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to
h
a
m
m
in
g
s
p
ac
e
w
h
er
e
cr
o
s
s
-
m
o
d
al
s
i
m
ilar
it
y
ar
e
ca
lc
u
lated
b
y
h
a
m
m
i
n
g
d
is
tan
ce
.
T
h
o
u
g
h
th
e
s
p
ac
e
co
m
p
lex
i
t
y
w
as
r
ed
u
ce
d
,
th
e
d
ata
r
etr
iev
al
p
r
o
ce
s
s
w
a
s
co
m
p
li
ca
ted
.
A
n
e
w
f
u
zz
y
c
-
m
ea
n
s
(
FC
M)
m
o
d
el
w
it
h
s
p
ar
s
e
r
eg
u
lar
izat
io
n
w
a
s
i
n
t
r
o
d
u
ce
d
in
[
6
]
th
r
o
u
g
h
r
ef
o
r
m
u
lati
n
g
th
e
FC
M
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
n
to
w
e
ig
h
t
ed
b
et
w
ee
n
-
clu
s
ter
s
u
m
o
f
s
q
u
ar
e
f
o
r
m
a
n
d
r
eq
u
ir
ed
th
e
s
p
ar
s
e
r
eg
u
lar
izatio
n
o
n
w
e
ig
h
t
s
.
B
u
t,
d
ata
r
etr
iev
al
ti
m
e
w
a
s
n
o
t
r
ed
u
ce
d
u
s
i
n
g
F
C
M
m
o
d
el.
I
n
ter
est
in
g
S
u
b
s
p
ac
e
C
l
u
s
ter
i
n
g
(
I
SC
)
alg
o
r
it
h
m
w
as
p
r
ese
n
te
d
in
[
7
]
u
til
ized
th
e
a
ttrib
u
te
d
ep
en
d
en
c
y
m
ea
s
u
r
e
f
r
o
m
R
o
u
g
h
Set
th
eo
r
y
to
r
ec
o
g
n
ize
t
h
e
s
u
b
s
p
ac
es.
Ho
wev
er
,
it
f
ailed
to
h
a
n
d
le
t
h
e
p
r
o
b
lem
o
f
d
en
s
el
y
p
o
p
u
lated
d
ata
p
o
in
ts
.
Mo
d
el
-
b
ased
clu
s
ter
in
g
late
n
t
tr
ait
(
MCL
T
)
m
o
d
els
w
a
s
in
tr
o
d
u
ce
d
in
[
8
]
w
it
h
b
lo
ck
ef
f
e
ct
p
r
esen
t
s
u
i
tab
le
alter
n
ati
v
e
f
o
r
s
a
m
p
led
d
ata.
T
h
e
MCL
T
m
o
d
e
w
a
s
n
o
t
co
n
s
id
er
ed
s
p
ac
e
a
n
d
ti
m
e
co
m
p
lex
it
y
d
u
r
i
n
g
th
e
clu
s
ter
i
n
g
p
r
o
ce
s
s
.
P
r
ed
ictiv
e
Su
b
s
p
ac
e
C
l
u
s
ter
i
n
g
(
P
SC
)
w
as
in
tr
o
d
u
ce
d
in
[
9
]
f
o
r
clu
s
ter
i
n
g
t
h
e
h
i
g
h
-
d
i
m
en
s
io
n
a
l
d
ata.
Ho
w
e
v
er
,
P
SC
is
n
o
t
s
u
itab
le
f
o
r
clu
s
ter
i
n
g
o
f
d
e
n
s
el
y
p
o
p
u
lated
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
p
o
in
ts
.
A
n
ef
f
icien
t
h
i
g
h
-
d
i
m
e
n
s
io
n
a
l
in
d
ex
in
g
lib
r
ar
y
ca
lled
HDI
d
x
was
in
tr
o
d
u
ce
d
in
[
1
0
]
f
o
r
esti
m
ated
NN
s
ea
r
ch
.
I
t
tr
an
s
f
o
r
m
ed
t
h
e
i
n
p
u
t
h
i
g
h
-
d
i
m
en
s
io
n
a
l
v
ec
to
r
s
in
to
co
m
p
a
ct
b
in
ar
y
co
d
es
in
e
f
f
icie
n
t
a
n
d
s
ca
lab
le
m
a
n
n
er
f
o
r
NN
s
ea
r
ch
w
it
h
less
er
s
p
a
ce
co
m
p
lex
it
y
.
T
h
o
u
g
h
s
p
ac
e
co
m
p
lex
it
y
w
as
r
ed
u
ce
d
,
d
at
a
r
etr
iev
al
w
as
n
o
t
ca
r
r
ied
o
u
t
in
e
f
f
icie
n
t
m
a
n
n
er
.
Ma
h
alan
o
b
is
d
is
ta
n
ce
b
as
ed
lo
ca
l
d
is
tr
ib
u
tio
n
o
r
ien
ted
s
p
ec
tr
al
clu
s
ter
i
n
g
tech
n
iq
u
e
w
as
d
ev
elo
p
ed
in
[
1
1
]
to
g
r
o
u
p
th
e
d
ata
in
d
im
en
s
io
n
al
s
p
ac
e.
Ho
w
e
v
er
,
d
ata
r
etr
iev
al
w
as
n
o
t
ca
r
r
ied
o
u
t.
I
n
o
r
d
e
r
to
o
v
er
c
o
m
e
th
e
ab
o
v
e
m
en
tio
n
ed
is
s
u
es
s
u
c
h
as
le
s
s
tr
u
e
p
o
s
it
iv
e
r
ate,
h
ig
h
s
p
ac
e
an
d
ti
m
e
co
m
p
le
x
it
y
d
u
r
in
g
clu
s
te
r
in
g
,
lac
k
o
f
d
ata
r
etr
iev
al,
h
an
d
le
d
en
s
el
y
p
o
p
u
lated
d
ata
p
o
in
ts
an
d
s
o
o
n
.
I
n
o
r
d
er
to
o
v
er
co
m
e
s
u
c
h
k
in
d
o
f
is
s
u
es,
Sp
ec
tr
al
C
l
u
s
ter
i
n
g
b
ased
Van
tag
e
P
o
in
t
T
r
ee
I
n
d
ex
in
g
(
SC
-
VP
T
I
)
T
ec
h
n
iq
u
e
is
in
tr
o
d
u
ce
d
.
T
h
e
SC
-
VP
T
I
tech
n
i
q
u
e
i
s
d
esi
g
n
ed
f
o
r
e
f
f
ic
ien
t
d
ata
r
etr
iev
a
l
b
ased
o
n
t
h
e
u
s
er
q
u
er
y
w
it
h
m
in
i
m
u
m
ti
m
e.
T
h
e
co
n
tr
ib
u
tio
n
o
f
o
u
r
r
esear
ch
w
o
r
k
i
n
clu
d
es
as
f
o
llo
w
s
:
a
Sp
ec
tr
al
C
lu
s
ter
in
g
B
ased
VP
T
r
ee
I
n
d
ex
i
n
g
(
S
C
-
VP
T
I
)
T
ec
h
n
iq
u
e
clu
s
ter
s
an
d
in
d
e
x
es
t
h
e
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
i
m
e
n
s
i
o
n
al
d
ata
p
o
in
ts
f
o
r
ef
f
icien
t
d
ata
r
etr
iev
al
b
ased
o
n
th
e
u
s
er
q
u
er
y
.
T
h
e
SC
-
V
PT
I
tech
n
iq
u
e
co
n
tai
n
s
t
h
r
ee
m
aj
o
r
co
n
tr
ib
u
tio
n
s
.
A
t
f
ir
s
t,
a
No
r
m
alize
d
Sp
ec
tr
a
l
C
l
u
s
ter
i
n
g
Alg
o
r
it
h
m
clu
s
ter
s
th
e
s
i
m
ilar
h
ig
h
d
i
m
e
n
s
io
n
al
d
ata
p
o
in
ts
b
ased
o
n
s
i
m
i
lar
i
t
y
s
co
r
e
o
f
d
ata
p
o
in
ts
.
Seco
n
d
,
Va
n
ta
g
e
P
o
in
t
T
r
ee
in
d
ex
es
t
h
e
cl
u
s
ter
ed
h
i
g
h
d
i
m
e
n
s
io
n
al
d
ata
p
o
in
ts
f
o
r
ef
f
icie
n
t
d
ata
r
etr
iev
al.
T
h
e
in
d
ex
ed
d
ata
p
o
in
ts
ar
e
r
ep
r
esen
ted
b
y
a
cir
cle.
T
h
e
V
P
in
d
ex
in
g
r
ed
u
ce
s
th
e
s
p
ac
e
co
m
p
le
x
it
y
f
o
r
s
to
r
in
g
th
e
m
u
lt
i
p
le
h
ig
h
d
i
m
e
n
s
io
n
a
l
d
ata
p
o
in
ts
.
