Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
24
,
No.
2
,
N
ov
em
ber
20
21
, pp.
108
4
~
10
90
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
24
.i
2
.
p
p
108
4
-
10
9
0
1084
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
IPOC:
a
n
efficie
nt appr
oach fo
r dynami
c
associati
on rul
e
ge
n
eration u
sing i
ncreme
ntal data
with upd
ating sup
ports
P.
Na
res
h, R.
Sugun
a
Depa
rtment
o
f
C
om
pute
r
Scie
n
ce a
nd
Engi
n
ee
rin
g
,
Vel
T
ec
h
Ran
gar
ajan
Dr.
Sagu
ntha
l
a
R&D
Instit
ute of
Sc
ie
n
ce
and
Te
chno
log
y
,
Ch
enna
i
,
Ind
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
y
25
,
2021
Re
vised
Sep
16
,
2021
Accepte
d
Se
p
21
,
2021
Acc
ording
to
r
e
ce
nt
statistic
s
,
t
her
e
was
dra
sti
c
growth
in
online
business
sec
tor
where
m
ore
num
ber
of
c
ustom
ers
int
ends
to
purc
hase
i
t
ems
.
Due
to
the
se
r
et
a
ilers
a
c
cumulat
es
hug
e
volumes
of
data
from
da
y
to
da
y
oper
ations
and
engr
oss
ed
in
ana
l
y
zi
ng
th
e
d
at
a
to
watc
h
th
e
beha
vior
of
c
ustom
ers
at
it
ems
which
strengt
hen
the
busin
ess
prom
oti
ons
and
ca
t
al
og
m
ana
gement.
It
rev
eals
the
cust
om
er
int
er
esti
ng
ness
and
fre
qu
e
nt
item
s
from
la
rge
data.
To
ca
rr
y
out this
there
was known a
l
gorit
hm
s pre
sent
which
deals wi
t
h
stat
ic
and
d
y
nami
c
data.
Som
e
of
the
m
are
l
ag
ti
m
e
an
d
m
emory
consum
ing
and
invol
ves
unnece
ss
ar
y
proc
ess.
T
his
pape
r
int
ents
to
implement
an
eff
icient
inc
rement
al
pr
e
orde
red
code
d
tr
ee
(IPO
C)
gene
r
at
ion
for
d
ata
u
pdat
es
an
d
appl
i
es
fre
quen
t
it
em
set
ge
n
erati
on
al
gori
thm
on
the
tr
ee.
W
hil
e
i
ncr
emental
gene
ra
ti
on
of
tr
ee
,
new
data
it
e
m
s
will
li
nk
to
pre
vious
nodes
in
tre
e
b
y
inc
re
asing
i
ts
support
coun
t.
T
his
removes
the
la
gging
issues
in
ex
isti
n
g
al
gorit
hm
s
and
d
oes
not
nee
d
to
m
ine
from
scra
tch
and
al
so
r
educes
the
t
ime,
m
emory
consu
m
pti
on
b
y
th
e
use
of
nodese
t
dat
a
struct
ur
e.
The
r
esult
s
of
proposed
m
et
hod
was
observe
d
and
an
aly
z
ed
with
exi
st
ing
m
et
hods.
Th
e
ant
i
ci
pa
te
d
m
ethod
show
s
impr
oved
result
s
b
y
m
ea
ns
of
generat
ed
item
s,
ti
m
e
and
m
emory
.
Ke
yw
or
d
s
:
Dataset
In
c
rem
ental
tree g
e
ner
at
io
n
IP
OC
Nodese
t
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
P.
Nar
es
h
Dep
a
rtm
ent o
f
Com
pu
te
r
Scie
nce
a
nd
E
ng
i
ne
erin
g
Vel Tec
h
Ra
ng
araj
a
n Dr. Sa
gunt
hala R&
D
I
ns
ti
tute o
f
Scie
nce a
nd Tec
hnology
Chen
nai,
India
Em
a
il
:
pan
na
ngina
resh@
gm
a
il
.co
m
1.
INTROD
U
CTION
Now
a
day
the
re
is
m
or
e
co
m
pet
it
ion
in
business
sect
or
wh
ic
h
aim
s
to
at
tract
the
custom
ers
wit
h
la
te
st
and
inter
est
ed
it
e
m
s.
