u
ct
e
d
s
im
ilar
ly
to
th
e
cl
ass
ic
al
k
e
r
n
el
est
im
ato
r
.
I
t
is
d
ef
in
e
d
b
y
(
12
)
[
2
4
]
:
̂
(
)
=
1
ℎ
∑
1
(
,
)
(
(
,
)
ℎ
,
)
=
1
(
1
2
)
w
ith
,
is
a
E
u
c
li
d
e
an
d
is
t
an
ce
b
etw
ee
n
a
d
at
a
p
o
in
t
an
d
th
e
ℎ
n
ea
r
est
p
o
in
t
o
f
th
e
o
th
er
−
1
da
t
a
p
o
in
ts
.
2
.
2
.
3
.
Clus
t
er
v
a
lid
it
y
ind
ex
Fo
r
ev
e
r
y
clu
s
te
r
in
g
p
r
o
c
ess
,
a
g
r
o
u
p
o
f
clu
s
te
r
s
1
,
…
,
,
…
,
is
o
b
tain
e
d
f
r
o
m
a
g
iv
en
d
a
tas
et.
T
h
e
m
ea
s
u
r
em
en
t
is
th
e
r
el
ati
o
n
b
e
tw
ee
n
ea
ch
p
o
in
t
an
d
t
h
e
c
lu
s
te
r
,
f
o
r
=
1
,
…
,
.
Fo
r
a
ll
th
e
p
r
e
-
d
ef
in
e
d
clu
s
t
er
s
,
w
e
s
et
=
0
in
ca
s
e
∉
an
d
,
w
h
en
∈
,
>
0
,
w
e
h
av
e
[
1
2
,
1
7
,
2
3
]
:
∑
=
1
∈
,
=
1
,
…
,
k
(
1
3
)
E
ac
h
cl
ass
p
r
o
v
id
es
in
f
o
r
m
ati
o
n
w
h
ich
is
m
ea
s
u
r
e
d
u
s
in
g
th
e
en
tr
o
p
y
f
o
r
m
u
la
(
14
)
:
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
C
lu
s
ter
in
g
u
s
in
g
ke
r
n
el
en
tr
o
p
y
p
r
in
cip
a
l c
o
mp
o
n
en
t
a
n
a
lysi
s
…
(
Lo
u
b
n
a
E
l F
a
tta
h
i
)
2113
=
∑
=
1
(
)
(
1
4
)
Fin
ally
,
th
e
in
d
ex
is
r
ec
o
g
n
iz
e
d
as
an
en
tr
o
p
y
b
y
(
15
)
:
=
=
1
∑
=
1
+
(
∗
)
(
1
5
)
w
h
er
e
is
an
en
tr
o
p
y
an
d
∗
is
th
e
o
p
t
im
al
n
u
m
b
er
o
f
c
lass
es
f
o
r
w
h
ich
th
e
en
t
r
o
p
y
is
m
ax
im
al
.
2
.
2
.
4
.
Alg
o
rit
h
m
o
f
t
he
K
er
nel e
ntr
o
py
princip
a
l c
o
m
po
n
ent
a
na
ly
s
is
A
cc
o
r
d
in
g
t
o
th
e
k
e
r
n
el
m
eth
o
d
,
th
e
in
p
u
t
s
p
ac
e
ca
n
b
e
in
d
i
r
e
ctly
m
ap
p
e
d
in
to
a
h
ig
h
-
d
im
en
s
io
n
al
f
ea
tu
r
e
s
p
ac
e
th
r
o
u
g
h
w
h
ich
th
e
n
o
n
l
in
ea
r
ity
co
u
l
d
b
e
r
em
o
v
ed
o
r
r
e
d
u
c
ed
.
T
h
e
GR
B
Fu
n
c
tio
n
is
th
e
p
r
in
ci
p
a
l
elem
en
t
o
f
th
e
k
er
n
el
f
u
n
cti
o
n
b
ec
au
s
e
it
is
ty
p
ica
lly
u
s
ed
in
R
ep
r
o
d
u
cin
g
K
er
n
e
l
Hil
b
e
r
t
Sp
a
ce
(
R
KHS
)
w
ith
th
e
o
b
ject
iv
e
o
f
m
ax
im
izin
g
th
e
f
ea
tu
r
e
s
p
a
ce
v
a
r
ian
ce
o
f
th
e
o
u
tp
u
t
v
ar
ia
b
les
.
Su
b
s
e
q
u
en
tl
y
,
th
e
m
ap
p
ed
d
a
ta
w
er
e
r
ed
u
ce
d
u
s
in
g
th
e
E
P
C
A
as
a
lin
ea
r
m
eth
o
d
f
o
r
d
ata
r
e
d
u
cti
o
n
w
ith
th
e
u
lti
m
ate
o
b
j
e
ctiv
e
to
m
ain
tain
f
ea
tu
r
es e
x
p
e
cte
d
t
o
p
r
es
er
v
e
a
s
p
o
s
s
i
b
le
th
e
v
a
lu
ab
le
in
f
o
r
m
ati
o
n
.
E
v
en
tu
al
ly
,
a
s
im
p
le
alg
o
r
ith
m
o
f
clu
s
te
r
in
g
w
o
u
ld
b
e
ab
le
t
o
ac
h
iev
e
s
ig
n
i
f
ican
t
r
esu
l
ts
b
as
e
d
o
n
b
o
th
Pa
r
z
en
es
tim
ato
r
an
d
v
ar
ia
b
l
e
k
e
r
n
el
es
tim
ato
r
.
Ou
r
p
r
o
p
o
s
e
d
alg
o
r
ith
m
o
f
cl
u
s
ter
in
g
c
o
n
s
i
d
e
r
in
g
o
u
r
p
r
o
p
o
s
e
d
K
E
P
C
A
m
eth
o
d
,
is
r
esu
m
ed
in
th
e
n
ex
t ste
p
s
.
No
r
m
alize
th
e
in
p
u
t
d
at
a
;
Ma
p
th
e
in
p
u
t
d
ata
;
P
e
r
f
o
r
m
th
e
E
P
C
A
;
R
ed
u
c
e
th
e
t
r
an
s
f
o
r
m
ed
d
at
a;
C
o
m
p
u
te
th
e
b
an
d
w
id
th
;
C
o
m
p
u
te
th
e
p
ai
r
d
en
s
ity
-
d
is
ta
n
ce
o
f
r
e
d
u
c
ed
d
at
a;
Fo
r
=
1
,
…
,
Sele
ct
th
e
clu
s
t
er
p
ea
k
s
an
d
as
s
ig
n
ea
ch
e
lem
en
t in
t
o
its
clu
s
t
er
;
C
o
m
p
u
te
th
e
c
lu
s
te
r
v
a
li
d
ity
in
d
ex
;
T
h
e
co
r
r
e
ct
n
u
m
b
er
o
f
c
lu
s
te
r
s
an
d
th
e
b
es
t g
r
o
u
p
in
g
f
o
r
th
e
i
n
p
u
t
d
a
ta
c
o
r
r
es
p
o
n
d
s
t
o
th
e
o
n
e
th
at
h
av
e
m
ax
i
m
u
m
v
alu
e
o
f
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Ou
r
p
r
es
en
t
s
ec
t
io
n
h
as
as
co
n
c
er
n
,
d
em
o
n
s
tr
at
in
g
th
e
p
e
r
f
o
r
m
an
ce
q
u
e
r
y
o
f
o
u
r
ap
p
r
o
a
ch
b
y
r
e
d
u
cin
g
d
a
ta
an
d
ex
t
r
a
ctin
g
o
n
ly
th
e
v
alu
ab
le
in
f
o
r
m
atio
n
.
I
n
s
p
ir
e
d
b
y
co
m
p
u
tin
g
th
e
c
o
u
p
le
d
en
s
ity
-
d
is
tan
ce
v
alu
es
th
r
o
u
g
h
th
e
f
ast
s
ea
r
ch
o
f
clu
s
te
r
ce
n
t
er
s
.
T
h
e
u
s
e
o
f
eith
e
r
th
e
P
a
r
ze
n
est
im
ato
r
[
2
7
]
o
r
v
a
r
ia
b
l
e
k
er
n
e
l
esti
m
ato
r
in
teg
r
at
in
g
th
e
r
u
le
o
f
Sil
v
e
r
m
an
h
as
g
o
o
d
o
u
t
co
m
es
o
n
o
u
r
clu
s
t
er
in
g
r
es
u
lts
.