At
last
,
th
e
in
d
ex
ed
s
i
m
ilar
d
ata
p
o
in
ts
g
ets
r
etr
ie
v
ed
f
r
o
m
th
e
i
n
d
ex
i
n
g
tr
ee
b
ased
o
n
th
e
u
s
er
q
u
er
y
w
it
h
t
h
e
h
elp
o
f
Van
ta
g
e
P
o
in
t T
r
ee
b
ased
Data
R
etr
iev
al
A
lg
o
r
it
h
m
.
As a
r
es
u
lt,
SC
-
VPT
I
tech
n
iq
u
e
ac
h
iev
e
s
h
i
g
h
er
tr
u
e
p
o
s
iti
v
e
r
at
e
w
it
h
m
i
n
i
m
u
m
d
ata
r
etr
iev
al
t
i
m
e.
T
h
e
r
est
o
f
th
e
p
ap
er
o
r
g
an
ized
as
f
o
llo
w
s
.
I
n
Sectio
n
2
,
th
e
p
r
o
p
o
s
ed
SC
-
VPT
I
tech
n
iq
u
e
i
s
d
escr
ib
ed
w
it
h
th
e
h
elp
o
f
s
tr
u
ct
u
r
al
d
i
ag
r
a
m
.
I
n
Sectio
n
3
,
ex
p
er
i
m
en
tal
e
v
al
u
atio
n
i
s
d
is
cu
s
s
ed
an
d
r
esu
lt
a
n
al
y
s
i
s
is
ca
r
r
ied
o
u
t
w
it
h
tab
les
a
n
d
g
r
ap
h
i
n
Sec
tio
n
4
.
A
s
u
m
m
ar
y
o
f
d
i
f
f
er
en
t
clu
s
ter
i
n
g
tec
h
n
iq
u
es
f
o
r
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
i
s
r
ev
ie
w
ed
i
n
S
ec
tio
n
5
.
T
h
e
Secti
o
n
6
co
n
cl
u
d
es
th
e
p
r
esen
ted
w
o
r
k
s
.
2.
SPEC
T
RA
L
CL
U
ST
E
R
I
N
G
B
ASE
D
VP
T
R
E
E
I
ND
E
XI
NG
T
E
CH
N
I
Q
UE
T
h
e
S
p
ec
tr
al
C
lu
s
ter
in
g
B
ase
d
VP
T
r
ee
I
n
d
ex
in
g
(
S
C
-
VP
T
I
)
T
ec
h
n
iq
u
e
i
s
i
n
tr
o
d
u
ce
d
to
clu
s
ter
a
n
d
in
d
ex
t
h
e
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
i
m
e
n
s
io
n
a
l
d
ata
p
o
in
ts
f
o
r
ef
f
ec
ti
v
e
d
ata
r
etr
iev
al
b
ased
o
n
th
e
u
s
er
q
u
er
y
.
SC
-
VP
T
I
tech
n
iq
u
e
is
u
s
ed
f
o
r
clu
s
ter
i
n
g
t
h
e
d
en
s
e
d
at
a
p
o
in
ts
a
n
d
in
cr
ea
s
e
s
th
e
d
ata
r
etr
i
ev
al
r
ate.
SC
-
VP
T
I
tech
n
iq
u
e
in
tr
o
d
u
ce
s
No
r
m
ali
ze
d
Sp
ec
tr
al
C
lu
s
ter
in
g
A
l
g
o
r
ith
m
to
g
r
o
u
p
th
e
s
i
m
ilar
h
i
g
h
d
i
m
e
n
s
io
n
a
l
d
ata
o
b
j
ec
ts
.
T
h
en
,
SC
-
VP
T
I
tech
n
iq
u
e
co
n
s
tr
u
ct
s
Van
tag
e
P
o
in
t
tr
ee
f
o
r
in
d
ex
in
g
th
e
cl
u
s
t
er
ed
d
ata
p
o
in
ts
to
f
o
r
m
t
h
e
i
n
d
ex
i
n
g
d
atab
ase
w
i
th
m
i
n
i
m
u
m
s
p
ac
e
co
m
p
le
x
it
y
.
Fin
all
y
,
S
C
-
VP
T
I
tech
n
iq
u
e
u
s
e
s
Van
tag
e
P
o
in
t
tr
ee
b
ased
d
ata
r
etr
iev
al
alg
o
r
ith
m
to
ex
tr
ac
t
t
h
e
u
s
er
r
eq
u
e
s
ted
d
ata
f
r
o
m
i
n
d
ex
i
n
g
d
atab
ase
w
it
h
less
er
d
ata
r
etr
iev
al
ti
m
e
co
n
s
u
m
p
tio
n
.
T
h
e
o
v
er
all
s
tr
u
c
tu
r
al
d
esi
g
n
o
f
SC
-
VP
T
I
T
ec
h
n
iq
u
e
f
o
r
clu
s
ter
in
g
th
e
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
i
m
e
n
s
io
n
al
d
ata
p
o
in
ts
is
d
escr
ib
ed
in
Fi
g
u
r
e
1
.
Fro
m
F
ig
u
r
e
1
,
S
C
-
VP
T
I
T
ec
h
n
iq
u
e
i
n
it
iall
y
co
llect
s
t
h
e
d
en
s
el
y
p
o
p
u
lated
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
p
o
in
ts
f
r
o
m
E
l
Ni
n
o
w
ea
t
h
er
d
ataset
as
in
p
u
t
w
h
ic
h
c
o
m
p
r
i
s
es
co
llect
io
n
o
f
d
en
s
el
y
p
o
p
u
lated
h
i
g
h
d
i
m
en
s
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an
d
g
i
v
e
n
b
y
,
(
4
)
Fro
m
(
4
)
,
„
‟
i
s
t
h
e
L
ap
lacia
n
m
atr
i
x
,
D
r
ep
r
esen
ts
d
ia
g
o
n
al
m
atr
i
x
a
n
d
„
A
‟
d
en
o
tes
th
e
s
i
m
ilar
it
y
m
atr
ix
.
T
h
en
,
th
e
f
ir
s
t
„
‟
lar
g
e
s
t
e
ig
en
v
al
u
es
o
f
L
ap
lacia
n
m
atr
i
x
an
d
t
h
eir
co
r
r
esp
o
n
d
in
g
ei
g
e
n
v
ec
to
r
s
(
)
in
co
lu
m
n
s
i
s
d
eter
m
i
n
ed
an
d
th
e
m
atr
i
x
„
‟
is
co
n
s
tr
u
cted
b
y
,
(
5
)
Fro
m
(
5
)
,
m
a
tr
ix
i
s
co
n
s
tr
u
cted
.
T
h
en
,
n
o
r
m
al
ized
L
ap
lacia
n
m
a
tr
ix
„
‟
is
co
n
s
t
r
u
cted
th
r
o
u
g
h
r
en
o
r
m
alizi
n
g
ea
c
h
r
o
w
v
al
u
e
o
f
„
‟
m
a
tr
ix
.
T
h
e
n
o
r
m
alize
d
L
ap
lacia
n
m
atr
i
x
is
co
n
s
tr
u
cted
b
y
,
√
(
∑
)
(
6
)
Fro
m
(
6
)
,
ea
ch
r
o
w
o
f
ac
ts
a
s
a
v
er
tex
an
d
cl
u
s
ter
t
h
e
m
in
to
m
a
n
y
K
c
lu
s
ter
s
b
y
u
s
i
n
g
k
-
m
ea
n
s
cl
u
s
ter
i
n
g
alg
o
r
ith
m
.
K
-
m
ea
n
s
clu
s
ter
al
g
o
r
ith
m
is
ca
r
r
ied
o
u
t
w
it
h
i
n
clu
s
ter
s
u
m
o
f
s
q
u
ar
es b
y
,
∑
∑
‖
‖
(
7
)
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
S
p
ec
tr
a
l Cl
u
s
teri
n
g
a
n
d
V
a
n
ta
g
e
P
o
in
t I
n
d
ex
in
g
fo
r
E
fficien
t D
a
ta
R
etri
ev
a
l (
R
.
P
u
s
h
p
a
la
t
h
a
)
2265
Fro
m
(
7
)
,
k
n
u
m
b
er
o
f
clu
s
te
r
s
ar
e
f
o
r
m
ed
,
„
‟
r
ep
r
esen
ts
t
h
e
cl
u
s
te
r
m
ea
n
a
n
d
„
‟
s
y
m
b
o
lizes
th
e
d
ata
p
o
in
ts
.
T
h
e
alg
o
r
ith
m
ic
p
r
o
ce
s
s
o
f
n
o
r
m
a
lized
s
p
ec
tr
al
clu
s
te
r
in
g
al
g
o
r
ith
m
i
s
g
i
v
e
n
b
elo
w
,
A
l
g
o
r
ith
m
1
.
No
r
m
alize
d
Sp
e
ctr
al
C
lu
s
ter
in
g
A
l
g
o
r
ith
m
\
\
No
r
m
alize
d
Sp
ec
tr
al
C
l
u
s
ter
i
n
g
Alg
o
r
it
h
m
I
n
p
u
t: Set
o
f
d
ata
p
o
in
ts
„
{
}‟
,
C
lu
s
ter
Nu
m
b
er
.