At
the
sam
e
t
i
m
e
it
is
req
uire
d
t
o
ide
ntify
the
us
er
i
nterests
on
it
e
m
s
by
appl
yi
ng
associat
ion
it
em
analy
sis.
It
will
help
to
kn
ow
the
fr
e
que
nt
it
e
m
s
bo
ug
ht
by
di
ff
e
ren
t
use
rs
of
al
l
trans
act
ion
s
at
a
su
per
m
ark
et
or
sto
re.
B
y
analy
zi
ng
these
data
on
e
c
an
sugge
st
m
or
e
it
e
m
s
to
cus
tom
ers
dep
en
di
ng
on
their
fr
e
quency
wh
ic
h
inte
rn
i
ncr
ease
the
sal
es
and
al
so
it
assist
in
m
ai
ntain
in
g
a
g
oo
d
an
d
update
d
cat
al
og
of
it
e
m
s.
It
is
ach
ie
ved
by
t
he
i
m
ple
m
entat
ion
s
of
var
i
ous
tre
nd
y
data
m
ining
a
ppr
oach
e
s
a
t
analy
zi
ng
dat
a
a
nd
m
akes
ideal
de
ci
sion
s.
Data
m
ining
is
a
f
undam
ental
pr
oc
ess
in
kn
ow
le
dge
m
ining
w
hich
disc
overs
unkn
own
facts,
nee
dy
inf
o
rm
at
ion
an
d
interest
in
g
patte
rn
s
form
m
assive
data.
Fr
eq
ue
nt
it
em
se
t
m
ining
[
1]
and
associat
ion r
ul
e m
ining
play
s
a cr
ucial
role o
n fin
ding
us
er
interests
from
tran
sact
io
nal d
at
abase.
Associ
at
ion
rul
e
gen
e
rati
on
f
ro
m
fr
eq
ue
nt
it
e
m
s
fr
om
retai
l
and
real
wo
rld
dataset
s
em
plo
ys
a
vital
ro
le
.
Aprio
ri
and
fr
e
quent
patte
rn
gro
wth
(
FP
-
gro
wth
)
are
the
f
undam
ental
al
go
rithm
s
fo
r
m
i
ning
transacti
onal
da
ta
set
to
disco
ver
f
re
qu
e
nt
it
em
s
[2
]
.
Aprio
ri
gen
e
rates
can
did
at
e
key
at
each
it
e
m
set
s
and
then
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
IPO
C
: an ef
fi
ci
ent appro
ac
h
f
or
dy
namic
as
s
ociatio
n
r
ule
ge
ner
ation
us
i
ng inc
reme
nta
l
…
(
P. Na
res
h
)
1085
ver
ifie
s
the
s
uppo
r
t
thres
ho
l
d,
w
hic
h
is
a
tim
e
con
su
m
ing
proce
ss.
T
he
oth
er
F
P
-
gro
wth
does
n’
t
ge
ner
at
e
cand
i
date
key
bu
t
it
bu
il
ds
a
fr
e
qu
e
nt
patte
r
n
tree
(
FP
-
tree
)
f
or
al
l
tra
ns
a
ct
ion
al
it
em
s.
Wh
il
e
li
nkin
g
t
he
it
em
with
the
node
of
t
ree
it
chec
ks
it
s
sup
port
and
occ
urre
nc
es
at
each
tra
nsa
ct
ion
.
Sup
port
an
d
Co
nfi
de
nce
are
qu
al
it
at
ive
m
easur
e
s
for
ref
i
ning
the
transa
ct
ion
s
to
know
the
it
e
m
fr
equencie
s.
High
ut
il
i
ty
[3
]
-
[5
]
A
RM
is
ta
sk
wh
ic
h per
form
s
m
ining
by consi
der
in
g uti
li
ti
es o
f res
pecti
ve
it
em
s [
6]
,
[
7]
:
Suppor
t
–
It is
the c
ount
of o
cc
urren
ce
of a
p
a
rtic
ular
it
em
I
at al
l t
ran
sact
io
ns
.
