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v
e
m
o
r
e
p
r
ec
is
io
n
i
n
t
h
e
p
r
ed
ictio
n
,
it
is
e
s
s
e
n
tia
l
to
w
o
r
k
o
n
a
h
o
m
o
g
e
n
eo
u
s
d
a
taset,
th
at
's
w
h
y
w
e
p
r
o
p
o
s
e
t
o
p
ar
titi
o
n
th
e
in
itial
cu
b
e
in
d
en
s
e
s
u
b
-
cu
b
e
s
b
y
ap
p
ly
i
n
g
m
e
th
o
d
s
o
f
clu
s
ter
in
g
th
e
n
ap
p
l
y
i
n
g
a
r
eg
r
es
s
i
o
n
tr
ee
tech
n
iq
u
e
f
o
r
th
e
c
o
n
s
tr
u
ct
io
n
o
f
th
e
p
r
ed
ictio
n
m
o
d
el.
2.
R
E
L
AT
E
D
WO
RK
Sev
er
al
ap
p
r
o
ac
h
es
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
co
u
p
lin
g
d
ata
m
i
n
i
n
g
an
d
o
n
li
n
e
a
n
al
y
s
is
to
ex
te
n
d
OL
A
P
to
p
r
ed
ictio
n
.
I
n
th
e
w
o
r
k
o
f
R
iad
B
en
Me
s
s
ao
u
d
[
6
]
,
th
e
au
t
h
o
r
h
as
d
e
f
i
n
ed
t
h
r
ee
co
u
p
li
n
g
ap
p
r
o
ac
h
es,
a
p
r
o
ce
s
s
o
f
tr
an
s
f
o
r
m
i
n
g
m
u
ltid
i
m
en
s
io
n
al
d
at
a
in
to
t
w
o
-
d
i
m
e
n
s
io
n
al
d
ata,
t
h
e
s
ec
o
n
d
ap
p
r
o
ac
h
is
b
ased
o
n
t
h
e
e
x
p
lo
itatio
n
o
f
to
o
ls
o
f
f
er
ed
b
y
m
u
l
tid
i
m
e
n
s
i
o
n
al
d
atab
ase
m
an
a
g
e
m
en
t
s
y
s
te
m
s
,
a
n
d
th
e
t
h
ir
d
is
to
ev
o
lv
e
t
h
e
d
ata
m
i
n
i
n
g
al
g
o
r
ith
m
s
to
ad
ap
t th
e
m
w
it
h
t
h
e
t
y
p
es o
f
d
ata
h
an
d
led
b
y
t
h
e
cu
b
es.
As
p
ar
t
o
f
t
h
e
co
u
p
lin
g
,
n
e
w
p
r
o
p
o
s
als
ar
e
e
m
er
g
i
n
g
.
T
h
e
y
co
n
s
i
s
t
o
f
u
s
in
g
s
tati
s
tical
a
n
d
m
ac
h
i
n
e
lear
n
in
g
m
et
h
o
d
s
f
o
r
p
r
ed
ictio
n
i
n
o
r
d
er
to
en
r
ich
t
h
e
ca
p
ab
i
liti
es
o
f
o
n
li
n
e
a
n
al
y
s
i
s
.
Sar
a
w
a
g
i
a
n
d
al
[
7
]
u
s
e
p
r
e
d
ictio
n
b
y
b
u
ild
i
n
g
a
cu
b
e
o
f
p
r
ed
icted
v
alu
es
f
r
o
m
t
h
e
i
n
itial
d
ata
cu
b
e,
th
e
lear
n
i
n
g
b
ase
is
th
e
o
r
ig
in
a
l
cu
b
e,
an
d
t
h
e
m
o
d
el
i
s
b
ased
o
n
a
lo
g
-
li
n
ea
r
r
eg
r
es
s
io
n
.
De
v
iatio
n
s
b
et
w
ee
n
t
h
e
t
w
o
c
u
b
es
ca
n
in
d
icate
to
th
e
u
s
er
ex
ce
p
tio
n
a
l
v
al
u
es.
T
h
es
e
ex
ce
p
t
io
n
al
ce
lls
ar
e
th
e
n
s
i
g
n
aled
to
th
e
u
s
er
w
h
e
n
n
a
v
i
g
atin
g
th
e
d
ata
cu
b
e
w
it
h
t
h
r
ee
in
d
icato
r
s
t
h
at
also
s
h
o
w
h
i
m
i
n
ter
es
tin
g
p
ath
s
to
ex
p
lo
r
e.
T
h
e
w
o
r
k
o
f
C
h
e
n
g
[
8
]
is
ai
m
ed
at
p
r
ed
ictin
g
n
e
w
f
ac
t
s
.
So
h
e
p
r
o
p
o
s
es
to
g
e
n
er
ate
a
n
e
w
c
u
b
e
u
s
i
n
g
a
g
en
er
alize
d
lin
ea
r
m
o
d
el.
