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p
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C
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[
1
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.
Mo
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[
2
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.
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w
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[
3
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4
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[
5
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SP
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7
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P
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[
8
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P
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[
9
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etc.
R
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B
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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C
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[
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ti
m
e
b
ec
au
s
e
th
e
iter
ati
v
e
p
r
o
ce
s
s
w
a
s
r
ep
ea
ted
f
o
r
lo
ts
o
f
d
ata.
Mo
r
eo
v
er
,
th
e
n
u
m
b
er
o
f
g
e
n
er
ated
s
eq
u
e
n
tia
l
p
atter
n
s
w
a
s
o
v
er
m
u
c
h
a
n
d
m
o
s
tl
y
t
h
e
y
w
er
e
s
h
o
r
t
an
d
tr
i
v
ial
to
u
s
er
s
s
o
th
at
t
h
e
y
b
u
r
d
en
ed
t
h
e
n
e
x
t
class
i
f
icatio
n
p
r
o
ce
s
s
.
Hen
ce
,
th
e
cla
s
s
i
f
icatio
n
p
r
o
ce
s
s
u
s
i
n
g
A
p
r
io
r
iL
i
k
e
s
e
q
u
en
tial
p
atter
n
m
i
n
i
n
g
to
o
k
lo
n
g
er
ti
m
e.
Mo
r
eo
v
er
,
f
r
o
m
b
u
s
i
n
es
s
p
o
in
t
o
f
v
ie
w
,
u
s
er
s
o
f
d
ata
m
i
n
in
g
s
o
m
eti
m
es
o
n
l
y
r
eq
u
ir
e
th
e
d
ata
an
al
y
s
is
f
r
o
m
a
ce
r
tai
n
p
er
s
p
ec
tiv
e.
T
h
is
v
ie
w
p
o
in
t
i
s
ad
o
p
ted
f
r
o
m
th
e
o
r
g
an
izatio
n
n
ee
d
s
.
Fo
r
ex
a
m
p
le,
u
s
er
s
ar
e
g
en
er
all
y
m
o
r
e
in
ter
ested
in
g
etti
n
g
k
n
o
w
led
g
e
o
f
t
h
e
late
s
t
d
ata
t
h
an
o
f
th
e
o
ld
o
n
es.
T
h
er
ef
o
r
e,
th
er
e
'
s
a
n
ec
es
s
it
y
to
i
m
p
r
o
v
e
s
eq
u
e
n
tial
p
atter
n
m
i
n
i
n
g
p
er
f
o
r
m
a
n
ce
i
n
p
r
ep
r
o
ce
s
s
i
n
g
b
y
i
m
p
r
o
v
i
n
g
ex
ec
u
tio
n
ti
m
e
to
g
et
s
eq
u
en
tial p
atter
n
s
a
n
d
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
s
eq
u
e
n
tia
l p
atter
n
s
to
o
n
l
y
th
o
s
e
th
at
s
atis
f
y
th
e
u
s
er
's n
ee
d
.
C
o
n
s
tr
ain
t
i
n
s
eq
u
e
n
tial
p
atter
n
m
i
n
i
n
g
i
s
ex
p
ec
ted
to
an
s
wer
th
is
n
ec
e
s
s
it
y
.
T
h
e
s
eq
u
en
t
ial
p
atter
n
m
i
n
in
g
al
g
o
r
it
h
m
is
d
e
v
elo
p
ed
b
ased
o
n
P
r
o
g
r
ess
iv
e
Min
i
n
g
o
f
Seq
u
e
n
tial
P
atter
n
s
,
P
I
S
A
.
P
I
SA
a
lg
o
r
it
h
m
ar
r
an
g
es
a
s
eq
u
e
n
ce
d
atab
ase
in
t
h
e
f
o
r
m
o
f
P
r
o
g
r
ess
i
v
e
Seq
u
en
ce
T
r
ee
,
P
S
-
tr
ee
,
an
d
d
o
es
n
o
t
g
e
n
er
ate
s
eq
u
en
ce
ca
n
d
id
ates
s
o
t
h
at
t
h
e
m
i
n
in
g
p
r
o
ce
s
s
b
ec
o
m
es
f
aster
.
W
e
n
a
m
ed
t
h
e
s
in
g
le
c
o
n
s
tr
ain
t
p
r
o
g
r
ess
iv
e
m
i
n
in
g
o
f
s
eq
u
e
n
tial
p
atter
n
s
,
as
P
I
SA*
.
I
n
ad
d
itio
n
to
its
ab
ilit
y
to
g
e
n
er
ate
s
eq
u
en
t
ial
p
atter
n
s
t
h
at
s
ati
s
f
y
th
e
u
s
er
s’
n
ee
d
,
co
n
s
tr
ai
n
t
ca
n
r
ed
u
ce
th
e
n
u
m
b
er
o
f
s
h
o
r
t
an
d
t
r
iv
ial
s
eq
u
e
n
tial
p
atter
n
s
[
1
3
]
.
T
h
e
l
ess
er
n
u
m
b
er
o
f
s
eq
u
e
n
tia
l
p
atter
n
s
w
ill
r
ed
u
ce
w
o
r
k
lo
ad
o
f
th
e
n
ex
t
cla
s
s
i
f
icat
io
n
p
r
o
ce
s
s
.
I
t
is
b
eliev
ed
th
at
t
h
e
class
i
f
icatio
n
p
r
o
ce
s
s
w
ill
b
e
f
aster
w
it
h
b
etter
ac
c
u
r
ac
y
le
v
el.
T
h
er
ef
o
r
e,
t
h
is
s
t
u
d
y
is
e
x
p
ec
ted
to
p
r
o
v
id
e
s
o
lu
tio
n
s
to
t
h
e
p
r
o
b
le
m
(
1
)
w
h
et
h
er
s
eq
u
e
n
tial
p
atter
n
m
i
n
in
g
,
e
s
p
ec
iall
y
P
I
SA*
ca
n
lo
w
er
t
h
e
n
u
m
b
er
o
f
s
eq
u
en
tial
p
atter
n
s
an
d
,
(
2
)
im
p
r
o
v
e
clas
s
if
icatio
n
t
i
m
e
p
er
f
o
r
m
an
ce
a
n
d
m
ain
tain
ac
c
u
r
ac
y
le
v
el
o
f
th
e
class
i
f
icatio
n
p
r
o
ce
s
s
.
I
n
o
r
d
er
to
s
o
lv
e
t
h
e
p
r
o
b
le
m
,
w
e
p
r
o
p
o
s
e
a
m
et
h
o
d
C
la
s
s
i
f
y
-
By
-
Seq
u
e
n
ce
_
C
la
s
s
*
,
C
B
S_
C
L
A
S
S
*
w
h
ic
h
in
teg
r
at
es P
I
SA*
to
f
i
n
d
s
eq
u
e
n
tial p
a
tter
n
s
a
n
d
class
i
f
icat
io
n
p
r
o
ce
s
s
.
T
h
e
o
b
j
ec
tiv
e
o
f
th
is
r
esear
ch
is
to
class
if
y
d
ata
b
ased
o
n
s
eq
u
en
tial
p
atter
n
s
th
at
w
er
e
f
o
u
n
d
u
s
in
g
P
I
SA*
.
T
h
er
ef
o
r
e,
C
B
S_
C
L
ASS
is
m
o
d
if
ied
to
in
te
g
r
ate
P
I
SA*
al
g
o
r
ith
m
a
n
d
clas
s
if
ic
atio
n
p
r
o
ce
s
s
.
