I
AE
S In
t
er
na
t
io
na
l J
o
urna
l o
f
Art
if
icia
l In
t
ellig
ence
(
I
J
-
AI)
Vo
l.
8
,
No
.
3
,
Sep
tem
b
er
201
9
,
p
p
.
237
~
243
I
SS
N:
2
2
5
2
-
8938
,
DOI
: 1
0
.
1
1
5
9
1
/i
j
ai.
v
8
.i
3
.
p
p
237
-
2
4
3
237
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e
.
co
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
J
AI
An ef
ficien
t
m
e
th
o
d t
o
i
m
pro
v
e t
h
e
clusteri
ng
per
form
a
nce
using
hybrid ro
b
ust prin
cipa
l co
mpo
nent
a
na
ly
sis
-
spectral
biclustering
in rai
nfall pa
tt
e
rns ide
ntif
ica
tion
Sh
a
zly
n M
illea
na
Sh
a
ha
rudin
1
,
Sh
u
ha
ida
I
s
m
a
il
2
,
Siti
M
a
ria
na
Che
M
a
t
N
o
r
3
,
No
rha
iza
Ah
m
a
d
4
1,
3
De
p
a
rtm
e
n
t
o
f
M
a
th
e
m
a
ti
c
s,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
a
n
d
M
a
th
e
m
a
ti
c
s
,
Un
iv
e
rsiti
P
e
n
d
id
ik
a
n
S
u
l
tan
I
d
r
is,
M
a
lay
sia
2
De
p
a
rtme
n
t
o
f
M
a
th
e
m
a
ti
c
s a
n
d
S
tatisti
c
s,
F
a
c
u
lt
y
o
f
A
p
p
li
e
d
S
c
ien
c
e
s a
n
d
T
e
c
h
n
o
l
o
g
y
,
Un
iv
e
rsiti
T
u
n
Hu
ss
e
in
On
n
M
a
lay
sia
,
M
a
la
y
sia
4
De
p
a
rtme
n
t
o
f
M
a
th
e
m
a
ti
c
a
l
S
c
ien
c
e
s,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
,
Un
iv
e
r
siti
T
e
k
n
o
lo
g
i
M
a
lay
sia
,
M
a
la
y
si
a
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
M
ay
1
2
,
2
0
1
9
R
ev
i
s
ed
J
u
l
2
5
,
2
0
1
9
A
cc
ep
ted
A
ug
10
,
2
0
1
9
In
th
is
st
u
d
y
,
h
y
b
rid
RP
CA
-
sp
e
c
tral
b
iclu
ste
rin
g
m
o
d
e
l
is
p
ro
p
o
se
d
in
id
e
n
ti
f
y
in
g
th
e
P
e
n
i
n
su
lar
M
a
la
y
sia
ra
in
f
a
ll
p
a
tt
e
rn
.
T
h
is
m
o
d
e
l
is
a
c
o
m
b
in
a
ti
o
n
b
e
tw
e
e
n
Ro
b
u
st
P
ri
n
c
ip
a
l
C
o
m
p
o
n
e
n
t
A
n
a
ly
sis
(RP
CA
)
a
n
d
b
i
-
c
lu
ste
rin
g
in
o
rd
e
r
t
o
o
v
e
rc
o
m
e
th
e
sk
e
w
n
e
ss
p
ro
b
lem
th
a
t
e
x
i
ste
d
in
th
e
P
e
n
in
su
lar
M
a
lay
sia
r
a
in
f
a
ll
d
a
ta.
T
h
e
a
b
il
it
y
o
f
Ro
b
u
st
P
C
A
is
m
o
re
re
sili
e
n
t
to
o
u
tl
ier
g
iv
e
n
th
a
t
it
a
ss
e
ss
e
s
e
v
e
r
y
o
b
se
rv
a
ti
o
n
a
n
d
d
o
w
n
w
e
ig
h
ts
th
e
o
n
e
s
w
h
ich
d
e
v
iate
f
ro
m
th
e
d
a
ta
c
e
n
ter
c
o
m
p
a
re
d
to
c
las
s
ica
l
P
CA
.
M
e
a
n
w
h
il
e
,
tw
o
w
a
y
-
c
lu
ste
rin
g
a
b
le
to
sim
u
lt
a
n
e
o
u
sly
c
lu
ste
r
a
lo
n
g
tw
o
v
a
riab
les
a
n
d
e
x
h
ib
it
a
h
ig
h
c
o
r
re
latio
n
c
o
m
p
a
re
d
to
o
n
e
-
w
a
y
c
lu
ste
r
a
n
a
ly
sis.
T
h
e
e
x
p
e
ri
m
e
n
t
a
l
re
su
lt
s
sh
o
w
e
d
th
a
t
th
e
b
e
st
c
u
m
u
lativ
e
p
e
rc
e
n
tag
e
o
f
v
a
ri
a
ti
o
n
i
n
b
e
tw
e
e
n
6
5
%
-
7
0
%
f
o
r
b
o
th
R
o
b
u
st
a
n
d
c
las
sic
a
l
P
CA
.
M
e
a
n
w
h
il
e
,
th
e
n
u
m
b
e
r
o
f
c
lu
st
e
rs
h
a
s
i
m
p
ro
v
e
d
f
ro
m
si
x
d
isjo
i
n
ted
c
lu
ste
r
in
Ro
b
u
st
P
CA
-
k
M
e
a
n
s
to
e
ig
h
t
d
isjo
in
ted
c
lu
st
e
r
f
o
r
th
e
p
ro
p
o
se
d
m
o
d
e
l.
F
u
rt
h
e
r
a
n
a
ly
sis
sh
o
w
s
th
a
t
th
e
p
ro
p
o
se
d
m
o
d
e
l
h
a
s
s
m
a
ll
e
r
v
a
riatio
n
w
it
h
th
e
v
a
lu
e
s
o
f
0
.
0
0
3
4
c
o
m
p
a
re
d
to
0
.
0
3
0
i
n
R
o
b
u
st
P
CA
-
k
M
e
a
n
s
m
o
d
e
l.
Ev
id
e
n
t
f
ro
m
th
is
a
n
a
ly
si
s,
it
is
p
r
o
v
e
n
th
a
t
t
h
e
p
ro
p
o
se
d
RP
CA
-
sp
e
c
tral
b
iclu
ste
ri
n
g
m
o
d
e
l
is
p
re
d
o
m
in
a
n
tl
y
a
c
c
li
m
a
ti
z
e
d
to
t
h
e
id
e
n
ti
f
y
in
g
r
a
in
f
a
ll
p
a
tt
e
rn
s
in
P
e
n
in
su
lar
M
a
lay
sia
d
u
e
to
th
e
sm
a
l
l
v
a
riatio
n
o
f
th
e
c
lu
ste
rin
g
re
su
lt
.
K
ey
w
o
r
d
s
:
C
lu
s
ter
an
al
y
s
is
P
r
in
cip
al
co
m
p
o
n
e
n
t a
n
al
y
s
is
R
o
b
u
s
t
p
r
in
cip
al
co
m
p
o
n
e
n
t
an
al
y
s
is
Sp
ec
tr
al
b
iclu
s
ter
i
n
g
T
u
k
e
y
’
s
b
i
w
ei
g
h
t c
o
r
r
elatio
n
Co
p
y
rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Sh
az
l
y
n
M
illea
n
a
Sh
a
h
ar
u
d
i
n
,
Dep
ar
t
m
en
t o
f
Ma
th
e
m
at
ics,
Facu
lt
y
o
f
Sc
ien
ce
a
n
d
Ma
th
e
m
atic
s
,
Un
i
v
er
s
iti P
en
d
id
ik
a
n
S
u
lta
n
I
d
r
is
,
Ma
la
y
s
ia
.
E
m
ail:
s
h
az
l
y
n
@
f
s
m
t.u
p
s
i.e
d
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
R
ain
f
all
p
atter
n
s
id
e
n
ti
f
icati
o
n
is
k
e
y
to
ca
te
g
o
r
ize
h
y
d
r
o
lo
g
ic
e
v
e
n
ts
f
o
r
cli
m
a
t
o
lo
g
is
t
o
r
h
y
d
r
o
lo
g
i
s
t to
b
e
ab
le
to
s
tr
ea
m
li
n
e
h
y
d
r
o
lo
g
ic
co
n
v
o
l
u
tio
n
.
So
m
e
o
f
t
h
e
m
o
s
t p
o
p
u
lar
m
e
th
o
d
s
i
n
id
en
t
if
y
i
n
g
th
e
r
ai
n
f
al
l
p
atter
n
s
th
r
o
u
g
h
d
ata
m
i
n
i
n
g
ap
p
r
o
ac
h
es
ar
e
P
r
in
cip
al
C
o
m
p
o
n
e
n
t
An
a
l
y
s
i
s
(
P
C
A
)
an
d
clu
s
ter
an
a
l
y
s
is
.
T
h
ese
ap
p
r
o
ac
h
es
h
a
v
e
b
ee
n
w
ell
-
k
n
o
w
n
f
o
r
m
a
n
y
y
ea
r
s
an
d
ap
p
lied
in
a
w
id
e
r
an
g
e
o
f
r
esear
ch
f
ield
s
s
u
ch
as
clas
s
if
icatio
n
o
f
w
ea
t
h
er
t
y
p
es,
c
li
m
ate
r
eg
io
n
aliza
tio
n
a
n
d
ci
r
cu
latio
n
p
atter
n
s
ass
o
ciate
d
to
cli
m
ate
e
x
tr
e
m
e
s
[
1
-
3
]
.
P
C
A
r
ed
u
ce
s
t
h
e
d
i
m
en
s
io
n
o
f
t
h
e
d
ata
m
atr
i
x
w
h
ic
h
is
co
m
m
o
n
l
y
e
m
p
lo
y
ed
as
a
p
r
e
-
p
r
o
ce
s
s
i
n
g
m
et
h
o
d
f
o
r
th
e
b
en
e
f
it
o
f
g
u
id
in
g
t
h
e
cla
s
s
i
f
icatio
n
p
r
o
ce
s
s
.
A
clas
s
ical
ap
p
r
o
ac
h
in
P
C
A
r
eq
u
ir
es
th
e
u
s
e
o
f
co
n
f
i
g
u
r
atio
n
p
o
in
ts
o
f
e
n
titi
e
s
b
et
w
ee
n
th
e
r
o
w
s
a
n
d
co
lu
m
n
s
o
f
th
e
d
ata
b
ased
o
n
P
ea
r
s
o
n
co
r
r
ela
tio
n
m
a
tr
ix
.
I
n
t
h
is
in
s
tan
ce
,
P
e
ar
s
o
n
co
r
r
elatio
n
m
atr
ix
is
o
f
t
en
e
m
p
lo
y
ed
in
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
l.
8
,
No
.
3
,
Sep
tem
b
er
201
9
:
2
3
7
–
2
4
3
238
d
er
iv
atio
n
o
f
T
-
m
o
d
e
co
r
r
el
atio
n
to
ev
alu
ate
t
h
e
s
i
m
ila
r
it
y
o
cc
u
r
r
en
ce
b
et
w
ee
n
d
ai
l
y
r
ain
f
all
s
[
4
-
7
]
.
A
k
e
y
c
h
ar
ac
ter
is
tic
o
f
P
ea
r
s
o
n
co
r
r
elatio
n
is
it
g
iv
e
s
eq
u
al
w
ei
g
h
t to
ea
ch
p
air
o
f
th
e
o
b
s
e
r
v
atio
n
s
.