Confide
nce
of
X
Y
–
It
is
the
pr
oba
bili
ty
of
occurre
nce
of
m
or
e
than
on
e
it
e
m
or
it
e
m
co
m
bin
at
ion
s
in
a
sing
le
or all
tra
ns
act
io
ns
.
T
h
e
T
a
b
l
e
1
c
o
n
t
a
i
n
s
s
a
m
pl
e
t
r
a
n
s
a
c
t
i
o
n
a
l
d
a
t
a
w
i
t
h
t
r
a
n
s
a
c
t
i
o
n
i
d
a
n
d
r
e
s
p
e
c
t
i
v
e
i
t
e
m
s
w
h
i
c
h
w
e
r
e
b
r
o
u
g
h
t
t
o
g
e
t
h
e
r
.
T
h
e
T
a
b
l
e
2
h
o
l
d
s
t
he
i
n
f
o
r
m
a
t
i
o
n
a
b
o
u
t
a
l
l
i
t
e
m
s
a
n
d
t
h
e
i
r
r
e
s
p
e
c
t
i
v
e
s
u
p
p
o
r
t
s
.
M
o
b
i
l
e
C
h
a
r
g
e
r
(
c
o
n
f
i
d
e
n
c
e
7
0
%
)
m
e
a
n
s
t
ha
t
7
0
%
o
f
t
h
e
c
u
s
t
om
e
r
s
w
h
o
b
o
u
g
h
t
m
o
b
i
l
e
a
l
s
o
b
u
y
a
c
h
a
r
g
e
r
.
Table
1.
Sam
pl
e transacti
on
al
data
Tr
an
sactio
n
s
Ite
m
s
T50
1
I2,I5,I6
T50
2
I3,I4,I6
T50
3
I1,I3,I5,
I6
T50
4
I2,I4,I5
T50
5
I1,I3,I5,
I6
Table
2
.
Item
s
with s
upport c
ount
Ite
m
Su
p
p
o
rt
I1
2
I2
2
I3
3
I4
2
I5
4
In
real
tim
e,
new
data
ge
ne
rated
dr
ast
ic
a
l
ly
as
con
ti
nuou
s
t
ran
sact
i
ons
[
8
]
wer
e
pe
rfor
m
ed
by
diff
e
re
nt
custo
m
ers
at
retai
l
stores.
Furth
erm
or
e
existi
ng
dataset
ca
n
be
up
dated
with
ne
w
in
form
ation
con
ti
nu
ously
wh
ic
h
m
akes
the
dataset
asy
m
m
e
tric
al
du
e
to
u
pdat
es
[
9
]
,
an
d
it
is
very
diff
ic
ult
to
a
naly
ze
t
hese
kinds
of
dataset
s
[1
0]
and
al
so
inc
re
ase
the
com
pl
exity
on
m
ining
fr
e
quent
it
em
s.
Pr
evio
us
m
et
ho
ds
wh
ic
h
deal
with
fr
e
quent
it
em
s
m
ining
we
re
ap
plica
ble
to
sta
ti
c
dataset
s
wh
e
re
no
c
hanges
wer
e
m
ad
e
furthe
r.
T
he
re
e
xist
so
m
e
al
gorithm
s
li
ke
f
r
equ
e
nt
i
te
m
set
with
node
set
(F
I
N)
[11
]
w
hi
ch
will
inc
rea
se
the
fast of m
ining
process
but
unawar
e
of
handl
ing
with i
ncr
e
m
ental
o
r dyna
m
ic
d
at
a.
C
hiu
et
al
.
[
12]
i
m
ple
m
ented
a
tree
base
d
m
et
hod
f
or
deali
ng
with
dynam
ic
data
us
i
ng
F
CFP
tree.
It
dep
e
nds
on
ge
ner
at
io
n
of
f
ul
l
com
pr
essio
n
tree
ge
ne
rati
on.
A
fter
ward
D
eng
[
13
]
disc
overe
d
a
no
vel
data
structu
re
cal
le
d
no
deset,
to
increase
th
e
m
ining
acc
ur
a
cy
.
In
t
heir
pa
per
t
hey
ge
nerat
ed
pre
orde
r
code
d
(
PO
C
)
tree
an
d
pre
–
post
order
c
od
e
d
(
P
PC
)
tree
de
pends
on
or
der
e
d
transacti
onal
it
e
m
s
to
fast
m
ining.