T
h
is
s
tu
d
y
is
e
x
p
ec
ted
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
clas
s
i
f
icat
io
n
’
s
to
tal
ex
ec
u
tio
n
t
i
m
e
w
h
i
le
m
ai
n
tai
n
in
g
t
h
e
ac
cu
r
ac
y
le
v
el.
T
h
is
p
ap
er
is
o
r
g
an
is
ed
a
s
f
o
ll
o
w
s
.
Sectio
n
I
co
n
tain
s
i
n
tr
o
d
u
ctio
n
,
r
elate
d
w
o
r
k
,
C
B
S
ap
p
r
o
ac
h
an
d
P
I
SA*
.
Sectio
n
I
I
ex
p
lain
s
a
b
o
u
t
C
B
S_
C
L
A
SS
*
w
it
h
P
I
SA*
:
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
Sectio
n
I
I
I
ex
p
lain
s
ab
o
u
t
th
e
r
esu
lts
a
n
d
an
al
y
s
i
s
.
Sectio
n
I
V
co
n
tai
n
s
co
n
c
lu
s
io
n
o
f
t
h
is
p
ap
er
an
d
f
u
tu
r
e
r
ese
ar
ch
.
1
.
1
.
Rela
t
ed
Wo
rk
Seq
u
en
t
ial
p
atter
n
m
i
n
i
n
g
is
o
n
e
o
f
th
e
d
ev
elo
p
m
e
n
t
o
f
f
r
eq
u
en
t
ite
m
s
e
t
m
i
n
i
n
g
[
5
]
.
Den
o
ted
b
y
I
=
{i
1
,
i
2
,
.
.
.
,
i
k
}
w
h
ic
h
is
a
s
et
o
f
all
ite
m
s
,
s
u
b
s
et
o
f
I
is
c
alled
ite
m
s
e
t.
Seq
u
e
n
ce
α
=
⟨
t
1
,
t
2
,
.
.
.
,
t
m
⟩
w
h
er
e
(t
i
⊆
I
)
is
o
r
d
er
ed
lis
t
.
E
ac
h
ite
m
s
e
t
in
a
s
eq
u
e
n
ce
r
ep
r
esen
ts
t
h
e
s
et
o
f
e
v
en
ts
t
h
at
o
cc
u
r
at
th
e
s
a
m
e
ti
m
e
(
s
a
m
e
ti
m
es
ta
m
p
)
.
Di
f
f
er
e
n
t
ite
m
s
et
ap
p
ea
r
s
at
d
if
f
er
e
n
t
t
i
m
e
[
1
4
]
.
Seq
u
en
ce
α
=
⟨
a
1
,
a
2
,
.
.
.
,
a
n
⟩
is
a
s
u
b
s
eq
u
en
ce
o
f
s
eq
u
e
n
ce
=
⟨
b
1
, b
2
, . . . , b
m
⟩
i
f
t
h
er
e
e
x
is
t
i
n
teg
er
s
i
1
< i
2
<
…
<
i
n
s
u
ch
t
h
at
a
1
b
i1
, a
2
b
i2
,
…,
a
n
b
in
[
6
]
.
R
esear
ch
o
n
t
h
e
m
i
n
in
g
s
eq
u
en
ce
a
s
f
ea
t
u
r
es
f
o
r
class
i
f
i
ca
tio
n
h
ad
b
ee
n
d
o
n
e
to
cla
s
s
i
f
y
s
tep
s
s
eq
u
en
ce
i
n
o
r
d
er
to
p
r
ed
ict
w
h
et
h
er
t
h
e
s
tep
s
w
i
ll
lead
t
o
v
icto
r
y
o
r
d
e
f
ea
t
[
2
]
.
T
h
e
s
t
u
d
y
i
n
tr
o
d
u
ce
d
a
Featu
r
e
Mi
n
i
n
g
ap
p
r
o
ac
h
.
I
n
th
is
s
t
u
d
y
,
t
h
er
e
w
er
e
3
s
te
p
s
tak
e
n
,
i.e
.
(
1
)
th
e
r
ep
ea
te
d
s
i
m
u
latio
n
s
tep
to
g
en
er
ate
e
x
ec
u
t
io
n
tr
ac
es,
(
2
)
m
i
n
in
g
t
h
e
s
i
m
u
lated
ex
ec
u
tio
n
tr
ac
es
to
o
b
tain
f
ea
tu
r
e
s
an
d
(
3
)
t
r
ain
class
i
f
ier
u
s
i
n
g
f
ea
t
u
r
es
to
p
r
ed
ict
t
h
e
s
u
cc
es
s
o
r
f
a
ilu
r
e
o
f
s
i
m
u
la
ted
tr
ac
es.
T
h
is
s
tu
d
y
u
s
ed
t
w
o
p
r
o
ce
s
s
es,
s
eq
u
e
n
tial
p
atter
n
m
i
n
i
n
g
p
r
o
ce
s
s
to
o
b
tain
s
eq
u
e
n
tial
p
atter
n
s
t
h
at
co
r
r
elate
w
it
h
tar
g
e
t
clas
s
an
d
th
e
clas
s
i
f
icatio
n
p
r
o
ce
s
s
u
s
i
n
g
f
ea
tu
r
e
s
o
b
tain
ed
f
r
o
m
t
h
e
p
r
ev
io
u
s
p
r
o
c
ess
[
2
]
.
Ho
w
e
v
er
,
C
B
S
w
as
p
r
o
v
en
to
h
a
v
e
b
etter
ac
cu
r
ac
y
p
er
f
o
r
m
a
n
ce
t
h
a
n
th
e
Featu
r
e
Mi
n
i
n
g
s
i
n
ce
C
B
S
in
te
g
r
ates
A
p
r
io
r
iL
i
k
e
s
eq
u
en
tial
p
atter
n
m
in
in
g
w
it
h
p
r
o
b
ab
ilis
tic
in
d
u
ctio
n
s
o
th
at
s
eq
u
e
n
tia
l p
atter
n
s
ca
n
b
e
u
s
ed
as a
clas
s
if
ier
r
u
le
[
1
1
]
.
1
.
2
.
Cla
s
s
if
y
-
b
y
-
Sequ
ence
,
C
bs
A
pp
ro
a
ch
C
las
s
i
f
y
-
by
-
Seq
u
en
ce
,
C
B
S,
is
a
class
i
f
icatio
n
p
r
o
ce
s
s
th
at
b
u
ild
s
m
o
d
el
f
r
o
m
s
eq
u
e
n
tia
l
p
atter
n
s
.
As
s
h
o
w
n
i
n
Fi
g
u
r
e
1
,
C
B
S
p
er
f
o
r
m
s
t
w
o
p
r
o
ce
s
s
es
s
eq
u
e
n
tiall
y
,
(
1
)
s
ea
r
ch
es
f
o
r
s
eq
u
e
n
t
ial
p
atter
n
s
t
h
r
o
u
g
h
A
p
r
io
r
iL
i
k
e
s
eq
u
e
n
tial
p
atter
n
m
i
n
i
n
g
,
(
2
)
class
i
f
ie
s
b
ased
o
n
t
h
e
s
eq
u
e
n
tial
p
atter
n
s
w
h
i
c
h
ac
t
as
a
clas
s
i
f
ier
r
u
le
[
1
1
]
.
Seq
u
en
tial
p
atter
n
s
th
at
ar
e
o
b
tain
ed
f
r
o
m
A
p
r
io
r
i
L
i
k
e
s
eq
u
e
n
tia
l
p
atter
n
m
in
in
g
ar
e
also
ca
lled
as
C
las
s
i
f
iab
le
Seq
u
en
t
ial
P
atter
n
s
,
C
SP
.