A
co
m
p
ar
is
o
n
b
etw
ee
n
th
e
r
esu
lts
u
s
in
g
o
u
r
clu
s
te
r
in
g
alg
o
r
ith
m
b
ase
d
o
n
KE
P
C
A
d
at
a
t
r
an
s
f
o
r
m
atio
n
a
n
d
o
th
er
alg
o
r
ith
m
s
o
f
c
lu
s
te
r
in
g
is
g
iv
en
.
T
h
e
a
r
tif
icia
l,
th
e
r
ea
l
w
ell
-
k
n
o
w
n
(
I
r
is
,
See
d
s
,
Fl
am
e
an
d
He
ar
t)
d
at
as
ets w
er
e
u
s
e
d
[
2
8
]
as w
ell
as
a
v
eh
ic
le
t
r
a
ject
o
r
y
d
at
ase
t.
Ou
r
an
aly
s
is
s
tu
d
y
is
d
em
o
n
s
tr
at
ed
o
n
MA
T
L
A
B
en
v
ir
o
n
m
en
t.
3
.
1
.
Si
m
ula
t
ed
s
t
u
dy
W
e
co
n
s
id
er
as
a
f
ir
s
t
ap
p
licat
io
n
,
a
s
i
m
u
late
d
d
ata
th
at
co
n
s
is
ts
o
f
t
h
r
ee
r
an
d
o
m
cl
u
s
ter
s
laid
in
6
0
0
b
y
2
m
atr
i
x
.
All
clu
s
ter
s
wer
e
g
en
er
ated
b
y
a
n
o
r
m
a
l
d
is
tr
ib
u
tio
n
b
u
t
w
i
th
d
if
f
er
e
n
t
r
an
d
o
m
co
v
ar
iate
m
atr
ices
an
d
ce
n
ter
s
.
C
l
u
s
ter
co
n
tain
s
2
0
0
d
ata
p
o
in
ts
f
o
r
e
ac
h
.
Fi
g
u
r
e
1
,
r
ev
ea
l
s
t
h
e
p
lo
t
o
f
t
h
e
i
n
itial
d
ata
o
f
th
e
t
w
o
v
ar
iab
les o
f
th
e
i
n
p
u
t
s
p
ac
e
b
ef
o
r
e
co
n
s
id
er
in
g
o
u
r
clu
s
ter
i
n
g
alg
o
r
it
h
m
.
A
s
it
is
s
h
o
w
n
in
Fig
u
r
e
2
(
a)
,
w
e
ca
n
o
b
s
e
r
v
e
th
at
af
te
r
ex
ec
u
tin
g
th
e
KE
P
C
A
d
a
ta
t
r
an
s
f
o
r
m
atio
n
r
esu
lt
h
as
g
iv
en
th
r
e
e
d
im
en
s
io
n
s
as th
e
r
e
d
u
ce
d
d
im
en
s
io
n
af
ter
d
at
a
m
ap
p
in
g
.
T
h
u
s
,
f
o
r
s
y
n
th
etic
d
a
ta
,
th
r
ee
-
d
im
en
s
io
n
al
ar
r
ay
ar
e
en
o
u
g
h
to
r
e
p
r
esen
t
in
p
u
t
d
at
a
in
f
e
atu
r
e
s
p
ac
e
.
T
h
e
Fig
u
r
e
2
(
b
)
d
is
c
lo
s
es
th
at
th
e
ce
n
te
r
s
a
r
e
i
d
en
tif
i
ed
as
th
r
e
e.
T
h
ey
ar
e
l
o
ca
t
ed
at
th
e
u
p
p
er
-
r
ig
h
t
c
o
r
n
er
o
f
th
e
d
e
n
s
ity
-
d
is
tan
ce
p
l
o
t
,
d
is
c
r
im
in
ate
d
in
r
e
d
co
lo
r
,
an
d
ci
r
cl
ed
s
h
a
p
e
.
B
esi
d
es
,
o
n
t
h
e
Fig
u
r
e
2
(
c
)
i
t
ca
n
b
e
e
asil
y
u
n
d
e
r
s
t
o
o
d
th
a
t
th
e
s
o
r
te
d
q
u
an
tity
(
p
r
o
d
u
ct
o
f
d
e
n
s
ity
an
d
d
is
t
an
ce
)
h
as
h
ig
h
v
alu
e
f
o
r
th
e
f
i
r
s
t
th
r
e
e
d
at
a
p
o
i
n
ts
.
T
h
is
m
ag
n
itu
d
e
is
b
y
its
o
w
n
d
ef
in
iti
o
n
la
r
g
e,
s
ta
r
ts
in
c
r
ea
s
in
g
a
b
n
o
r
m
ally
b
etw
ee
n
clu
s
t
er
c
en
te
r
s
an
d
g
ettin
g
v
e
r
y
n
ar
r
o
w
b
etw
ee
n
o
th
e
r
s
am
p
les.
C
o
n
s
eq
u
en
t
ly
,
b
o
th
te
ch
n
iq
u
es
s
h
o
w
th
e
s
am
e
n
u
m
b
er
o
f
c
en
te
r
s
,
w
h
ich
ev
en
tu
ally
co
n
f
i
r
m
s
th
e
ex
is
ten
c
e
o
f
th
r
ee
c
lu
s
te
r
s
.
T
h
e
o
b
t
ain
e
d
r
esu
lts
c
an
b
e
ex
p
la
in
e
d
th
an
k
s
t
o
th
e
f
ac
t
th
at
ea
ch
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.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
1
0
9
-
2119
2114
ce
n
te
r
is
r
e
co
g
n
iz
e
d
b
y
h
ig
h
er
lo
ca
l
d
en
s
ity
an
d
r
el
ativ
e
ly
lar
g
e
d
is
t
an
c
e
aw
ay
f
r
o
m
th
e
o
t
h
er
d
a
ta
p
o
in
ts
w
ith
h
ig
h
er
d
en
s
ity
.
Hen
ce
,
o
u
r
a
lg
o
r
ith
m
is
ca
p
a
b
l
e
o
f
d
if
f
er
en
ti
atin
g
am
o
n
g
s
t
ce
n
te
r
s
an
d
o
th
er
d
at
a
p
o
i
n
ts
.
N
ex
t
,
to
ex
am
in
e
th
e
v
a
li
d
ity
o
f
o
u
r
clu
s
te
r
in
g
r
esu
l
t,
w
e
in
v
esti
g
at
e
b
o
th
c
r
ite
r
i
o
n
an
d
th
e
E
l
b
o
w
m
eth
o
d
[
2
9
]
.
T
h
e
g
iv
en
r
esu
lts
a
r
e
d
is
p
l
ay
ed
o
n
th
e
s
am
e
Fig
u
r
e
2
.
On
th
e
F
ig
u
r
e
2
(
d
)
,
w
e
ca
n
o
b
s
er
v
e
th
e
p
r
o
g
r
ess
o
f
th
e
in
d
ex
th
r
o
u
g
h
w
h
ich
th
e
o
p
t
im
al
n
u
m
b
er
o
f
clu
s
t
e
r
s
is
i
d
en
tif
i
e
d
t
o
b
e
th
r
ee
clu
s
t
er
s
ap
p
ly
in
g
th
e
m
ax
i
m
u
m
en
tr
o
p
y
p
r
in
ci
p
le
.
L
ik
e
w
is
e,
s
am
e
r
esu
lt
w
as
g
iv
en
o
n
Fig
u
r
e
2
(
e
)
b
y
in
v
esti
g
atin
g
th
e
E
l
b
o
w
m
eth
o
d
,
w
h
ich
r
eli
es
o
n
th
e
m
in
im
izatio
n
o
f
th
e
s
u
m
o
f
th
e
s
q
u
a
r
e
d
e
r
r
o
r
s
w
ith
in
ea
ch
c
lu
s
ter
.
T
h
r
e
e
c
lu
s
te
r
s
w
er
e
p
ick
e
d
.
On
th
e
last
Fi
g
u
r
e
2
(
f
)
w
e
ca
n
s
ee
th
e
s
am
p
les
ass
ig
n
ati
o
n
to
th
ei
r
co
n
v
en
i
en
t
clu
s
te
r
s
co
n
s
i
d
e
r
in
g
th
e
ce
n
t
e
r
s
el
ec
ti
o
n
o
u
t
c
o
m
e.
E
v
e
r
y
s
in
g
le
p
o
i
n
t
is
ass
ig
n
e
d
t
o
th
e
n
e
ar
est
ce
n
te
r
b
as
ed
o
n
th
e
E
u
cl
i
d
e
an
d
is
t
an
ce
ca
lcu
la
ti
o
n
.