Ou
tp
u
t: Gr
o
u
p
in
g
o
f
d
a
ta
p
o
in
ts
in
d
i
f
f
er
e
n
t c
l
u
s
ter
Step
1
:
B
eg
in
Step
2
:
F
o
r
ea
ch
d
ata
p
o
in
t in
E
l N
in
o
w
ea
t
h
er
d
ataset
Step
3
:
C
o
n
s
tr
u
ct
s
i
m
il
ar
it
y
m
a
tr
ix
„
‟
u
s
in
g
(
1
)
Step
4
:
Dete
r
m
in
e
L
ap
lacia
n
m
atr
ix
„
‟
u
s
in
g
(
4
)
Step
5
:
C
o
m
p
u
t
e
No
r
m
alize
d
L
ap
lacia
n
m
atr
i
x
u
s
in
g
(
6
)
Step
6
:
I
d
en
ti
f
y
f
ir
s
t
eig
e
n
v
ec
to
r
s
o
f
an
d
d
en
o
te
it
as
u
s
i
n
g
(
7
)
Step
7
:
Use k
-
m
ea
n
s
to
g
r
o
u
p
th
e
m
in
to
clu
s
ter
s
.
Step
8
:
C
lu
s
ter
t
h
e
d
ata
p
o
in
ts
to
clu
s
ter
if
an
d
o
n
l
y
if
r
o
w
o
f
th
e
m
atr
ix
w
a
s
ass
ig
n
ed
to
clu
s
t
er
Step
9
:
E
n
d
fo
r
Step
1
0
:
R
etu
r
n
C
lu
s
ter
i
n
g
r
es
u
lts
o
f
d
ata
p
o
in
ts
Step
1
1
:
E
n
d
A
l
g
o
r
ith
m
1
d
escr
ib
es
th
e
n
o
r
m
alize
d
s
p
ec
tr
al
cl
u
s
ter
in
g
a
lg
o
r
ith
m
ic
p
r
o
ce
s
s
.
B
y
co
n
s
tr
u
cti
n
g
th
e
s
i
m
ilar
it
y
m
atr
i
x
an
d
lap
laci
an
m
a
tr
ix
,
t
h
e
s
i
m
ilar
d
ata
p
o
in
ts
ar
e
id
en
ti
f
ied
.
T
h
en
,
n
o
r
m
al
ized
lap
lacia
n
m
atr
i
x
g
et
s
co
n
s
tr
u
cted
a
n
d
id
en
ti
f
ied
k
-
ei
g
en
v
ec
to
r
s
.
Af
ter
t
h
e
id
en
ti
f
icat
io
n
,
K
-
m
ea
n
s
al
g
o
r
ith
m
is
e
m
p
lo
y
ed
to
g
r
o
u
p
t
h
e
s
i
m
ilar
d
ata
p
o
in
ts
to
f
o
r
m
k
-
cl
u
s
ter
s
.
T
h
u
s
,
t
h
e
d
ata
p
o
in
ts
i
n
d
e
n
s
el
y
p
o
p
u
lated
h
i
g
h
d
i
m
en
s
io
n
d
ata
s
i
g
n
i
f
ican
tl
y
g
r
o
u
p
ed
in
m
an
y
cl
u
s
ter
s
b
ased
o
n
th
e
d
ata
t
y
p
e.
2
.
2
.
Va
nta
g
e
po
int
t
re
e
f
o
r
ind
ex
ing
clus
t
er
ed
hig
h
di
m
en
s
io
n
a
l da
t
a
I
n
SC
-
VP
T
I
tech
n
iq
u
e,
v
a
n
ta
g
e
p
o
in
t
tr
ee
is
u
s
ed
f
o
r
i
n
d
ex
in
g
th
e
cl
u
s
ter
ed
h
ig
h
d
i
m
e
n
s
io
n
al
d
ata.
I
n
itiall
y
,
S
C
-
VP
T
I
tech
n
iq
u
e
u
s
ed
n
o
r
m
alize
d
s
p
ec
tr
al
clu
s
t
er
in
g
a
lg
o
r
it
h
m
f
o
r
cl
u
s
ter
in
g
th
e
d
ata
p
o
in
t
s
s
u
c
h
as
s
ea
s
u
r
f
ac
e
te
m
p
er
atu
r
e
s
,
r
elativ
e
h
u
m
id
it
y
,
r
ai
n
f
a
ll,
s
u
b
s
u
r
f
ac
e
te
m
p
er
at
u
r
es
air
te
m
p
er
at
u
r
e
d
ata,
etc.
Af
ter
cl
u
s
ter
i
n
g
th
e
d
ata
p
o
i
n
t
s
,
in
d
ex
in
g
p
r
o
ce
s
s
i
s
ca
r
r
ied
o
u
t
b
y
Va
n
ta
g
e
P
o
in
t
T
r
ee
f
o
r
r
ed
u
cin
g
t
h
e
s
p
ac
e
co
m
p
le
x
it
y
.
T
h
e
VP
-
T
r
ee
I
n
d
e
x
in
g
H
i
g
h
Di
m
en
s
io
n
al
Da
ta
P
r
o
ce
s
s
is
d
escr
ib
ed
in
F
ig
u
r
e
3
.
Fig
u
r
e
3
.
P
r
o
ce
s
s
o
f
VP
-
T
r
ee
I
n
d
ex
i
n
g
Hig
h
Di
m
e
n
s
io
n
al
Da
ta
Fig
u
r
e
3
s
h
o
w
s
t
h
e
p
r
o
ce
s
s
o
f
VP
-
tr
ee
i
n
d
ex
i
n
g
h
i
g
h
d
im
en
s
io
n
a
l
d
ata.
T
h
e
SC
-
VP
T
I
tech
n
iq
u
e
u
s
ed
VP
-
tr
ee
f
o
r
i
n
d
ex
in
g
t
h
e
clu
s
ter
ed
d
ata
p
o
i
n
ts
.
I
n
VP
-
tr
ee
,
th
e
s
to
r
in
g
o
f
cl
u
s
ter
ed
d
at
a
p
o
in
ts
is
d
e
n
o
ted
b
y
a
cir
cle.
E
ac
h
n
o
d
e
o
f
VP
tr
ee
co
n
s
i
s
ts
o
f
an
i
n
p
u
t
p
o
in
t
an
d
a
r
ad
iu
s
.
A
ll
t
h
e
le
f
t
ch
i
l
d
r
en
o
f
g
i
v
e
n
n
o
d
e
ar
e
p
lace
d
in
s
id
e
t
h
e
cir
cle
a
n
d
all
th
e
r
ig
h
t
c
h
ild
r
en
o
f
a
g
i
v
en
n
o
d
e
ar
e
p
lace
d
o
u
t
s
id
e
t
h
e
cir
cle.
T
h
e
tr
ee
its
el
f
n
o
t
n
ee
d
ed
to
k
n
o
w
an
y
in
f
o
r
m
atio
n
r
eg
ar
d
in
g
w
h
at
i
s
s
to
r
ed
an
d
its
n
ee
d
is
t
h
e
d
is
ta
n
ce
f
u
n
ctio
n
w
h
ich
s
atis
f
ies
t
h
e
m
etr
ic
s
p
ac
e
p
r
o
p
er
ties
.
A
cir
cle
i
s
ta
k
en
in
to
a
co
n
s
id
er
atio
n
w
i
th
a
r
ad
iu
s
.
T
h
e
le
f
t
c
h
ild
r
en
ar
e
all
p
lace
d
in
s
id
e
th
e
cir
cle
a
n
d
th
e
r
ig
h
t c
h
ild
r
en
ar
e
p
lace
d
o
u
ts
id
e
t
h
e
cir
cle.
El
Nin
o
w
e
a
th
e
r
d
a
tas
e
t
S
p
e
c
tral
Clu
ste
rin
g
VP
-
tree
I
n
d
e
x
in
g
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.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
2
2
6
1
–
2
2
7
1
2266
L
et
u
s
co
n
s
id
er
E
l
Nin
o
w
ea
th
er
d
ataset
i
s
cl
u
s
ter
ed
in
to
k
n
u
m
b
er
o
f
cl
u
s
ter
s
co
n
s
is
t
o
f
d
ata
p
o
in
ts
.
Fo
r
ea
c
h
n
o
d
e
in
tr
e
e,
a
d
ata
p
o
in
t
cl
u
s
ter
is
c
h
o
s
en
to
b
e
t
h
e
v
a
n
tag
e
p
o
in
t
b
y
Va
n
ta
g
e
P
o
in
t
Selectio
n
.
L
e
t
u
s
co
n
s
id
er
clu
s
ter
ed
d
ata
p
o
in
t
is
ch
o
s
en
f
o
r
t
h
e
r
o
o
t
n
o
d
e
is
an
d
μ
b
e
m
ed
i
an
o
f
d
is
tan
ce
v
alu
e
s
o
f
all
t
h
e
o
th
er
cl
u
s
ter
e
d
d
ata
p
o
in
ts
i
n
w
i
t
h
r
esp
ec
t
to
.
is
p
ar
titi
o
n
ed
in
to
t
w
o
s
u
b
s
ets
o
f
ap
p
r
o
x
i
m
atel
y
eq
u
al
s
ize
s
a
s
an
d
is
g
iv
e
n
b
y
,
{
|
(
8
)
{
|
(
9
)
Fro
m
(
8
)
an
d
(
9
)
,
s
y
m
b
o
lizes
th
e
d
is
ta
n
ce
b
et
w
ee
n
d
ata
p
o
i
n
t
cl
u
s
ter
s
„
‟
an
d
.