A
p
r
io
r
iL
i
k
e
s
ee
k
s
s
e
q
u
en
tial
p
atter
n
s
w
i
th
le
n
g
th
-
(
n
+1
)
f
r
o
m
le
n
g
th
-
n
.
B
y
t
h
e
iter
ati
v
e
p
r
o
ce
s
s
,
A
p
r
io
r
iL
i
k
e
r
eq
u
ir
es a
lo
n
g
ti
m
e
to
g
et
s
eq
u
e
n
tia
l p
atter
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
2
1
4
2
–
2
1
5
1
2144
Fig
u
r
e
1
.
C
B
S Sch
e
m
e
[
1
3
]
Data
t
h
at
ar
e
p
r
o
ce
s
s
ed
in
C
B
S
ar
e
ca
teg
o
r
ical
d
ata
.
E
ac
h
r
ec
o
r
d
is
as
s
o
ciate
d
to
a
p
ar
ticu
lar
cla
s
s
lab
el.
Den
o
te
D
i
t
h
at
co
n
s
is
t
s
o
f
a
ti
m
e
s
er
ies
o
f
d
ata
as
s
o
ciate
d
w
it
h
cla
s
s
n
,
D
=
{
D
1
,
D
2
,D
3
,
…,
D
n
}
.
A
p
r
io
r
iL
i
k
e
s
ea
r
ch
e
s
f
o
r
C
las
s
if
iab
le
Seq
u
e
n
tia
l
P
atter
n
s
(
C
SP
)
as
c
lass
if
ier
r
u
le
s
.
T
h
er
ef
o
r
e,
a
s
eq
u
en
tial
p
atter
n
i c
o
r
r
esp
o
n
d
s
to
class
m
,
SP
i
C
m
,
w
it
h
SP
i
is
a
s
eq
u
en
ce
o
f
a
1
a
3
a
7
a
n
d
C
m
is
th
e
clas
s
m
[
1
1
]
.
C
B
S a
lg
o
r
it
h
m
is
d
i
v
id
ed
in
to
t
w
o
t
y
p
es,
n
a
m
el
y
C
B
S_
A
L
L
an
d
C
B
S_
C
L
ASS.
C
B
S_
AL
L
m
i
n
es a
l
l
d
ata
in
t
h
e
d
atab
ase
w
h
ile
C
B
S_
C
L
ASS
f
ir
s
t
d
iv
id
es
th
e
d
ata
b
ased
o
n
co
r
r
esp
o
n
d
in
g
class
to
b
e
m
i
n
ed
f
u
r
t
h
er
.
Sin
ce
C
B
S_
C
L
A
S
S
b
u
ild
s
clas
s
i
f
icatio
n
m
o
d
el
f
r
o
m
ea
ch
cla
s
s
,
C
B
S_
C
L
ASS
was
p
r
o
v
en
to
ac
h
iev
e
b
etter
ac
cu
r
ac
y
co
m
p
ar
ed
to
C
B
S_
AL
L
[
1
1
]
.
T
h
e
C
B
S_
C
L
A
S
S
m
eth
o
d
is
a
s
f
o
llo
w
s
,
(
1
)
d
iv
id
es
th
e
d
ata
b
ased
o
n
t
h
e
co
r
r
esp
o
n
d
in
g
c
l
ass
o
r
lab
el,
(
2
)
f
r
o
m
ea
ch
cla
s
s
,
A
p
r
io
r
iLik
e
s
ea
r
ch
e
s
th
e
s
eq
u
en
tial
p
atter
n
s
,
(
3
)
class
i
f
ies
d
ata
u
s
i
n
g
t
h
e
s
e
q
u
en
tial
p
atter
n
s
t
h
at
ac
t
a
s
C
lass
i
f
iab
le
Seq
u
e
n
tial
P
atter
n
s
,
C
SP
.
T
h
e
C
SP
is
u
s
ed
as
a
clas
s
i
f
ier
r
u
le.
T
o
f
i
n
d
s
eq
u
e
n
tial
p
atter
n
s
,
A
p
r
io
r
iL
i
k
e
u
s
e
s
t
h
e
m
in
i
m
u
m
s
u
p
p
o
r
t.
E
ac
h
C
SP
w
il
l
b
e
g
iv
en
a
s
co
r
e
b
ased
o
n
th
e
len
g
t
h
o
f
s
eq
u
e
n
tial
p
atte
r
n
.
T
h
en
,
C
SP
s
co
r
e
is
n
o
r
m
alize
d
s
o
th
at
t
h
e
m
ax
i
m
u
m
s
co
r
e
is
1
[
1
1
]
.
Fig
u
r
e
2
s
h
o
w
s
ab
o
u
t
C
B
S_
C
L
A
SS
al
g
o
r
it
h
m
t
h
at
c
o
n
s
is
ts
o
f
A
p
r
io
r
iLik
e
al
g
o
r
ith
m
a
n
d
class
i
f
icatio
n
p
r
o
ce
s
s
[
1
1
]
.
Fig
u
r
e
2
.
C
B
S_
C
L
ASS al
g
o
r
it
h
m
[
1
1
]
Input:
dataset, minimum support
Output:
class of sequential patterns
Method:
CBS_CLASS
(Dataset D, min_sup)
{
For
each c
i
ϵ class_
set(D)
do
D
i
=
class_dataset(D,
c
i
);
CSP
i
=
FindSP(D
i
,
mi
n
_s
up
)
//to get CSP using AprioriLike
End
}
//Start
program
of
AprioriLike
algorithm
for
finding
sequential patterns
FindSP
(Dataset D, min_sup)
{
Sp
1
= {large
-
1
it
em
s
}
For
(i=2; Sp
i
-
1
;i
++)
do
SP_C
i
= gen
_candidat
eSP(Sp
i
-
1
);
For
each data d
ϵ
D
do
SP
s
= SP_C
i
∩ subseq(
d);
For
each sp
ϵ
SP
s
do
Sp.sup++;
End
End
Sp
i
= {sp | sp
ϵ
SP
s
,
s
p.
su
p
≥
mi
n
su
p}
End
Return
∪
SP
i
}
//This is the end of AprioriLike algorithm
//S
tart program for classifying test data
Class_of_sequence
(x
)
{
Total_score = new array[class_count(D)];
For
each csp
i
ϵ CSP
do
Total_score[csp
i
.c
la
ss
]
+=
c
sp
i
.sp.lengt
h;
End
Score_array[]=new
array
[class_count(D)];
For
each csp
i
ϵ CSP
do
If
csp
i
ϵ subseq(
x
)
For
each c
m
ϵ belong
_class_set(csp
i
)
Score_array
y[m]
+=
csp
i
.sp.length/total
_score[m];
//count score for test data
End
End if
End
k = index_of(max{score_array[]});
return c
k
;
}
//End program for classifying test data
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
C
la
s
s
i
fica
tio
n
w
ith
S
in
g
le
C
o
n
s
tr
a
in
t P
r
o
g
r
ess
ive
Min
in
g
o
f S
eq
u
en
tia
l P
a
tter
n
s
(
R
eg
in
a
Yu
lia
Ya
s
min
)
2145
1
.
3
.
P
ro
g
re
s
s
iv
e
M
ini
ng
o
f
Sequ
ent
ia
l P
a
t
t
er
ns
,
P
I
SA
A
co
n
s
tr
ai
n
t
i
s
a
li
m
i
tatio
n
s
et
b
y
u
s
er
b
ef
o
r
e
t
h
e
m
in
in
g
p
r
o
ce
s
s
b
eg
in
s
.