E
v
en
tu
ally
,
th
e
r
esu
lt
o
f
th
e
clu
s
te
r
in
g
o
f
th
e
p
r
o
p
o
s
e
d
alg
o
r
ith
m
is
g
iv
en
o
n
th
r
e
e
-
d
im
en
s
io
n
al
f
ea
tu
r
e
s
p
a
ce
p
l
o
t
f
o
r
th
e
s
y
n
th
etic
d
at
a
s
et
s
in
ce
th
e
d
im
en
s
io
n
w
as
r
e
d
u
ce
d
in
t
o
th
r
e
e
f
ea
tu
r
es a
f
te
r
p
e
r
f
o
r
m
in
g
KE
PC
A
Fig
u
r
e
2
(
a
)
.
T
h
e
th
r
e
e
c
lu
s
ter
s
w
er
e
p
r
o
p
er
ly
d
is
tin
g
u
is
h
e
d
o
n
e
f
r
o
m
an
o
th
e
r
b
y
d
if
f
er
en
t
s
h
a
p
es
an
d
co
lo
r
s
as
th
e
b
est
g
r
o
u
p
in
g
f
o
r
s
am
p
les,
w
h
ich
d
em
o
n
s
tr
at
es
o
u
r
cl
u
s
ter
in
g
alg
o
r
i
th
m
ass
u
m
p
tio
n
s
.
Fig
u
r
e
1
.
T
w
o
-
d
im
en
s
io
n
al
p
l
o
t
o
f
th
e
in
iti
al
a
r
tif
i
cia
l
d
a
tase
t
Fig
u
r
e
1
.
R
esu
lts
o
b
t
ain
e
d
o
n
ar
t
if
ici
al
d
atas
et
(
a
)
R
esu
lt o
f
t
h
e
o
p
ti
m
al
co
m
p
o
n
e
n
t
s
n
u
m
b
er
u
s
i
n
g
t
h
e
KE
P
C
A
,
(
b
)
d
ec
is
io
n
g
r
ap
h
f
o
r
ce
n
ter
s
s
elec
tio
n
o
f
t
h
e
d
en
s
i
t
y
d
is
ta
n
ce
p
lo
t,
(
c)
t
he
p
r
o
d
u
c
t o
f
th
e
d
en
s
it
y
an
d
d
is
tan
ce
p
lo
tted
in
d
ec
r
ea
s
in
g
o
r
d
er
,
(
d
)
n
u
m
b
er
o
f
clu
s
te
r
s
v
alid
atio
n
g
i
v
en
b
y
in
d
ex
,
(
e)
th
e
E
lb
o
w
m
et
h
o
d
f
o
r
ar
tif
icial
d
ataset
,
(
f
)
th
e
ass
i
g
n
m
e
n
t o
f
s
a
m
p
le
s
to
clu
s
ter
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
C
lu
s
ter
in
g
u
s
in
g
ke
r
n
el
en
tr
o
p
y
p
r
in
cip
a
l c
o
mp
o
n
en
t
a
n
a
lysi
s
…
(
Lo
u
b
n
a
E
l F
a
tta
h
i
)
2115
T
h
e
cl
ass
if
ic
ati
o
n
r
at
e
o
f
o
u
r
p
r
o
p
o
s
e
d
a
lg
o
r
ith
m
w
ith
KE
PC
A
d
ata
t
r
an
s
f
o
r
m
atio
n
an
d
t
h
e
VKE
i
s
ab
o
u
t
9
7
.
1
7
%
f
o
r
th
e
s
im
u
lated
d
at
aset
,
w
h
er
ea
s
th
e
K
-
m
e
an
s
alg
o
r
ith
m
ac
h
iev
e
d
9
6
.
8
3
%.
T
h
en
,
u
s
in
g
o
u
r
alg
o
r
ith
m
o
f
clu
s
te
r
in
g
w
ith
th
e
VKE
an
d
E
P
C
A
h
as
g
iv
en
8
2
.
3
3
%.
T
h
e
r
ef
o
r
e,
th
e
p
r
esen
t
alg
o
r
ith
m
w
ith
th
e
k
er
n
el
d
at
a
tr
an
s
f
o
r
m
ati
o
n
h
as
g
iv
en
r
ela
tiv
ely
h
ig
h
er
cl
ass
if
i
ca
ti
o
n
r
ate
th
an
th
e
o
th
er
c
lu
s
t
er
in
g
alg
o
r
ith
m
s
.
3
.
2
.
T
he
I
ris da
t
a
s
et
T
h
e
I
r
is
b
en
ch
m
ar
k
is
o
n
e
o
f
t
h
e
m
ac
h
in
e
-
lea
r
n
in
g
d
atas
ets;
Fis
h
er
f
ir
s
t
u
s
e
d
i
t
in
[
3
0
]
.
I
t
c
o
n
s
is
ts
o
f
1
5
0
m
ea
s
u
r
em
en
ts
o
f
th
r
e
e
d
i
s
tin
ct
ty
p
es
o
f
th
e
I
r
is
p
lan
t
(
I
r
is
s
et
o
s
a
,
I
r
is
v
i
r
g
in
ic
a
an
d
I
r
is
v
e
r
s
ic
o
l
o
r
)
o
f
th
e
f
o
u
r
v
a
r
i
ab
les:
w
id
th
an
d
len
g
th
f
o
r
s
e
p
al
an
d
p
et
al
.
I
t
is
w
o
r
th
m
en
tio
n
in
g
th
at
,
o
n
e
o
f
th
e
cl
ass
es
is
l
in
ea
r
ly
s
ep
ar
ab
le
,
w
h
er
ea
s
th
e
tw
o
o
t
h
er
s
ar
e
n
o
t
[
3
0
]
.
C
o
n
s
i
d
er
in
g
th
e
c
o
m
b
in
ati
o
n
o
f
k
er
n
el
d
at
a
t
r
an
s
f
o
r
m
ati
o
n
(
m
ap
p
in
g
)
an
d
th
e
E
P
C
A
as
a
p
r
e
p
r
o
c
ess
in
g
f
o
r
in
p
u
t
d
ata
,
t
h
e
f
ig
u
r
e
p
r
esen
ts
r
es
u
lts
o
b
tai
n
ed
o
n
I
r
is
d
at
ase
t,
Fig
u
r
e
3
(
a
)
illu
s
t
r
at
es th
e
r
e
d
u
ce
d
f
e
atu
r
es
in
th
e
h
ig
h
-
d
im
en
s
io
n
al
s
p
ac
e
(
1
5
0
f
ea
tu
r
es
)
.
W
e
r
est
r
i
ct
o
u
r
p
l
o
t to
o
n
ly
2
5
f
ea
tu
r
es
o
n
th
e
F
ig
u
r
e
3
f
o
r
th
e
s
ak
e
o
f
c
le
ar
n
ess
as
t
h
e
en
t
r
o
p
y
ev
o
lv
es in
d
e
c
r
ea
s
i
n
g
o
r
d
e
r
.
T
h
er
ef
o
r
e
,
th
e
s
ev
en
te
en
m
ain
tain
e
d
n
o
n
lin
ea
r
f
ea
tu
r
es
in
te
r
p
r
et
th
e
m
o
r
e
r
el
ev
an
t
o
n
es
f
o
r
o
u
r
c
lu
s
ter
in
g
alg
o
r
ith
m
in
ter
m
o
f
in
f
o
r
m
ati
o
n
co
n
ten
t
.
O
n
th
e
Fig
u
r
es
3
(
b
)
an
d
3
(
c
)
b
o
t
h
g
r
ap
h
s
a
r
e
g
iv
en
r
e
ly
in
g
o
n
th
e
m
ea
s
u
r
em
en
t o
f
th
e
p
ai
r
d
en
s
ity
an
d
d
is
t
an
ce
.
C
o
n
s
id
er
in
g
th
e
f
ir
s
t
p
l
o
t
o
n
th
e
Fig
u
r
e
3
(
b
)
,
it
p
r
es
en
ts
a
d
en
s
ity
-
d
is
tan
ce
p
l
o
t
,
w
h
er
ea
s
th
e
F
ig
u
r
e
3
(
c)
it
p
r
esen
ts
th
e
s
o
r
te
d
q
u
an
t
ity
o
f
th
e
d
en
s
ity
an
d
d
is
t
an
ce
p
r
o
d
u
ct.