E
ac
h
s
u
b
s
et
lin
k
ed
to
o
n
e
n
o
d
e
o
f
VP
-
tr
ee
.
Fo
r
ea
ch
n
o
d
e,
a
v
an
tag
e
p
o
in
t
is
c
h
o
s
en
to
s
to
r
e
th
e
cl
u
s
t
er
ed
d
ata
p
o
in
ts
in
re
s
u
lta
n
t
s
u
b
s
e
t.
VP
-
tr
ee
s
to
r
es
m
an
y
d
ata
p
o
in
ts
a
t
o
n
e
leaf
n
o
d
e.
Fi
n
all
y
,
t
h
e
w
h
o
le
cl
u
s
ter
ed
d
ata
p
o
in
t
i
s
s
o
r
ted
o
u
t a
s
b
alan
ce
d
tr
ee
.
T
h
e
VP
-
tr
ee
s
tr
u
c
tu
r
e
i
s
s
i
m
p
le
w
h
er
e
ea
c
h
n
o
d
e
is
in
f
o
r
m
(
)
.
„
‟
s
y
m
b
o
lize
s
v
an
ta
g
e
p
o
in
t
an
d
d
en
o
tes
m
ed
ian
d
is
ta
n
ce
a
m
o
n
g
all
d
ata
p
o
in
ts
i
n
d
ex
ed
b
elo
w
t
h
at
n
o
d
e
w
h
er
ea
s
an
d
ar
e
p
o
in
ter
s
o
f
r
ig
h
t a
n
d
lef
t b
r
an
c
h
es r
esp
ec
ti
v
el
y
.
L
e
f
t
b
r
an
ch
o
f
n
o
d
e
in
d
ex
es c
lu
s
te
r
ed
d
ata
p
o
in
ts
w
h
o
s
e
d
is
tan
ce
s
f
r
o
m
ar
e
less
t
h
a
n
o
r
eq
u
al
to
.
C
o
n
s
e
q
u
en
tl
y
,
r
i
g
h
t
b
r
an
ch
o
f
n
o
d
e
in
d
ex
e
s
t
h
e
clu
s
ter
ed
d
ata
p
o
in
t
s
w
h
o
s
e
d
is
tan
ce
s
f
r
o
m
ar
e
g
r
ea
ter
t
h
an
o
r
eq
u
al
to
.
I
n
leaf
n
o
d
es,
r
ath
er
t
h
a
n
p
o
in
ter
s
to
lef
t
an
d
r
ig
h
t
b
r
an
ch
es,
r
ef
er
e
n
ce
s
to
clu
s
ter
ed
d
ata
p
o
in
ts
ar
e
k
ep
t.
T
h
e
m
ed
ia
n
d
is
ta
n
ce
b
et
w
ee
n
v
an
ta
g
e
p
o
in
t
an
d
th
e
cl
u
s
ter
e
d
d
ata
p
o
in
ts
„
‟
i
s
d
eter
m
i
n
ed
b
y
,
√
∑
(1
0)
Fro
m
(
1
0
)
,
m
ed
ia
n
d
is
tan
ce
is
m
ea
s
u
r
ed
.
Gi
v
en
a
d
ata
s
et
o
f
clu
s
ter
ed
d
ata
p
o
in
ts
{
,
an
d
a
m
ed
ia
n
d
is
ta
n
ce
f
u
n
ctio
n
,
a
VP
tr
ee
is
co
n
s
tr
u
cted
b
y
u
s
i
n
g
th
e
f
o
llo
w
i
n
g
alg
o
r
it
h
m
ic
p
r
o
ce
s
s
,
A
l
g
o
r
ith
m
2
.
VP
T
r
ee
b
as
ed
C
lu
s
ter
ed
Data
P
o
in
t I
n
d
ex
in
g
A
l
g
o
r
ith
m
// VP
tr
ee
b
ased
C
lu
s
ter
ed
Data
P
o
in
t I
n
d
ex
in
g
A
l
g
o
r
ith
m
I
n
p
u
t:
C
lu
s
ter
ed
d
ata
p
o
in
ts
„
{
‟
Ou
tp
u
t: C
r
ea
te
VP
tr
ee
f
o
r
I
n
d
ex
in
g
o
f
C
l
u
s
ter
ed
Data
P
o
in
ts
Step
1
: B
eg
in
Step
2
:
if
|
DP
C
|
=0
,
t
h
e
n
co
n
s
tr
u
ct
a
e
m
p
t
y
tr
ee
Step
3
:
M
=
m
ed
ian
o
f
{
)
|
}
Step
4
:
F
o
r
ea
ch
clu
s
ter
ed
d
ata
p
o
in
t „
‟
Step
5
:
R
an
d
o
m
l
y
s
elec
t
v
an
ta
g
e
p
o
in
t
„
‟
Step
6
:
C
alcu
late
t
h
e
d
is
tan
ce
f
r
o
m
v
an
tag
e
p
o
in
t
„
‟
to
th
e
d
ata
p
o
in
t „
‟
u
s
in
g
(
1
0
)
Step
7
:
C
o
m
p
u
te
m
ea
n
an
d
v
ar
ian
ce
o
f
d
is
ta
n
ce
Step
8
:
if
,
th
en
Step
9
:
C
lu
s
t
er
ed
d
ata
p
o
in
t
„
‟
is
s
to
r
ed
in
lef
t
b
r
an
ch
o
f
tr
ee
Step
1
0
:
else
Step
1
1
:
C
lu
s
te
r
ed
d
ata
p
o
in
t
„
‟
i
s
s
to
r
ed
in
r
ig
h
t
b
r
an
ch
o
f
tr
ee
Step
1
2
:
e
n
d
if
Step
1
3
:
else fo
r
Step
1
4
:
E
n
d
B
y
u
s
i
n
g
t
h
e
ab
o
v
e
alg
o
r
ith
m
2
,
clu
s
ter
ed
d
ata
p
o
in
ts
ar
e
ef
f
icie
n
tl
y
s
to
r
ed
in
VP
tr
e
e
s
tr
u
ctu
r
e
b
ased
o
n
d
ata
ty
p
e.
VP
tr
ee
i
n
d
ex
i
n
g
m
i
n
i
m
izes
t
h
e
o
v
er
la
p
s
p
ac
e
an
d
o
p
tim
izes
t
h
e
r
etr
iev
al
p
ath
o
f
i
n
d
ex
.
T
h
is
i
n
tu
r
n
h
e
lp
s
to
r
ed
u
ce
th
e
s
p
ac
e
co
m
p
le
x
it
y
.
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
S
p
ec
tr
a
l Cl
u
s
teri
n
g
a
n
d
V
a
n
ta
g
e
P
o
in
t I
n
d
ex
in
g
fo
r
E
fficien
t D
a
ta
R
etri
ev
a
l (
R
.
P
u
s
h
p
a
la
t
h
a
)
2267
2
.
3
.
VP
-
t
re
e
ba
s
ed
da
t
a
re
t
riev
a
l
pro
ce
s
s
Af
ter
i
n
d
ex
i
n
g
th
e
cl
u
s
ter
ed
d
ata
p
o
in
ts
,
S
C
-
VP
T
I
tech
n
iq
u
e
p
er
f
o
r
m
s
VP
-
tr
ee
b
ased
d
ata
r
etr
iev
al
p
r
o
ce
s
s
f
o
r
ef
f
icie
n
t
d
ata
r
etr
iev
al
p
r
o
ce
s
s
b
ased
o
n
t
h
e
u
s
e
r
q
u
er
y
.
Da
ta
r
etr
iev
al
i
s
a
p
r
o
ce
s
s
o
f
r
etr
iev
in
g
th
e
r
elev
a
n
t
d
ata
f
r
o
m
th
e
i
n
d
ex
ed
d
atab
ase
b
ased
o
n
u
s
er
r
eq
u
ested
d
ata.
Fo
r
r
etr
iev
in
g
th
e
d
ata,
u
s
er
q
u
er
y
is
g
i
v
en
as
a
n
in
p
u
t.
T
h
en
,
th
e
u
s
er
q
u
er
ied
d
ata
ar
e
s
ea
r
ch
ed
an
d
r
etr
iev
ed
.
Fin
all
y
,
th
e
r
etr
iev
ed
d
ata
ar
e
tr
an
s
m
itted
to
th
e
co
r
r
esp
o
n
d
i
n
g
u
s
er
.
T
h
e
d
ata
r
etr
iev
al
p
r
o
ce
s
s
is
s
h
o
w
n
in
b
elo
w
Fi
g
u
r
e
4
.
F
ig
u
r
e
4
.
Data
r
tr
iev
al
p
r
o
ce
s
s
es
Fig
u
r
e
4
ex
p
lai
n
s
th
e
b
lo
ck
d
iag
r
a
m
o
f
d
ata
r
etr
ie
v
al
p
r
o
ce
s
s
.