C
o
n
s
tr
ai
n
t
i
n
s
eq
u
en
tial
p
atter
n
m
i
n
in
g
is
e
x
p
ec
ted
to
r
ed
u
ce
th
e
n
u
m
b
er
o
f
s
eq
u
e
n
tial
p
atter
n
s
[
1
3
]
.
T
h
er
e
ar
e
m
an
y
t
y
p
e
s
o
f
u
s
er
co
n
s
tr
ain
ts
,
s
u
c
h
as
ite
m
,
len
g
th
,
s
u
p
er
-
p
atter
n
,
ag
g
r
eg
ate,
r
eg
u
lar
ex
p
r
es
s
io
n
,
d
u
r
atio
n
an
d
g
ap
co
n
s
tr
ai
n
t
[
1
5
]
.
C
o
n
s
tr
ain
t
ca
n
b
e
ei
th
er
(
1
)
ite
m
co
n
s
tr
ain
t,
is
a
li
m
ita
tio
n
w
h
er
e
a
s
eq
u
en
tial
p
atter
n
s
h
o
u
ld
co
n
tai
n
o
r
n
o
t
co
n
tai
n
ce
r
tain
ite
m
,
(
2
)
l
en
g
t
h
les
s
co
n
s
tr
ain
t,
r
eq
u
ir
es
th
at
th
e
le
n
g
th
o
f
s
eq
u
e
n
tial
p
atter
n
s
h
o
u
ld
b
e
s
h
o
r
ter
th
an
t
h
e
g
i
v
en
v
alu
e,
(
3
)
len
g
th
m
o
r
e
co
n
s
tr
ai
n
t,
r
eq
u
ir
es
th
at
t
h
e
len
g
t
h
o
f
s
eq
u
e
n
tial
p
atter
n
s
h
o
u
ld
b
e
lo
n
g
er
th
a
n
th
e
g
iv
e
n
v
al
u
e,
(
4
)
s
u
p
er
-
p
atter
n
co
n
s
tr
ain
t,
i
s
a
c
o
n
s
tr
ain
t
ad
o
p
ted
to
lo
o
k
f
o
r
s
eq
u
e
n
tia
l
p
atter
n
th
a
t
co
n
tai
n
s
a
p
ar
ticu
l
ar
p
atter
n
as
a
s
et
o
f
s
u
b
-
p
atte
r
n
,
(
5
)
ag
g
r
e
g
ate
co
n
s
tr
ain
t,
is
a
co
n
s
tr
ai
n
t
o
n
th
e
ag
g
r
e
g
ate
o
f
ite
m
s
in
t
h
e
p
att
er
n
,
(
6
)
r
eg
u
lar
ex
p
r
ess
io
n
co
n
s
tr
ai
n
t,
is
a
co
n
s
tr
ain
t
w
it
h
r
eg
u
lar
e
x
p
r
ess
io
n
,
s
u
c
h
as
d
is
j
u
n
tio
n
a
n
d
Klee
n
e
clo
s
u
r
e
o
f
th
e
s
e
t
o
f
ite
m
s
,
(
7
)
d
u
r
atio
n
co
n
s
tr
ai
n
t,
is
a
co
n
s
tr
ain
t
o
n
th
e
s
eq
u
en
ce
d
atab
ase
t
h
at
r
eq
u
ir
es
s
eq
u
e
n
tial
p
atter
n
to
s
ati
s
f
y
th
e
ti
m
e
d
if
f
er
e
n
ce
b
et
w
ee
n
p
r
ed
eter
m
in
ed
s
tar
t
an
d
en
d
tr
an
s
ac
tio
n
s
,
(
8
)
g
ap
co
n
s
tr
ain
t,
r
eq
u
ir
es
to
s
atis
f
y
p
r
ed
ef
in
ed
ti
m
e
d
i
f
f
er
en
ce
b
et
w
ee
n
t
w
o
ad
j
ac
en
t
tr
an
s
ac
tio
n
s
[
1
5
]
.
B
ased
o
n
h
o
w
to
ch
ec
k
co
n
s
tr
ai
n
t
o
n
s
eq
u
en
t
ial
p
atter
n
s
,
co
n
s
tr
ain
t
s
ca
n
b
e
ca
teg
o
r
ized
in
to
m
o
n
o
to
n
ic
o
r
a
n
ti
-
m
o
n
o
to
n
ic
co
n
s
tr
ain
t.
C
o
n
s
tr
ai
n
t
ch
ec
k
i
n
g
u
t
ilizes
c
h
ar
ac
ter
is
t
ic
o
f
s
u
b
s
eq
u
en
ce
a
n
d
s
u
p
er
s
eq
u
en
ce
.
A
co
n
s
t
r
ain
t,
d
e
n
o
ted
b
y
C
M
,
i
s
s
aid
a
s
a
m
o
n
o
t
o
n
ic
co
n
s
tr
ain
t
if
th
er
e
i
s
a
s
e
q
u
en
ce
α
m
ee
ts
C
M
co
n
s
tr
ain
t
th
e
n
an
y
s
u
p
er
-
s
eq
u
en
ce
o
f
α
al
s
o
s
atis
f
ie
s
co
n
s
tr
a
in
t
C
M
.
Me
an
w
h
ile,
a
co
n
s
tr
ai
n
t,
d
en
o
ted
b
y
C
A
,
is
s
aid
as
an
ti
-
m
o
n
o
to
n
ic
co
n
s
tr
ain
t
if
t
h
er
e
is
a
s
eq
u
e
n
ce
o
f
α
s
ati
s
f
y
th
e
co
n
s
tr
ai
n
t
C
A
t
h
e
n
an
y
s
u
b
s
eq
u
e
n
ce
o
f
α
also
s
at
is
f
ies co
n
s
tr
ai
n
t C
A
[
1
5
]
.
P
I
SA
r
ep
r
esen
ts
a
s
eq
u
e
n
ce
d
atab
ase
in
to
a
p
r
o
g
r
ess
i
v
e
s
eq
u
en
t
ial
tr
ee
,
P
S
-
tr
ee
[
9
]
.
P
I
S
A
u
s
e
s
th
e
co
n
ce
p
t
o
f
a
ti
m
e
f
r
a
m
e
n
a
m
e
d
as
P
er
io
d
o
f
I
n
ter
e
s
t,
P
OI
,
w
h
ic
h
i
s
a
s
lid
i
n
g
w
i
n
d
o
w
a
n
d
m
o
v
e
c
o
n
ti
n
u
o
u
s
l
y
in
t
i
m
e
[
9
]
.
P
OI
m
ad
e
P
I
S
A
t
o
b
e
f
le
x
ib
le
in
ad
d
in
g
o
r
d
el
etin
g
d
ata
[
9
]
.
P
I
S
A
p
r
o
ce
s
s
e
s
s
eq
u
en
ce
d
atab
ase
th
at
i
s
co
m
p
o
s
ed
f
r
o
m
ite
m
s
e
t
f
r
o
m
ea
c
h
s
eq
u
e
n
ce
I
D
b
as
ed
o
n
o
cc
u
r
r
en
ce
ti
m
es
ta
m
p
.
P
S
-
tr
ee
w
it
h
P
I
SA
alg
o
r
ith
m
[
9
]
r
ec
o
r
d
s
s
eq
u
e
n
c
e
I
D,
lab
el
an
d
ti
m
es
ta
m
p
.
P
I
S
A
al
g
o
r
ith
m
tr
a
v
er
s
es
f
r
o
m
t
h
e
r
o
o
t
n
o
d
e
to
th
e
leaf
o
n
e
a
n
d
ca
lc
u
late
t
h
e
o
c
cu
r
r
en
ce
f
r
eq
u
en
c
y
o
f
ite
m
.