T
h
u
s
,
i
d
en
ti
ca
l
r
esu
lt
w
as
g
iv
en
b
y
b
o
th
tech
n
iq
u
es
,
th
r
ee
c
en
tr
o
i
d
s
h
av
e
b
e
en
d
et
er
m
in
ed
f
r
o
m
d
ata
.
T
h
e
o
b
tain
ed
r
esu
lts
a
r
e
in
ter
p
r
et
e
d
th
an
k
s
t
o
th
e
c
o
m
in
g
ass
u
m
p
tio
n
:
E
v
e
r
y
ce
n
te
r
i
s
d
is
t
in
g
u
is
h
ed
f
r
o
m
th
e
o
th
e
r
d
a
ta
p
o
in
ts
b
y
its
h
ig
h
er
lo
ca
l
d
en
s
i
ty
an
d
r
ela
ti
v
ely
lar
g
e
d
is
t
an
ce
.
Hen
c
e,
o
u
r
alg
o
r
ith
m
is
ca
p
a
b
l
e
o
f
d
if
f
er
en
ti
atin
g
am
o
n
g
ce
n
te
r
s
an
d
th
e
o
th
er
d
a
ta
p
o
i
n
ts
.
T
o
d
em
o
n
s
tr
at
e
o
u
r
clu
s
t
er
in
g
alg
o
r
ith
m
p
er
f
o
r
m
an
ce
,
w
e
in
co
r
p
o
r
at
e
th
e
clu
s
te
r
v
a
li
d
ity
in
d
ex
f
o
u
n
d
e
d
th
e
m
ax
i
m
u
m
en
tr
o
p
y
p
r
in
cip
le
in
F
ig
u
r
e
3
(
d
)
an
d
th
e
E
l
b
o
w
m
eth
o
d
in
Fig
u
r
e
3
(
e
)
.
B
o
th
cr
ite
r
i
a
p
e
r
f
o
r
m
s
am
e
r
esu
lt
,
w
h
ich
c
o
n
s
eq
u
en
tly
co
n
f
i
r
m
s
th
e
ex
is
t
en
ce
o
f
th
r
ee
clu
s
t
er
s
.
Fig
u
r
e
2
.
R
esu
lts
o
b
t
ain
e
d
o
n
I
r
is
d
atas
et
(
a
)
r
esu
lt o
f
th
e
o
p
ti
m
al
co
m
p
o
n
e
n
t
s
n
u
m
b
er
u
s
i
n
g
th
e
KE
P
C
A
,
(
b
)
d
ec
is
io
n
g
r
ap
h
f
o
r
ce
n
ter
s
s
e
le
ctio
n
o
f
t
h
e
d
en
s
it
y
d
is
ta
n
ce
p
l
o
t,
(
c)
t
h
e
p
r
o
d
u
ct
o
f
th
e
d
en
s
it
y
an
d
d
is
ta
n
ce
p
lo
tted
in
d
ec
r
ea
s
in
g
o
r
d
er
,
(
d
)
n
u
m
b
er
o
f
cl
u
s
ter
s
v
al
id
atio
n
g
iv
e
n
b
y
in
d
ex
a
n
d
(
e)
th
e
E
lb
o
w
m
et
h
o
d
f
o
r
I
r
is
d
ataset
T
h
er
ef
o
r
e
,
o
u
r
c
lu
s
te
r
in
g
a
lg
o
r
ith
m
is
a
b
l
e
t
o
i
d
en
tif
y
au
to
m
atica
lly
th
e
ce
n
te
r
o
f
ea
ch
c
lu
s
ter
.
T
h
e
class
if
i
ca
t
io
n
r
a
te
f
o
r
I
r
is
d
at
a
u
s
in
g
o
u
r
alg
o
r
ith
m
o
f
clu
s
te
r
i
n
g
c
o
n
s
id
e
r
in
g
th
e
K
E
P
C
A
d
at
a
tr
an
s
f
o
r
m
atio
n
as
a
p
r
ep
r
o
c
ess
in
g
s
t
ep
is
8
9
.
3
3
%
in
c
o
r
p
o
r
atin
g
v
ar
ia
b
le
k
e
r
n
el
esti
m
ato
r
w
h
ile
it
is
e
q
u
als
t
o
8
8
%
in
co
r
p
o
r
atin
g
P
a
r
ze
n
esti
m
ato
r
,
f
o
r
th
e
E
P
C
A
d
at
a
t
r
an
s
f
o
r
m
ati
o
n
in
teg
r
a
t
in
g
VKE
,
it
is
u
n
a
b
le
t
o
d
ete
ct
all
th
r
ee
clu
s
t
er
s
an
d
c
o
n
s
id
er
s
o
n
ly
2
clu
s
ter
s
,
lik
ew
is
e
f
o
r
K
-
m
ed
o
i
d
s
.
T
h
en
,
th
e
K
-
m
ea
n
s
h
as
r
ea
ch
e
d
o
n
l
y
8
2
%.
T
h
er
ef
o
r
e
,
o
u
r
au
t
o
m
atic
alg
o
r
ith
m
in
teg
r
at
in
g
KE
P
C
A
d
ata
t
r
an
s
f
o
r
m
ati
o
n
an
d
th
e
v
a
r
i
ab
le
k
e
r
n
el
esti
m
ato
r
is
ca
p
a
b
l
e
o
f
c
lass
if
y
in
g
p
a
tte
r
n
s
w
ith
a
h
ig
h
er
cl
ass
if
ic
ati
o
n
r
a
te
c
o
m
p
ar
e
d
to
th
e
o
th
e
r
alg
o
r
ith
m
s
.
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.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
1
0
9
-
2119
2116
3
.
3
.
Seeds
da
t
a
ba
s
e
T
h
e
Seed
s
d
ataset
co
m
p
o
s
ed
o
f
2
1
0
s
a
m
p
les
r
e
f
er
r
in
g
to
t
h
r
ee
w
h
ea
t
v
ar
ieties,
7
0
ele
m
en
t
s
f
o
r
ea
ch
,
d
escr
ib
ed
b
y
7
g
eo
m
etr
ic
f
e
atu
r
es
[
2
9
]
.
C
o
n
s
id
er
in
g
t
h
e
co
m
b
i
n
atio
n
o
f
th
e
k
er
n
el
d
ata
tr
an
s
f
o
r
m
a
tio
n
(
m
ap
p
in
g
)
a
n
d
t
h
e
E
P
C
A
a
s
a
n
e
f
f
icien
t
p
r
e
p
r
o
ce
s
s
in
g
f
o
r
in
p
u
t
d
ata,
t
h
e
Fi
g
u
r
e
4
(
a)
ill
u
s
tr
ates
t
h
e
r
ed
u
ce
d
n
u
m
b
er
o
f
f
ea
t
u
r
es
in
t
h
e
h
i
g
h
-
d
i
m
e
n
s
io
n
al
s
p
ac
e
(
2
1
0
f
ea
tu
r
es).
Fo
r
th
e
s
ak
e
o
f
clea
r
n
es
s
,
w
e
li
m
it
o
u
r
p
lo
t
to
2
5
f
ea
tu
r
es
b
ec
au
s
e
o
f
t
h
e
d
ec
r
ea
s
in
g
e
v
o
lu
t
io
n
o
f
t
h
e
en
tr
o
p
y
.
T
h
er
ef
o
r
e,
th
e
s
ev
e
n
m
ain
tai
n
ed
n
o
n
l
in
ea
r
f
ea
t
u
r
es
in
ter
p
r
et
th
e
m
o
r
e
r
el
ev
an
t
o
n
es
in
ter
m
o
f
in
f
o
r
m
a
tio
n
co
n
ten
t
f
o
r
o
u
r
clu
s
ter
i
n
g
alg
o
r
ith
m
.
I
n
th
e
Fig
u
r
e
4
(
b
)
an
d
4
(
c)
t
h
e
d
is
p
lay
ed
r
esu
lts
ar
e
g
iv
e
n
b
ase
d
o
n
t
h
e
s
a
m
e
m
ag
n
it
u
d
es
(
t
h
e
d
en
s
it
y
a
n
d
t
h
e
d
is
tan
ce
)
.
Fo
r
th
e
p
lo
t
in
Fi
g
u
r
e
4
(
b
)
it
is
a
d
en
s
it
y
-
d
is
tan
ce
p
l
o
t
w
h
er
ea
s
t
h
e
p
lo
t
in
Fi
g
u
r
e
4
(
c)
,
it r
ev
ea
ls
th
e
s
o
r
ted
p
r
o
d
u
ct
o
f
d
en
s
i
t
y
an
d
d
is
tan
ce
.