Fo
r
t
h
e
g
iv
e
n
u
s
er
q
u
er
y
„
‟
,
s
et
o
f
d
ata
p
o
in
ts
th
at
ar
e
w
it
h
i
n
th
e
d
is
tan
ce
„
‟
o
f
ar
e
r
etr
iev
ed
b
y
s
ea
r
ch
alg
o
r
ith
m
.
T
h
e
alg
o
r
ith
m
ic
p
r
o
ce
s
s
o
f
VP
-
T
r
ee
B
ased
Data
R
etr
iev
al
A
l
g
o
r
ith
m
is
e
x
p
lai
n
ed
b
elo
w
.
A
l
g
o
r
ith
m
3
.
VP
-
T
r
ee
B
ased
Data
R
etr
iev
a
l
A
lg
o
r
it
h
m
// VP
-
T
r
ee
B
ased
Data
R
etr
iev
al
A
l
g
o
r
ith
m
I
n
p
u
t: U
s
er
q
u
er
y
,
Qu
er
y
r
an
g
e
„
‟,
v
a
n
ta
g
e
p
o
in
t
„
‟
,
an
d
Me
d
ian
d
is
tan
ce
„
M
‟
Ou
tp
u
t: I
m
p
r
o
v
ed
T
r
u
e
P
o
s
iti
v
e
R
ate
o
f
Da
ta
R
etr
ie
v
al
an
d
R
ed
u
ce
d
Data
R
etr
ie
v
al
ti
m
e
Step
1
:
B
eg
in
Step
2
:
F
o
r
ea
ch
User
q
u
er
y
„
‟
Step
3
:
if
,
th
en
v
an
tag
e
p
o
i
n
t a
t th
e
r
o
o
t
Step
4
:
if
,
th
en
Step
5
:
Sear
ch
r
ig
h
t
b
r
an
ch
o
f
tr
ee
Step
6
:
else
,
th
en
Step
7
:
S
ea
r
ch
lef
t b
r
an
c
h
o
f
tr
ee
Step
8
:
E
n
d
if
Step
9
:
E
n
d
if
Step
1
0
:
if
b
o
th
s
ea
r
ch
co
n
d
it
io
n
s
ar
e
s
atis
f
ied
,
th
en
Step
1
1
:
B
o
th
b
r
an
ch
es
o
f
tr
ee
is
s
ea
r
ch
ed
f
o
r
r
etr
iev
i
n
g
u
s
er
q
u
er
ied
d
ata
p
o
in
ts
Step
1
2
:
Dis
p
lay
s
ea
r
c
h
e
d
d
ata
p
o
in
t to
u
s
er
Step
1
2
:
E
n
d
if
Step
1
3
:
E
n
d
f
o
r
Step
1
4
:
E
n
d
B
y
u
s
in
g
ab
o
v
e
al
g
o
r
ith
m
3
,
SC
-
VP
T
I
tech
n
iq
u
e
e
f
f
icien
tl
y
r
etr
iev
e
s
d
ata
p
o
in
ts
f
r
o
m
t
h
e
VP
tr
ee
in
d
ex
i
n
g
d
atab
ase
b
ased
o
n
th
e
u
s
er
q
u
er
y
.
As
a
r
esu
lt,
SC
-
VPT
I
tech
n
iq
u
e
i
n
cr
ea
s
es
t
h
e
tr
u
e
p
o
s
itiv
e
r
ate
o
f
d
ata
r
etr
iev
al
an
d
r
ed
u
ce
s
d
ata
r
etr
iev
al
ti
m
e.
3.
E
XP
E
R
I
M
E
NT
A
L
SE
T
T
I
N
G
T
h
e
Sp
ec
tr
al
C
lu
s
ter
in
g
B
ase
d
VP
T
r
ee
I
n
d
ex
in
g
(
SC
-
VP
T
I
)
T
ec
h
n
iq
u
e
is
i
m
p
le
m
e
n
te
d
in
J
av
a
L
a
n
g
u
a
g
e
w
it
h
aid
o
f
E
l
Ni
n
o
d
ataset
f
r
o
m
U
C
I
m
ac
h
i
n
e
le
ar
n
in
g
r
ep
o
s
ito
r
y
.
T
h
e
E
l
Nin
o
d
ataset
co
m
p
r
is
e
s
th
e
o
ce
an
o
g
r
ap
h
ic
an
d
s
u
r
f
ac
e
m
eteo
r
o
lo
g
ical
r
ea
d
in
g
s
f
r
o
m
s
eq
u
e
n
ce
o
f
b
u
o
y
s
s
i
ted
all
o
v
er
th
e
eq
u
ato
r
ial
P
ac
if
ic.
T
h
e
d
ata
is
p
r
ed
ictab
le
to
ass
is
t
in
a
n
d
p
r
ed
ictio
n
o
f
E
l
Nin
o
/So
u
t
h
er
n
Oscill
at
i
o
n
(
E
NSO)
cy
c
les.
T
h
e
d
ataset
ch
ar
ac
ter
is
tics
ar
e
s
p
atio
-
te
m
p
o
r
al
an
d
attr
ib
u
te
ch
ar
ac
ter
is
t
ics
is
b
o
th
r
ea
l
an
d
in
teg
er
.
I
n
ad
d
itio
n
,
n
u
m
b
er
o
f
i
n
s
ta
n
ce
s
ar
e
1
7
8
0
8
0
an
d
n
u
m
b
er
o
f
attr
ib
u
tes
ar
e
1
2
.
E
l
Nin
o
d
ataset
in
c
lu
d
es
t
h
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.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
2
2
6
1
–
2
2
7
1
2268
attr
ib
u
tes
li
k
e
d
ate,
latitu
d
e,
l
o
n
g
it
u
d
e,
zo
n
al
w
i
n
d
s
(
w
e
s
t<
0
,
ea
s
t>0
)
,
m
er
id
io
n
al
w
i
n
d
s
(
s
o
u
th
<0
,
n
o
r
t
h
>0
)
,
r
elativ
e
h
u
m
id
it
y
,
air
te
m
p
er
a
tu
r
e,
s
ea
s
u
r
f
ac
e
te
m
p
er
atu
r
e
an
d
s
u
b
s
u
r
f
ac
e
te
m
p
er
at
u
r
es
d
o
w
n
to
a
d
ep
th
o
f
5
0
0
m
eter
s
.
4.
RE
SU
L
T
S AN
D
D
I
S
CU
SS
I
O
NS
T
h
e
r
esu
lt
an
al
y
s
is
o
f
S
C
-
VP
T
I
tech
n
iq
u
e
is
co
m
p
ar
ed
ag
ai
n
s
t
w
it
h
ex
i
s
ti
n
g
t
w
o
ap
p
r
o
ac
h
es
n
a
m
el
y
L
o
ca
lit
y
-
Sen
s
iti
v
e
Has
h
i
n
g
(
L
SH)
[
1
]
an
d
in
cr
e
m
en
ta
l
s
em
i
s
u
p
er
v
is
ed
clu
s
ter
in
g
en
s
e
m
b
le
(
I
SS
C
E
)
[
2
]
r
esp
ec
tiv
el
y
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
SC
-
VP
T
I
tech
n
iq
u
e
i
s
ev
a
lu
ated
o
n
v
ar
io
u
s
f
ac
t
o
r
s
s
u
c
h
a
s
s
p
ac
e
co
m
p
le
x
it
y
,
d
ata
r
etr
iev
al
ti
m
e
an
d
tr
u
e
p
o
s
itiv
e
r
ate
w
it
h
h
el
p
o
f
tab
les an
d
g
r
ap
h
s
.
4
.
1
.
Sp
a
ce
co
m
plex
it
y
Sp
ac
e
co
m
p
le
x
it
y
i
s
d
ef
in
ed
as
th
e
a
m
o
u
n
t
o
f
m
e
m
o
r
y
s
p
ac
e
r
eq
u
ir
ed
f
o
r
clu
s
ter
in
g
an
d
in
d
ex
in
g
th
e
d
en
s
el
y
p
o
p
u
lated
h
i
g
h
d
i
m
e
n
s
io
n
a
l
d
ata.
T
h
e
s
p
ac
e
co
m
p
le
x
it
y
i
s
m
ea
s
u
r
ed
in
ter
m
s
o
f
Me
g
a
B
y
tes (
MB
)
an
d
f
o
r
m
u
l
ated
as,
(
1
1
)
Fro
m
(
1
1
)
,
„
‟
d
en
o
tes
th
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
tak
en
f
o
r
cl
u
s
ter
i
n
g
p
r
o
ce
s
s
.
W
h
en
t
h
e
s
p
ac
e
co
m
p
lex
it
y
i
s
less
er
,
th
e
tec
h
n
iq
u
e
is
s
aid
to
b
e
m
o
r
e
ef
f
icie
n
t.