I
f
t
h
e
o
cc
u
r
r
en
ce
f
r
eq
u
e
n
c
y
o
f
ite
m
i
s
lar
g
e
r
th
a
n
m
i
n
i
m
u
m
s
u
p
p
o
r
t
th
en
it
w
i
ll
b
e
co
n
s
id
er
ed
as
s
eq
u
e
n
tial
p
atter
n
.
Ho
w
e
v
er
,
o
r
ig
i
n
al
P
I
S
A
ap
p
r
o
ac
h
h
as
n
o
t
ac
co
m
m
o
d
ated
co
n
s
tr
ai
n
t
ch
ec
k
in
g
w
h
en
s
ea
r
c
h
in
g
f
o
r
s
eq
u
en
tial
p
atter
n
s
.
T
h
er
ef
o
r
e,
P
I
SA*
h
as
b
ee
n
d
ev
elo
p
ed
s
o
th
at
it is
ab
le
to
ch
ec
k
s
in
g
le
co
n
s
tr
ai
n
t
.
2.
CB
S_
CL
ASS*
W
I
T
H
P
I
SA
*
:
T
H
E
P
RO
P
O
SE
D
AP
P
R
O
ACH
C
las
s
i
f
icatio
n
C
B
S
*
w
i
th
Si
n
g
le
C
o
n
s
tr
ain
t
P
r
o
g
r
ess
i
v
e
Mi
n
in
g
o
f
Seq
u
e
n
tial
P
atter
n
s
o
r
P
I
SA*
,
is
a
class
if
icatio
n
ap
p
r
o
ac
h
th
at
in
teg
r
ate
s
s
eq
u
e
n
tial
p
atter
n
m
i
n
in
g
P
I
SA*
w
it
h
class
i
f
icatio
n
p
r
o
ce
s
s
.
C
las
s
i
f
icatio
n
p
r
o
ce
s
s
n
ee
d
s
s
eq
u
en
t
ial
p
atter
n
s
a
s
in
p
u
t
.
Fig
u
r
e
3
s
h
o
w
s
t
h
at
s
eq
u
e
n
tial
p
atter
n
s
w
er
e
o
b
tain
ed
f
r
o
m
s
eq
u
e
n
tial
p
att
er
n
m
i
n
i
n
g
P
I
SA*
t
h
at
w
as
c
o
n
d
u
cted
b
ef
o
r
e
th
e
class
i
f
ic
atio
n
s
tar
ts
.
Si
n
g
le
co
n
s
tr
ain
t
P
I
SA
,
P
I
SA*
s
ea
r
c
h
es
f
o
r
s
eq
u
en
t
ial
p
atter
n
s
t
h
at
m
ee
t
a
m
i
n
i
m
u
m
s
u
p
p
o
r
t,
a
s
in
g
le
co
n
s
tr
ain
t
w
it
h
i
n
t
h
e
u
s
er
-
d
ef
i
n
ed
P
OI
.
Min
i
m
u
m
s
u
p
p
o
r
t,
s
in
g
le
co
n
s
tr
ain
t
a
n
d
P
OI
w
er
e
s
et
b
e
f
o
r
e
s
eq
u
e
n
tia
l
p
atter
n
m
i
n
in
g
p
r
o
ce
s
s
s
tar
ts
.
T
h
e
ad
v
an
ta
g
e
s
o
f
P
I
SA*
ar
e
(
1
)
th
e
f
lex
ib
ili
t
y
i
n
ad
d
in
g
o
r
s
u
b
tr
ac
tin
g
d
ata,
(
2
)
th
e
co
n
f
o
r
m
a
n
ce
o
f
s
eq
u
en
tial p
at
ter
n
s
w
it
h
u
s
er
’
s
n
ee
d
,
(
3
)
th
e
r
e
m
o
v
al
o
f
s
h
o
r
t a
n
d
tr
i
v
ial
s
e
q
u
en
tial p
atter
n
s
.
Seq
u
en
t
ial
p
atter
n
w
ill
b
e
u
s
e
d
as
a
C
SP
,
C
las
s
if
iab
le
Seq
u
en
tial
P
atter
n
th
at
ac
t
as
a
cla
s
s
i
f
icatio
n
r
u
le
,
w
h
ic
h
i
s
d
e
n
o
ted
as
Sp
i
C
m
,
s
eq
u
en
t
ial
p
atter
n
-
i
b
el
o
n
g
s
to
t
h
e
clas
s
m
.
C
las
s
if
ic
atio
n
r
u
les
ar
e
u
s
ed
to
d
eter
m
i
n
e
t
h
e
class
o
f
n
e
w
d
ata
[
1
1
]
.
Fig
u
r
e
3.
C
lass
if
ica
tio
n
b
y
s
eq
u
en
ce
w
i
th
p
r
io
r
p
r
o
ce
s
s
P
I
SA
*
[
1
3
]
T
h
is
ap
p
r
o
ac
h
p
r
o
v
ed
to
p
er
f
o
r
m
b
etter
in
s
ea
r
ch
i
n
g
f
o
r
s
eq
u
en
tial
p
atter
n
s
b
ased
o
n
a
m
i
n
i
m
u
m
s
u
p
p
o
r
t
an
d
a
s
in
g
le
u
s
er
-
d
ef
i
n
ed
co
n
s
tr
ain
t.
Si
n
g
le
co
n
s
tr
ai
n
t
th
at
h
a
s
b
ee
n
test
ed
ar
e
co
n
s
tr
ain
t
ite
m
,
len
g
t
h
less
co
n
s
tr
ai
n
t
a
n
d
le
n
g
th
m
o
r
e
co
n
s
tr
ai
n
t.
Mo
r
eo
v
er
,
t
h
is
a
p
p
r
o
ac
h
w
as
also
p
r
o
v
e
n
to
d
ec
r
ea
s
e
th
e
n
u
m
b
er
o
f
s
h
o
r
t a
n
d
tr
i
v
ial
s
eq
u
en
t
ial
p
atter
n
s
an
d
p
er
f
o
r
m
ed
i
n
f
a
s
t
er
ti
m
e
th
a
n
t
h
e
o
r
ig
i
n
al
P
I
SA
alg
o
r
ith
m
.
L
i
k
e
C
B
S_
C
L
ASS,
C
B
S_
C
L
ASS
*
al
s
o
s
p
lits
d
atab
ase
b
ased
o
n
th
e
co
r
r
esp
o
n
d
in
g
class
.
Den
o
tes,
D
m
co
n
tai
n
s
s
eq
u
en
t
ial
d
ata
th
at
co
r
r
esp
o
n
d
s
to
class
m
.
Da
tab
ase
is
r
ep
r
esen
ted
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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A
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1
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2
1
4
2
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2
1
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D
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w
it
h
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e
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elate
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atter
n
s
t
h
at
m
ee
t
m
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m
u
m
s
u
p
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d
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s
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le
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ai
n
t.
Seq
u
en
t
ial
p
atter
n
o
b
tain
ed
i
s
ca
lled
C
SP
,
C
la
s
s
i
f
iab
le
Se
q
u
en
tial
P
atter
n
.
C
SP
is
w
ei
g
h
ted
b
ased
o
n
th
e
len
g
th
o
f
s
eq
u
e
n
tial
p
atter
n
.
L
o
n
g
er
s
eq
u
e
n
tial
p
atter
n
i
s
g
iv
en
a
g
r
ea
ter
w
ei
g
h
t.
Ma
x
i
m
u
m
w
e
ig
h
t
o
f
ea
c
h
C
SP
is
1
.