T
h
i
s
q
u
a
n
tit
y
is
b
y
its
d
e
f
i
n
itio
n
lar
g
e
an
d
b
eg
in
s
to
g
r
o
w
b
et
w
ee
n
clu
s
ter
ce
n
tr
o
id
s
p
r
o
g
r
ess
iv
el
y
af
ter
w
ar
d
s
it
b
ec
o
m
e
s
tig
h
t
b
et
w
ee
n
t
h
e
r
est
o
f
p
o
in
ts
.
T
h
u
s
,
th
e
s
a
m
e
r
esu
lt
is
g
iv
e
n
b
y
b
o
th
tec
h
n
iq
u
e
s
,
it
i
s
clea
r
l
y
s
ee
n
th
at
th
r
ee
ce
n
tr
o
i
d
s
w
er
e
d
eter
m
i
n
ed
f
r
o
m
d
ata
,
w
h
ic
h
d
ec
lar
es
i
n
ad
v
an
ce
th
e
e
x
is
te
n
ce
o
f
t
h
r
ee
clu
s
ter
s
.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
co
n
f
ir
m
ed
th
a
n
k
s
to
th
e
as
s
u
m
p
tio
n
t
h
at
ea
ch
ce
n
ter
is
d
is
tin
g
u
is
h
ed
b
y
its
h
ig
h
lo
ca
l
d
en
s
it
y
an
d
r
elativ
e
l
y
lar
g
e
d
is
ta
n
ce
a
w
a
y
f
r
o
m
t
h
e
o
th
er
d
ata
p
o
in
ts
w
it
h
h
i
g
h
er
d
en
s
i
t
y
.
He
n
ce
,
o
u
r
alg
o
r
it
h
m
is
ap
t to
ex
tr
ac
t c
en
ter
s
f
r
o
m
d
ata
p
o
i
n
ts
a
s
a
f
ir
s
t step
.
T
o
p
r
o
v
e
its
ef
f
icien
c
y
,
w
e
o
p
t
to
i
n
v
est
ig
ate
t
h
e
cl
u
s
ter
v
alid
it
y
i
n
d
ex
in
F
i
g
u
r
e
4
(
d
)
an
d
t
h
e
E
lb
o
w
m
et
h
o
d
in
Fig
u
r
e
4
(
e)
.
Fig
u
r
e
3
.
R
esu
lts
o
b
t
ain
e
d
o
n
S
ee
d
s
d
a
tas
et
(
a)
r
esu
lt o
f
th
e
o
p
tim
a
l c
o
m
p
o
n
e
n
ts
n
u
m
b
er
u
s
in
g
t
h
e
KE
P
C
A
,
(
b
)
d
ec
is
io
n
g
r
ap
h
f
o
r
ce
n
ter
s
s
elec
tio
n
o
f
t
h
e
d
en
s
it
y
d
is
ta
n
ce
p
lo
t,
(
c)
t
h
e
p
r
o
d
u
ct
o
f
th
e
d
en
s
it
y
an
d
d
is
tan
ce
p
lo
tted
in
d
ec
r
ea
s
in
g
o
r
d
er
,
(
d
)
n
u
m
b
er
o
f
clu
s
ter
s
v
alid
atio
n
g
i
v
e
n
b
y
in
d
ex
an
d
(
e)
th
e
E
lb
o
w
m
et
h
o
d
f
o
r
Seed
s
d
ataset
T
h
e
class
if
icat
io
n
r
ate
g
i
v
en
b
y
o
u
r
clu
s
ter
i
n
g
alg
o
r
ith
m
co
n
s
id
er
in
g
th
e
KE
P
C
A
d
ata
tr
an
s
f
o
r
m
atio
n
is
eq
u
a
l
to
8
7
.
6
2
%
u
s
i
n
g
V
KE
,
w
h
er
ea
s
b
y
u
s
i
n
g
th
e
P
ar
ze
n
es
ti
m
ato
r
w
e
g
o
t
8
9
.
5
2
%,
an
d
co
n
s
id
er
in
g
E
P
C
A
d
ata
r
ed
u
ctio
n
w
i
th
VKE
w
e
o
b
tai
n
8
7
.
6
2
%
an
d
t
h
e
k
-
m
ed
o
id
s
an
d
t
h
e
k
-
m
ea
n
s
,
r
es
u
lts
ar
e
eq
u
al
to
8
4
%.
A
s
a
co
m
p
ar
is
o
n
,
w
e
co
n
c
lu
d
e
t
h
at
o
u
r
alg
o
r
ith
m
h
a
s
b
etter
r
esu
lt
t
h
an
i
ts
co
u
n
ter
p
ar
t
alg
o
r
ith
m
s
o
f
clu
s
ter
i
n
g
.
3
.
4
.
T
ra
j
ec
t
o
ries da
t
a
ba
s
e
T
h
e
L
C
P
C
(
L
ab
o
r
at
o
i
r
e
C
en
t
r
al
d
es
Po
n
ts
et
C
h
an
s
s
ée
s
)
m
ak
es
it
p
o
s
s
i
b
l
e
t
o
p
r
o
v
i
d
e
a
d
a
tab
ase
o
f
ex
p
e
r
im
en
tal
t
r
a
j
e
ct
o
r
ies
b
y
m
ea
s
u
r
in
g
th
e
p
a
r
am
eter
s
o
f
tr
a
ject
o
r
y
in
th
e
b
en
d
d
u
r
in
g
th
e
v
eh
icle
p
ass
ag
e
at
a
d
is
c
r
ete
in
te
r
v
als
o
f
t
im
e.
T
o
ac
h
iev
e
t
h
e
p
u
r
p
o
s
e
,
th
ey
u
tili
ze
a
d
at
a
a
c
q
u
is
iti
o
n
s
y
s
tem
in
co
r
p
o
r
at
e
d
t
o
a
t
est
v
eh
icle
th
at
c
an
r
est
o
r
e
th
e
p
o
s
it
io
n
s
,
s
p
e
ed
s
an
d
ac
ce
l
er
at
io
n
s
.
T
h
e
s
u
r
v
ey
w
as
co
n
d
u
c
ted
w
ith
v
o
lu
n
tee
r
d
r
iv
e
r
s
,
w
h
er
e
e
ac
h
d
r
iv
er
h
as
to
g
o
th
r
o
u
g
h
d
if
f
e
r
en
t
tr
a
j
e
ct
o
r
ies
.
Hen
ce
,
th
e
d
a
ta
b
as
e
o
f
p
h
y
s
ical
t
r
a
ject
o
r
ie
s
w
as
f
o
u
n
d
ed
[
3
1
]
.
T
h
er
ef
o
r
e
,
in
th
e
p
r
es
en
t
s
tu
d
y
,
w
e
ar
e
m
o
tiv
ated
t
o
in
v
esti
g
ate
th
e
t
r
a
j
e
ct
o
r
i
es
d
ata
b
ase
,
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
C
lu
s
ter
in
g
u
s
in
g
ke
r
n
el
en
tr
o
p
y
p
r
in
cip
a
l c
o
mp
o
n
en
t
a
n
a
lysi
s
…
(
Lo
u
b
n
a
E
l F
a
tta
h
i
)
2117
w
h
ich
co
n
s
is
ts
o
f
2
3
2
t
r
a
jec
to
r
ies
w
ith
6
v
a
r
ia
b
l
es
(
l
o
n
g
itu
d
in
al
p
o
s
iti
o
n
,
l
at
er
al
p
o
s
iti
o
n
,
lo
n
g
itu
d
in
al
s
p
e
e
d
,
late
r
a
l
s
p
e
ed
,
l
o
n
g
itu
d
in
al
ac
ce
l
er
ati
o
n
an
d
l
ate
r
al
a
cc
ele
r
ati
o
n
)
.
T
h
u
s
,
w
e
co
n
s
i
d
e
r
o
u
r
a
p
p
r
o
ac
h
f
o
r
d
at
a
tr
an
s
f
o
r
m
atio
n
c
o
m
b
in
in
g
th
e
k
er
n
el
f
u
n
cti
o
n
th
e
E
P
C
A
.
T
h
e
F
ig
u
r
e
5
p
r
es
en
ts
r
esu
lts
o
b
t
ain
e
d
o
n
t
r
a
ject
o
r
i
es
d
at
ase
t,
Fig
u
r
e
5
(
a
)
d
em
o
n
s
tr
a
te
s
th
e
r
e
d
u
c
e
d
f
ea
tu
r
es
in
th
e
h
ig
h
-
d
i
m
en
s
io
n
al
s
p
ac
e
(
2
3
2
f
ea
tu
r
es)
.