I
n
an
al
y
zi
n
g
t
h
e
f
ea
tu
r
e
s
o
f
r
ai
n
f
a
ll p
atter
n
in
Ma
la
y
s
ia,
t
h
e
f
o
ca
l p
r
in
cip
al
is
t
h
at
th
e
d
ail
y
r
ain
f
al
l i
s
n
o
r
m
all
y
i
n
h
er
e
n
tl
y
s
k
e
w
ed
t
h
e
r
ig
h
t.
T
h
is
is
r
e
f
lecte
d
b
y
h
o
w
th
e
d
ata
h
as
h
ig
h
te
n
d
en
c
y
to
b
e
s
k
e
w
ed
to
w
ar
d
s
h
ig
h
er
an
d
o
n
l
y
p
o
s
it
iv
e
v
a
lu
e
s
.
C
o
n
s
eq
u
e
n
tl
y
,
af
f
ec
ted
o
b
s
er
v
atio
n
s
ar
e
d
is
ti
n
g
u
is
h
ed
as
o
u
tl
y
i
n
g
.
P
ea
r
s
o
n
co
r
r
elatio
n
p
r
o
g
r
ess
iv
el
y
r
ed
u
ce
s
it
s
ad
v
a
n
tag
e
s
i
n
s
i
g
n
if
ican
t
l
y
s
k
e
w
ed
d
is
tr
ib
u
tio
n
s
[
8
]
.
I
t
w
o
u
ld
lo
w
er
t
h
e
d
i
s
cr
i
m
in
ato
r
y
p
o
wer
d
u
e
to
t
h
e
f
ac
t
t
h
at
o
u
tlier
s
u
n
d
o
u
b
ted
l
y
s
tic
k
o
u
t
i
n
o
n
e
o
b
s
er
v
atio
n
,
ca
u
s
in
g
th
e
i
n
f
o
r
m
atio
n
in
an
o
b
s
er
v
atio
n
to
b
e
w
ea
k
e
n
ed
[
9
]
.
T
h
er
ef
o
r
e,
P
ea
r
s
o
n
co
r
r
elatio
n
m
i
g
h
t
n
o
t
b
e
s
u
itab
l
y
ap
p
licab
le
s
in
ce
th
e
w
ei
g
h
t
f
o
r
ea
ch
d
a
y
s
ar
e
u
n
eq
u
al,
s
e
ein
g
h
o
w
it
is
i
n
ter
co
n
n
ec
ted
w
i
t
h
t
h
e
cl
u
s
ter
in
g
r
esu
lt
i
n
h
ig
h
li
g
h
ti
n
g
th
e
r
ai
n
f
all
p
atter
n
s
.
C
l
u
s
ter
an
al
y
s
i
s
h
as
b
ee
n
d
e
v
elo
p
ed
to
s
u
b
d
iv
id
e
o
b
s
er
v
atio
n
s
o
f
s
i
m
ilar
p
atter
n
s
a
n
d
d
is
s
i
m
il
ar
p
atter
n
s
ac
co
r
d
in
g
l
y
i
n
to
d
if
f
er
e
n
t
cl
u
s
ter
s
.
T
y
p
icall
y
,
class
ical
cl
u
s
ter
in
g
tech
n
iq
u
es
i
n
cli
m
ate
d
ata
ap
p
ly
t
h
e
alg
o
r
it
h
m
s
to
eith
er
th
e
r
o
w
s
o
r
th
e
co
l
u
m
n
s
w
i
th
i
n
ti
m
e
o
r
s
p
ac
e
d
o
m
ai
n
s
o
f
t
h
e
d
ata
m
atr
i
x
s
e
p
ar
ately
[
1
0
-
1
4
]
.
I
n
tim
e
-
cl
u
s
ter
in
g
tec
h
n
iq
u
es,
s
e
g
m
en
t
s
o
f
ti
m
e
ar
e
d
etec
ted
w
h
er
e
th
e
v
al
u
es
o
f
t
h
e
ti
m
e
s
er
ies
ar
e
s
i
m
ilar
to
ea
ch
o
th
er
[
1
5
]
.
A
ls
o
,
class
ical
c
l
u
s
ter
i
n
g
tech
n
iq
u
e
t
y
p
icall
y
d
i
v
id
es
t
h
e
d
atab
ase
o
f
r
ain
f
a
ll
p
atter
n
s
i
n
to
clu
s
te
r
s
w
it
h
t
h
e
ass
u
m
p
tio
n
t
h
at
ev
er
y
r
ai
n
f
a
ll
p
atter
n
b
elo
n
g
s
to
o
n
l
y
o
n
e
s
p
ec
i
f
ic
clu
s
ter
.
T
h
is
i
m
p
lies
th
a
t
t
h
e
m
e
m
b
er
s
o
f
ea
c
h
cl
u
s
ter
ar
e
ex
cl
u
s
i
v
e
a
n
d
ex
h
a
u
s
tiv
e
to
o
n
e
a
n
d
o
n
l
y
o
n
e
clu
s
ter
.
Ho
w
ev
er
,
i
n
p
r
ac
tice,
th
is
i
s
r
ar
el
y
tr
u
e.
I
n
th
i
s
p
ap
er
,
tw
o
s
tatis
t
ical
s
t
r
ateg
ies
ar
e
p
r
esen
ted
b
ased
o
n
d
ata
m
i
n
i
n
g
ap
p
r
o
ac
h
es
to
id
en
tify
t
h
e
to
r
r
en
tial
r
ain
f
a
ll
p
atter
n
s
i
n
P
en
in
s
u
lar
Ma
la
y
s
ia
b
y
co
n
s
i
d
er
in
g
th
e
i
s
s
u
es
m
en
t
io
n
ed
ab
o
v
e.
R
o
b
u
s
t
P
C
A
-
b
ased
T
u
k
e
y
'
s
b
i
w
ei
g
h
t
co
r
r
elatio
n
is
in
tr
o
d
u
ce
d
.
A
lter
n
ati
v
el
y
,
t
h
is
i
s
a
n
e
w
o
p
tio
n
al
co
r
r
elatio
n
m
ea
s
u
r
e
to
P
ea
r
s
o
n
co
r
r
elatio
n
m
atr
i
x
i
n
P
C
A
ap
p
r
o
ac
h
[
1
6
]
.
T
u
k
e
y
'
s
b
i
w
ei
g
h
t
co
r
r
elatio
n
is
b
ased
o
n
T
u
k
e
y
's
b
i
w
e
ig
h
t
f
u
n
ctio
n
t
h
at
r
elies
o
n
M
-
e
s
ti
m
ato
r
s
u
s
ed
in
r
o
b
u
s
t
co
r
r
elatio
n
esti
m
ate
s
.
T
h
is
ap
p
r
o
ac
h
is
m
o
r
e
r
esil
ie
n
t
to
o
u
tl
y
i
n
g
v
al
u
es
g
i
v
e
n
t
h
at
i
t
ass
es
s
es
e
v
er
y
o
b
s
er
v
atio
n
a
n
d
d
o
w
n
w
e
ig
h
ts
t
h
e
o
n
e
s
w
h
ic
h
d
ev
iate
f
r
o
m
t
h
e
d
ata
ce
n
ter
.
T
h
is
esti
m
ato
r
i
s
m
o
r
e
ef
f
icie
n
t,
f
le
x
ib
le
an
d
f
ai
r
l
y
f
u
n
ctio
n
u
n
d
er
d
iv
er
s
e
d
at
a
d
is
tr
ib
u
tio
n
s
[
1
7
]
.
So
as
to
co
u
n
ter
t
h
e
i
s
s
u
e
i
n
c
lu
s
ter
i
n
g
tec
h
n
iq
u
e,
a
s
er
ies
o
f
t
w
o
-
w
a
y
cl
u
s
ter
i
n
g
m
e
th
o
d
s
k
n
o
w
n
a
s
s
p
ec
tr
al
b
iclu
s
ter
i
n
g
is
i
n
tr
o
d
u
ce
d
to
s
i
m
u
lta
n
eo
u
s
l
y
clu
s
ter
alo
n
g
t
w
o
v
ar
iab
le
s
.
T
h
e
ai
m
o
f
co
n
cu
r
r
en
t
cl
u
s
ter
in
g
i
s
to
f
in
d
s
u
b
-
m
atr
ice
s
,
w
h
ic
h
ar
e
s
u
b
g
r
o
u
p
s
o
f
r
o
w
s
an
d
s
u
b
g
r
o
u
p
s
o
f
co
lu
m
n
s
t
h
at
s
h
o
w
a
h
ig
h
co
r
r
elatio
n
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Da
t
a
T
h
e
d
aily
r
ain
f
all
d
ata
f
r
o
m
th
e
in
ter
v
al
o
f
1
9
7
5
to
2
0
0
7
w
as
g
at
h
er
ed
f
r
o
m
t
h
e
Dep
ar
t
m
en
t
o
f
I
r
r
ig
atio
n
an
d
Dr
ain
a
g
e,
Ma
la
y
s
ia,
o
r
J
ab
atan
P
en
g
air
an
d
a
n
Salira
n
(
J
P
S).
T
h
e
d
ata
w
er
e
co
llected
f
r
o
m
7
5
s
tatio
n
s
in
d
i
f
f
er
e
n
t
g
eo
g
r
ap
h
ical
co
o
r
d
in
ates
o
n
f
o
u
r
r
eg
io
n
s
in
P
en
i
n
s
u
lar
Ma
la
y
s
i
a
w
h
ich
ar
e
ea
s
t
,
s
o
u
t
h
w
est,
w
e
s
t
a
n
d
n
o
r
th
w
e
s
t.
P
r
im
ar
il
y
,
th
is
s
tu
d
y
’
s
m
ai
n
in
ter
est
i
s
e
x
tr
e
m
e
r
ai
n
f
all
e
v
e
n
t
w
h
ic
h
is
k
n
o
w
n
as
th
e
to
r
r
en
t
ial
r
ain
f
all.
He
n
ce
,
it
w
a
s
i
m
p
o
r
ta
n
t
to
s
elec
t
s
o
m
e
cr
iter
ia
to
lead
an
d
es
tab
lis
h
a
t
h
r
e
s
h
o
ld
to
f
in
d
a
ce
r
tain
d
is
tin
ct
io
n
b
et
w
ee
n
w
h
at
d
o
es
o
r
d
o
es
n
o
t
co
n
s
titu
te
a
d
a
y
o
f
to
r
r
en
tial
r
ain
f
a
ll
in
th
e
P
en
i
n
s
u
lar
Ma
la
y
s
ia
r
e
g
io
n
s
.
T
h
e
m
o
s
t
co
m
m
o
n
an
d
ap
p
licab
le
th
r
esh
o
ld
in
a
tr
o
p
ical
cli
m
ate
f
o
r
th
is
w
a
s
6
0
m
m
/d
a
y
[
1
8
]
.
T
h
e
f
ilter
ed
d
ay
s
w
it
h
r
ain
f
all
t
h
at
ex
ce
ed
ed
6
0
m
m
i
n
at
leas
t
2
%
o
f
th
e
s
tat
io
n
s
w
er
e
u
s
ed
[
1
9
]
.
T
h
e
o
u
tco
m
e
w
a
s
2
5
0
d
ay
s
a
n
d
1
5
r
ain
f
all
s
tatio
n
s
-
an
a
m
p
le
f
ig
u
r
e
to
ex
e
m
p
li
f
y
th
e
m
ain
to
r
r
en
tial c
en
ter
s
.
2
.
2
.