C
B
S_
C
L
A
S
S
*
w
i
th
P
I
S
A*
i
s
ex
p
lain
ed
as
f
o
llo
w
s
:
1.
Fo
r
ea
ch
d
atab
ase
D
m
p
er
class
m
,
m
in
i
m
u
m
s
u
p
p
o
r
t,
s
in
g
le
co
n
s
tr
ain
t
a
n
d
P
OI
ar
e
p
r
ed
ef
in
ed
b
ased
o
n
u
s
er
r
eq
u
ir
e
m
e
n
ts
.
Si
n
g
le
co
n
s
tr
ai
n
t
m
a
y
b
e
a
n
ite
m
o
r
l
en
g
t
h
les
s
o
r
len
g
t
h
m
o
r
e
co
n
s
tr
ai
n
t.
Fin
d
s
eq
u
en
tial p
atter
n
s
u
s
in
g
P
I
SA*
as
f
o
llo
w
s
:
a.
T
r
an
s
f
o
r
m
t
h
e
d
atab
ase
i
n
to
s
eq
u
en
ce
d
atab
ase
t
h
at
h
as
p
r
o
p
er
ty
o
f
s
eq
u
e
n
ce
id
,
ti
m
e
s
ta
m
p
a
n
d
lab
el.
L
ab
el
is
also
ca
lled
as it
e
m
s
et.
b.
Usi
n
g
P
r
o
ce
d
u
r
e
T
r
av
er
s
e:
De
v
elo
p
an
d
tr
a
v
er
s
e
P
S
-
tr
ee
o
f
i
te
m
s
e
t
ele
m
e
n
ts
w
it
h
in
P
OI
.
E
v
er
y
n
e
w
ele
m
e
n
t
i
s
r
ec
o
r
d
ed
at
t
h
e
r
o
o
t
n
o
d
e,
w
h
ile
ev
er
y
ele
m
e
n
t
t
h
at
h
a
s
p
r
ed
ec
ess
o
r
is
r
e
co
r
d
ed
at
co
m
m
o
n
n
o
d
e.
W
h
ile
tr
a
v
er
s
i
n
g
,
ch
ec
k
w
h
et
h
er
s
eq
u
en
tial
p
atter
n
s
ati
s
f
ies
m
in
i
m
u
m
s
u
p
p
o
r
t,
w
h
ic
h
is
th
e
s
eq
u
en
ce
l
is
t s
ize
≥
m
i
n
i
m
u
m
s
u
p
p
o
r
t
*
n
u
m
b
er
o
f
s
eq
u
en
ce
.
c.
Usi
n
g
P
r
o
ce
d
u
r
e
P
is
aCo
n
s
tr
ai
n
tI
te
m
:
T
o
o
b
tain
s
eq
u
en
t
ial
p
atter
n
s
t
h
at
s
ati
s
f
y
t
h
e
s
i
n
g
le
co
n
s
tr
ain
t,
ch
ec
k
s
eq
u
en
t
ial
p
atter
n
ag
ai
n
s
t
s
i
n
g
le
co
n
s
tr
ai
n
t
in
P
OI
ti
m
e
f
r
a
m
e.
C
h
ec
k
co
n
s
tr
ain
t
b
ased
o
n
p
r
o
p
er
ty
an
ti
m
o
n
o
to
n
ic
o
r
m
o
n
o
to
n
ic
co
n
s
tr
ain
t a
n
d
ap
p
l
y
it
to
all
s
eq
u
en
tia
l p
a
tter
n
s
.
Fo
r
an
ti
-
m
o
n
o
to
n
ic
co
n
s
tr
ai
n
t
s
u
c
h
a
s
le
n
g
th
les
s
co
n
s
tr
ain
t
,
if
s
eq
u
e
n
ce
o
f
α
s
ati
s
f
ies
t
h
e
co
n
s
tr
ai
n
t
an
ti
-
m
o
n
o
to
n
ic
C
A
t
h
e
n
an
y
s
u
b
s
eq
u
e
n
ce
o
f
α
al
s
o
s
ati
s
f
ies
co
n
s
tr
ain
t C
A
.
I
f
t
h
e
SP
Existin
g
s
atis
f
ies t
h
e
co
n
s
tr
ain
t a
n
d
i
f
SP
is
s
u
b
s
eq
u
en
ce
o
f
SP
Existin
g
t
h
en
SP
also
s
atis
f
ies t
h
e
co
n
s
tr
ai
n
t.
Fo
r
m
o
n
o
to
n
ic
co
n
s
tr
ai
n
t
s
u
c
h
as
ite
m
,
le
n
g
t
h
m
o
r
e,
s
u
p
er
p
atter
n
co
n
s
tr
ain
t,
if
th
er
e
i
s
a
s
eq
u
en
ce
α
s
atis
f
ies
co
n
s
tr
ai
n
t
m
o
n
o
to
n
ic
C
M
th
e
n
a
n
y
s
u
p
er
-
s
eq
u
e
n
ce
o
f
α
al
s
o
s
atis
f
ie
s
co
n
s
tr
ai
n
t
C
M
.
I
f
t
h
e
SP
Existing
m
ee
t
s
th
e
co
n
s
tr
ai
n
t
an
d
if
SP
Existin
g
i
s
s
u
b
s
eq
u
e
n
ce
o
f
SP
o
r
SP
is
s
u
p
er
-
s
e
q
u
en
ce
o
f
SP
Existing
t
h
e
n
SP
also
s
atis
f
ie
s
th
e
co
n
s
tr
ain
t.
2.
Usi
n
g
P
r
o
ce
d
u
r
e
C
lass
_
o
f
_
s
eq
u
en
ce
:
C
las
s
i
f
y
t
h
e
d
ata
a.
Fo
r
ea
ch
o
b
tain
ed
s
eq
u
en
tia
l
p
atter
n
o
r
C
SP
,
co
m
p
u
te
C
SP
s
co
r
e
b
y
ac
cu
m
u
lati
n
g
len
g
t
h
o
f
s
eq
u
en
tial p
atter
n
.
b.
Fo
r
ea
ch
C
SP
,
n
o
r
m
aliza
tio
n
o
f
s
co
r
es is
co
u
n
ted
.
I
f
C
SP
is
a
s
u
b
s
eq
u
e
n
ce
o
f
t
h
e
e
x
is
ti
n
g
C
SP
ar
r
ay
,
th
en
s
co
r
e
=
ac
cu
m
u
lated
o
f
(
l
en
g
t
h
o
f
s
eq
u
e
n
ce
/ to
tal
s
co
r
e)
.
c.
C
h
ec
k
th
e
s
eq
u
e
n
tial
p
atter
n
s
f
o
u
n
d
f
r
o
m
tes
t
d
ata
ag
ain
s
t
li
s
t
o
f
C
SP
.
I
f
th
e
co
r
r
esp
o
n
d
in
g
class
i
s
f
ailed
to
g
et,
t
h
en
c
h
ec
k
t
h
e
s
u
b
s
eq
u
e
n
ce
o
f
s
eq
u
e
n
tial
p
att
er
n
s
f
r
o
m
te
s
t
d
ata,
f
r
o
m
t
h
e
lo
n
g
e
s
t
to
th
e
s
h
o
r
test
le
n
g
t
h
,
ag
a
in
s
t th
e
lis
t o
f
C
SP
r
ec
u
r
s
iv
e
l
y
u
n
til it
s
co
r
r
esp
o
n
d
en
ce
class
is
f
o
u
n
d
.
d.
B
ased
o
n
th
e
s
co
r
es
o
b
tain
ed
in
p
o
in
t
4
,
in
d
e
x
k
w
ill
b
e
o
b
tain
ed
,
w
h
er
e
k
i
s
t
h
e
m
a
x
i
m
u
m
s
co
r
e.