W
e
lim
it
o
u
r
p
l
o
t to
o
n
ly
2
5
f
ea
tu
r
es o
n
th
e
Fig
u
r
e
5
(
a)
f
o
r
th
e
s
ak
e
o
f
cle
ar
n
ess
s
in
ce
th
e
en
tr
o
p
y
ev
o
lv
es in
d
ec
r
e
asin
g
o
r
d
er
.
Hen
c
e,
th
e
th
r
e
e
m
ain
tain
ed
n
o
n
l
in
ea
r
f
ea
tu
r
es
a
r
e
s
e
l
ec
t
ed
t
o
h
av
e
th
e
h
ig
h
est
v
alu
e
o
f
en
tr
o
p
y
,
w
h
ic
h
m
ea
n
s
th
e
y
in
ter
p
r
et
th
e
m
o
r
e
r
e
lev
an
t
o
n
es
f
o
r
o
u
r
clu
s
t
er
in
g
alg
o
r
ith
m
in
ter
m
o
f
in
f
o
r
m
ati
o
n
c
o
n
ten
t
.
A
f
ter
w
ar
d
s
,
o
n
th
e
Fig
u
r
es
5
(
b
)
an
d
5
(
c
)
b
o
th
ch
a
r
ts
a
r
e
g
iv
e
n
b
as
ed
o
n
th
e
p
a
ir
d
en
s
ity
-
d
is
tan
ce
m
ea
s
u
r
em
en
t.
T
h
e
f
ir
s
t
p
l
o
t
o
n
th
e
Fig
u
r
e
5
(
b
)
p
r
es
en
ts
a
d
en
s
ity
-
d
is
tan
ce
p
l
o
t
,
w
h
er
ea
s
th
e
F
ig
u
r
e
5
(
c
)
i
llu
s
tr
ates
th
e
s
o
r
t
e
d
q
u
an
tity
o
f
th
e
d
en
s
ity
-
d
is
tan
c
e
p
r
o
d
u
c
t.
H
en
ce
,
i
d
en
ti
ca
l
r
e
s
u
lt
w
as
g
iv
en
b
y
b
o
th
te
ch
n
i
q
u
es,
f
o
u
r
c
en
tr
o
i
d
s
h
av
e
b
ee
n
d
et
er
m
in
ed
.
T
h
e
o
b
tain
e
d
r
esu
lts
ar
e
j
u
s
tif
i
e
d
th
a
n
k
s
to
th
e
ass
u
m
p
tio
n
th
at
d
ef
in
es
ev
e
r
y
ce
n
te
r
t
o
b
e
d
is
tin
g
u
is
h
e
d
f
r
o
m
th
e
o
th
er
d
ata
p
o
in
ts
b
y
its
h
ig
h
er
lo
c
al
d
en
s
ity
an
d
r
el
ativ
ely
lar
g
e
d
is
t
an
ce
.
T
h
u
s
,
o
u
r
alg
o
r
ith
m
is
ca
p
a
b
le
o
f
d
if
f
e
r
en
tiat
in
g
b
etw
ee
n
ce
n
t
er
s
an
d
th
e
o
th
e
r
p
o
in
ts
.
T
o
d
em
o
n
s
tr
at
e
o
u
r
clu
s
t
e
r
in
g
alg
o
r
ith
m
p
e
r
f
o
r
m
an
ce
,
w
e
i
n
v
esti
g
ate
th
e
clu
s
t
er
v
ali
d
ity
in
d
ex
in
Fig
u
r
e
5
(
d
)
a
n
d
th
e
E
lb
o
w
m
eth
o
d
in
Fig
u
r
e
5
(
e
)
.
B
o
th
c
r
it
er
ia
p
er
f
o
r
m
s
am
e
r
esu
lt,
w
h
ich
co
n
f
ir
m
s
th
e
ex
is
ten
c
e
o
f
f
o
u
r
clu
s
te
r
s
f
o
r
t
h
e
b
eh
av
io
r
o
f
d
r
iv
e
r
s
.
On
Fig
u
r
e
5
(
f
)
,
w
e
d
is
p
lay
ed
th
e
s
am
p
les
(
tr
a
ject
o
r
i
es)
ass
ig
n
at
io
n
t
o
th
ei
r
ap
p
r
o
p
r
ia
te
clu
s
t
er
s
b
ase
d
o
n
th
e
c
en
tr
o
i
d
s
s
el
ec
t
io
n
r
esu
lt
w
h
er
e
th
e
r
em
ain
in
g
p
o
in
ts
ar
e
ass
ig
n
ed
t
o
th
e
c
lo
s
est
ce
n
tr
o
i
d
b
as
ed
o
n
th
e
m
ea
s
u
r
em
en
t
o
f
th
e
E
u
clid
ea
n
d
is
tan
c
e.
T
h
e
g
iv
en
r
esu
lt
is
d
is
p
lay
ed
o
n
th
r
e
e
-
d
im
en
s
io
n
al
p
l
o
t
s
in
ce
th
e
r
e
d
u
ce
d
d
im
en
s
io
n
af
te
r
p
er
f
o
r
m
in
g
KE
P
C
A
w
as
d
ed
u
ce
d
t
o
b
e
a
th
r
ee
-
f
ea
tu
r
e
Fig
u
r
e
5
(
a
)
.
T
h
e
f
o
u
r
c
lu
s
te
r
s
ar
e
d
is
co
v
er
e
d
an
d
c
le
ar
ly
d
is
tin
g
u
is
h
ed
f
r
o
m
o
n
e
to
an
o
th
e
r
a
n
d
r
e
p
r
es
en
te
d
b
y
d
if
f
er
en
t
co
l
o
r
s
an
d
s
h
a
p
es.
E
ac
h
c
lu
s
te
r
r
e
p
r
es
en
ts
a
d
r
i
v
er
’
s
b
eh
av
io
r
.
T
h
e
f
ir
s
t
clas
s
C
1
,
c
o
r
r
esp
o
n
d
s
to
th
e
f
a
m
il
y
o
f
th
e
s
lo
w
est
tr
a
jec
to
r
i
es
o
f
ca
lm
ed
d
r
iv
in
g
.
T
h
e
s
e
c
o
n
d
cl
ass
C
2
,
co
r
r
es
p
o
n
d
s
t
o
th
e
f
am
il
y
o
f
th
e
s
lo
w
est
tr
ajec
t
o
r
ies
o
f
s
p
o
r
t
in
g
d
r
iv
in
g
.
T
h
e
th
ir
d
cl
ass
C
3
,
r
e
p
r
esen
ts
th
e
f
am
ily
o
f
th
e
f
astes
t
t
r
a
ject
o
r
ies
o
f
ca
lm
ed
d
r
iv
in
g
.
T
h
e
f
o
u
r
th
cl
ass
C
4
,
c
o
r
r
ela
tes
w
it
h
th
e
f
am
ily
o
f
th
e
f
ast
est
tr
a
je
cto
r
i
es
o
f
s
p
o
r
tin
g
d
r
iv
in
g
.
Fig
u
r
e
4
.
R
esu
lts
o
b
t
ain
e
d
o
n
t
r
a
ject
o
r
i
es
d
a
tase
t
(
a)
r
esu
lt o
f
th
e
o
p
ti
m
al
co
m
p
o
n
en
t
s
n
u
m
b
er
u
s
i
n
g
t
h
e
KE
P
C
A
,
(
b
)
d
ec
is
io
n
g
r
ap
h
f
o
r
ce
n
ter
s
s
elec
tio
n
o
f
t
h
e
d
en
s
i
t
y
d
is
ta
n
ce
p
lo
t,
(
c)
t
h
e
p
r
o
d
u
ct
o
f
th
e
d
en
s
it
y
an
d
d
is
tan
ce
p
lo
t
ted
in
d
ec
r
ea
s
in
g
o
r
d
er
,
(
d
)
n
u
m
b
e
r
o
f
clu
s
te
r
s
v
alid
atio
n
g
i
v
en
b
y
in
d
ex
a
n
d
(
e)
th
e
E
lb
o
w
m
et
h
o
d
,
(
f
)
T
h
r
ee
-
d
i
m
e
n
s
io
n
al
p
lo
t p
er
f
o
r
m
ed
o
n
m
a
p
p
ed
tr
a
j
ec
to
r
ies d
ata
in
th
e
r
e
d
u
ce
d
s
p
ac
e
o
f
th
r
ee
f
ea
t
u
r
es,
s
a
m
p
les ar
e
co
l
o
r
ed
ac
co
r
d
in
g
to
th
e
clu
s
ter
t
o
w
h
ich
t
h
e
y
ar
e
as
s
i
g
n
ed
w
it
h
d
if
f
er
en
t c
o
lo
r
an
d
s
h
ap
e
As
a
co
m
p
ar
is
o
n
to
o
th
er
w
o
r
k
s
r
elate
d
to
s
am
e
tr
aj
ec
to
r
ies
d
ataset
as
in
[
3
1
]
,
s
a
m
e
n
u
m
b
er
o
f
clu
s
ter
s
a
n
d
o
f
d
r
iv
er
’
s
b
eh
a
v
io
r
w
er
e
d
etec
ted
u
s
i
n
g
o
u
r
u
n
s
u
p
er
v
i
s
ed
alg
o
r
it
h
m
b
as
ed
o
n
k
er
n
el
d
at
a
tr
an
s
f
o
r
m
atio
n
an
d
v
ar
iab
le
k
er
n
el
esti
m
ato
r
f
o
r
d
en
s
it
y
e
s
ti
m
atio
n
t
h
at
is
cr
itical
f
o
r
clu
s
t
er
in
g
.