T
ab
le
1
d
escr
ib
es
th
e
s
p
ac
e
co
m
p
le
x
it
y
v
a
lu
e
s
o
b
tain
ed
b
ased
o
n
d
if
f
er
en
t
n
u
m
b
er
o
f
d
ata
p
o
in
ts
tak
en
in
th
e
r
a
n
g
e
o
f
5
0
-
5
0
0
.
Fro
m
th
e
tab
le
v
al
u
e,
p
r
o
p
o
s
ed
SC
-
VP
T
I
tech
n
iq
u
e
h
a
s
les
s
er
s
p
ac
e
co
m
p
le
x
it
y
d
u
r
in
g
clu
s
ter
in
g
an
d
i
n
d
ex
i
n
g
th
e
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
i
m
en
s
io
n
al
d
ata
p
o
in
t
s
w
h
e
n
co
m
p
ar
ed
to
L
SH
T
ec
h
n
iq
u
e
an
d
I
SS
C
E
A
p
p
r
o
ac
h
r
esp
ec
tiv
el
y
.
B
esid
es,
w
h
e
n
th
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
d
u
r
in
g
clu
s
ter
in
g
an
d
in
d
ex
i
n
g
p
r
o
ce
s
s
in
cr
ea
s
e
s
,
th
e
s
p
ac
e
co
m
p
le
x
it
y
also
g
et
s
i
n
cr
ea
s
ed
in
all
t
h
r
ee
m
et
h
o
d
s
.
T
ab
le
1
.
T
ab
u
latio
n
f
o
r
Sp
ac
e
C
o
m
p
le
x
it
y
N
u
mb
e
r
o
f
D
a
t
a
P
o
i
n
t
s
S
p
a
c
e
C
o
mp
l
e
x
i
t
y
(
M
B
)
L
S
H
Te
c
h
n
i
q
u
e
I
S
S
C
E
A
p
p
r
o
a
c
h
SC
-
V
P
TI
t
e
c
h
n
i
q
u
e
50
2
6
.
3
6
2
3
.
7
8
1
4
.
3
2
1
0
0
2
8
.
1
2
2
5
.
1
4
1
6
.
3
4
1
5
0
2
9
.
8
9
2
7
.
9
6
1
7
.
9
8
2
0
0
3
1
.
7
8
2
9
.
1
7
1
9
.
2
3
2
5
0
3
3
.
9
8
3
1
.
5
4
2
1
.
5
9
3
0
0
3
5
.
6
3
3
3
.
9
8
2
3
.
8
7
3
5
0
3
7
.
8
9
3
4
.
5
2
2
5
.
9
8
4
0
0
3
9
.
2
7
3
7
.
1
2
2
7
.
4
5
4
5
0
4
1
.
9
6
3
8
.
3
3
2
9
.
7
5
5
0
0
4
2
.
3
4
4
0
.
1
5
3
1
.
4
7
B
u
t,
th
e
s
p
a
ce
co
m
p
le
x
it
y
u
s
i
n
g
p
r
o
p
o
s
ed
SC
-
VP
T
I
te
ch
n
iq
u
e
is
less
er
.
T
h
is
is
b
ec
au
s
e
o
f
ap
p
licatio
n
o
f
n
o
r
m
alize
d
s
p
ec
tr
al
clu
s
ter
in
g
al
g
o
r
it
h
m
an
d
VP
b
ased
C
l
u
s
ter
ed
Da
ta
P
o
in
t
I
n
d
ex
i
n
g
A
l
g
o
r
ith
m
in
SC
-
VP
T
I
tech
n
iq
u
e
w
h
er
e
it
ef
f
icie
n
tl
y
g
r
o
u
p
an
d
in
d
e
x
t
h
e
h
ig
h
d
i
m
en
s
io
n
a
l
d
ata
.
I
n
n
o
r
m
alize
d
s
p
ec
tr
al
cl
u
s
ter
i
n
g
alg
o
r
it
h
m
,
t
h
e
s
i
m
i
lar
it
y
m
atr
i
x
an
d
lap
lacia
n
m
atr
i
x
ar
e
co
n
s
tr
u
cted
to
id
en
ti
f
y
s
i
m
ilar
d
ata
p
o
in
ts
.
F
o
llo
w
ed
b
y
,
t
h
e
K
-
m
ea
n
s
al
g
o
r
ith
m
is
ap
p
lied
to
g
r
o
u
p
t
h
e
s
i
m
ilar
d
ata
p
o
i
n
ts
to
co
n
s
tr
u
ct
k
-
cl
u
s
ter
s
.
B
y
ap
p
ly
in
g
an
in
d
e
x
i
n
g
al
g
o
r
ith
m
,
s
et
o
f
d
ata
p
o
in
ts
t
h
at
ar
e
w
it
h
in
t
h
e
d
is
tan
ce
ar
e
co
r
r
ec
tly
i
n
d
ex
ed
i
n
r
i
g
h
t
an
d
lef
t
b
r
an
c
h
e
s
r
esp
ec
tiv
e
l
y
.
I
n
VP
tr
ee
,
lef
t
b
r
an
c
h
o
f
n
o
d
e
in
d
ex
e
s
cl
u
s
ter
ed
d
ata
p
o
in
ts
w
h
o
s
e
d
is
ta
n
ce
s
f
r
o
m
v
a
n
tag
e
p
o
in
t
ar
e
les
s
th
a
n
o
r
eq
u
al
to
Me
d
ian
d
is
tan
ce
.
A
cc
o
r
d
in
g
l
y
,
r
ig
h
t
b
r
an
ch
o
f
n
o
d
e
in
d
ex
es
t
h
e
cl
u
s
ter
ed
d
ata
p
o
in
ts
w
h
o
s
e
d
is
t
an
ce
s
f
r
o
m
v
a
n
tag
e
p
o
in
t
ar
e
g
r
ea
ter
th
an
o
r
eq
u
al
to
Me
d
ian
d
is
tan
ce
.
B
ased
o
n
in
d
e
x
in
g
al
g
o
r
ith
m
,
th
e
d
e
n
s
el
y
p
o
p
u
lated
clu
s
ter
ed
d
at
a
ar
e
s
to
r
ed
in
an
ef
f
icien
t
m
a
n
n
er
w
i
th
le
s
s
s
p
ac
e
co
m
p
le
x
it
y
.
A
s
a
r
esu
lt,
p
r
o
p
o
s
ed
SC
-
VP
T
I
tech
n
iq
u
e
r
ed
u
ce
s
th
e
s
p
ac
e
co
m
p
le
x
it
y
o
f
d
en
s
el
y
p
o
p
u
lat
ed
h
ig
h
d
i
m
en
s
io
n
al
d
ata
b
y
3
5
%
as
co
m
p
ar
ed
to
L
SH
T
ec
h
n
iq
u
e
[
1
]
an
d
3
0
%
as c
o
m
p
ar
ed
to
I
SS
C
E
A
p
p
r
o
ac
h
[
2
]
r
esp
ec
tiv
el
y.
4
.
2
.
T
rue
po
s
it
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e
ra
t
e
T
r
u
e
p
o
s
itiv
e
r
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(
T
P
R
)
o
f
d
ata
r
etr
iev
al
is
d
escr
ib
ed
as
th
e
r
atio
o
f
n
u
m
b
er
o
f
co
r
r
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tl
y
r
etr
iev
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d
ata
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o
in
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ased
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n
u
s
er
q
u
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r
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t
h
e
to
tal
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u
m
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er
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d
ata
p
o
in
ts
.
T
h
e
tr
u
e
p
o
s
iti
v
e
r
ate
o
f
d
ata
r
etr
ie
v
al
i
s
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u
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m
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g
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r
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ed
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tech
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iq
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e
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as
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i
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er
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e
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g
r
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ata
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o
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ts
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ased
o
n
th
e
u
s
er
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u
er
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r
o
m
th
e
in
d
e
x
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n
g
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ase
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h
e
n
co
m
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ar
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SH
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h
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n
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ed
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h
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ig
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i
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ith
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a
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ie
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al
A
l
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o
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ith
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i
n
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I
tech
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i
q
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e
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er
e
it
ef
f
ic
ien
tl
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ea
r
c
h
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n
d
r
etr
iev
es t
h
e
ex
ac
t u
s
er
r
eq
u
ested
d
ata
.
Fig
u
r
e
5
.
Me
asu
r
e
m
en
t o
f
T
r
u
e
P
o
s
itiv
e
r
ate
T
h
e
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an
ta
g
e
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o
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ee
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n
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cted
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o
r
in
d
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in
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r
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leaf
a
n
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ig
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t
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ee
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Af
ter
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ilar
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atab
ase
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ased
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n
u
s
er
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eq
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ested
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ata.
Fo
r
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h
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ata
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o
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lay
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h
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ata
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o
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ts
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u
s
er
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d
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g
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er
r
eq
u
ir
e
m
en
ts
.
T
h
is
h
elp
s
to
co
r
r
ec
tly
r
etr
ie
v
e
t
h
e
s
i
m
i
la
r
d
ata
p
o
in
ts
i
n
o
r
d
er
to
ar
ch
iv
e
h
i
g
h
tr
u
e
p
o
s
iti
v
e
r
ate
i
n
a
n
ef
f
icien
t
w
a
y
.