C
las
s
o
b
tain
ed
is
a
class
w
ith
i
n
d
ex
k
.
C
B
S_
C
L
A
S
S
*
w
i
th
P
I
S
A*
al
g
o
r
ith
m
is
d
escr
ib
ed
in
Fi
g
u
r
e
4
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
C
la
s
s
i
fica
tio
n
w
ith
S
in
g
le
C
o
n
s
tr
a
in
t P
r
o
g
r
ess
ive
Min
in
g
o
f S
eq
u
en
tia
l P
a
tter
n
s
(
R
eg
in
a
Yu
lia
Ya
s
min
)
2147
Fig
u
r
e
4
.
T
h
e
p
r
o
p
o
s
ed
C
B
S_
C
L
ASS
*
al
g
o
r
ith
m
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
E
x
p
er
i
m
e
n
t
u
s
es
e
-
co
m
m
er
ce
s
ales
d
ata
w
h
ich
co
n
tai
n
s
c
ateg
o
r
ical
d
ata.
T
h
e
am
o
u
n
t
o
f
d
ata
is
ab
o
u
t
2
2
,
6
9
9
tr
an
s
ac
tio
n
s
w
it
h
attr
ib
u
te
s
ar
e
p
r
o
d
u
ct
I
D,
d
ate
o
f
s
ale
s
,
cu
s
to
m
er
I
D,
o
r
d
er
I
D.
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
ex
p
er
i
m
en
ts
i
s
to
co
m
p
ar
e
th
e
cla
s
s
i
f
icatio
n
ti
m
e
p
er
f
o
r
m
a
n
ce
a
n
d
th
e
ac
cu
r
ac
y
b
et
w
ee
n
C
B
S_
C
L
A
S
S
an
d
C
B
S_
C
L
A
S
S
*
.
I
n
o
r
d
er
to
g
et
th
e
ac
cu
r
ac
y
lev
el,
k
-
f
o
ld
s
tr
atif
ied
cr
o
s
s
v
alid
atio
n
is
u
s
ed
as
test
in
g
s
ce
n
ar
io
.
I
n
t
h
i
s
ex
p
er
i
m
en
t,
C
B
S_
C
L
A
S
S
u
s
es
o
r
i
g
in
a
l
P
I
S
A
m
e
th
o
d
f
o
r
s
ea
r
ch
i
n
g
s
eq
u
en
t
ial
p
atter
n
s
,
an
d
C
B
S_
C
L
A
S
S
*
u
s
e
s
P
I
SA*
w
i
th
s
i
n
g
le
co
n
s
tr
ai
n
t.
C
o
n
s
tr
ain
t
u
s
ed
is
ei
th
er
a
n
it
e
m
co
n
s
tr
ai
n
t
o
r
len
g
t
h
le
s
s
o
r
len
g
th
m
o
r
e
co
n
s
tr
ai
n
t.
I
te
m
co
n
s
tr
ai
n
t
r
eq
u
ir
es seq
u
e
n
ti
al
p
atter
n
s
to
co
n
tain
1
s
p
ec
i
f
ic
ite
m
.
L
en
g
t
h
les
s
co
n
s
tr
ai
n
t r
eq
u
ir
es t
h
at
l
en
g
t
h
o
f
s
eq
u
e
n
tia
l
p
atter
n
s
m
u
s
t
b
e
less
t
h
an
a
ce
r
tain
n
u
m
b
er
.
On
th
e
co
n
tr
ar
y
,
len
g
th
m
o
r
e
co
n
s
tr
ain
t
r
eq
u
ir
es
th
a
t
len
g
th
o
f
s
eq
u
en
tial p
atter
n
s
m
u
s
t b
e
m
o
r
e
o
r
th
e
s
am
e
t
h
a
n
a
ce
r
tain
n
u
m
b
er
.
First,
d
ata
in
ea
ch
d
atab
ase
D
m
t
h
at
co
r
r
esp
o
n
d
s
to
class
m
,
w
er
e
r
ep
r
esen
ted
in
s
eq
u
e
n
ce
d
atab
ase
b
ased
o
n
s
ales
d
ate
an
d
tim
e
.
Fig
u
r
e
5
r
ep
r
esen
ts
th
e
s
eq
u
en
ce
d
atab
ase.
Seq
u
e
n
ce
I
D
o
r
SID
r
ep
r
esen
ts
s
eq
u
en
ce
s
b
ased
o
n
u
s
er
’
s
p
o
in
t
o
f
v
ie
w
to
an
al
y
ze
.
I
n
t
h
is
ca
s
e,
s
eq
u
en
ce
I
D
is
b
ased
o
n
s
ales
d
ate.
E
ac
h
Input:
dataset,
minimum
suppo
rt,
POI
and
single
con
straint
criteria,
for
example
item constraint
Output:
class of sequent
ial patterns
Method:
CBS_CLASS*
(Dataset D, min_sup, POI, label)
{
For
each c
i
ϵ class_set(D)
do
D
i
= class_dataset(D,c
i
);
CSP
i
= PISA*(D
i
, min_sup, POI, label)
End
}
PISA*
(Dataset D, min_sup, POI, label)
{
1.
Var PS; //PS Tree
2.
Var currentTime; //tim
estamp now
3.
Var eleSet; //used to store elements ele
4.
While (there is still new transaction)
5.
eleSet = read all ele at currentTime;
6.
traverse(currentTime, PS);
7.
PisaConstraintItem(sp, label); //item constraint checking
8.
currentTime++;
//This i
s the start of modified PISA algorithm
Procedure traverse
(
currentTime,PS
)
For
(each node of
PS
in post order)
do
If
(
node
is Root)
For
(
ele
of every
seq
in
eleSet
)
do
For
(all combination of elements in the
ele
)
do
If
(
element
==label of one of
node.ch
ild
)
Update timestamp of
seq
to
currentTime
;
Else
Create a new sequence with
currentTime
;
Else
//create a child
Create a new child with
element
,
seq
and
currentTime
;
Else
//the node is a common node
For
(every
seq
in the
seq_list
)
do
If
(
seq.timestamp
<=
currentTime
-
POI
Delete
seq
from
seq_list
and continue to the next
seq
;
If
(there is new
ele
of the seq in
eleSet
)
For
(all combination of elements in the
ele
)
do
If
(
element
is not on the path from Root)
If
(
element
==label of one of
node.child
)
Child.seq_list.seq.timestamp
=
seq.timestamp
;
Else
Create
a
new
sequence
with
seq.timestamp
;
Endif
Else
//create a child
Create
a
new
child
with
element,
seq
and
seq.timestamp
;
Endif
EndFor
Endif
Endif
If
(
seq_list.size
==0)
Delete this node and all of its children from its parent;
If
(
seq_list.size
>=support*sequence number)
Output the labels of path from Root to this node as a SP
End
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
4
,
A
u
g
u
s
t
2
0
1
7
:
2
1
4
2
–
2
1
5
1
2148
SID
co
n
s
i
s
ts
o
f
s
er
ies
o
f
ite
m
s
et.
E
ac
h
i
te
m
s
et
co
n
s
is
ts
o
f
p
r
o
d
u
ct
I
D.
I
te
m
s
et
in
ea
c
h
SID
is
g
r
o
u
p
ed
b
y
t
h
e
s
a
m
e
ti
m
es
ta
m
p
.
I
n
th
is
ex
p
er
i
m
e
n
t,
ti
m
e
o
r
ti
m
e
s
ta
m
p
i
s
in
s
ales
h
o
u
r
u
n
it.