T
h
e
r
esu
lti
n
g
cu
b
e
co
r
r
es
p
o
n
d
in
g
to
th
e
p
r
ed
ictio
n
m
o
d
el.
Han
a
n
d
al
[
9
]
p
r
o
p
o
s
es
to
p
r
ed
ict
a
n
e
w
f
ac
t
m
ea
s
u
r
e
b
y
id
en
t
if
y
i
n
g
s
u
b
s
ets
o
f
i
n
ter
esti
n
g
d
ata.
T
h
e
p
r
ed
ictiv
e
m
o
d
el
is
a
cu
b
e
w
h
er
e
th
e
m
ea
s
u
r
e
in
d
ic
ates
a
s
co
r
e
o
r
a
p
r
o
b
ab
ilit
y
d
i
s
tr
ib
u
tio
n
a
s
s
o
ciate
d
w
it
h
th
e
m
ea
s
u
r
e
v
al
u
e
t
h
at
ca
n
b
e
ex
p
ec
ted
in
th
e
o
r
ig
in
al
cu
b
e,
r
esu
lti
n
g
c
u
b
e
co
r
r
esp
o
n
d
s
to
th
e
m
o
d
el
to
b
e
u
s
ed
f
o
r
p
r
ed
ictio
n
.
Y.
C
h
e
n
a
n
d
P
ei's
p
r
o
p
o
s
al
[
10
]
co
n
s
is
ts
o
f
b
u
ild
in
g
c
u
b
es
b
ased
o
n
li
n
ea
r
r
eg
r
e
s
s
io
n
.
Fro
m
t
h
e
in
itial
d
ata
c
u
b
e,
a
cu
b
ic
m
ea
s
u
r
e
is
g
en
er
ated
w
h
er
e
ea
ch
v
alu
e
i
n
d
icate
s
t
h
e
w
ei
g
h
t
o
f
e
v
id
en
ce
.
C
o
n
t
in
u
i
n
g
o
n
th
e
w
o
r
k
o
f
Sar
a
w
a
g
i,
w
h
ich
f
o
cu
s
e
s
o
n
t
h
e
aid
to
n
a
v
ig
atio
n
a
n
d
also
o
n
th
e
e
x
p
la
n
atio
n
o
f
t
h
e
f
ac
t
s
,
A
.
Sa
ir
[
11
]
p
u
s
h
e
s
t
h
e
li
m
its
o
f
e
x
p
lo
r
a
to
r
y
n
av
i
g
atio
n
b
y
i
n
j
ec
tin
g
p
r
ed
ictio
n
tech
n
iq
u
es
at
t
h
e
h
ea
r
t
o
f
OL
A
P
p
r
o
ce
s
s
es,
th
i
s
w
o
r
k
is
b
ased
o
n
t
h
e
i
n
te
g
r
atio
n
o
f
a
co
m
p
lete
lear
n
in
g
p
r
o
ce
s
s
in
OL
A
P
f
o
r
o
n
li
n
e
d
ata
m
in
i
n
g
.
A
co
m
p
lete
p
r
o
ce
s
s
th
e
n
i
n
cl
u
d
es
a
s
elec
tio
n
p
h
ase
o
f
t
h
e
ex
p
la
n
ato
r
y
v
a
r
i
ab
les,
a
f
ac
t
s
h
ar
i
n
g
p
h
ase
in
a
lear
n
i
n
g
s
a
m
p
le
an
d
a
test
s
a
m
p
le.
Nex
t,
a
lear
n
in
g
p
h
ase
a
n
d
a
v
alid
atio
n
p
h
ase
ar
e
ex
ec
u
ted
.
A
.
Sa
ir
[
11
]
p
r
o
p
o
s
es
an
ap
p
r
o
ac
h
b
ased
o
n
au
to
m
atic
lear
n
in
g
w
i
th
r
eg
r
es
s
io
n
tr
ee
s
i
n
o
r
d
er
to
p
r
ed
ict
th
e
v
alu
e
o
f
an
a
g
g
r
e
g
a
te
o
r
a
m
ea
s
u
r
e.
Oth
er
w
o
r
k
in
v
o
lv
e
s
ap
p
l
y
i
n
g
m
eth
o
d
s
f
o
r
p
ar
titi
o
n
i
n
g
O
L
A
P
cu
b
es.
T
h
e
r
esear
c
h
o
f
R
.
Mis
s
ao
u
i
an
d
C
.
Go
u
tte
[
1
2
]
p
r
o
p
o
s
es
to
an
al
y
ze
th
e
p
o
te
n
tial
o
f
a
p
r
o
b
ab
ilis
tic
m
o
d
elin
g
tech
n
iq
u
e,
ca
lled
“n
o
n
-
n
eg
at
iv
e
m
u
lt
i
-
w
a
y
ar
r
a
y
f
ac
to
r
izatio
n
”,
f
o
r
ap
p
r
o
x
i
m
atin
g
a
g
g
r
e
g
a
te
a
n
d
m
u
lt
id
i
m
e
n
s
io
n
al
v
alu
e
s
.