P
rincipa
l c
o
m
po
nent
a
n
a
ly
s
is
I
n
cli
m
ate
d
ata,
th
e
t
y
p
ical
to
r
r
en
tial
r
ain
f
all
p
atter
n
s
ar
e
d
er
iv
ed
u
s
i
n
g
p
r
in
cip
al
co
m
p
o
n
e
n
t
an
al
y
s
is
(
P
C
A
)
m
et
h
o
d
b
ased
o
n
T
-
m
o
d
e
ap
p
r
o
ac
h
.
T
-
m
o
d
e
w
as
u
s
ed
w
it
h
t
h
e
ai
m
o
f
a
n
al
y
zin
g
s
p
atia
l
f
ield
s
i
n
d
if
f
er
e
n
t
ti
m
e
s
.
T
h
is
is
p
r
ac
t
ical
f
o
r
ex
tr
ac
t
in
g
a
n
d
r
ep
r
o
d
u
cin
g
t
h
e
t
y
p
e
s
o
f
c
ir
cu
lati
o
n
,
m
ea
s
u
r
i
n
g
th
e
ir
f
r
eq
u
en
c
y
an
d
d
is
p
la
y
i
n
g
t
h
e
p
er
io
d
s
o
f
d
o
m
i
n
a
n
t
w
ea
t
h
e
r
[
2
0
]
.
T
h
e
m
ai
n
p
u
r
p
o
s
e
o
f
u
s
in
g
P
C
A
is
to
d
ec
r
ea
s
e
th
e
lar
g
e
d
i
m
e
n
s
io
n
a
l
d
ata
in
to
lo
w
d
i
m
en
s
io
n
a
l
d
ata
w
h
ile
co
n
c
u
r
r
en
tl
y
r
etai
n
i
n
g
th
e
s
i
g
n
if
ica
n
ce
in
f
o
r
m
atio
n
o
f
t
h
e
d
ata
s
et
[
2
1
]
.
I
n
ad
d
itio
n
,
th
i
s
m
eth
o
d
is
q
u
ite
p
o
p
u
lar
f
o
r
f
in
d
i
n
g
p
atter
n
s
in
h
i
g
h
d
i
m
en
s
io
n
al
d
ata
[
2
2
]
.
T
h
e
m
ai
n
p
ar
t
in
P
C
A
co
v
er
s
s
ta
n
d
ar
d
d
ev
ia
tio
n
,
co
v
ar
ia
n
ce
o
r
co
r
r
elatio
n
an
d
eig
e
n
v
ec
to
r
.
T
h
e
alg
o
r
ith
m
o
f
P
C
A
ap
p
r
o
ac
h
w
o
r
k
s
as
f
o
llo
w
s
:
=
(
11
,
12
,
13
⋯
1
21
,
22
.
.
.
,
23
⋱
2
1
,
2
,
3
⋯
)
(
1
)
Giv
e
n
m
atr
i
x
is
th
e
r
ain
f
al
l
d
ata
in
P
en
in
s
u
lar
Ma
la
y
s
ia
co
m
p
r
is
e
s
o
b
s
er
v
atio
n
s
(
i.e
.
r
ain
f
all
d
a
y
s
)
d
escr
ib
ed
b
y
v
ar
iab
les
(
i.e
.
r
ain
f
all
s
tatio
n
s
)
an
d
it
is
r
ep
r
esen
ted
b
y
th
e
×
m
atr
i
x
,
w
h
o
s
e
g
en
er
ic
ele
m
e
n
t is
,
.
T
h
en
,
th
e
s
p
atial
T
-
m
o
d
e
m
a
tr
ix
i
s
d
ef
i
n
ed
as
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
A
n
efficien
t m
eth
o
d
to
imp
r
o
ve
t
h
e
clu
s
teri
n
g
p
erfo
r
ma
n
ce
u
s
in
g
…
(
S
h
a
z
lyn
Mil
lea
n
a
S
h
a
h
a
r
u
d
in
)
239
′
=
′
T
(
2
)
w
h
er
e
th
e
tr
a
n
s
p
o
s
e
o
p
er
atio
n
is
d
en
o
ted
b
y
t
h
e
s
u
p
er
s
cr
ip
t
T
.
Su
b
s
eq
u
e
n
tl
y
,
t
h
e
m
atr
i
x
ca
n
b
e
d
ef
in
ed
th
r
o
u
g
h
t
h
e
co
r
r
elatio
n
m
atr
i
x
=
(
′
)
=
∑
(
′
−
̅
′
)
(
′
−
̅
′
)
=
1
√
∑
(
′
−
̅
′
)
2
∑
(
′
−
̅
′
)
2
=
1
=
1
(
3
)
A
cc
o
r
d
in
g
to
th
e
(
3
)
,
eig
en
v
e
cto
r
s
an
d
eig
en
v
a
lu
e
s
ar
e
ca
lcu
lated
u
s
i
n
g
th
i
s
ex
p
r
ess
io
n
.
T
h
e
f
o
llo
w
in
g
s
ar
e
th
e
s
tep
s
i
n
v
o
lv
ed
in
P
C
A
al
g
o
r
ith
m
:
Step
1
: A
cq
u
ir
e
t
h
e
in
p
u
t
m
atr
ix
.
Step
2
: Co
m
p
u
te
T
-
m
o
d
e
b
ase
d
P
ea
r
s
o
n
co
r
r
elatio
n
m
atr
i
x
.
Step
3
: Co
m
p
u
te
t
h
e
ei
g
en
v
ec
t
o
r
s
an
d
eig
en
v
al
u
es o
f
t
h
e
co
r
r
elatio
n
m
atr
i
x
.
Step
4
: Ch
o
o
s
e
th
e
m
o
s
t i
m
p
o
r
tan
t p
r
in
cip
al
co
m
p
o
n
e
n
ts
b
a
s
ed
o
n
cu
m
u
la
tiv
e
p
er
ce
n
ta
g
e
o
f
to
tal
v
ar
iatio
n
.
Step
5
: O
b
tain
th
e
n
e
w
d
ata
s
e
t
2
.
3
.
Ro
bu
s
t
P
rincipa
l C
o
m
p
o
nent
Ana
ly
s
is
T
u
k
e
y
'
s
b
i
w
ei
g
h
t
co
r
r
elatio
n
i
s
b
ased
o
n
T
u
k
e
y
'
s
b
i
w
ei
g
h
t
f
u
n
ct
io
n
w
h
ich
d
ep
en
d
s
o
n
M
-
esti
m
ato
r
s
ap
p
lied
in
r
o
b
u
s
t
co
r
r
elatio
n
esti
m
ates.
M
-
e
s
ti
m
ate
h
a
s
a
d
er
iv
ativ
e
f
u
n
ctio
n
,
w
h
ic
h
d
ef
in
es
t
h
e
w
ei
g
h
ts
allo
tted
to
th
e
o
b
s
er
v
atio
n
s
i
n
th
e
d
ata
s
et.
I
t
h
as
th
e
ab
i
lit
y
to
d
o
w
n
w
eig
h
t
o
b
s
er
v
ati
o
n
s
to
e
m
u
late
its
in
f
lu
e
n
ce
f
r
o
m
t
h
e
ce
n
tr
e
o
f
t
h
e
d
ata
[
1
7
]
.
T
h
e
d
er
iv
ativ
e
f
u
n
ctio
n
is
o
b
tain
ed
as
f
o
llo
w
s
:
(
)
=
{
(
1
−
)
2
|
|
≤
1
0
|
|
>
1
(
4
)
E
v
id
en
tl
y
,
if
|
|
is
lar
g
e
en
o
u
g
h
,
th
en
(
)
r
ed
u
ce
s
to
ze
r
o
.
A
n
i
m
p
o
r
tan
t
asp
ec
t
to
ev
alu
ate
t
h
e
r
es
is
t
an
ce
to
o
u
tl
y
i
n
g
d
ata
v
al
u
es
o
f
M
-
est
i
m
ato
r
s
is
its
b
r
ea
k
d
o
w
n
p
o
i
n
t.
B
y
d
ef
i
n
itio
n
,
a
b
r
ea
k
d
o
w
n
p
o
in
t
m
ea
n
s
t
h
e
s
m
al
lest
f
r
ac
tio
n
o
f
co
n
ta
m
i
n
a
tio
n
w
h
ich
m
a
y
i
n
s
tig
a
te
in
ac
cu
r
ate
r
es
u
lt
[
2
3
]
.
I
n
th
i
s
s
t
u
d
y
,
T
u
k
e
y
's
b
i
w
ei
g
h
t
w
it
h
b
r
ea
k
d
o
w
n
p
o
in
ts
o
f
0
.
2
,
0
.
4
,
0
.
6
an
d
0
.
8
w
er
e
co
m
p
ar
ed
u
s
i
n
g
s
i
m
u
lated
d
ata
an
d
b
r
ea
k
d
o
w
n
p
o
in
t
o
f
0
.
4
p
er
f
o
r
m
ed
t
h
e
b
est.
A
cc
o
r
d
in
g
to
[
2
4
]
,
a
b
r
ea
k
d
o
w
n
p
o
in
t
o
f
0
.
4
g
e
n
er
all
y
p
er
f
o
r
m
s
b
etter
in
m
o
s
t
cir
cu
m
s
ta
n
ce
s
i
n
w
h
ic
h
t
h
e
r
esu
lt
i
s
m
o
r
e
p
r
ec
is
e
an
d
ef
f
ec
t
iv
e
w
h
e
n
co
m
p
ar
ed
to
a
lo
w
e
r
b
r
ea
k
d
o
w
n
p
o
in
t.
T
h
e
b
i
w
ei
g
h
t
esti
m
ate
o
f
co
r
r
elatio
n
i
s
estab
li
s
h
ed
b
y
f
ir
s
t
d
eter
m
in
i
n
g
t
h
e
lo
ca
tio
n
esti
m
ate,
T
̃
an
d
f
u
r
th
er
,
u
p
d
atin
g
th
e
s
h
ap
e
esti
m
ate,
S ̃.
T
h
e
(
,
)
ℎ
ele
m
e
n
t
o
f
S ̃,
i.e
.
̃
s
er
v
es
as
a
r
esi
s
tan
t
esti
m
ate
o
f
th
e
co
v
a
r
ian
ce
b
et
w
ee
n
t
h
e
t
w
o
v
ec
to
r
s
,
an
d
.
T
h
e
ca
lcu
latio
n
o
f
b
i
w
eig
h
t c
o
r
r
elatio
n
o
f
b
o
th
v
ec
to
r
s
is
:
̃
=
̃
√
̃
̃
(
5
)
W
ith
(
+
1
)
=
∑
(
(
)
)
=
1
∑
(
(
)
)
=
1
k
=
0
,
1
,
2
,
…
(
6
)
(
+
1
)
=
∑
(
(
)
)
(
−
(
+
1
)
)
(
−
(
+
1
)
)
=
1
∑
(
(
)
)
(
(
)
=
1
)
(
7
)
w
h
er
e
(
+
1
)
is
a
lo
ca
tio
n
v
ec
to
r
an
d
(
+
1
)
i
s
a
s
h
ap
e
m
a
tr
ix
s
u
c
h
th
a
t
=
0
,
1
,
2
,
…
.
T
h
u
s
,
a
P
C
A
-
b
ased
T
u
k
e
y
’
s
b
i
w
ei
g
h
t
co
r
r
elatio
n
f
o
r
K
-
m
ea
n
s
clu
s
ter
a
n
al
y
s
i
s
h
as
th
e
te
n
d
en
c
y
to
estab
li
s
h
a
b
etter
clu
s
ter
p
ar
titi
o
n
w
h
ich
i
s
m
o
r
e
r
esil
ie
n
t to
w
ar
d
s
th
e
o
u
tl
y
in
g
v
alu
e
s
t
h
an
P
ea
r
s
o
n
co
r
r
elatio
n
in
P
C
A
.