Wh
e
ne
ver
n
e
w
data
ad
de
d
to ex
ist
ing,
it
is
toug
h
to
m
ine
accuratel
y
an
d
s
om
eti
m
es
earlier
ge
ne
rated
it
e
m
s
or
ru
le
s
gets
i
nv
a
li
d.
All
this
pr
ocess
e
ntirel
y
beco
m
es
w
or
t
hless
du
e
to
st
art
f
ro
m
s
cratch
re
cu
rsively
f
or
al
l
new
ly
ad
de
d
data.
To
c
onquer
the
se
issu
es
and
to
dea
l
with
dynam
i
c
dataset
[14
]
,
this
pap
e
r
ai
m
s
to
i
m
ple
m
ent
a
no
vel
a
nd
e
ff
ic
i
ent
al
gorithm
cal
le
d
increm
e
ntal
pr
e
order
e
d
co
de
d
tree.
I
t
wo
r
ks
with
node
set
data
struct
ur
e
creati
o
n
a
nd
app
li
es
f
reque
nt
it
e
m
se
t
m
ining
(
F
IM
)
on
th
e
tree
[15
].
The
fo
rt
hc
om
ing
sect
ions
of
this
pa
pe
r
exp
l
or
es
a
bout
li
te
ratur
e
surve
y
of
existi
ng
a
ppr
oach
es
relat
ed
to
ARM
and
dynam
ic
it
e
m
set
m
ining
,
pro
pos
ed
al
gorithm
wh
ic
h
ha
ndle
s
th
e
dy
nam
ic
data
by
t
he
us
e
of
nodeset
data
st
ru
ct
ur
e,
a
naly
sis
of
resu
lt
s
(co
m
par
is
on
with e
xis
ti
ng
alg
ori
thm
s
)
a
nd f
inall
y e
nds
with c
oncl
usi
on secti
on.
Dynam
ic
it
e
mset
m
ining
a
nd
associat
io
n
r
ul
e
m
ining
[16]
has
bee
n
c
halle
ng
in
g
e
ra
i
n
data
m
ining
from
increm
en
ta
l
dataset
s.
A
s
the
data
in
retai
l
industry
or
supe
rm
ark
et
intends
to
changes
,
co
nti
nuous
m
ining
bec
ome
a
co
m
plex
t
ask.
S
o
it
is
e
ssentia
l
to
devel
op
a
data
structu
re
m
os
tl
y
su
it
able
for
ha
nd
li
ng
updat
in
g
data
or
ne
w
data.
It
m
a
intai
ns
inform
at
ion
reg
a
rd
i
ng
a
dd
ed
tran
sact
ions
dynam
ic
al
l
y
[17
].
This
proces
s
di
scov
e
rs
ne
w
f
reque
nt
it
e
m
se
ts
by
el
i
m
inatin
g
in
fr
e
quent
it
e
m
set
s
dep
en
ding
on
their
update
d
su
pp
or
t
[
18
]
th
reshold
s.
E
xist
ing
m
et
hods
sc
an
the
d
at
a
ba
s
e
from
scratch f
or
eac
h
a
dded
transacti
on
w
hi
ch
is
a
tim
e
con
s
umi
ng
an
d
ha
d
un
necessa
ry
ta
sks.
S
o
finall
y
th
is
survey
ai
m
s
on
ide
ntifyi
ng
novel
a
nd
im
pr
ove
d
al
gorithm
s f
or
fast m
ining
a
nd assim
il
a
te
s wi
th d
ynam
ic
d
a
ta
set
s
us
in
g
m
achine lea
ning a
ppr
oac
hes
[1
9]
.
Sun
et
al
.
[1
]
in
their
pa
per
“
In
c
rem
ental
Fr
equ
e
nt
Item
sets
Mi
nin
gwit
h
FCFP
Tree”
im
ple
m
ented
a
new
tr
ee
base
d
data
struct
ur
e
for
m
ai
ntaining
both
fr
e
quen
t
and
in
fr
e
que
nt
it
e
m
s
to
ov
e
rco
m
e
tim
e
wastage.