Usi
n
g
s
u
c
h
a
tec
h
n
iq
u
e,
th
e
y
co
m
p
u
te
t
h
e
s
et
o
f
co
m
p
o
n
e
n
ts
(
cl
u
s
ter
s
)
th
at
b
es
t
f
i
t
th
e
in
itial
d
ata
s
et
an
d
w
h
o
s
e
s
u
p
er
p
o
s
itio
n
ap
p
r
o
x
i
m
ates
th
e
o
r
ig
in
al
d
ata.
T
h
e
g
en
er
ated
co
m
p
o
n
e
n
t
s
ca
n
t
h
en
b
e
e
x
p
lo
ited
f
o
r
ap
p
r
o
x
im
a
tel
y
a
n
s
w
er
i
n
g
O
L
A
P
q
u
er
ies s
u
c
h
as r
o
ll
-
u
p
,
s
li
ce
an
d
d
ice
o
p
er
atio
n
s
.
3.
O
UR
AP
P
RO
ACH
Ou
r
w
o
r
k
is
p
ar
t
o
f
ap
p
r
o
ac
h
o
f
th
e
co
u
p
li
n
g
b
et
w
ee
n
d
ata
m
i
n
in
g
a
n
d
o
n
l
in
e
a
n
al
y
s
is
to
p
r
ed
ict
th
e
m
ea
s
u
r
ed
v
al
u
e
f
o
r
n
o
n
-
e
x
is
te
n
t
f
ac
ts
o
r
f
ac
ts
w
it
h
a
m
is
s
i
n
g
v
a
lu
e.
T
h
e
id
ea
i
s
to
p
ar
titi
o
n
,
u
s
i
n
g
m
et
h
o
d
s
o
f
clu
s
ter
i
n
g
,
an
i
n
itia
l
d
ata
cu
b
e
in
to
d
en
s
e
s
u
b
-
c
u
b
es
th
a
t
c
o
u
ld
s
er
v
e
as
a
lear
n
i
n
g
s
et
t
o
b
u
ild
a
p
r
ed
ictio
n
m
o
d
el.
T
h
e
ch
o
ice
to
u
s
i
n
g
d
en
s
e
s
u
b
-
c
u
b
es
i
s
j
u
s
tifie
d
b
y
th
e
q
u
alit
y
o
f
t
h
e
in
f
o
r
m
at
io
n
o
b
tain
ed
b
y
t
h
es
e
d
en
s
e
s
u
b
-
cu
b
e
s
,
an
d
it
w
ill
b
e
m
o
r
e
in
ter
es
tin
g
to
s
ea
r
ch
in
th
e
p
r
ed
ictiv
e
m
o
d
el
o
f
s
u
b
-
c
u
b
e
w
h
ic
h
co
n
tain
s
th
e
ce
ll d
esi
g
n
a
ted
b
y
t
h
e
u
s
er
th
an
lo
o
k
t
h
r
o
u
g
h
o
f
all
d
ata
cu
b
e.
I
n
th
i
s
w
o
r
k
,
w
e
d
is
c
u
s
s
t
h
e
f
i
r
s
t
p
ar
t
co
n
ce
r
n
in
g
t
h
e
ap
p
licatio
n
o
f
cl
u
s
ter
i
n
g
f
o
r
t
h
e
p
ar
titi
o
n
in
g
o
f
th
e
i
n
itia
l
cu
b
e;
w
e
f
ir
s
t
m
a
k
e
an
e
x
p
er
i
m
e
n
tal
s
t
u
d
y
o
f
t
h
e
clu
s
ter
in
g
m
et
h
o
d
s
a
n
d
th
e
n
ap
p
l
y
th
e
c
h
o
s
e
n
m
et
h
o
d
o
n
o
u
r
r
ea
l
cu
b
e.
I
n
t
h
e
s
ec
o
n
d
p
ar
t,
w
e
ap
p
l
y
th
e
r
eg
r
ess
io
n
tr
ee
m
et
h
o
d
f
o
r
t
h
e
co
n
s
tr
u
ctio
n
an
d
v
alid
atio
n
o
f
th
e
p
r
ed
ictio
n
m
o
d
el
f
o
r
ea
ch
s
u
b
-
c
u
b
e;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
0
8
8
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8708
I
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E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
3
,
J
u
n
e
2
0
1
9
:
2
0
9
4
-
2
1
0
2
2096
Fin
all
y
,
w
e
p
r
o
ce
ed
to
th
e
p
r
ed
ictio
n
o
f
t
h
e
v
al
u
e
o
f
t
h
e
ce
ll
d
esig
n
ated
b
y
t
h
e
u
s
er
th
r
o
u
g
h
t
h
e
m
o
d
el
o
f
th
e
s
u
b
-
cu
b
e
i
n
w
h
ic
h
is
t
h
e
s
elec
ted
ce
ll.