2
.
4
.
k
-
M
ea
ns
T
h
e
in
itial
s
tep
w
a
s
to
r
an
d
o
m
l
y
s
elec
t
k
o
b
j
ec
ts
,
w
h
er
e
ea
ch
i
n
itiall
y
r
ep
r
ese
n
ts
a
clu
s
ter
m
ea
n
o
r
ce
n
ter
.
Nex
t,
t
h
e
r
esp
ec
tiv
e
d
ata
p
o
in
t,
is
allo
tted
to
th
e
n
ea
r
est
cl
u
s
ter
ce
n
tr
e.
E
u
clid
ea
n
d
is
tan
c
e
m
et
h
o
d
w
as
co
m
m
o
n
l
y
ap
p
lie
d
to
ca
lcu
late
th
e
d
is
tan
ce
,
(
,
)
b
e
t
w
ee
n
ea
ch
d
ata
p
o
in
ts
,
an
d
c
en
tr
o
id
,
as sh
o
w
n
in
(
7
)
.
(
,
)
=
√
∑
(
−
)
2
=
1
(8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
l.
8
,
No
.
3
,
Sep
tem
b
er
201
9
:
2
3
7
–
2
4
3
240
W
h
en
all
t
h
e
d
ata
p
o
in
t
s
wer
e
ass
ig
n
ed
to
ea
ch
o
f
t
h
e
clu
s
ter
s
,
th
e
cl
u
s
ter
ce
n
tr
o
i
d
w
as
r
ec
alc
u
lated
.
k
-
Me
an
s
clu
s
ter
in
g
al
g
o
r
ith
m
f
u
n
ctio
n
s
i
n
th
e
f
o
llo
w
i
n
g
s
tep
s
:
Step
1
: Ran
d
o
m
l
y
ch
o
o
s
e
o
b
jects f
r
o
m
t
h
e
s
et
o
f
d
ata
as in
i
t
ial
clu
s
ter
ce
n
tr
o
id
.
Ste
p
2
:
Dete
r
m
i
n
e
t
h
e
d
is
ta
n
c
e
b
et
w
ee
n
ea
ch
d
ata
p
o
in
ts
an
d
ass
i
g
n
ea
c
h
ite
m
to
th
e
cl
u
s
ter
w
h
ic
h
h
as
th
e
clo
s
est ce
n
tr
o
id
.
R
ec
alcu
la
te
th
e
clu
s
ter
ce
n
tr
o
id
f
o
r
ea
ch
clu
s
ter
u
n
ti
l c
o
n
v
er
g
e
n
ce
cr
iter
ia
is
r
ea
ch
ed
.
2
.
5
.
Sp
ec
t
ra
l
B
iclus
t
er
ing
T
h
e
s
p
ec
tr
al
b
iclu
s
ter
in
g
al
g
o
r
ith
m
w
as
p
r
o
p
o
s
ed
as
a
m
et
h
o
d
to
id
en
tify
s
u
b
s
ets
o
f
f
ea
tu
r
es
a
n
d
co
n
d
itio
n
s
w
i
th
c
h
ec
k
er
b
o
ar
d
s
tr
u
ct
u
r
e
w
h
ic
h
ca
n
b
e
d
escr
ib
ed
as
a
co
m
b
in
a
tio
n
o
f
co
n
s
tan
t
b
icl
u
s
ter
s
in
a
s
in
g
le
d
ata
m
atr
ix
.
I
n
th
i
s
s
t
u
d
y
,
t
h
e
s
p
ec
tr
al
b
icl
u
s
ter
i
n
g
w
as
ap
p
lied
in
o
r
d
er
to
o
b
tain
th
e
r
ain
f
all
p
atter
n
s
.
T
h
is
m
eth
o
d
h
a
s
ef
f
icie
n
t
p
er
f
o
r
m
a
n
ce
,
s
u
i
tab
le
f
o
r
w
o
r
k
i
n
g
w
it
h
lar
g
e
m
atr
ice
s
[
2
5
]
.
A
s
et
o
f
m
atr
i
x
d
ata,
m
atr
i
x
A
w
as
r
ep
r
esen
ted
alo
n
g
t
w
o
v
ar
iab
les
d
i
m
en
s
io
n
,
M
an
d
N
as
(
)
.
Ma
tr
ix
A
th
e
n
s
u
p
p
o
s
ed
to
b
e
b
iclu
s
ter
in
to
K
an
d
L
s
u
b
m
atr
ices.
T
h
en
,
let
(
,
)
b
e
th
e
s
u
b
m
atr
i
x
an
d
d
en
o
ted
w
it
h
th
e
av
er
ag
e
o
f
all
v
alu
e
s
o
f
th
e
s
u
b
m
atr
i
x
as
(
.
)
.
B
y
u
s
i
n
g
(
.
)
,
th
e
v
ar
iatio
n
o
f
th
e
m
atr
i
x
co
u
ld
b
e
i
d
en
tif
ied
w
h
i
ch
d
ef
in
e
s
th
e
er
r
o
r
.
T
h
e
g
o
al
o
f
a
b
iclu
s
t
er
in
g
is
to
f
i
n
d
t
h
e
p
ar
titi
o
n
with
m
i
n
i
m
u
m
er
r
o
r
.
T
h
e
p
r
o
b
l
e
m
r
e
m
ai
n
s
as
h
o
w
to
ch
o
o
s
e
th
e
b
est
v
al
u
e
f
o
r
K
an
d
L
.
Fo
r
th
is
p
ar
t,
a
m
et
h
o
d
p
r
o
p
o
s
ed
in
[
1
1
]
w
a
s
r
ef
er
r
ed
w
h
ic
h
e
x
p
lain
ed
th
at
th
e
er
r
o
r
d
ec
r
ea
s
ed
as
K
an
d
L
i
n
cr
ea
s
ed
.
As
t
h
e
s
p
ec
t
r
al
b
iclu
s
ter
in
g
ap
p
r
o
ac
h
w
a
s
ap
p
lied
to
th
e
d
ata
s
et,
th
e
v
al
u
e
o
f
K
∈
{2
5
,
2
6
,
2
7
}
an
d
L
∈
{4
}.
T
h
e
alg
o
r
ith
m
w
as
ap
p
lied
r
an
d
o
m
l
y
f
o
r
5
0
ti
m
es
to
o
b
tain
th
e
o
p
ti
m
al
v
al
u
es o
f
(
K,
L
)
.
T
h
e
f
o
llo
w
i
n
g
s
ar
e
th
e
s
tep
s
r
eq
u
ir
ed
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
:
Step
1
: A
cq
u
ir
e
t
h
e
in
p
u
t
m
atr
ix
.
Step
2
: Stan
d
ar
d
ize
th
e
d
ata
w
ith
m
ed
ian
a
n
d
m
ea
n
ab
s
o
lu
te
d
ev
iatio
n
(
M
A
D)
,
i.e
.
∗
=
−
̅
(
|
−
(
)
|
)
(
9
)
s
u
c
h
th
a
t
r
ef
er
s
to
ele
m
en
t
s
in
th
e
in
p
u
t
m
atr
ix
.
Step
3
: A
r
r
an
g
e
th
e
d
ata
to
o
b
tain
a
T
-
m
o
d
e
d
ec
o
m
p
o
s
it
io
n
.
Step
4
: Set
th
e
b
r
ea
k
d
o
w
n
p
o
in
t,
0
.
4
f
o
r
th
e
R
o
b
u
s
t P
C
A
.
Step
5
: Co
m
p
u
te
t
h
e
r
o
b
u
s
t c
o
r
r
elatio
n
m
ea
s
u
r
e,
P
C
A
-
T
u
k
e
y
's b
i
w
ei
g
h
t
co
r
r
elatio
n
m
atr
i
x
.
Step
6
: Co
m
p
u
te
t
h
e
ei
g
en
v
ec
t
o
r
s
an
d
eig
en
v
al
u
es o
f
t
h
e
R
o
b
u
s
t P
C
A
.
Step
7
: Ch
o
o
s
e
th
e
s
ig
n
i
f
ica
n
c
e
co
m
p
o
n
e
n
t
s
b
ased
o
n
cu
m
u
l
ativ
e
p
er
ce
n
ta
g
e
o
f
to
tal
v
ar
iat
io
n
.
Step
8
: Co
m
p
u
te
t
h
e
m
atr
ix
o
f
co
m
p
o
n
e
n
t lo
ad
in
g
s
Step
9
: A
p
p
l
y
s
p
ec
tr
al
b
iclu
s
te
r
in
g
to
m
atr
ix
o
f
co
m
p
o
n
e
n
t l
o
ad
in
g
s
.
3.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
T
h
er
e
ar
e
tw
o
m
ain
d
is
c
u
s
s
io
n
s
i
n
t
h
is
s
ec
tio
n
:
t
h
e
s
elec
t
io
n
s
o
f
c
u
m
u
lati
v
e
p
er
ce
n
tag
e
t
o
r
em
o
v
e
th
e
a
m
o
u
n
t
o
f
p
r
i
n
cip
al
co
m
p
o
n
en
t
s
a
n
d
th
e
s
e
n
s
i
tiv
it
y
o
f
t
h
e
a
m
o
u
n
t
o
f
cl
u
s
ter
to
t
h
e
c
h
o
ice
o
f
clu
s
ter
i
n
g
ap
p
r
o
ac
h
es.
T
h
e
ef
f
ec
t
o
n
cl
u
s
ter
in
g
r
es
u
lt
w
h
en
u
s
i
n
g
h
y
b
r
i
d
R
o
b
u
s
t
P
C
A
a
g
ai
n
s
t
clas
s
ic
al
P
C
A
ap
p
r
o
ac
h
es
w
il
l
also
b
e
s
h
o
w
n
.
As
n
o
ted
f
r
o
m
T
ab
le
1
,
th
e
a
m
o
u
n
t
o
f
co
m
p
o
n
en
t
s
o
b
tain
ed
f
r
o
m
b
o
th
ap
p
r
o
ac
h
es
in
P
C
A
at
r
esp
ec
tiv
e
lev
e
l
o
f
c
u
m
u
lati
v
e
p
er
ce
n
ta
g
e
o
f
v
ar
iati
o
n
s
d
i
f
f
er
.
A
p
p
ar
en
tl
y
,
r
o
b
u
s
t
P
C
A
e
n
tai
led
les
s
n
u
m
b
er
o
f
co
m
p
o
n
e
n
ts
to
e
x
t
r
ac
t
to
ac
h
iev
e
at
least
7
0
%
o
f
cu
m
u
lati
v
e
p
er
ce
n
ta
g
e
o
f
v
a
r
iatio
n
,
co
n
tr
ar
y
to
P
C
A
.
T
o
illu
s
tr
ate,
at
8
0
%
c
u
m
u
lat
iv
e
p
er
ce
n
tag
e
o
f
v
ar
i
atio
n
,
t
h
er
e
w
er
e
2
8
co
m
p
o
n
en
ts
r
etain
ed
w
h
e
n
u
s
i
n
g
R
o
b
u
s
t
P
C
A
w
h
i
le
as
f
o
r
C
lass
ical
P
C
A
,
t
h
er
e
w
er
e
3
5
co
m
p
o
n
e
n
ts
.
E
x
ce
s
s
i
v
e
i
n
clu
s
io
n
o
f
p
r
in
cip
al
co
m
p
o
n
e
n
t
s
o
v
er
s
tated
th
e
s
i
g
n
i
f
ica
n
ce
o
f
o
u
tlier
,
cr
ea
tin
g
p
o
o
r
r
esu
lts
i
n
d
is
ti
n
g
u
is
h
i
n
g
r
ai
n
f
al
l
p
atter
n
s
.