They
us
e
d
c
om
pr
ession
te
ch
nique
to
sa
ve
s
p
ace
w
hile
sto
r
ing
it
em
set
s.
Wh
e
n
s
upport
of
it
em
s
chan
ge
s
ev
e
n
that t
i
m
e also it
show
e
d g
ood resu
lt
s.
Un
il
a
nd
Lee
[20],
w
r
ote
a
pap
e
r
on
"I
ncre
m
ental
m
ining
of
weig
hted
m
axi
m
al
fr
equent
it
e
m
set
s
from
dyna
m
ic
databases”
,
dis
cusse
d
how
to
m
ine
m
axi
m
a
l
fr
eq
uen
t
it
em
set
s
by
con
si
de
rin
g
it
e
m
wei
gh
ts
.
Dep
e
nds
on
it
e
m
set
weigh
ts,
tho
se
set
s
wit
h
m
axi
m
u
m
weigh
t
will
be
ta
ken
first
as
m
os
t
fr
equ
e
n
t
it
e
m
s.
Deng
[11],
“
F
ast
m
ining
fr
e
qu
e
nt
it
em
set
s
us
in
g
N
o
de
set
s”,
de
fine
d
a
ne
w
data
str
uctur
e
nam
ed
no
de
set
.
It
stores
t
he
it
e
m
s infor
m
at
ion
in
tree str
uctu
re
s eit
her
pre
ord
er or
post o
r
de
r
of their a
rr
i
va
l i
n
each tra
ns
a
ct
ion
.
Ther
e
after
ap
plied
a
m
ining
al
gorithm
on
that
tree
to
m
i
ne
fa
st.
T
hey
pro
ved
t
heir
pro
posal
incre
as
es
the
m
ining
sp
ee
d
a
nd
acc
ur
acy
.
Y
ao
an
d
Ham
il
t
on
[21],
in
thei
r
arti
cl
e
“M
ining
it
em
set
uti
liti
es
fr
om
transacti
on
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
24
, N
o.
2
,
N
ove
m
ber
2
02
1
:
108
4
-
10
9
0
1086
databases”
,
m
e
ntion
e
d
util
it
y
for
each
it
em
and
dep
e
nds
on
it
em
utilit
y
m
ining
of
it
em
se
ts
and
r
ules
was
done.
Item
s
with
highest
util
it
y
will
be
pr
e
ferred
as
m
axim
u
m
pr
iority
and
it
will
be
con
si
der
e
d
as
first
it
e
m
set
.
Ba
gu
i
a
nd
St
anley
[
22
]
,
i
n
their
researc
h
arti
cl
e
“M
inin
g
fr
e
qu
e
nt
it
e
m
set
s
fr
om
strea
m
ing
transacti
on
data
us
in
g
ge
netic
al
gorithm
s”,
con
si
der
e
d
st
rea
m
ing
da
ta
a
s
input
to
m
ine
and
ge
ne
rate
f
re
qu
e
nt
it
e
m
set
s.
Stream
ing
data
[
23]
,
[24]
m
eans
wh
e
re
data
in
and
out
ta
kes
place
on
a
pa
r
ti
cular
databa
s
e.
It
is
su
bject
e
d
to
co
ntinuo
us
cha
nges
res
pect
to
tim
e.
So
these
kinds
of
datase
ts
wer
e
ve
ry
diff
ic
ult
to
m
ine.
T
he
auth
or
s
pr
oj
ect
ed
a
ge
netic
al
gorithm
wh
ic
h
acce
pts
data
i
n
sli
di
ng
wi
ndow
f
or
m
at
as
input
a
nd
use
d
dr
ift
con
ce
pt to
p
ic
k fr
e
quent it
em
s
.
Chiu
et
al
.
[12
]
,
“In
c
rem
enta
l
m
ining
of
cl
os
e
d
inter
-
tran
sact
ion
it
em
sets
ov
e
r
data
str
ea
m
sli
din
g
windows”,
a
ppl
ie
d
a
novel
m
echan
ism
to
fi
nd
cl
os
e
d
it
e
m
set
s.
T
hey
al
so
co
ns
ide
re
d
str
ea
m
ing
data
to
m
ine.