3
.
1
.
Clus
t
er
ing
m
et
ho
d
s
W
ith
t
h
e
in
cr
e
a
s
e
o
f
t
h
e
i
n
f
o
r
m
atio
n
o
b
tain
ed
d
u
r
in
g
t
h
e
wo
r
k
o
f
in
f
o
r
m
a
tio
n
p
r
o
ce
s
s
e
s
,
tr
ea
t
m
e
n
t
b
ec
o
m
e
s
d
if
f
ic
u
lt.
T
h
e
n
ee
d
f
o
r
an
in
it
ial
tr
ea
t
m
en
t
o
f
t
h
e
i
n
f
o
r
m
atio
n
f
o
r
its
s
tr
u
ctu
r
i
n
g
,
th
e
i
s
o
latio
n
o
f
th
e
ch
ar
ac
ter
is
tic
f
ea
t
u
r
es,
g
e
n
er
al
izatio
n
,
s
o
r
tin
g
ap
p
ea
r
s
.
Fo
r
th
is
p
u
r
p
o
s
e,
clas
s
i
f
icatio
n
a
n
d
clu
s
ter
i
n
g
p
r
o
ce
s
s
es a
r
e
u
s
ed
to
p
er
f
o
r
m
t
h
e
r
eq
u
ir
ed
i
n
f
o
r
m
atio
n
tr
ea
t
m
e
n
t
f
o
r
later
an
al
y
s
is
b
y
a
s
p
ec
ialis
t.
P
ar
titi
o
n
in
g
o
b
s
er
v
atio
n
s
i
n
to
g
r
o
u
p
s
o
f
s
i
m
il
ar
o
b
j
ec
ts
m
a
k
es
it
p
o
s
s
ib
le
to
s
i
m
p
li
f
y
t
h
e
f
u
r
t
h
e
r
tr
ea
t
m
e
n
t
o
f
d
ata
an
d
d
ec
i
s
i
o
n
-
m
a
k
in
g
b
y
ap
p
l
y
in
g
to
ea
c
h
cl
u
s
ter
its
m
et
h
o
d
o
f
an
al
y
s
i
s
.
C
l
u
s
ter
in
g
is
t
h
e
p
r
o
ce
s
s
o
f
g
r
o
u
p
in
g
s
i
m
ilar
o
b
j
ec
ts
in
to
d
if
f
er
e
n
t
g
r
o
u
p
s
,
o
r
m
o
r
e
p
r
ec
is
el
y
,
t
h
e
p
ar
titi
o
n
in
g
o
f
a
d
ata
s
et
in
to
s
u
b
s
ets,
s
o
th
at
t
h
e
d
ata
in
ea
ch
s
u
b
s
e
t
a
cc
o
r
d
in
g
to
s
o
m
e
d
ef
i
n
ed
d
is
tan
ce
m
ea
s
u
r
e
[
1
3
].
T
h
e
s
tar
tin
g
p
o
in
t
o
f
o
u
r
ap
p
r
o
ac
h
is
to
co
n
d
u
ct
e
x
p
er
i
m
e
n
t
s
o
n
th
r
ee
d
i
f
f
er
e
n
t
al
g
o
r
ith
m
s
,
th
e
f
ir
s
t
is
b
ased
o
n
a
h
ier
ar
ch
ica
l
m
eth
o
d
,
w
e
u
s
e
H
A
C
al
g
o
r
ith
m
,
t
h
e
s
ec
o
n
d
i
s
b
ased
o
n
t
h
e
d
is
ta
n
ce
,
w
e
u
s
e
th
e
K
-
m
ea
n
s
alg
o
r
it
h
m
,
a
n
d
t
h
e
last
is
a
m
o
d
el
-
b
ased
m
et
h
o
d
,
th
e
E
M
al
g
o
r
ith
m
.
T
h
ese
a
l
g
o
r
ith
m
s
r
eq
u
ir
e
to
s
p
ec
if
y
th
e
n
u
m
b
er
o
f
cl
u
s
ter
s
as in
p
u
t p
ar
a
m
e
ter
s
.
T
h
e
ch
o
ice
o
f
th
e
cl
u
s
ter
i
n
g
m
et
h
o
d
u
s
ed
in
o
u
r
s
tu
d
y
i
s
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ased
o
n
t
h
e
e
v
alu
a
tio
n
o
f
t
h
e
q
u
alit
y
o
f
th
e
r
es
u
lt.