T
h
ese
f
in
d
i
n
g
s
ar
e
in
lin
e
with
th
o
s
e
i
n
[
2
6
]
.
Me
an
w
h
i
le
,
ir
r
esp
ec
tiv
e
o
f
th
e
cu
m
u
lat
iv
e
p
er
ce
n
tag
e
o
f
v
ar
iatio
n
,
t
h
e
n
u
m
b
er
o
f
clu
s
t
er
s
as
an
o
u
tco
m
e
o
f
P
C
A
co
m
b
in
ed
w
it
h
t
w
o
cl
u
s
ter
i
n
g
a
p
p
r
o
ac
h
es
s
tab
ilized
at
o
n
l
y
t
w
o
clu
s
ter
s
.
T
h
i
s
i
s
i
n
d
icativ
e
o
f
s
o
m
e
i
n
f
lu
e
n
tia
l
o
b
s
er
v
atio
n
s
in
t
h
e
d
ata.
I
n
c
li
m
ato
lo
g
y
s
t
u
d
ies
esp
ec
iall
y
in
id
en
ti
f
y
i
n
g
r
ai
n
f
all
p
atter
n
s
,
o
b
tai
n
in
g
m
o
r
e
th
a
n
t
w
o
cl
u
s
ter
s
to
d
escr
ib
e
th
e
v
ar
iatio
n
s
o
f
p
atter
n
s
o
f
r
ai
n
f
all
i
s
m
o
r
e
p
e
r
tin
en
t.
T
h
is
r
esu
lt
w
as
s
u
p
p
o
r
ted
b
y
[
2
7
]
w
h
ic
h
d
en
o
ted
th
at
s
o
m
e
a
m
o
u
n
t
o
f
clu
s
ter
s
i.e
.
a
co
u
p
le
o
f
cl
u
s
ter
s
w
o
u
ld
n
o
t
b
e
ad
eq
u
ate
t
o
d
eter
m
in
e
r
ain
f
all
p
atter
n
w
h
il
s
t
it
co
m
e
s
to
co
n
d
u
cti
n
g
co
n
s
id
er
ab
le
r
ain
f
all
p
atter
n
s
a
n
al
y
s
i
s
.
T
h
er
ef
o
r
e,
t
w
o
cl
u
s
ter
s
e
ts
ar
e
e
v
id
en
tl
y
u
n
f
itti
n
g
s
i
n
c
e
th
e
y
co
v
er
th
e
ac
t
u
al
co
n
s
tr
u
ct
o
f
th
e
d
ata.
Fig
u
r
e
1
d
em
o
n
s
tr
ate
s
th
e
a
m
o
u
n
t
o
f
cl
u
s
ter
s
ac
q
u
ir
ed
b
y
t
h
e
m
ea
n
s
o
f
R
o
b
u
s
t
P
C
A
co
m
b
in
ed
w
it
h
k
-
m
ea
n
s
cl
u
s
ter
a
n
al
y
s
i
s
a
n
d
p
r
o
p
o
s
ed
m
o
d
el
o
f
R
o
b
u
s
t
P
C
A
co
m
b
i
n
ed
w
it
h
s
p
ec
tr
al
b
icl
u
s
ter
i
n
g
.
E
v
id
en
tl
y
,
r
elativ
e
to
clu
s
ter
p
ar
titi
o
n
s
,
F
ig
u
r
e
1
d
is
p
la
y
s
h
o
w
i
n
co
m
p
ar
is
o
n
to
P
C
A
a
s
s
h
o
w
n
i
n
T
ab
le
1
,
R
o
b
u
s
t
P
C
A
h
as
h
i
g
h
er
s
en
s
iti
v
it
y
to
th
e
s
u
m
o
f
cl
u
s
ter
s
e
m
p
lo
y
ed
,
b
ased
o
n
th
e
c
u
m
u
lati
v
e
p
er
ce
n
ta
g
e
o
f
v
ar
iatio
n
.
Fo
r
an
i
n
s
ta
n
ce
,
i
n
Fi
g
u
r
e
1
,
w
h
e
n
t
h
e
7
0
%
cu
m
u
lati
v
e
p
er
ce
n
tag
e
w
a
s
s
elec
ted
,
t
h
e
to
tal
cl
u
s
ter
s
to
m
a
in
ta
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
A
n
efficien
t m
eth
o
d
to
imp
r
o
ve
t
h
e
clu
s
teri
n
g
p
erfo
r
ma
n
ce
u
s
in
g
…
(
S
h
a
z
lyn
Mil
lea
n
a
S
h
a
h
a
r
u
d
in
)
241
w
er
e
s
ix
an
d
ei
g
h
t
f
o
r
b
o
th
ap
p
r
o
ac
h
es,
r
esp
ec
tiv
el
y
.
W
h
e
n
5
%
ad
d
itio
n
al
cu
m
u
lati
v
e
p
er
ce
n
tag
e
o
f
v
ar
ia
n
ce
w
a
s
u
s
ed
,
th
e
s
u
m
o
f
c
lu
s
ter
s
d
ev
iated
f
r
o
m
s
i
x
to
ten
f
o
r
R
o
b
u
s
t
P
C
A
w
ith
k
-
Me
a
n
s
a
p
p
r
o
ac
h
w
h
i
le
th
e
n
u
m
b
er
o
f
clu
s
ter
b
ec
a
m
e
3
5
f
o
r
h
y
b
r
id
R
P
C
A
-
s
p
ec
tr
al
b
iclu
s
ter
i
n
g
.
T
h
e
m
o
s
t
s
ig
n
i
f
ica
n
t
ef
f
ec
t
s
f
o
r
R
o
b
u
s
t
P
C
A
w
er
e
s
h
o
w
n
o
n
th
e
c
h
o
ice
o
f
clu
s
ter
i
n
g
ap
p
r
o
ac
h
w
h
ic
h
w
as se
n
s
iti
v
e
to
th
e
ac
q
u
ir
ed
n
u
m
b
er
o
f
clu
s
ter
.
Ho
w
e
v
er
,
th
e
s
elec
tio
n
o
f
c
u
m
u
lat
iv
e
p
er
ce
n
tag
e
o
f
v
ar
iati
o
n
ab
o
v
e
7
0
%
f
o
r
th
e
p
u
r
p
o
s
e
o
f
id
en
ti
f
y
i
n
g
th
e
r
ai
n
f
all
p
atter
n
w
a
s
a
w
ea
k
d
ec
is
io
n
as
a
c
u
t
o
f
f
f
o
r
th
e
n
u
m
b
er
o
f
p
r
in
cip
al
co
m
p
o
n
en
t
s
.
I
n
Fig
u
r
e
1
,
th
e
r
esu
lti
n
g
n
u
m
b
er
o
f
clu
s
ter
f
o
r
h
y
b
r
id
R
P
C
A
-
s
p
ec
tr
al
b
iclu
s
ter
in
g
n
o
ticea
b
l
y
tu
r
n
s
m
u
ch
b
ig
g
er
af
ter
r
etain
i
n
g
7
0
%
cu
m
u
lati
v
e
p
er
ce
n
tag
e
o
f
v
ar
iatio
n
.
I
n
id
en
ti
f
y
in
g
r
ain
f
all
p
atter
n
s
,
to
o
m
u
c
h
clu
s
ter
s
in
d
icate
d
th
at
th
e
g
r
o
u
p
i
n
g
co
u
ld
b
e
d
is
ad
v
an
tag
eo
u
s
f
r
o
m
an
i
m
p
ac
t
o
u
tlo
o
k
s
o
as
to
d
e
s
cr
ib
e
th
e
v
ar
iatio
n
o
f
r
ain
f
al
l
p
atter
n
s
i
n
P
en
i
n
s
u
lar
Ma
la
y
s
ia
[
2
8
]
.
I
n
o
r
d
er
to
ex
a
m
i
n
e
t
h
e
cl
u
s
ter
s
o
lu
t
io
n
s
,
t
h
e
v
ar
iatio
n
b
et
w
ee
n
t
w
o
cl
u
s
ter
ap
p
r
o
ac
h
es
w
er
e
test
ed
.
A
s
a
r
esu
l
t
,
th
e
v
ar
iab
ilit
y
o
f
th
e
h
y
b
r
id
R
P
C
A
-
s
p
ec
tr
al
b
iclu
s
ter
i
n
g
m
o
d
el
w
as
s
m
a
ll
er
w
h
ich
i
s
0
.
0
0
3
4
co
m
p
ar
ed
to
P
C
A
co
u
p
led
w
it
h
k
-
Me
a
n
s
cl
u
s
ter
a
n
al
y
s
i
s
w
h
ic
h
i
s
0
.
0
3
0
0
.
E
v
id
en
ce
f
o
r
m
t
h
i
s
w
a
s
p
r
o
v
id
ed
b
y
[
2
9
]
w
h
ic
h
i
n
d
icate
d
t
h
at
h
i
g
h
er
v
a
r
iatio
n
i
n
cl
u
s
ter
in
g
r
ep
r
esen
ted
m
o
r
e
n
o
is
e
an
d
wea
k
er
s
i
g
n
al
w
i
th
in
d
is
co
v
er
ed
clu
s
ter
i
n
g
ap
p
r
o
ac
h
es.
T
h
er
ef
o
r
e,
it
s
h
o
w
ed
t
h
at
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
R
P
C
A
-
s
p
ec
tr
al
b
iclu
s
ter
in
g
h
ad
a
r
elativ
el
y
b
etter
clu
s
ter
i
n
g
r
esu
l
t
in
ter
m
s
o
f
th
e
v
ar
iatio
n
w
h
e
n
co
m
p
ar
ed
to
P
C
A
w
it
h
k
-
Me
an
s
ap
p
r
o
ac
h
.
C
o
n
cl
u
s
i
v
el
y
,
h
y
b
r
id
R
P
C
A
-
s
p
ec
tr
al
b
iclu
s
ter
i
n
g
is
p
r
o
v
en
to
b
e
an
ef
f
icie
n
t
r
o
b
u
s
t
m
et
h
o
d
co
m
b
i
n
ed
w
i
th
a
s
er
ies
o
f
t
w
o
-
w
a
y
cl
u
s
ter
i
n
g
ap
p
r
o
ac
h
w
h
e
n
d
ea
lin
g
w
i
th
h
y
d
r
o
lo
g
ical
d
at
a
esp
ec
iall
y
i
n
r
ain
f
all
d
ata
w
h
er
e
th
er
e
w
as
a
s
i
g
n
if
ican
t
i
m
p
r
o
v
e
m
e
n
t
i
n
th
e
clu
s
ter
p
ar
titi
o
n
.
T
h
is
p
r
ev
e
n
te
d
th
e
r
ain
f
a
ll d
ata
f
r
o
m
h
av
in
g
er
r
o
n
eo
u
s
u
n
b
alan
ce
d
clu
s
te
r
s
.
T
ab
le
1
.
T
h
e
n
u
m
b
er
o
f
co
m
p
o
n
en
t
s
an
d
clu
s
ter
s
ac
q
u
ir
ed
u
s
in
g
t
w
o
ap
p
r
ao
ch
es o
n
to
r
r
en
tial r
ain
f
all
d
ata
C
u
m
.