A
s
a
r
esu
lt,
p
r
o
p
o
s
ed
SC
-
VP
T
I
tec
h
n
iq
u
e
i
n
cr
ea
s
es
th
e
tr
u
e
p
o
s
i
tiv
e
r
ate
o
f
d
e
n
s
el
y
p
o
p
u
lated
h
i
g
h
d
i
m
e
n
s
io
n
al
d
ata
b
y
2
2
% a
s
co
m
p
ar
ed
to
L
SH T
ec
h
n
iq
u
e
[
1
]
an
d
1
2
% a
s
co
m
p
ar
ed
to
I
SS
C
E
A
p
p
r
o
ac
h
[
2
]
r
esp
ec
tiv
ely
.
4
.
3
.
Da
t
a
re
t
riev
a
l t
i
m
e
Data
R
etr
iev
al
T
i
m
e
is
d
ef
in
ed
as
am
o
u
n
t
o
f
ti
m
e
ta
k
e
n
f
o
r
r
etr
iev
in
g
th
e
d
a
ta
p
o
in
ts
f
r
o
m
th
e
in
d
ex
i
n
g
d
atab
ase.
I
t is
m
ea
s
u
r
ed
in
ter
m
s
o
f
m
ill
is
ec
o
n
d
s
(
m
s
)
.
Data
R
e
tr
iev
al
T
i
m
e
is
f
o
r
m
u
la
ted
as,
(
1
3
)
Fro
m
(
1
3
)
,
„
‟
r
ep
r
esen
ts
n
u
m
b
er
o
f
d
ata
p
o
in
ts
.
W
h
en
t
h
e
d
ata
r
etr
iev
al
ti
m
e
is
le
s
s
er
,
th
e
m
et
h
o
d
is
s
aid
to
b
e
m
o
r
e
ef
f
icie
n
t.
Fig
u
r
e
6
d
escr
ib
es
th
e
d
ata
r
etr
iev
al
ti
m
e
m
ea
s
u
r
e
o
f
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
i
m
e
n
s
io
n
al
d
ata
v
er
s
u
s
n
u
m
b
er
o
f
d
ata
p
o
in
ts
i
n
r
an
g
e
o
f
5
0
-
5
0
0
.
Fro
m
f
i
g
u
r
e,
p
r
o
p
o
s
ed
SC
-
VP
T
I
tech
n
iq
u
e
co
n
s
u
m
es
le
s
s
er
ti
m
e
d
u
r
i
n
g
r
etr
iev
i
n
g
t
h
e
d
ata
p
o
in
ts
b
ased
o
n
t
h
e
u
s
er
q
u
e
r
y
f
r
o
m
th
e
i
n
d
ex
in
g
d
atab
ase
w
h
e
n
co
m
p
ar
ed
to
L
SH
T
ec
h
n
iq
u
e
a
n
d
I
SS
C
E
A
p
p
r
o
ac
h
r
esp
ec
ti
v
el
y
.
I
n
ad
d
itio
n
,
w
h
en
th
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
d
u
r
in
g
clu
s
ter
i
n
g
an
d
in
d
e
x
i
n
g
p
r
o
ce
s
s
i
n
cr
ea
s
es,
t
h
e
d
ata
r
etr
iev
a
l
ti
m
e
al
s
o
g
ets
i
n
cr
ea
s
ed
in
all
th
r
ee
m
e
th
o
d
s
.
Ho
w
e
v
er
,
th
e
d
ata
r
etr
iev
al
ti
m
e
u
s
i
n
g
p
r
o
p
o
s
ed
SC
-
VP
T
I
tech
n
iq
u
e
is
le
s
s
er
.
T
h
is
is
d
u
e
to
th
e
Van
tag
e
P
o
in
t
b
ased
C
lu
s
ter
ed
Data
Po
in
t
I
n
d
ex
i
n
g
A
l
g
o
r
ith
m
a
n
d
R
etr
iev
al
A
l
g
o
r
ith
m
i
n
SC
-
V
PT
I
tech
n
iq
u
e
w
h
er
e
it
ef
f
icie
n
tl
y
s
ea
r
ch
e
s
d
ata
an
d
r
etr
iev
es
w
it
h
m
in
i
m
al
ti
m
e
.
An
i
n
d
ex
i
n
g
al
g
o
r
it
h
m
e
f
f
ec
ti
v
el
y
s
to
r
es
t
h
e
d
ata
w
ith
t
w
o
d
if
f
er
e
n
t
b
r
an
c
h
es
n
a
m
e
l
y
le
f
t
an
d
r
ig
h
t
an
d
it
is
d
en
o
tes
as
cir
cles.
T
h
is
h
e
lp
s
to
e
f
f
ec
ti
v
el
y
s
to
r
e
t
h
e
cl
u
s
ter
ed
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
i
n
t
h
ese
t
w
o
b
r
an
ch
es
o
f
n
o
d
e.
Af
ter
in
d
e
x
in
g
t
h
e
d
ata,
d
ata
r
etr
iev
al
f
r
o
m
i
n
d
ex
d
atab
ase
is
ca
r
r
ied
o
u
t
u
s
i
n
g
VP
-
T
r
ee
B
ased
Data
R
etr
ie
v
al
Alg
o
r
it
h
m
.
Fo
r
ea
c
h
r
eq
u
e
s
ted
u
s
er
q
u
er
y
,
th
e
s
i
m
ilar
d
ata
p
o
in
ts
ar
e
s
ea
r
c
h
ed
f
r
o
m
th
e
in
d
ex
i
n
g
d
atab
ase.
T
h
is
h
elp
s
to
r
ed
u
ce
th
e
d
ata
r
etr
iev
al
tim
e
o
f
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
im
e
n
s
io
n
al
d
ata.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
0
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-
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I
n
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&
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,
No
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As
a
r
es
u
lt,
p
r
o
p
o
s
ed
SC
-
VP
T
I
tech
n
iq
u
e
r
ed
u
ce
s
d
ata
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etr
iev
al
t
i
m
e
o
f
d
en
s
el
y
p
o
p
u
late
d
h
i
g
h
d
i
m
e
n
s
io
n
al
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ata
b
y
1
7
% a
s
co
m
p
ar
ed
to
L
SH T
ec
h
n
iq
u
e
[
1
]
an
d
3
0
% a
s
co
m
p
ar
ed
to
I
SS
C
E
A
p
p
r
o
ac
h
[
2
]
r
esp
ec
tiv
ely
.
Fig
u
r
e
6
.
Me
a
s
u
r
e
m
en
t o
f
Dat
a
R
etr
iev
al
T
i
m
e
5.
RE
L
AT
E
D
WO
RK
S
A
s
u
r
p
r
is
i
n
g
s
i
m
p
le
m
et
h
o
d
w
a
s
i
n
tr
o
d
u
ce
d
in
[
1
2
]
f
o
r
ad
d
r
ess
in
g
th
e
ANN
i
s
s
u
es
w
i
th
h
i
g
h
ac
cu
r
ac
y
r
es
u
lt
s
an
d
n
ee
d
s
les
s
er
n
u
m
b
er
o
f
r
a
n
d
o
m
I
/O.
B
u
t,
a
b
in
ar
y
in
d
e
x
s
tr
u
ct
u
r
e
r
ed
u
ce
s
t
h
e
s
p
ac
e
an
d
it
f
ailed
to
co
n
s
id
er
th
e
p
er
f
o
r
m
a
n
ce
o
f
tr
u
e
p
o
s
iti
v
e
r
at
e
in
th
e
p
r
o
ce
s
s
o
f
d
ata
r
etr
iev
al.
A
n
e
w
s
e
m
i
-
s
u
p
er
v
i
s
ed
h
as
h
in
g
m
e
th
o
d
was
i
n
tr
o
d
u
ce
d
i
n
[
1
3
]
w
ith
p
air
w
i
s
e
s
u
p
er
v
is
ed
i
n
f
o
r
m
atio
n
c
o
m
p
r
i
s
in
g
o
f
m
u
s
t
-
lin
k
an
d
ca
n
n
o
t
-
li
n
k
.
T
h
e
d
e
s
ig
n
ed
m
et
h
o
d
in
cr
ea
s
ed
th
e
in
f
o
r
m
a
tio
n
p
r
o
v
id
ed
b
y
ev
er
y
b
it
alo
n
g
w
ith
lab
eled
d
ata
an
d
th
e
u
n
lab
ele
d
d
ata.
A
c
lu
s
ter
in
g
al
g
o
r
it
h
m
ca
lled
SUB
SC
AL
E
w
as
in
tr
o
d
u
ce
d
in
[
1
4
]
to
id
en
ti
f
y
th
e
n
o
n
-
tr
iv
ial
s
u
b
s
p
ac
e
clu
s
ter
s
w
i
th
les
s
er
co
s
t
a
n
d
it
n
ee
d
ed
o
n
l
y
k
d
at
ab
ase
s
ca
n
s
f
o
r
k
-
d
i
m
en
s
io
n
al
d
atase
ts
.