I
n
d
ee
d
th
e
e
v
al
u
ati
o
n
o
f
a
clu
s
ter
i
n
g
al
w
a
y
s
co
n
t
ain
s
a
p
ar
t
o
f
s
u
b
j
ec
tiv
i
t
y
an
d
th
at
i
t
is
i
m
p
o
s
s
ib
le
to
d
ef
in
e
a
u
n
i
v
er
s
al
cr
iter
io
n
w
h
ic
h
w
o
u
ld
allo
w
a
n
u
n
b
ia
s
ed
ev
al
u
atio
n
o
f
all
th
e
r
esu
l
ts
p
r
o
d
u
ce
d
b
y
all
th
e
m
et
h
o
d
s
o
f
clu
s
ter
i
n
g
.
Ho
w
e
v
er
,
a
n
u
m
b
er
o
f
cr
iter
ia
ex
is
t
an
d
ar
e
u
s
ed
r
ec
u
r
r
en
tl
y
b
y
m
a
n
y
r
esear
c
h
er
s
to
co
m
p
ar
e
t
h
e
r
es
u
lt
s
o
b
tain
ed
.
Sin
ce
t
h
er
e
ar
e
a
lar
g
e
n
u
m
b
er
o
f
p
o
s
s
ib
le
cl
u
s
ter
in
g
r
esu
lt
s
f
o
r
th
e
s
a
m
e
d
ataset,
th
e
g
o
al
i
s
to
ev
al
u
ate
w
h
et
h
er
o
n
e
o
f
th
e
s
e
r
es
u
lts
i
s
b
etter
th
an
an
o
t
h
er
.
B
o
th
alg
o
r
it
h
m
s
h
a
v
e
b
ee
n
i
m
p
le
m
en
ted
o
n
t
h
e
s
a
m
e
d
ataset
to
a
n
al
y
s
e
th
e
ir
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er
f
o
r
m
an
ce
s
,
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y
ta
k
i
n
g
s
a
m
e
n
u
m
b
er
o
f
clu
s
ter
s
(
3
clu
s
ter
s
)
an
d
s
a
m
e
n
u
m
b
er
o
f
iter
atio
n
s
.
A
f
ter
i
m
p
l
e
m
en
tatio
n
o
f
th
e
s
e
alg
o
r
ith
m
s
,
t
h
e
f
o
llo
w
in
g
r
es
u
lts
h
a
v
e
b
ee
n
o
b
tai
n
ed
(
T
ab
le
1
)
.
T
ab
le
1
.
C
o
m
p
ar
ativ
e
R
es
u
lt
s
of
B
o
th
A
lg
o
r
it
h
m
s
A
l
g
o
r
i
t
h
m
C
o
mp
u
t
a
t
i
o
n
t
i
me
(
ms)
Er
r
o
r
R
a
t
i
o
EM
1
5
1
4
0
,
2
1
K
m
e
a
n
s
8
1
4
0
,
3
4
H
A
C
9
8
0
0
,
4
I
n
th
i
s
co
m
p
ar
ati
v
e
s
t
u
d
y
f
o
u
n
d
th
a
t
E
M
alg
o
r
it
h
m
g
i
v
es
th
e
b
etter
p
er
f
o
r
m
a
n
ce
a
s
co
m
p
ar
e
to
K
-
Me
a
n
s
a
n
d
H
AC
w
i
th
m
in
i
m
u
m
er
r
o
r
r
ate
.
A
s
r
esu
lt
o
f
o
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r
ex
p
er
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m
e
n
t,
t
h
e
E
M
al
g
o
r
ith
m
s
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m
s
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e
th
e
m
o
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t
s
tr
o
n
g
e
s
t
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o
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s
ter
i
n
g
,
i
t
allo
w
s
th
e
p
r
o
ce
s
s
i
n
g
o
f
h
u
g
e
d
atab
ase
s
an
d
o
f
f
er
h
i
g
h
ac
cu
r
ac
y
.
T
h
e
E
M
alg
o
r
ith
m
is
d
e
f
i
n
ed
as: [
1
4
]
Giv
e
n
a
s
tati
s
tical
m
o
d
el
w
h
i
ch
g
e
n
er
ates
a
s
e
t
X
o
f
o
b
s
er
v
ed
d
ata,
a
s
et
o
f
u
n
o
b
s
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v
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laten
t
d
ata
or
m
i
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v
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Z
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an
d
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r
o
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eter
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alo
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it
h
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(
1
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(
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X
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(
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T
h
e
m
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li
k
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ate
(
ML
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o
f
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n
k
n
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n
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am
eter
s
is
d
eter
m
in
ed
b
y
t
h
e
m
ar
g
in
al
lik
eli
h
o
o
d
o
f
th
e
o
b
s
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v
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d
ata
(
2
)
:
L
(
θ
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X
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∑
p
(
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(
2
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T
h
e
E
M
alg
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r
ith
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s
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s
to
f
i
n
d
th
e
m
a
x
i
m
u
m
li
k
eli
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o
o
d
esti
m
ate
(
M
L
E
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o
f
th
e
m
ar
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al
lik
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h
o
o
d
b
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iter
ati
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el
y
ap
p
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w
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tatio
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E
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C
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h
e
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p
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th
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f
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w
i
th
r
esp
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th
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co
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cu
r
r
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p
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θ
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t)
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t
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θ
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t
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[
l
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(
θ
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(
3
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t
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d
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as
a
m
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s
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p
r
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m
.