%
N
u
mb
e
r
o
f
c
o
m
p
o
n
e
n
t
s
N
u
mb
e
r
o
f
c
l
u
s
t
e
r
,
k
P
C
A
R
o
b
u
st
P
C
A
P
C
A
w
i
t
h
k
-
M
e
a
n
s
R
o
b
u
st
P
C
A
w
i
t
h
k
-
M
e
a
n
s
P
C
A
w
i
t
h
S
p
e
c
t
r
a
l
b
i
c
l
u
st
e
r
i
n
g
H
y
b
r
i
d
R
P
C
A
-
S
p
e
c
t
r
a
l
b
i
c
l
u
st
e
r
i
n
g
65
70
75
80
85
90
14
19
26
35
39
42
13
15
22
28
30
35
2
2
2
2
2
2
6
6
10
10
12
12
2
2
2
2
2
2
8
8
35
52
52
95
Fig
u
r
e
1
.
T
h
e
n
u
m
b
er
o
f
cl
u
s
t
er
s
o
b
tain
ed
u
s
i
n
g
R
o
b
u
s
t P
C
A
co
m
b
i
n
ed
w
it
h
d
if
f
er
en
t c
l
u
s
ter
an
al
y
s
is
ap
p
r
o
ac
h
es.
4.
CO
NCLU
SI
O
N
T
h
e
R
o
b
u
s
t
P
C
A
s
to
o
d
o
u
t
as
a
n
e
n
g
a
g
i
n
g
co
n
te
n
d
er
t
o
th
e
c
u
r
r
en
t
cla
s
s
ica
l
P
C
A
ap
p
r
o
ac
h
.
Sp
ec
if
icall
y
,
R
o
b
u
s
t
P
C
A
s
h
o
w
ed
an
ex
ten
s
i
v
e
p
r
o
g
r
es
s
i
n
t
h
e
p
ar
tit
io
n
o
f
cl
u
s
ter
s
as
co
m
p
ar
ed
to
class
ical
P
C
A
.
I
n
cl
i
m
a
to
lo
g
y
s
tu
d
ies
e
s
p
ec
i
all
y
i
n
id
e
n
ti
f
y
i
n
g
r
ai
n
f
all
p
atter
n
s
,
o
b
tain
in
g
m
o
r
e
t
h
a
n
a
p
air
o
f
clu
s
ter
s
to
ex
p
lai
n
t
h
e
v
ar
iatio
n
s
o
f
p
atter
n
s
o
f
r
ain
f
all
is
m
o
r
e
p
er
tin
en
t.
I
n
ad
d
itio
n
,
i
t
ap
p
ea
r
ed
th
at
R
o
b
u
s
t
P
C
A
r
eq
u
ir
ed
f
e
w
er
co
m
p
o
n
en
t
s
to
ex
tr
ac
t
s
o
as
to
ac
h
iev
e
at
least
7
0
%
o
f
s
ig
n
i
f
ica
n
ce
c
u
m
u
lat
iv
e
0
20
40
60
80
100
65
70
75
80
85
90
N
o
.
o
f
C
l
u
ste
r
C
u
mu
l
ati
v
e
Pe
r
c
e
n
tag
e
(
%
)
N
u
m
b
e
r
o
f Cl
u
ste
r
s
Ob
taine
d
u
si
n
g
R
o
b
u
st
PCA
Co
m
b
i
n
e
d
wi
th
Di
ff
e
r
e
n
t
Cl
u
ste
r
i
n
g
Ap
p
r
o
ac
h
e
s
PC
A
w
i
th
k
-Me
an
s
PC
A
w
i
th
S
p
e
c
t
ral
b
i
c
l
u
s
te
ri
n
g
R
o
b
u
s
t
P
CA
w
i
t
h
k-Me
an
s
R
o
b
u
s
t
P
CA
w
i
t
h
S
p
e
c
tr
al b
i
c
l
u
s
te
ri
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
l.
8
,
No
.
3
,
Sep
tem
b
er
201
9
:
2
3
7
–
2
4
3
242
p
er
ce
n
tag
e
i
n
co
n
tr
ac
t
to
P
ea
r
s
o
n
.
T
o
o
f
e
w
co
m
p
o
n
en
t
s
w
o
u
ld
a
f
f
ec
t t
h
e
o
b
s
er
v
a
tio
n
s
i
n
a
w
a
y
t
h
at
t
h
e
y
w
er
e
p
o
o
r
ly
e
m
b
o
d
ied
an
d
w
o
u
l
d
b
e
clu
s
ter
ed
to
g
eth
er
b
ec
au
s
e
o
f
lo
w
s
co
r
es
o
n
e
v
e
r
y
co
m
p
o
n
e
n
t
s
.
On
th
e
co
n
tr
ar
y
,
if
m
o
r
e
n
u
m
b
e
r
o
f
co
m
p
o
n
e
n
ts
to
m
a
in
tai
n
o
r
m
o
r
e
cu
m
u
lati
v
e
p
er
ce
n
t
ag
e
w
er
e
u
s
ed
,
th
er
e
w
o
u
ld
b
e
p
o
o
r
r
esu
lt
i
n
id
e
n
t
if
y
in
g
r
ai
n
f
all
p
atter
n
s
s
i
n
ce
i
t
a
m
p
li
f
ie
s
t
h
e
s
i
g
n
i
f
ica
n
ce
o
f
n
o
is
e.
He
n
ce
,
t
h
e
o
p
tim
u
m
c
u
m
u
lati
v
e
p
er
ce
n
ta
g
e
to
id
en
ti
f
y
r
ai
n
f
a
ll p
atter
n
s
is
b
et
w
ee
n
6
5
%
u
n
til
7
0
%.
T
h
is
s
tu
d
y
h
ad
s
h
o
wn
th
at
t
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
R
P
C
A
-
s
p
ec
tr
al
b
iclu
s
ter
in
g
is
p
ar
ticu
lar
l
y
w
el
l
ad
ap
ted
in
id
en
tify
i
n
g
r
ain
f
all
p
atter
n
s
in
P
en
i
n
s
u
lar
Ma
la
y
s
i
a
d
u
e
to
th
e
s
m
a
ll
v
ar
iatio
n
o
f
th
e
clu
s
ter
in
g
r
esu
lt.
Hav
i
n
g
m
en
tio
n
ed
th
i
s
,
it
is
r
en
o
u
n
ce
d
t
h
at
a
ll
o
f
th
e
r
e
s
u
lt
is
s
tr
ictl
y
allied
to
t
h
e
ca
s
es
b
ased
o
n
r
ai
n
f
al
l
d
ata
i
n
P
en
in
s
u
lar
Ma
la
y
s
i
a
w
h
er
e
th
e
w
ea
t
h
er
an
d
s
ea
s
o
n
s
d
if
f
er
f
r
o
m
o
t
h
er
zo
n
es.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
au
th
o
r
s
w
is
h
to
e
x
p
r
ess
g
r
atit
u
d
e
to
w
ar
d
s
Un
iv
er
s
iti
P
en
d
id
ik
an
Su
l
tan
I
d
r
is
f
o
r
t
h
eir
s
u
p
p
o
r
t
an
d
f
i
n
an
c
ial
f
u
n
d
in
g
v
ia
GP
U
g
r
an
t V
o
te
No
.
2
0
1
8
-
0
1
5
4
-
1
0
1
-
01.
RE
F
E
R
E
NC
E
S
[1
]
V
.
M
o
ro
n
,
e
t
a
l
.
,
“
W
e
a
th
e
r
Ty
p
e
s
A
c
ro
ss
th
e
M
a
rit
i
m
e
Co
n
ti
n
e
n
t:
f
ro
m
th
e
Diu
rn
a
l
C
y
c
le
t
o
In
tera
n
n
u
a
l
V
a
riatio
n
s,”
Fro
n
ti
e
rs
in
En
v
iro
n
me
n
ta
l
S
c
ien
c
e
.
3
(
4
4
),
2
0
1
5
.
[2
]
N.
H.
A
h
m
a
d
,
e
t
a
l
.
,
“
Hie
ra
rc
h
ica
l
Clu
ste
r
A
p
p
ro
a
c
h
f
o
r
Re
g
io
n
a
li
z
a
ti
o
n
o
f
P
e
n
in
s
u
lar
M
a
lay
si
a
b
a
se
d
o
n
th
e
P
re
c
ip
it
a
ti
o
n
Am
o
u
n
t,
”
J
o
u
rn
a
l
o
f
Ph
y
sic
s: Co
n
fer
e
n
c
e
S
e
rie
s.
4
2
3
,
p
p
.
1
-
1
0
,
2
0
1
3
.
[3
]
G
.
S
.
S
iv
a
,
e
t
a
l
.
,
“
Clu
ste
r
A
n
a
l
y
sis
A
p
p
ro
a
c
h
to
S
t
u
d
y
th
e
Ra
in
f
a
ll
P
a
tt
e
rn
in
V
isa
k
h
a
p
a
tn
a
m
Di
strict,
”
W
e
e
k
l
y
S
c
ien
c
e
Res
e
a
rc
h
J
o
u
rn
a
l
.
1
(
3
1
),
2
0
1
4
.
[4
]
R.
Ro
m
e
ro
,
e
t
a
l
.
,
“
Da
il
y
Ra
in
fa
ll
P
a
tt
e
rn
s
in
th
e
S
p
a
n
is
h
M
e
d
it
e
rra
n
e
a
n
A
re
a
:
A
n
Ob
jec
ti
v
e
Clas
sif
ic
a
ti
o
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Cl
ima
t
o
l
o
g
y
.
1
9
,
p
p
.
95
-
1
1
2
,
1
9
9
9
.
[5
]
D.
P
e
n
a
rro
c
h
a
,
“
Clas
si
f
ica
ti
o
n
o
f
Da
il
y
Ra
in
f
a
ll
P
a
tt
e
rn
s
in
a
M
e
d
it
e
rra
n
e
a
n
A
re
a
w
it
h
Ex
tre
m
e
I
n
ten
sity
L
e
v
e
ls:
T
h
e
V
a
len
c
ia Reg
io
n
,
”
In
ter
n
a
ti
o
n
J
o
u
r
n
a
l
o
f
Cli
ma
t
o
l
o
g
y
.
2
2
,
p
p
.
6
7
7
-
6
9
5
,
2
0
0
2
.
[6
]
G
.
S
u
m
n
e
r,
e
t
a
l
.
,
“
T
h
e
I
m
p
a
c
t
o
f
S
u
rf
a
c
e
Cir
c
u
la
ti
o
n
s
o
n
th
e
Da
il
y
Ra
in
fa
ll
o
v
e
r
M
a
ll
o
rc
a
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Cli
m
a
to
l
o
g
y
.
15
,
p
p
.
6
7
3
–
6
9
6
,
1
9
9
5
.
[7
]
P
.
W
ick
ra
m
a
g
a
m
a
g
e
,
“
S
e
a
so
n
a
li
ty
a
n
d
sp
a
ti
a
l
p
a
tt
e
rn
o
f
ra
in
f
a
l
l
o
f
S
ri
L
a
n
k
a
:
Ex
p
lo
ra
to
ry
fa
c
to
r
a
n
a
ly
sis,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Cl
ima
t
o
l
o
g
y
.
3
0
,
p
p
.
1
2
3
5
-
1
2
4
5
,
2
0
1
0
.
[8
]
N.
S
.
C
h
o
k
,
“
P
e
a
rso
n
’s
V
e
rsu
s
S
p
e
r
m
a
n
’s an
d
Ke
n
d
a
ll
’s C
o
rre
latio
n
Co
e
f
f
icie
n
ts
f
o
r
Co
n
t
in
u
o
u
s
Da
ta”
,
2
0
0
8
.
[9
]
Do
re
sw
a
m
y
a
n
d
C.
M
.