Fr
om
that
they
first
m
ine
sli
di
ng
wind
ow
in
form
ation
a
fter
that
sli
de
will
m
ov
e
to
nex
t
pa
rt
of
dataset
.
Th
os
e
it
e
m
s
wh
ic
h
a
r
e
ver
y
cl
os
e
re
la
ti
on
to
f
ulfill
stron
g
ass
ocia
ti
on
wer
e
give
n
highest
pri
or
it
y
in
m
ining
.
They
pro
ved it
is b
et
te
r
ap
plica
ble
f
or stream
ing
dat
a.
Vige
r
et
al
.
[
25]
,
“F
HM+:
fa
ste
r
hi
gh
util
it
y
it
e
m
set
m
ini
ng
us
i
ng
le
ngth
upper
-
bound
reducti
on”,
discusse
d
high
util
it
y
m
ining
.
They
def
in
ed
FH
M+
al
go
rith
m
fo
r
fast
m
ini
ng
de
pe
nd
s
on
it
e
m
s
util
i
ty
.
Wh
il
e
ta
kin
g i
te
m
s u
t
il
ities
, also
fo
c
us
e
d on up
per
bound o
f
al
l t
ra
ns
act
io
ns
to
r
e
du
ce
in
fr
e
qu
e
nt
it
e
m
s.
Deng
a
nd
Lv
[26],
ti
tl
ed
“PreP
os
t
+
:
A
n
eff
ic
ie
nt
N
-
li
sts
-
base
d
al
gorithm
fo
r
m
ining
fr
e
quent
it
e
m
set
s
via
C
hildr
e
n
–
Pare
nt
Equ
iv
al
ence
pru
ning”,
w
r
ote
an
al
go
rithm
nam
ed
Pr
ePos
t
+
fo
r
ef
fici
ent
m
inin
g
process
.
A
tree
was
generate
d
with
le
ft
and
r
igh
t
child
’s
by
m
ake
us
e
of
N
-
li
st
as
anetwork
[
27]
,
an
d
ap
plied
pru
ning
at
le
ft
par
t
a
nd
rig
ht
par
t
of
t
he
tre
e
ref
e
rr
e
d
as
e
qu
i
valence
pru
ning.
It
pro
ve
d
m
or
e
ef
fici
ent
than
existi
ng appr
oa
ches.
Han
et
al
.
[
28
]
,
“M
ining
fr
e
qu
e
nt
patte
r
ns
without
cand
i
date
gen
e
rati
on:
a
fr
eq
ue
nt
-
patte
rn
tree
appr
oach
”
,
is
a
gen
e
ral
ap
proach
for
m
ining
freq
ue
nt
it
em
s.
It
do
esn’
t
gen
e
rates
can
di
date
key
for
e
ach
1
-
it
e
m
,
2
-
it
em
se
ts.
It
st
or
es
sup
port
c
ount o
f
a
ll
it
e
m
s
in
a
ta
ble
an
d
ge
ner
at
ed
a
n
fp
-
tree w
her
e
each
no
de
li
nk
s
with
res
pecte
d
it
e
m
s
[2
9].
Daw
ar
da
n
G
oya
[30],
“UP
-
Hist
tree:
An
eff
i
ci
ent
data
struc
ture
f
or
m
ining
hig
h
util
it
y
patte
rn
s
from
transacti
on
data
bases”,
de
rive
d
a
no
vel
tree
struct
ur
e
nam
ed
UP
-
Hist
tree.
It
m
ai
ntain
s
a
histo
gr
am
of
e
ach
tra
ns
act
io
nal
it
em
s
and
associ
at
e
it
wi
th
eac
h
node
of
the
t
ree.
T
he
histo
gr
am
al
lows
cal
culat
ion
of
enh
a
nce
d
e
ff
ic
acy
estim
at
es f
or ef
fectual
prun
i
ng of t
he
se
arch space
.
Tsen
g
et
al
.
[31],
“Ef
fici
ent
al
gorithm
s
fo
r
m
ining
high
util
it
y
ite
m
set
s
fr
om
transacti
onal
databases”
,
im
plem
ent
ed
UP
-
Grow
t
h
an
d
U
P
-
G
r
ow
t
h+
al
gorithm
s
fo
r
m
i
ning
high
util
ity
it
e
m
set
s.