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n
t
h
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t
h
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ith
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all
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ltip
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a
d
if
f
er
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n
t
n
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m
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cl
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s
.
T
h
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r
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co
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ased
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a
s
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cr
iter
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n
t
h
at
allo
w
s
y
o
u
to
ch
o
o
s
e
t
h
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est s
o
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tio
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.
T
h
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p
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ab
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f
r
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m
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On
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o
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i
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f
o
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m
atio
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s
u
c
h
B
I
C
(
B
ay
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n
I
n
f
o
r
m
a
tio
n
C
r
iter
io
n
)
[1
5
]
.
T
h
e
s
e
cr
iter
ia
ar
e
g
en
er
all
y
b
ased
o
n
s
tr
o
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tatis
t
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ases
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n
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ap
p
ly
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at
u
r
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p
r
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ab
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s
ter
i
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m
et
h
o
d
s
.
So
w
e
ch
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s
e
to
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s
e
t
h
e
m
o
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s
elec
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I
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to
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atic
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t th
e
n
u
m
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o
f
clu
s
t
er
s
.
B
IC
=
−
2
ln
(
)
+
ln
(
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(
5
)
w
it
h
L
is
th
e
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e
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o
d
f
u
n
ctio
n
,
N
i
s
t
h
e
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
,
K
i
s
t
h
e
n
u
m
b
e
r
o
f
clu
s
ter
s
to
b
e
esti
m
ated
.
3
.
2
.
Reg
re
s
s
io
n t
re
e
A
clas
s
i
f
icatio
n
o
r
r
eg
r
ess
io
n
tr
ee
is
a
p
r
ed
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n
m
o
d
el
th
at
ca
n
b
e
r
ep
r
esen
ted
as
a
d
e
cisi
o
n
tr
ee
.
R
eg
r
es
s
io
n
tr
ee
s
ar
e
f
o
r
d
ep
en
d
en
t
v
ar
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les
th
at
ta
k
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n
ti
n
u
o
u
s
o
r
o
r
d
er
e
d
d
is
cr
ete
v
alu
es,
w
it
h
p
r
ed
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n
er
r
o
r
ty
p
icall
y
m
ea
s
u
r
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b
y
th
e
s
q
u
ar
ed
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
o
b
s
er
v
ed
an
d
p
r
ed
icted
v
alu
es.
A
r
e
g
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io
n
tr
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s
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ilt
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n
a
n
iter
ati
v
e
w
a
y
,
b
y
d
iv
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i
n
g
i
n
ea
c
h
s
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t
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e
p
o
p
u
latio
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i
n
t
o
t
w
o
o
r
k
s
u
b
s
et
s
.
T
h
e
d
iv
is
io
n
is
ca
r
r
i
ed
o
u
t
ac
co
r
d
in
g
to
s
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m
p
le
r
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les
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n
ex
p
lan
a
to
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y
v
ar
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b
y
d
eter
m
in
i
n
g
th
e
o
p
tim
a
l
r
u
le
w
h
ic
h
m
a
k
es
it
p
o
s
s
ib
le
to
co
n
s
tr
u
ct
t
w
o
o
r
m
o
r
e
m
o
s
t
d
i
f
f
er
e
n
tiated
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o
p
u
latio
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s
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n
ter
m
s
o
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v
alu
e
s
o
f
t
h
e
v
ar
iab
le
to
b
e
ex
p
lain
ed
.
T
h
e
ev
alu
at
io
n
cr
iter
ia
o
f
a
r
e
g
r
ess
io
n
tr
ee
ar
e
t
h
e
a
v
er
ag
e
e
r
r
o
r
r
ate
an
d
th
e
r
ed
u
ctio
n
o
f
er
r
o
r
.
T
h
e
er
r
o
r
r
ate
in
d
icate
s
th
e
a
v
er
ag
e
d
ev
iatio
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b
et
w
ee
n
th
e
o
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s
er
v
ed
v
al
u
e
an
d
t
h
e
tr
u
e
v
al
u
e
o
f
th
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v
ar
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le
to
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I
f
th
e
er
r
o
r
r
ate
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clo
s
e
to
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en
th
i
s
m
ea
n
s
t
h
at
t
h
e
p
r
ed
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n
m
o
d
el
(
th
e
tr
ee
)
is
ac
cu
r
ate.