V
a
stra
d
,
“
Id
e
n
ti
f
ica
ti
o
n
o
f
Ou
tl
iers
in
Ox
a
z
o
li
n
e
s
a
n
d
Ox
a
z
o
les
Hig
h
Di
m
e
n
sio
n
M
o
lec
u
lar
De
sc
rip
to
r
Da
tas
e
t
u
sin
g
P
r
in
c
ip
a
l
Co
m
p
o
n
e
n
t
Ou
tl
ier
De
tec
ti
o
n
A
l
g
o
rit
h
m
a
n
d
Co
m
p
a
ra
ti
v
e
Nu
m
e
rica
l
S
tu
d
y
o
f
Oth
e
r
Ro
b
u
st
Esti
m
a
to
rs,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Da
t
a
M
in
in
g
a
n
d
K
n
o
wle
d
g
e
M
a
n
a
g
e
me
n
t
Pr
o
c
e
ss
.
3
(4
),
p
p
.
75
-
9
3
,
2
0
1
3
.
[1
0
]
M
.
G
.
S
e
f
id
m
a
z
g
i,
e
t
a
l
.
,
“
T
re
n
d
a
n
a
l
y
sis
u
sin
g
n
o
n
-
sta
ti
o
n
a
ry
ti
m
e
s
e
ries
c
lu
ste
rin
g
b
a
se
d
o
n
th
e
f
in
it
e
e
le
m
e
n
t
m
e
th
o
d
,
”
N
o
n
l
in
e
a
r P
r
o
c
e
ss
e
s in
Ge
o
p
h
y
sic
s
,
v
o
l.
2
1
,
n
o
.
3
,
p
p
.
6
0
5
–
6
1
5
,
2
0
1
4
.
[1
1
]
H.
W
a
n
,
e
t
a
l
.
,
“
A
tt
rib
u
ti
n
g
n
o
r
th
e
rn
h
ig
h
-
lat
it
u
d
e
p
re
c
ip
it
a
ti
o
n
c
h
a
n
g
e
o
v
e
r
th
e
p
e
ri
o
d
1
9
6
6
–
2
0
0
5
t
o
h
u
m
a
n
in
f
lu
e
n
c
e
,
”
Cli
ma
te Dy
n
a
mic
s
,
v
o
l.
4
5
,
n
o
.
7
,
p
p
.
1
7
1
3
–
1
7
2
6
,
2
0
1
5
.
[1
2
]
A
.
M
.
Ra
d
a
n
d
D.
Kh
a
li
l,
“
A
p
p
ro
p
riate
n
e
ss
o
f
Clu
ste
re
d
Ra
in
g
a
u
g
e
S
tatio
n
s
f
o
r
S
p
a
ti
o
-
T
e
m
p
o
ra
l
M
e
teo
ro
l
o
g
ica
l
Dro
u
g
h
t
A
p
p
li
c
a
ti
o
n
s,”
W
a
ter
Re
so
u
rc
e
s M
a
n
a
g
e
me
n
t
,
v
o
l.
2
9
,
n
o
.
1
1
,
p
p
.
4
1
5
7
–
4
1
7
1
,
2
0
1
5
.
[1
3
]
Y.
Zh
a
n
g
,
e
t
a
l
.
,
“
Op
ti
m
a
l
Clu
ste
r
A
n
a
l
y
sis
f
o
r
Ob
jec
ti
v
e
Re
g
io
n
a
li
z
a
ti
o
n
o
f
S
e
a
so
n
a
l
P
re
c
ip
it
a
ti
o
n
in
Re
g
io
n
s
o
f
Hig
h
S
p
a
ti
a
l
–
T
e
m
p
o
ra
l
V
a
riab
il
i
ty
:
A
p
p
li
c
a
ti
o
n
to
W
e
ste
rn
Et
h
i
o
p
ia,”
J
o
u
r
n
a
l
o
f
Cli
m
a
te
,
v
o
l.
2
9
,
n
o
.
1
0
,
p
p
.
3
6
9
7
–
3
7
1
7
,
2
0
1
6
.
[1
4
]
X
.
Hu
a
n
g
,
e
t
a
l
.
,
“
A
n
a
ly
sis
o
f
d
y
n
a
m
ic
tren
d
-
b
a
se
d
c
lu
ste
rin
g
o
n
Ce
n
tral
G
e
r
m
a
n
y
p
re
c
ip
it
a
ti
o
n
,
”
i
n
Fi
f
t
h
In
ter
n
a
t
io
n
a
l
W
o
rk
sh
o
p
o
n
Cli
ma
te In
fo
rm
a
ti
c
s
,
(Bo
u
ld
e
r),
2
0
1
5
.
[1
5
]
M
.
G
.
S
e
f
id
m
a
z
g
i
a
n
d
C.
T
.
M
a
rriso
n
,
“
S
p
a
ti
o
tem
p
o
ra
l
A
n
a
l
y
sis
o
f
s
e
a
so
n
a
l
P
re
c
ip
it
a
ti
o
n
o
v
e
r
US
u
sin
g
Co
-
c
lu
ste
rin
g
,
”
in
6
th
In
ter
n
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
Cli
ma
te
In
fo
rm
a
ti
c
s,
2
0
1
6
.
Pro
c
e
e
d
i
n
g
s
o
f
th
e
6
th
In
ter
n
a
t
io
n
a
l
W
o
rk
sh
o
p
o
n
Cl
ima
te I
n
fo
rm
a
ti
c
s,
p
p
.
4
1
-
4
4
,
2
0
1
6
.
[1
6
]
S
.
M
.
S
h
a
h
a
r
u
d
i
n
,
e
t
a
l
.
,
“
Id
e
n
ti
f
ica
ti
o
n
o
f
Ra
in
f
a
ll
P
a
tt
e
rn
s
o
n
H
y
d
ro
lo
g
ica
l
S
im
u
latio
n
u
sin
g
R
o
b
u
st
P
ri
n
c
ip
a
l
Co
m
p
o
n
e
n
t
A
n
a
l
y
sis,”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
,
”
v
o
l.
1
1
,
n
o
.
3
,
p
p
.
1
1
6
2
-
1
1
6
7
,
S
e
p
tem
b
e
r
2
0
1
8
.
[1
7
]
J.
Ha
rd
in
,
e
t
a
l.
,
“
A
Ro
b
u
st
M
e
a
su
re
o
f
Co
rre
latio
n
b
e
tw
e
e
n
Tw
o
G
e
n
e
s
o
n
a
M
icro
a
rra
y
,
”
BM
C
Bi
o
in
fo
rm
a
t
ics
,
8
(2
2
0
),
2
0
0
7
.
[1
8
]
S
.
M
.
S
h
a
h
a
r
u
d
i
n
,
e
t
a
l
.
,
“
M
o
d
i
f
ied
S
in
g
u
lar
S
p
e
c
tru
m
A
n
a
l
y
sis
in
Id
e
n
ti
fy
in
g
Ra
in
fa
ll
T
re
n
d
o
v
e
r
P
e
n
in
su
la
r
M
a
la
y
sia
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
C
o
mp
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
,
”
v
o
l.
1
5
,
n
o
.
1
,
p
p
.
283
-
2
9
3
,
Ju
ly
2
0
1
9
.
[1
9
]
R.
Ro
m
e
ro
,
e
t
a
l
.
,
“
A
Clas
sif
i
c
a
ti
o
n
o
f
th
e
A
t
m
o
sp
h
e
ric
Circu
latio
n
P
a
tt
e
r
n
s
P
r
o
d
u
c
in
g
S
ig
n
if
ica
n
t
Da
il
y
Ra
in
f
a
ll
in
t
h
e
S
p
a
n
ish
M
e
d
it
e
rra
n
e
a
n
A
re
a
”
,
In
t.
J
.
Cl
ima
t
o
l
.
1
9
,
p
p
.
7
6
5
-
7
8
5
,
1
9
9
9
.
[2
0
]
R.
H.
Co
m
p
a
g
n
u
c
c
i,
e
t
a
l
.
,
“
P
r
in
c
ip
a
l
S
e
q
u
e
n
c
e
P
a
tt
e
rn
A
n
a
ly
sis:
A
N
e
w
A
p
p
ro
a
c
h
to
C
las
sify
in
g
t
h
e
Ev
o
lu
ti
o
n
o
f
A
t
m
o
sp
h
e
ric S
y
ste
m
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Cli
ma
to
l
o
g
y
.
2
1
,
p
p
.
1
9
7
-
2
1
7
,
2
0
0
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
A
n
efficien
t m
eth
o
d
to
imp
r
o
ve
t
h
e
clu
s
teri
n
g
p
erfo
r
ma
n
ce
u
s
in
g
…
(
S
h
a
z
lyn
Mil
lea
n
a
S
h
a
h
a
r
u
d
in
)
243
[2
1
]
S
.
M
.
S
h
a
h
a
ru
d
in
,
e
t
a
l
.
,
“
T
h
e
Co
m
p
a
riso
n
o
f
T
-
m
o
d
e
a
n
d
P
e
a
rso
n
Co
rre
latio
n
M
a
tri
c
e
s
in
Clas
sif
ica
ti
o
n
o
f
Da
il
y
Ra
in
f
a
ll
P
a
tt
e
rn
s i
n
P
e
n
in
s
u
lar M
a
la
y
sia
,
”
M
a
tem
a
ti
k
a
,
p
p
.
1
8
7
-
1
9
4
,
2
0
1
3
.
[2
2
]
J.
M
e
n
g
,
a
n
d
Y.
Ya
n
g
,
“
S
y
m
m
e
tr
ica
l
Tw
o
-
Di
m
e
n
sio
n
a
l
P
CA
w
it
h
Im
a
g
e
M
e
a
su
re
s in
F
a
c
e
Re
c
o
g
n
it
io
n
,
”
I
n
t
J
A
d
v
Ro
b
o
ti
c
S
y
.
9
,
2
0
1
2
.
[2
3
]
P
.
Ro
u
ss
e
e
u
w
,
a
n
d
A
.
L
e
ro
y
,
“
R
o
b
u
st
Reg
re
ss
io
n
a
n
d
Ou
t
li
e
r
De
tec
ti
o
n
.
Ne
w
Yo
rk
,
USA
:
Jo
h
n
W
il
e
y
a
n
d
S
o
n
s
,
In
c
.
1
9
8
7
.
[2
4
]
M
.
Ow
e
n
,
“
T
u
k
e
y
'
s Bi
we
ig
h
t
Co
r
re
latio
n
a
n
d
t
h
e
Bre
a
k
d
o
w
n
T
h
e
sis,”
P
o
m
o
n
a
Co
ll
e
g
e
.
2
0
1
0
.
[2
5
]
M
.
G
.
S
e
f
id
m
a
z
g
a
n
d
C.
T
.
M
o
rriso
n
,
“
S
p
a
ti
o
tem
p
o
ra
l
A
n
a
l
y
si
s
o
f
S
e
a
so
n
a
l
P
re
c
ip
i
tatio
n
o
v
e
r
US
u
sin
g
Co
-
c
lu
ste
rin
g
,
”
6
th
In
ter
n
a
ti
o
n
a
l
W
o
r
k
sh
o
p
o
n
Cli
ma
te I
n
fo
rm
a
ti
c
s,
p
p
4
1
-
4
4
.
2
0
1
6
.
[2
6
]
G
.
M
.
M
imm
a
c
k
,
e
t
a
l
.
,
“
Ch
o
ice
o
f
Dista
n
c
e
M
a
tri
c
e
s
in
Clu
ste
r
An
a
ly
sis:
D
e
f
in
in
g
Re
g
io
n
s,”
J
o
u
r
n
a
l
o
f
Cli
m
a
te.
14
,
p
p
.
2
7
9
0
-
2
7
9
7
,
2
0
0
2
.
[2
7
]
W
.
C.