A
n
e
w
p
en
al
ized
f
o
r
w
ar
d
s
e
lectio
n
tec
h
n
iq
u
e
in
[
1
5
]
m
i
n
i
m
ized
h
ig
h
d
i
m
e
n
s
io
n
al
o
p
ti
m
izat
io
n
is
s
u
es
to
m
a
n
y
o
n
e
d
i
m
e
n
s
i
o
n
al
o
p
ti
m
izatio
n
i
s
s
u
es
t
h
r
o
u
g
h
s
elec
t
in
g
th
e
b
est
p
r
ed
icto
r
.
B
u
t,
th
e
d
ata
r
etr
iev
al
ti
m
e
w
as
n
o
t
r
ed
u
ce
d
u
s
i
n
g
p
en
alize
d
f
o
r
w
ar
d
s
elec
tio
n
tech
n
iq
u
e.
C
o
n
s
tr
ai
n
t
-
P
ar
titi
o
n
i
n
g
K
-
Me
a
n
s
(
C
OP
-
KM
E
A
N
S)
clu
s
ter
in
g
alg
o
r
ith
m
w
a
s
i
n
tr
o
d
u
ce
d
in
[
1
6
]
f
o
r
clu
s
ter
in
g
h
ig
h
d
i
m
e
n
s
io
n
al
d
ata
an
d
to
m
i
n
i
m
ize
t
h
e
co
s
t
t
h
r
o
u
g
h
r
e
m
o
v
i
n
g
th
e
n
o
is
y
d
i
m
en
s
io
n
s
.
P
r
ed
ictiv
e
S
u
b
s
p
ac
e
C
l
u
s
ter
in
g
(
P
SC
)
w
as
in
tr
o
d
u
ce
d
i
n
[
1
7
]
f
o
r
clu
s
ter
i
n
g
t
h
e
h
ig
h
-
d
i
m
e
n
s
io
n
al
d
ata.
B
u
t,
P
SC
is
n
o
t
s
u
itab
le
f
o
r
d
en
s
el
y
p
o
p
u
lated
h
ig
h
d
i
m
en
s
io
n
al
d
ata
p
o
in
t
s
.
Dis
cr
i
m
in
at
iv
e
E
m
b
ed
d
ed
C
l
u
s
ter
i
n
g
(
DE
C
)
w
a
s
ca
r
r
ied
o
u
t
i
n
[
1
8
]
th
at
co
m
b
i
n
es
th
e
s
u
b
s
p
ac
e
lear
n
in
g
an
d
clu
s
ter
i
n
g
.
Ho
wev
er
,
DE
C
co
n
s
u
m
ed
lar
g
e
a
m
o
u
n
t
o
f
ti
m
e
f
o
r
d
ata
r
etr
iev
al.
H
-
K
cl
u
s
ter
i
n
g
alg
o
r
ith
m
w
a
s
d
esi
g
n
ed
i
n
[
1
9
]
to
m
i
n
i
m
ize
t
h
e
s
p
ac
e
co
m
p
lex
i
t
y
d
u
r
in
g
h
ig
h
d
i
m
en
s
i
o
n
al
d
ata
clu
s
ter
in
g
.
Hier
ar
ch
ical
A
cc
u
m
u
lativ
e
C
l
u
s
ter
i
n
g
A
l
g
o
r
ith
m
w
a
s
i
n
tr
o
d
u
ce
d
in
[
2
0
]
to
clu
s
ter
t
h
e
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
w
it
h
h
ig
h
er
cl
u
s
ter
i
n
g
ac
c
u
r
ac
y
.
Ho
w
e
v
er
,
th
e
d
esi
g
n
ed
alg
o
r
ith
m
n
ee
d
s
lar
g
e
a
m
o
u
n
t
o
f
m
e
m
o
r
y
s
p
ac
e.
A
r
o
b
u
s
t
m
u
lti
o
b
j
ec
tiv
e
s
u
b
s
p
ac
e
clu
s
ter
i
n
g
(
MO
S
C
L
)
alg
o
r
ith
m
w
as
p
r
esen
ted
in
[
2
1
]
f
o
r
h
ig
h
-
d
i
m
e
n
s
io
n
a
l
clu
s
ter
i
n
g
w
it
h
h
ig
h
er
ac
cu
r
a
c
y
o
f
s
u
b
s
p
ac
e
cl
u
s
ter
i
n
g
.
B
u
t,
th
e
s
p
ac
e
co
m
p
lex
it
y
r
e
m
ain
ed
u
n
ad
d
r
ess
ed
u
s
i
n
g
MO
SC
L
a
lg
o
r
it
h
m
.
Gr
ap
h
-
b
ased
cl
u
s
ter
in
g
w
a
s
d
ev
e
l
o
p
ed
in
[
2
2
]
to
clu
s
ter
th
e
w
e
b
s
ea
r
ch
r
es
u
lt
s
w
i
th
h
ig
h
cl
u
s
ter
i
n
g
q
u
al
it
y
.
Ho
w
e
v
er
,
th
e
d
en
s
el
y
p
o
p
u
late
d
clu
s
ter
in
g
o
n
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
w
as
n
o
t
p
er
f
o
r
m
ed
.
An
in
cr
e
m
en
tal
-
c
l
u
s
ter
i
n
g
ap
p
r
o
ac
h
w
as
d
e
v
elo
p
ed
in
[
2
3
]
f
o
r
co
n
s
tr
u
cti
n
g
a
clu
s
ter
b
ased
o
n
s
elec
ti
n
g
a
n
o
p
ti
m
al
t
h
r
es
h
o
ld
v
alu
e.
B
u
t,
ef
f
icie
n
t d
ata
r
etr
iev
al
w
as
n
o
t p
er
f
o
r
m
ed
w
ith
m
in
i
m
u
m
ti
m
e.
6.
CO
NCLU
SI
O
N
An
ef
f
icie
n
t
Sp
ec
tr
al
C
lu
s
ter
i
n
g
B
as
ed
VP
T
r
ee
I
n
d
ex
in
g
(
SC
-
VP
T
I
)
T
ec
h
n
iq
u
e
is
d
e
v
elo
p
ed
t
o
en
h
a
n
ce
th
e
d
ata
r
etr
ie
v
al
p
e
r
f
o
r
m
an
ce
b
ased
o
n
u
s
er
q
u
e
r
y
w
it
h
les
s
er
s
p
ac
e
co
m
p
lex
it
y
a
n
d
h
i
g
h
er
tr
u
e
p
o
s
itiv
e
r
ate.
E
x
i
s
ti
n
g
lo
ca
lit
y
s
en
s
iti
v
e
h
a
s
h
i
n
g
(
L
SH)
tech
n
iq
u
e
s
e
m
p
lo
y
ed
f
o
r
n
ea
r
-
n
ei
g
h
b
o
r
s
ea
r
ch
i
s
s
u
e
s
b
u
t
it
f
ailed
to
ad
d
r
ess
r
etr
i
ev
al
o
f
h
i
g
h
d
i
m
en
s
io
n
al
d
ata.
An
i
n
cr
e
m
en
ta
l
s
e
m
i
s
u
p
er
v
is
ed
cl
u
s
ter
i
n
g
en
s
e
m
b
le
ap
p
r
o
ac
h
n
o
t
co
n
s
i
d
er
ed
th
e
r
etr
iev
al
p
r
o
ce
s
s
.
T
h
ese
p
r
o
b
le
m
s
ar
e
ad
d
r
ess
ed
b
y
u
s
in
g
SC
-
VP
T
I
T
ec
h
n
iq
u
e.
T
h
r
ee
p
r
o
ce
s
s
in
g
s
tep
s
ar
e
p
r
esen
ted
f
o
r
i
m
p
r
o
v
in
g
th
e
h
i
g
h
d
i
m
e
n
s
io
n
al
d
ata
clu
s
ter
i
n
g
.
A
t
f
ir
s
t,
No
r
m
a
lized
Sp
ec
tr
al
C
lu
s
ter
i
n
g
tec
h
n
iq
u
e
in
S
C
-
VP
T
I
tec
h
n
iq
u
e
g
r
o
u
p
s
t
h
e
s
i
m
ilar
h
i
g
h
d
i
m
en
s
io
n
a
l
d
ata
p
o
in
ts
to
f
o
r
m
cl
u
s
ter
s
b
ased
o
n
s
i
m
ilar
it
y
m
a
tr
ix
w
h
ic
h
co
m
p
r
i
s
es
a
q
u
a
n
ti
tati
v
e
esti
m
at
io
n
f
o
r
ea
ch
p
air
o
f
d
ata
in
d
ataset.
Af
ter
t
h
at,
v
an
tag
e
p
o
in
t
tr
ee
i
n
d
ex
i
n
g
is
p
er
f
o
r
m
ed
f
o
r
clu
s
ter
in
g
t
h
e
d
ata
p
o
in
ts
.
T
h
ese
p
o
in
ts
ar
e
s
to
r
ed
in
lef
t
an
d
r
ig
h
t
b
r
an
ch
e
s
o
f
tr
ee
.
T
h
is
h
e
lp
s
to
r
ed
u
ce
th
e
s
p
ac
e
co
m
p
lex
it
y
.
Fi
n
all
y
,
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.