T
h
e
r
ed
u
ctio
n
o
f
er
r
o
r
:
1
-
R
2
,
w
it
h
R
2
t
h
e
co
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f
f
icien
t
o
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d
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m
i
n
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w
h
ic
h
m
ea
s
u
r
es
th
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p
r
o
p
o
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tio
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o
f
v
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ce
e
x
p
lai
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b
y
th
e
m
o
d
el
t
h
at
i
s
to
s
a
y
t
h
e
q
u
al
it
y
o
f
t
h
e
r
e
g
r
ess
io
n
.
Am
o
n
g
t
h
e
m
et
h
o
d
s
f
o
r
co
n
s
tr
u
ct
in
g
a
r
eg
r
es
s
io
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t
r
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th
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t
w
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m
o
s
t c
o
m
m
o
n
tech
n
iq
u
e
s
ar
e
C
A
R
T
[
16]
an
d
A
I
D
[
1
7
]
.
I
n
o
u
r
ca
s
e,
w
e
u
s
e
C
AR
T
to
b
u
ild
th
e
r
eg
r
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io
n
tr
ee
.
A
d
ec
is
io
n
tr
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b
u
ilt
w
it
h
th
e
C
AR
T
alg
o
r
ith
m
ca
n
w
o
r
k
w
it
h
all
ty
p
e
s
o
f
v
ar
iab
les:
q
u
alita
tiv
e,
o
r
d
in
a
l
an
d
co
n
tin
u
o
u
s
q
u
a
n
ti
tativ
e.
T
hi
s
m
et
h
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d
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ak
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s
it p
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s
ib
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to
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te
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s
m
ix
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o
f
in
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atio
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.
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g
en
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al
p
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in
cip
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o
f
C
AR
T
is
to
p
a
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titi
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n
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u
r
s
iv
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l
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th
e
in
p
u
t
s
p
ac
e
in
a
b
in
ar
y
w
a
y
,
th
e
n
d
eter
m
in
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a
n
o
p
ti
m
al
s
u
b
s
et
f
o
r
th
e
p
r
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n
.
B
u
ild
in
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a
C
AR
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tr
ee
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d
o
n
e
in
t
w
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s
tep
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A
f
ir
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t p
h
a
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t
h
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co
n
s
tr
u
ct
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o
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a
m
a
x
i
m
al
tr
ee
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w
h
ic
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a
x
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izes
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o
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en
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t
y
o
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p
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ataset,
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n
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ase,
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p
r
u
n
ed
f
r
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m
th
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m
a
x
i
m
al
tr
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.
3
.
3
.
G
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W
e
tak
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th
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d
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n
itio
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s
p
r
o
p
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s
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in
[
3
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o
f
a
d
ata
cu
b
e.
C
is
a
d
ata
cu
b
e
w
it
h
:
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p
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m
}.
H
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Di.
H
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L
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a
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s
A
ij
.
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66
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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2
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u
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An
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ce
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s
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p
ly
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s
u
p
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lear
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m
eth
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ter
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d
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p
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lear
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eth
o
d
: Re
g
r
es
s
io
n
tr
ee
.
RE
F
E
R
E
NC
E
S
[1
]
Kim
b
a
ll
R.
,
“
T
h
e
Da
ta
W
a
re
h
o
u
se
T
o
o
lk
it
,
”
Jo
h
n
W
il
e
y
&
S
o
n
s
,
1
9
9
6
.
[2
]
In
m
o
n
W
.
H.,
“
Bu
il
d
in
g
t
h
e
Da
ta W
a
re
h
o
u
se
,
”
Jo
h
n
W
il
e
y
&
S
o
n
s
,
1
9
9
6
.
[3
]
Ha
n
J.,
“
O
LA
P
M
in
in
g
:
a
n
In
teg
ra
ti
o
n
o
f
OLA
P
w
it
h
Da
ta
M
in
in
g
,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
7
th
IFI
P
Co
n
fer
e
n
c
e
o
n
Da
ta
S
e
ma
n
t
ics
,
L
e
y
sin
,
S
wit
ze
rla
n
d
,
1
9
9
7
.
[4
]
G
.
S
a
th
e
a
n
d
S
.
S
a
ra
w
a
g
i
,
“
In
telli
g
e
n
t
ro
ll
u
p
s
i
n
m
u
lt
id
im
e
n
sio
n
a
l
OL
A
P
d
a
ta
,”
Pro
c
e
e
d
in
g
s
o
f
th
e
2
7
t
h
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
Ver
y
L
a
rg
e
D
a
ta
Ba
se
s,
M
o
rg
a
n
Ka
u
f
ma
n
n
Pu
b
li
sh
e
rs
In
c
.,
p
p
.
5
3
1
-
5
4
0
,
2
0
0
1
.
[5
]
S
.
G
o
il
a
n
d
A
.
Ch
o
u
d
h
a
ry
,
“
P
A
RS
IM
ON
Y
:
a
n
in
f
ra
stru
c
tu
re
f
o
r
p
a
ra
ll
e
l
m
u
lt
id
im
e
n
sio
n
a
l
a
n
a
l
y
sis
a
n
d
d
a
ta
m
in
in
g
,”
J
.