T
h
e
KE
P
C
A
h
as
s
h
o
w
n
i
ts
p
o
ten
tial
o
v
er
d
if
f
er
en
t
d
ataset
f
r
o
m
ar
t
if
ic
ial
an
d
r
ea
l
w
o
r
ld
d
atab
ase.
Am
o
n
g
all
o
f
t
h
e
m
,
t
h
e
p
r
o
p
o
s
ed
KE
P
C
A
p
r
esen
t
a
n
ad
v
an
ta
g
e
o
f
e
x
tr
ac
tin
g
o
n
l
y
v
alu
ab
le
i
n
f
o
r
m
atio
n
an
d
m
ap
p
in
g
i
n
p
u
t
d
ata
i
n
to
h
ig
h
s
p
ac
e,
w
h
er
e
t
h
e
n
o
n
-
li
n
ea
r
it
y
ca
n
b
e
o
m
itted
ea
s
il
y
.
T
h
e
r
ed
u
ce
d
n
u
m
b
er
o
f
f
ea
tu
r
es
in
th
e
h
i
g
h
s
p
ac
e
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.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
1
0
9
-
2119
2118
i
m
p
r
o
v
es
th
e
r
es
u
lts
.
Firstl
y
,
i
n
t
h
e
P
DF
e
s
ti
m
atio
n
u
s
i
n
g
t
h
e
r
ed
u
ce
d
d
i
m
e
n
s
io
n
w
h
er
e
m
o
s
t
o
f
th
e
en
tr
o
p
y
in
f
o
r
m
atio
n
is
co
m
p
ac
ted
an
d
t
h
e
s
elec
t
io
n
o
f
t
h
e
k
er
n
el
p
ar
a
m
eter
b
ec
o
m
e
m
o
r
e
r
o
b
u
s
t
.
Seco
n
d
l
y
,
i
n
th
e
clu
s
ter
i
n
g
task
as
it
is
s
h
o
w
n
o
n
th
e
T
ab
le
1
,
th
e
ex
p
er
im
e
n
t
r
es
u
lts
r
ev
ea
l
t
h
e
i
m
p
r
o
v
e
m
e
n
t
o
f
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
al
g
o
r
ith
m
u
s
i
n
g
KE
P
C
A
o
v
er
its
co
u
n
te
r
p
ar
t
E
P
C
A
.
Fu
r
t
h
er
m
o
r
e,
t
h
e
u
s
e
o
f
VKE
,
o
f
ten
m
ak
e
s
KE
P
C
A
m
o
r
e
e
f
f
icie
n
t
th
a
n
t
h
e
u
s
e
o
f
P
ar
ze
n
esti
m
a
to
r
,
w
h
ich
ca
n
b
e
ex
p
lai
n
ed
with
t
h
e
f
ac
t
th
a
t
t
h
e
v
ar
iab
le
k
er
n
el
es
ti
m
ato
r
ad
ap
ts
t
h
e
a
m
o
u
n
t
o
f
s
m
o
o
t
h
i
n
g
t
o
th
e
lo
ca
l
d
en
s
it
y
d
ata
d
u
e
t
o
th
e
ad
ap
tiv
e
s
ca
le
th
at
ca
n
v
ar
y
f
r
o
m
o
n
e
d
ata
p
o
in
t to
an
o
t
h
er
.
T
ab
le
1
.
C
o
m
p
ar
is
o
n
o
f
th
e
d
i
f
f
er
en
t c
l
u
s
ter
i
n
g
alg
o
r
it
h
m
s
o
v
er
ar
tif
icial
a
n
d
r
ea
l
w
o
r
ld
d
ata.
D
a
t
a
se
t
W
i
t
h
o
u
t
d
a
t
a
t
r
a
n
sf
o
r
m
a
t
i
o
n
EP
C
A
-
V
K
E
K
EPCA
-
P
a
r
z
e
n
K
EPCA
-
V
K
E
k
-
me
a
n
s
A
r
t
i
f
i
c
i
a
l
9
6
.
8
3
8
2
.
3
3
9
6
.
6
7
9
7
.
1
7
9
6
.
8
3
I
r
i
s
-
-
88
8
9
.
3
3
8
9
.
3
3
F
l
a
me
8
4
.
1
7
80
85
85
85
h
e
a
r
t
6
2
.
5
9
6
5
.
1
9
7
9
.
2
6
8
2
.
5
9
5
9
.
2
6
T
r
a
j
e
c
t
o
r
y
-
-
-
4
c
l
u
s
t
e
r
s
4
c
l
u
s
t
e
r
s
S
e
e
d
9
1
.
4
3
8
9
.
5
2
8
9
.
5
2
8
7
.
6
2
8
9
.
5
2
4.
CO
NCLU
SI
O
N
I
n
th
e
p
r
es
en
t
p
ap
er
,
w
e
p
r
o
p
o
s
e
an
ef
f
ic
ien
t
d
at
a
tr
an
s
f
o
r
m
atio
n
f
o
r
th
e
ex
is
te
d
E
P
C
A
m
eth
o
d
t
o
ex
tr
ac
t
th
e
o
p
tim
al
f
ea
tu
r
es
.
W
h
er
e
as th
e
E
P
C
A
g
iv
es th
e
o
p
t
im
al
en
tr
o
p
ic
co
m
p
o
n
en
t th
r
o
u
g
h
m
ax
i
m
izin
g
th
e
av
er
ag
e
o
f
th
e
in
f
o
r
m
atio
n
(
th
e
in
er
t
ia
)
p
r
o
v
id
ed
b
y
th
e
elem
en
ts
,
th
e
KE
P
C
A
in
d
ee
d
m
ak
es
a
m
ap
p
in
g
f
o
r
d
at
a
b
ef
o
r
e
c
o
n
s
id
e
r
in
g
E
P
C
A
.
T
h
e
r
ef
o
r
e,
th
e
c
o
r
e
elem
en
t
o
f
th
e
k
e
r
n
el
u
s
e
d
in
K
E
P
C
A
is
to
m
ap
im
p
li
citly
th
e
in
p
u
t
d
ata
in
t
o
a
h
ig
h
-
d
i
m
en
s
io
n
al
f
ea
tu
r
e
s
p
a
ce
,
w
h
er
e
th
e
n
o
n
lin
e
a
r
p
a
tte
r
n
s
b
ec
o
m
e
lin
ea
r
an
d
th
e
s
ep
ar
ati
o
n
o
f
th
e
el
em
en
ts
b
ec
o
m
es
ea
s
ie
r
.
W
e
h
av
e
r
ev
e
al
e
d
th
e
ab
ilit
y
o
f
KE
P
C
A
t
o
r
eta
in
m
o
r
e
in
f
o
r
m
atio
n
in
th
e
h
ig
h
s
p
ac
e
in
b
o
th
PDF
esti
m
atio
n
an
d
clu
s
te
r
in
g
o
v
er
s
y
n
th
etic
an
d
r
e
al
w
o
r
l
d
d
atas
et
ex
am
p
les
.
R
esu
lts
s
h
o
w
th
e
p
er
f
o
r
m
an
ce
q
u
er
y
o
f
th
e
KE
P
C
A
o
v
er
its
co
u
n
te
r
p
ar
t
E
P
C
A
d
ata
t
r
an
s
f
o
r
m
ati
o
n
.