Mo
r
eo
v
er
,
POI
is
u
s
ed
as
a
u
s
er
d
ef
in
ed
t
i
m
e
s
l
id
in
g
w
i
n
d
o
w
b
et
w
ee
n
s
p
ec
i
f
ied
s
ale
s
h
o
u
r
s
i
n
ter
v
al.
T
h
er
ef
o
r
e,
b
ased
o
n
s
ale
s
h
o
u
r
s
,
m
ax
i
m
u
m
n
u
m
b
er
o
f
P
OI
is
2
3
.
I
n
th
is
ex
p
er
i
m
en
t,
P
OI
is
s
et
o
f
5
,
m
ea
n
s
t
h
at
ti
m
e
s
li
d
in
g
w
i
n
d
o
w
i
s
s
e
t
b
et
w
ee
n
5
h
o
u
r
s
.
Fig
u
r
e
5
.
Seq
u
en
tia
l d
atab
ase
r
ep
r
esen
tatio
n
i
n
ea
ch
D
m
[
1
3
]
Seq
u
en
t
ial
p
atter
n
s
ar
e
s
eq
u
en
ce
o
f
ite
m
s
ets t
h
at
co
n
tai
n
:
a.
Seq
u
en
t
ial
p
atter
n
1
: <
(
p
r
o
d
u
ct
11
)
,
<(
p
r
o
d
u
ct
12
)
,
.
.
.
,
<(
p
r
o
d
u
ct
1n
)
>,
b.
Seq
u
en
t
ial
p
atter
n
2
: <
(
p
r
o
d
u
ct
21
)
,
<(
p
r
o
d
u
ct
22
)
,
.
.
.
,
<(
p
r
o
d
u
ct
2n
)
>,
c.
Seq
u
en
t
ial
p
atter
n
m
: <
(
p
r
o
d
u
ct
m1
)
,
<(
p
r
o
d
u
ct
m2
)
,
.
.
.
,
<(
p
r
o
d
u
ct
mn
)
>.
I
n
th
i
s
ex
p
er
i
m
en
t,
cla
s
s
i
f
icat
io
n
p
r
o
ce
s
s
ca
teg
o
r
izes
s
eq
u
e
n
tial
p
atter
n
s
i
n
t
w
o
cla
s
s
e
s
,
p
r
o
s
p
ec
t
an
d
n
o
n
p
r
o
s
p
ec
t
p
r
o
d
u
cts.
Fo
r
ex
am
p
le,
s
eq
u
e
n
tial
p
atter
n
s
g
e
n
er
ated
b
y
P
I
S
A*
t
h
at
ac
t
as
f
ea
t
u
r
es
f
o
r
th
e
class
i
f
icatio
n
p
r
o
ce
s
s
ar
e
as f
o
llo
w
s
:
a.
C
las
s
o
f
p
r
o
s
p
ec
t p
r
o
d
u
ct
:
1)
Seq
u
en
t
ial
p
atter
n
s
1
: <
(
Sa
m
s
u
n
g
Gala
x
y
V
S
M
-
G3
1
3
H
Z
W
h
ite)
,
(
Sa
m
s
u
n
g
Gala
x
y
T
ab
S 8
.
4
"
-
SM
-
T
7
0
5
N
T
-
T
itan
iu
m
B
r
o
w
n
)
>,
2)
Seq
u
en
t
ial
p
atter
n
s
2
:
<(
P
r
eo
r
d
er
Mic
r
o
s
o
f
t
L
u
m
ia
5
3
5
B
lack
)
,
(
Sa
m
s
u
n
g
Ga
lax
y
V
SM
-
G3
1
3
HZ
W
h
ite)
>
an
d
s
o
o
n
.
b.
C
las
s
o
f
n
o
n
p
r
o
s
p
ec
t p
r
o
d
u
ct
:
1)
Seq
u
en
t
ial
p
atter
n
s
1
:
<(
E
m
te
c
USB
2
.
0
Flas
h
Dr
i
v
e
8
GB
B
lack
P
an
th
er
)
,
(
V
-
Ge
n
Mic
r
o
SDHC
1
6
GB
)
>
2)
Seq
u
en
t
ial
p
atter
n
s
2
:
<(
P
NY
Du
al
U
SB
Flas
h
Dr
i
v
e
-
OU1
1
6
GB
)
,
(
u
NiQu
e
L
ap
to
p
B
ac
k
p
ac
k
i
-
P
r
o
tect
B
ir
u
)
,
(
V
-
Gen
Mic
r
o
SDHC
1
6
GB
)
>
an
d
s
o
o
n
.
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
f
ir
s
t
e
x
p
er
i
m
en
t
w
as
to
co
m
p
ar
e
t
h
e
n
u
m
b
er
o
f
s
eq
u
en
tial
p
atter
n
s
f
r
o
m
P
I
SA
in
C
B
S_
C
L
A
SS
a
n
d
P
I
SA*
f
r
o
m
C
B
S_
C
L
A
S
S
*
.
T
h
e
e
x
p
er
i
m
en
t
w
as
co
n
d
u
cted
at
m
i
n
i
m
u
m
s
u
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I
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C
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I
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ip
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RE
F
E
R
E
NC
E
S
[1
]
X
.
Ya
n
,
“
De
sig
n
a
n
d
A
n
a
l
y
sis
o
f
P
a
ra
ll
e
l
M
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p
Re
d
u
c
e
b
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se
d
KN
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-
jo
in
A
lg
o
ri
th
m
f
o
r
Big
Da
ta
Clas
sif
ic
a
ti
o
n
”
,
In
d
o
n
e
s.
J
.
E
lec
tr.
En
g
.
C
o
mp
u
t.
S
c
i.
,
v
o
l
.
1
2
,
n
o
.
1
1
,
p
p
.
7
9
2
7
–
7
9
3
4
,
2
0
1
4
.
[2
]
N.
L
e
sh
,
M
.
J.
Zak
i,
M
.
Og
ih
a
ra
,
“
M
in
in
g
Fea
t
u
re
s
fo
r
S
e
q
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e
n
c
e
Cla
ss
if
ica
ti
o
n
”
,
in
P
r
o
c
e
e
d
in
g
s
o
f
th
e
f
i
f
th
A
CM
S
IG
KD
D In
tern
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ti
o
n
a
l
Co
n
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re
n
c
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o
n
K
n
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led
g
e
Disc
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v
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r
y
a
n
d
Da
ta M
in
in
g
,
AC
M
,
1
9
9
9
,
p
p
.
3
4
2
–
3
4
6
.
[3
]
R.
Y.
Ya
sm
in
,
G
.
A
.
P
.
S
a
p
taw
a
ti
,
B.
S
i
to
h
a
n
g
,
“
S
u
rv
e
y
o
n
S
e
q
u
e
n
ti
a
l
P
a
tt
e
rn
M
in
i
n
g
”
,
in
ICI
BA
,
2
0
1
3
.
[4
]
D.
W
u
,
J.
Re
n
,
“
S
e
q
u
e
n
c
e
Clu
st
e
rin
g
A
l
g
o
rit
h
m
Ba
se
d
o
n
W
e
ig
h
e
d
S
e
q
u
e
n
ti
a
l
P
a
t
tern
S
im
il
a
rit
y
”
,
In
d
o
n
e
s.
J
.
El
e
c
tr.
En
g
.
Co
m
p
u
t
.
S
c
i.
,
v
o
l.
1
2
,
n
o
.
7
,
p
p
.
5
5
2
9
–
5
5
3
6
,
2
0
1
4
.
[5
]
R.
Ag
ra
w
a
l,
R.
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rik
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