Pa
ra
ll
e
l
Distri
b
.
C
o
m
p
u
t.
,
v
o
l/
issu
e
:
6
1
(3
)
,
p
p
.
2
8
5
-
3
2
1
,
2
0
0
1
.
[6
]
R.
B
.
M
e
ss
a
o
u
d
,
“
Co
u
p
lag
e
d
e
l’an
a
ly
s
e
e
n
li
g
n
e
e
t
la
f
o
u
il
le
d
e
d
o
n
n
é
e
s
p
o
u
r
l’ex
p
l
o
it
a
ti
o
n
,
l’ag
ré
g
a
ti
o
n
e
t
l’ex
p
li
c
a
ti
o
n
d
e
s d
o
n
n
é
e
s c
o
m
p
lex
e
s
,”
P
h
D t
h
e
sis,
Un
iv
e
rsité L
u
m
ière
Ly
o
n
2
,
Ly
o
n
,
F
ra
n
c
e
,
2
0
0
6
.
[7
]
S
a
ra
wa
g
i
S
.
,
e
t
a
l
.,
“
Disc
o
v
e
r
y
-
d
riv
e
n
Ex
p
lo
ra
ti
o
n
o
f
OLA
P
Da
ta
Cu
b
e
s,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
6
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Exte
n
d
in
g
Da
t
a
b
a
se
T
e
c
h
n
o
l
o
g
y
(
EDBT
'
1
9
9
8
),
V
a
l
e
n
c
ia
,
S
p
a
in
:
S
p
ri
n
g
e
r
,
p
p
.
1
6
8
-
1
8
2
,
1
9
9
8
.
[8
]
Ch
e
n
g
S
.
,
“
S
tatisti
c
a
l
A
p
p
ro
a
c
h
e
s
to
P
re
d
ictiv
e
M
o
d
e
li
n
g
in
L
a
rg
e
D
a
tab
a
se
s,
”
M
a
ste
r’s
th
e
sis
,
S
im
o
n
F
ra
se
r
Un
iv
e
rsit
y
,
Br
it
ish
Co
lu
m
b
ia,
Ca
n
a
d
a
,
1
9
9
8
.
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
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g
,
Vo
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9
,
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3
,
J
u
n
e
2
0
1
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:
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2102
[9
]
J.
Ha
n
,
e
t
a
l
.
,
“
Cu
b
e
e
x
p
lo
re
r:
o
n
l
in
e
e
x
p
lo
ra
ti
o
n
o
f
d
a
ta
c
u
b
e
s
,”
S
IGM
OD
‟
0
2
:
Pro
c
e
e
d
in
g
s
o
f
th
e
2
0
0
2
ACM
S
IG
M
OD
in
ter
n
a
ti
o
n
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l
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o
n
fer
e
n
c
e
o
n
M
a
n
a
g
e
me
n
t
o
f
d
a
ta
,
Ne
w
Y
o
rk
,
NY
,
US
A
,
p
p
.
6
2
6
-
6
2
6
,
2
0
0
2
.
[1
0
]
Y.
Ch
e
n
a
n
d
J.
P
e
i
,
“
Re
g
re
ss
i
o
n
c
u
b
e
s
w
it
h
lo
ss
l
e
ss
c
o
m
p
re
ss
io
n
a
n
d
a
g
g
re
g
a
ti
o
n
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Kn
o
wled
g
e
a
n
d
D
a
ta
En
g
i
n
e
e
rin
g
,
v
o
l/
iss
u
e
:
1
8
(1
2
)
,
p
p
.
1
5
8
5
-
1
5
9
9
,
2
0
0
6
.
[1
1
]
A
.
S
a
ir,
e
t
a
l
.
,
“
P
re
d
ictio
n
in
O
LA
P
C
ube
,
”
IJ
CS
I
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
S
c
ien
c
e
Iss
u
e
s
,
v
ol
/i
ss
u
e
:
9
(
3
)
,
2
0
1
2
.
[1
2
]
R.
M
issa
o
u
i,
e
t
a
l
.
,
“
A
P
ro
b
a
b
il
ist
ic M
o
d
e
l
f
o
r
Da
ta Cu
b
e
Co
m
p
re
s
sio
n
a
n
d
Qu
e
ry
A
p
p
ro
x
i
m
a
ti
o
n
,
”
Pro
c
e
e
d
in
g
s o
f
th
e
Co
u
p
l
in
g
OLA
P
a
n
d
d
a
ta
mi
n
in
g
f
o
r
p
re
d
ict
io
n
1
5
1
0
t
h
AC
M
In
ter
n
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
D
a
ta
W
a
re
h
o
u
sin
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8
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,”
L
a
b
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ra
to
ire
ERIC,
Un
iv
e
rsité
L
u
m
ière
Ly
o
n
2
.
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