Ch
a
n
g
,
“
On
u
sin
g
p
ri
n
c
ip
a
l
c
o
m
p
o
n
e
n
ts b
e
f
o
re
se
p
a
ra
ti
n
g
a
m
i
x
tu
re
o
f
t
w
o
m
u
lt
iv
a
riate
n
o
rm
a
l
p
o
p
u
latio
n
s,”
J
.
Ap
p
l.
S
ta
t
.
3
2
,
p
p
.
2
6
7
–
2
7
5
,
1
9
8
3
.
[2
8
]
I.
M
a
h
lstei
n
a
n
d
R
.
Kn
u
tt
i,
“
Re
g
io
n
a
l
c
li
m
a
te
c
h
a
n
g
e
p
a
tt
e
rn
s
i
d
e
n
ti
f
ied
b
y
c
lu
ste
r
a
n
a
ly
sis,”
Cli
m.
Dy
n
.,
v
o
l.
3
5
,
p
p
.
5
8
7
-
6
0
0
,
2
0
1
0
.
[2
9
]
A
.
K
a
si
m
,
e
t
a
l
.
,
A
p
p
li
e
d
Biclu
ste
rin
g
M
e
th
o
d
s
f
o
r
Big
a
n
d
Hig
h
-
Dim
e
n
sio
n
a
l
Da
ta
Us
in
g
R,
T
a
y
lo
r
&
F
ra
n
c
is
G
ro
u
p
,
2
0
1
7
,
p
.
8
9
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
S
h
a
z
ly
n
M
il
lea
n
a
w
a
s
b
o
rn
in
J
o
h
o
r
Ba
h
ru
,
M
a
lay
sia
,
in
1
9
8
8
.
S
h
e
is
a
se
n
i
o
r
lec
tu
re
r
a
t
t
h
e
De
p
a
rtme
n
t
o
f
M
a
th
e
m
a
ti
c
s,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
a
n
d
M
a
th
e
m
a
ti
c
s
,
Un
iv
e
rsiti
P
e
n
d
id
ik
a
n
S
u
lt
a
n
Id
ris
(U
P
S
I).
S
h
e
g
ra
d
u
a
ted
w
it
h
a
b
a
c
h
e
lo
r
sc
ien
c
e
d
e
g
re
e
in
In
d
u
strial
M
a
th
e
m
a
ti
c
s
f
ro
m
Un
iv
e
rsiti
Tek
n
o
lo
g
i
M
a
la
y
sia
,
in
2
0
1
0
.
Up
o
n
g
ra
d
u
a
ti
o
n
,
sh
e
b
e
g
a
n
h
e
r
c
a
re
e
r
a
s
a
n
Ex
e
c
u
ti
v
e
in
b
a
n
k
in
g
in
stit
u
t
io
n
.
In
th
e
f
o
ll
o
win
g
y
e
a
r,
sh
e
re
c
e
iv
e
d
a
n
o
ffe
r
t
o
c
o
n
ti
n
u
e
h
e
r
stu
d
y
a
s
a
f
a
st
-
trac
k
P
h
D
stu
d
e
n
t
a
t
th
e
sa
m
e
u
n
iv
e
rsity
.
Du
rin
g
h
e
r
P
h
D
j
o
u
r
n
e
y
,
sh
e
d
e
v
e
lo
p
e
d
a
n
in
tere
st
i
n
m
u
lt
iv
a
riate
a
n
a
l
y
sis,
sp
e
c
if
ica
ll
y
in
f
in
d
in
g
p
a
tt
e
rn
s
w
h
ich
d
e
a
ls
w
it
h
b
ig
d
a
ta.
He
r
re
se
a
rc
h
f
o
c
u
se
s
o
n
th
e
a
r
e
a
o
f
d
i
m
e
n
sio
n
re
d
u
c
ti
o
n
m
e
th
o
d
s
sp
e
c
i
f
ica
ll
y
in
c
li
m
a
te
in
f
o
r
m
a
ti
c
s
w
h
ich
in
v
o
lv
e
s
a
n
a
l
y
sis
o
n
h
u
g
e
c
li
m
a
t
e
-
re
late
d
d
a
tas
e
ts
b
a
s
e
d
o
n
tec
h
n
iq
u
e
s
in
Da
ta
M
i
n
in
g
.
S
h
e
h
a
d
p
u
b
li
sh
e
d
h
e
r
re
se
a
rc
h
in
S
c
o
p
u
s
in
d
e
x
e
d
j
o
u
r
n
a
l
a
n
d
p
re
se
n
te
d
h
e
r
w
o
rk
in
v
a
rio
u
s
l
o
c
a
l
a
n
d
in
tern
a
ti
o
n
a
l
c
o
n
f
e
re
n
c
e
s.
S
h
e
c
o
m
p
lete
d
h
e
r
P
h
D
th
e
sis
a
t
th
e
e
n
d
o
f
2
0
1
6
a
n
d
w
a
s
c
o
n
fe
rre
d
a
d
o
c
to
ra
te
d
e
g
re
e
in
2
0
1
7
.
S
h
u
h
a
id
a
Ism
a
il
is a l
e
c
tu
re
r
a
t
th
e
De
p
a
rt
m
e
n
t
o
f
M
a
th
e
m
a
ti
c
s a
n
d
S
tatics
ti
c
s,
F
a
c
u
lt
y
o
f
A
p
p
li
e
d
S
c
ien
c
e
s
a
n
d
T
e
c
h
n
o
lo
g
y
,
Un
iv
e
r
siti
T
u
n
Hu
ss
e
in
On
n
M
a
lay
sia
(
UT
HM).
S
h
e
o
b
tain
e
d
h
e
r
f
irst
d
e
g
re
e
in
Co
m
p
u
ter
S
c
ien
c
e
s
m
a
jo
rin
g
f
ro
m
UT
M
.
S
h
e
a
lso
o
b
tai
n
e
d
a
M
a
ste
r
d
e
g
re
e
a
n
d
P
h
D
f
ro
m
th
e
s
a
m
e
u
n
iv
e
rsit
y
.
T
h
ro
u
g
h
o
u
t
h
e
r
stu
d
ies
,
sh
e
d
e
v
e
lo
p
e
d
a
n
in
tere
st
in
M
a
c
h
in
e
L
e
a
rn
in
g
re
se
a
rc
h
a
re
a
,
sp
e
c
if
ic
a
ll
y
in
p
r
e
d
ictiv
e
m
o
d
e
ll
in
g
,
c
las
si
f
ica
ti
o
n
,
a
n
d
c
lu
ste
rin
g
.
He
r
c
u
rre
n
t
re
se
a
rc
h
a
re
a
s a
re
in
h
y
d
ro
lo
g
ica
l
m
o
d
e
ll
in
g
,
b
ig
d
a
ta a
n
a
ly
ti
c
s a
n
d
d
e
e
p
lea
rn
i
n
g
.
S
it
i
M
a
rian
a
is
a
g
ra
d
u
a
te
o
f
Ba
c
h
e
lo
r
De
g
re
e
in
Ed
u
c
a
ti
o
n
(M
a
th
e
m
a
ti
c
s)
f
ro
m
Un
iv
e
rsit
i
P
e
n
d
i
d
ik
a
n
S
u
lt
a
n
Id
ris
(U
P
S
I)
in
2
0
1
8
.
S
h
e
is
c
u
rre
n
t
ly
p
u
rsu
in
g
h
e
r
stu
d
ies
in
M
a
ste
rs
o
f
S
c
ien
c
e
d
e
g
re
e
in
S
tatisti
c
s
w
h
il
e
w
o
rk
in
g
o
n
to
p
u
b
li
sh
p
a
p
e
rs
in
h
e
r
sc
o
p
e
o
f
f
ield
.
He
r
re
se
a
r
c
h
f
o
c
u
se
s
o
n
th
e
a
re
a
o
f
d
ime
n
sio
n
re
d
u
c
ti
o
n
m
e
th
o
d
s,
sp
e
c
if
ica
l
l
y
in
c
li
m
a
te
in
f
o
r
m
a
ti
c
s
w
h
ich
in
v
o
lv
e
s a
n
a
ly
sis o
n
h
u
g
e
c
li
m
a
te
-
re
late
d
d
a
tas
e
ts b
a
se
d
o
n
tec
h
n
iq
u
e
s in
Da
ta M
i
n
in
g
.
No
rh
a
iza
is
a
se
n
io
r
lec
tu
re
r
a
t
th
e
De
p
a
rtm
e
n
t
o
f
M
a
th
e
m
a
ti
c
a
l
S
c
ien
c
e
s,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
,
Un
iv
e
rsiti
Tek
n
o
lo
g
i
M
a
la
y
sia
(
UT
M
).
S
h
e
g
r
a
d
u
a
ted
w
it
h
a
n
h
o
n
o
rs
d
e
g
re
e
in
M
a
th
e
m
a
ti
c
s,
S
tatisti
c
s
a
n
d
Op
e
ra
ti
o
n
a
l
re
se
a
rc
h
f
ro
m
th
e
Un
iv
e
rsit
y
o
f
M
a
n
c
h
e
ste
r,
in
1
9
9
6
.
S
h
e
jo
in
e
d
UT
M
in
A
u
g
u
st
2
0
0
0
.
In
th
e
f
o
ll
o
w
in
g
y
e
a
r,
sh
e
c
o
n
ti
n
u
e
d
h
e
r
stu
d
ies
a
t
th
e
Un
iv
e
rsity
o
f
S
h
e
ff
i
e
ld
f
o
r
h
e
r
m
a
ste
r’s d
e
g
re
e
.
In
S
h
e
f
f
i
e
ld
,
sh
e
d
e
v
e
lo
p
e
d
a
n
i
n
tere
st i
n
m
u
lt
i
v
a
riate
a
n
a
l
y
sis,
sp
e
c
i
f
ica
ll
y
in
f
in
d
in
g
p
a
tt
e
rn
s
w
h
ich
lea
d
h
e
r
t
o
p
u
rsu
e
a
P
h
D
d
e
g
re
e
a
t
th
e
Un
iv
e
rsit
y
o
f
Ke
n
t.
S
h
e
c
o
m
p
lete
d
h
e
r
P
h
D
th
e
sis
a
t
th
e
e
n
d
o
f
2
0
0
7
a
n
d
w
a
s
c
o
n
f
e
rr
e
d
a
d
o
c
t
o
ra
te
d
e
g
re
e
in
2
0
0
8
.
F
i
n
d
i
n
g
p
a
tt
e
rn
s
in
a
n
y
d
a
ta
h
a
v
e
a
l
w
a
y
s
b
e
e
n
h
e
r
re
se
a
r
c
h
in
tere
sts.
S
h
e
sta
rted
t
h
e
in
tere
sts
in
p
ro
f
il
in
g
d
a
ta
–
f
in
d
in
g
sta
ti
stica
ll
y
d
isti
n
c
ti
v
e
a
n
d
sig
n
if
ica
n
t
g
ro
u
p
s
a
n
d
f
e
a
tu
re
s
in
th
e
o
b
jec
t
o
f
in
tere
st
w
h
il
st
a
t
S
h
e
ff
ield
.
Cu
rre
n
tl
y
,
h
e
r
re
se
a
rc
h
in
tere
sts
re
v
o
lv
e
a
ro
u
n
d
h
y
d
ro
in
f
o
r
m
a
ti
c
s
p
a
rti
c
u
larl
y
in
in
v
e
stig
a
ti
n
g
th
e
stre
a
m
f
lo
w
v
a
ria
b
il
it
y
o
f
th
e
lo
c
a
l
riv
e
rs.
Evaluation Warning : The document was created with Spire.PDF for Python.