B
esi
d
es
,
th
e
u
s
e
o
f
VKE
esti
m
ato
r
h
as
p
r
o
v
en
its
ef
f
icien
cy
in
d
en
s
ity
esti
m
atio
n
,
w
h
ich
h
as
cr
i
tica
l
ef
f
ec
t
o
n
th
e
clu
s
te
r
in
g
alg
o
r
ith
m
.
RE
F
E
R
E
NC
E
S
[1
]
D.
Na
p
o
leo
n
a
n
d
S
.
P
a
v
a
lak
o
d
i,
“
A
Ne
w
M
e
th
o
d
f
o
r
Dim
e
n
sio
n
a
li
ty
Re
d
u
c
ti
o
n
Us
i
n
g
KMea
n
s
Clu
ste
rin
g
A
l
g
o
rit
h
m
f
o
r
Hig
h
Di
m
e
n
sio
n
a
l
Da
ta S
e
t,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
1
3
,
n
o
.
7
,
p
p
.
4
1
–
4
6
,
Ja
n
.
2
0
1
1
.
[2
]
R.
H
a
n
d
A
.
T
,
“
F
e
a
tu
re
Ex
tra
c
ti
o
n
o
f
Ch
e
st
X
-
ra
y
I
m
a
g
e
s
a
n
d
A
n
a
l
y
si
s
u
sin
g
P
CA
a
n
d
k
P
CA
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
E
n
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
5
,
p
p
.
3
3
9
2
–
3
3
9
8
,
Oc
t.
2
0
1
8
,
d
o
i
:
1
0
.
1
1
5
9
1
/i
j
ec
e.
v
8
i5
.
p
p
3
3
9
2
-
3
3
9
8
.
[3
]
A
.
K.
Nik
h
a
th
a
n
d
K.
S
u
b
ra
h
m
a
n
y
a
m
,
“
F
e
a
tu
re
se
le
c
ti
o
n
,
o
p
ti
m
iza
ti
o
n
a
n
d
c
l
u
ste
rin
g
stra
teg
ies
o
f
te
x
t
d
o
c
u
m
e
n
ts,”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
&
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
EC
E
)
,
v
o
l.
9
,
n
o
.
2
,
p
p
.
1
3
1
3
–
1
3
2
0
,
A
p
r.
2
0
1
9
,
d
o
i
:
h
tt
p
:
//
d
o
i.
o
rg
/1
0
.
1
1
5
9
1
/i
jec
e
.
v
9
i2
.
p
p
1
3
1
3
-
1
3
2
0
.
[4
]
J.
M
a
c
Qu
e
e
n
,
“
S
o
m
e
m
e
th
o
d
s
f
o
r
c
la
ss
i
f
ica
ti
o
n
a
n
d
a
n
a
ly
sis
o
f
m
u
lt
iv
a
riate
o
b
se
rv
a
ti
o
n
s,”
p
re
se
n
ted
a
t
th
e
Pro
c
e
e
d
in
g
s
o
f
t
h
e
Fi
f
th
Ber
k
e
ley
S
y
mp
o
si
u
m o
n
M
a
t
h
e
ma
ti
c
a
l
S
t
a
ti
stics
a
n
d
Pro
b
a
b
il
i
ty,
1
9
6
7
.
[5
]
A
.
K.
Ja
in
,
“
Da
ta
c
lu
ste
rin
g
:
5
0
y
e
a
rs
b
e
y
o
n
d
K
-
m
e
a
n
s,”
Pa
tt
e
rn
Rec
o
g
n
it
.
L
e
tt
.
,
v
o
l.
3
1
,
n
o
.
8
,
p
p
.
6
5
1
–
6
6
6
,
J
u
n
.
2
0
1
0
,
d
o
i:
h
tt
p
s:/
/d
o
i.
o
rg
/1
0
.
1
0
1
6
/j
.
p
a
trec
.
2
0
0
9
.
0
9
.
0
1
1
.
[6
]
L
.
Ka
u
fm
a
n
a
n
d
P
.
J.
Ro
u
ss
e
e
u
w
,
“
F
in
d
in
g
g
ro
u
p
s
in
d
a
ta:
a
n
i
n
tro
d
u
c
ti
o
n
t
o
c
lu
ste
r
a
n
a
ly
sis,”
Ho
b
o
k
e
n
,
N
.
J
:
W
il
e
y
,
2
0
0
5
.
[7
]
U.
Oz
e
rte
m
,
e
t
a
l.
,
“
M
e
a
n
sh
if
t
s
p
e
c
tral
c
lu
ste
rin
g
,
”
Pa
tt
e
rn
Rec
o
g
n
it
.
,
v
o
l.
4
1
,
n
o
.
6
,
p
p
.
1
9
2
4
–
1
9
3
8
,
Ju
n
.
2
0
0
8
,
d
o
i:
h
tt
p
s://
d
o
i
.
o
rg
/1
0
.
1
0
1
6
/j
.
p
a
tc
o
g
.
2
0
0
7
.
0
9
.
0
0
9
.
[8
]
Y.
W
e
iss,
“
S
e
g
m
e
n
tatio
n
u
sin
g
e
ig
e
n
v
e
c
to
rs:
a
u
n
ify
in
g
v
ie
w
,
”
Pro
c
e
e
d
in
g
s
o
f
t
h
e
S
e
v
e
n
t
h
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Co
m
p
u
ter
Vi
si
o
n
,
Ke
rk
y
ra
,
Gr
e
e
c
e
,
v
o
l.
2
,
1
9
9
9
,
p
p
.
9
7
5
–
9
8
2
,
d
o
i:
1
0
.
1
1
0
9
/ICC
V
.
1
9
9
9
.
7
9
0
3
5
4
.
[9
]
E.
m
e
h
d
i
Ch
e
rra
t,
Ra
c
h
i
d
A
lao
u
i,
Ha
ss
a
n
e
Bo
u
z
a
h
ir
.
,
“
Im
p
ro
v
in
g
o
f
F
in
g
e
rp
rin
t
S
e
g
m
e
n
tatio
n
Im
a
g
e
s
Ba
se
d
o
n
K
-
M
EA
NS
a
n
d
DBSCA
N
Clu
ste
ri
n
g
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
4
,
p
p
.
2
4
2
5
–
2
4
3
2
,
A
u
g
.
2
0
1
9
,
d
o
i:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
9
i4
.
p
p
2
4
2
5
-
2
4
3
2
.
[1
0
]
A
.
Ro
d
rig
u
e
z
a
n
d
A
.
Laio
,
“
Clu
ste
rin
g
b
y
fa
st
se
a
rc
h
a
n
d
f
in
d
o
f
d
e
n
sity
p
e
a
k
s,”
S
c
ien
c
e
,
v
o
l.
3
4
4
,
n
o
.
6
1
9
1
,
p
p
.
1
4
9
2
–
1
4
9
6
,
Ju
n
.
2
0
1
4
,
d
o
i:
1
0
.
1
1
2
6
/sc
ien
c
e
.
1
2
4
2
0
7
2
.
[1
1
]
X.
-
F
.
W
a
n
g
a
n
d
Y.
Xu
,
“
F
a
st
c
lu
ste
rin
g
u
sin
g
a
d
a
p
ti
v
e
d
e
n
si
ty
p
e
a
k
d
e
tec
ti
o
n
,
”
S
ta
t.
M
e
th
o
d
s
M
e
d
.
Res
.
,
v
o
l.
2
6
,
n
o
.
6
,
p
p
.
2
8
0
0
–
2
8
1
1
,
De
c
.
2
0
1
7
,
d
o
i:
h
tt
p
s://
d
o
i
.
o
rg
/1
0
.
1
1
7
7
%
2
F
0
9
6
2
2
8
0
2
1
5
6
0
9
9
4
8
.
[1
2
]
L
.
E.
F
a
tt
a
h
i,
e
t
a
l.
,
“
Clu
ste
rin
g
b
a
se
d
o
n
d
e
n
sity
e
sti
m
a
ti
o
n
u
sin
g
v
a
riab
le k
e
rn
e
l
a
n
d
m
a
x
i
m
u
m
e
n
t
ro
p
y
p
rin
c
ip
le,
”
In
telli
g
e
n
t
S
y
ste
ms
a
n
d
Co
mp
u
ter
Vi
sio
n
(
IS
CV),
2
0
1
7
,
p
p
.
1
–
7.
Evaluation Warning : The document was created with Spire.PDF for Python.