At
each
sta
ge
pr
un
i
ng
was
done
t
o
fil
te
r
irrele
van
t
it
e
m
s
and
l
ow
ut
il
i
ty
it
e
m
s
[3
2]
.
Po
st
diff
set
a
lgorit
hm
[3
3]
in
ra
re
patte
rn
re
duces
can
did
at
es c
ount a
nd c
onsum
ed
le
ss ti
m
e f
or lo
ng transa
c
ti
on
al
d
at
a
base
s
.
2.
PROP
OSE
D MET
HO
DOL
OGY
Scan
ning
th
e
da
ta
base
is
not
m
uch
com
plex
w
hen
volum
e
of
data
is
fi
xe
d
bu
t
w
hen
it
is
grad
ually
increasin
g
the
n
it
’s
diff
ic
ult
to
m
ine.
In
this
reg
a
rd
it
is
ne
eded
t
hat
to
up
date
curre
nt
da
ta
structu
re
with
ne
w
data
with
ou
t
proces
sin
g
from
scratch.
T
o
ac
hieve
this
it
is
m
and
at
ory
to
def
i
ne
an
d
co
nst
ru
ct
a
datast
r
uctu
re
wh
ic
h
nee
ds
one
scan
f
or
dynam
ic
m
ining
.
More
ov
e
r
the
dataset
sh
ould
be
sorte
d
in
an
a
pp
r
opriat
e
order
t
o
fasten
the
proc
ess
an
d
rem
oves
barrier
on
s
earchi
ng
for
ra
ndom
it
e
m
s.
To
co
nque
r
the
m
entioned
pro
blem
s
a
nodeset
str
uctu
re
was
s
uggest
ed.
T
he
nodes
e
t
req
uire
s
ei
ther
pr
e o
r
der
o
r
post
orde
r
of
n
odes
in
the
tree
.
Her
e
pr
e
orde
r was t
aken
f
or im
ple
m
entat
ion
s
o
it
is re
qu
i
red to
gen
e
rate P
OC t
ree.
Along
with
no
deset,
FIN
al
gorithm
us
ed
to
disco
ver
fr
e
qu
ent
it
e
m
s
fr
om
scratch.
It
was
achieve
d
by
sel
ect
ing
node
by
node
in
se
t
enu
m
erati
on
tree,
an
d
al
so
avo
i
ds
re
petit
ive
searc
h
by
usi
ng
pru
ni
ng
at
each
node.
By
consi
der
i
ng
pre
ord
er
on
ly
it
is
po
ssible
to
sel
ect
fr
e
qu
e
nt
it
e
m
s
by
le
vel
wise
fr
om
tree.
To
achiev
e
desire
d
dynam
ic
it
e
m
set
m
ining
t
he
PO
C
t
ree
needs
dynam
ic
updations
incessa
ntly
f
or
each
ne
wly
ad
de
d
record
.
It
is
do
ne
by
m
ai
ntainin
g
a
dataset
that
store
s
each
and
e
ve
ry
transacti
on
inf
or
m
at
ion
and
c
al
le
d
as
In
c
rem
ental
p
r
e orde
red co
de
d (
IPOC
)
tree.
The
ste
ps
fo
ll
owed
in ge
ner
at
ion
of
dynam
ic
it
e
m
s
et
s b
y ad
diti
on
of
new da
ta
are:
Inp
ut
:
a
datase
t D
.
Gen
e
rate a
nor
m
al
pr
e
order
e
d
c
od
e
d (
P
OC
)
tree f
or
D
.
Appe
nd n
e
w d
at
a d
1 t
o o
rigina
l data D
.
Gen
e
rate I
PO
C
tree fo
r
e
xisti
ng a
nd n
e
w data
(lin
k
new it
e
m
s info wit
h
e
xis
ti
ng
nodes
)
.
Apply FIM
alg
or
it
hm
s o
n u
pd
at
ed
data
to
m
i
ne fre
qu
e
nt it
e
m
se
ts.
If
ne
w data
d2 a
dd
e
d
t
hen re
pe
at
step
3
a
nd
4
to
g
et
update
d
it
em
s
.
Ou
tp
ut:
F
re
quent it
em
se
ts for
dynam
ic
d
at
a
.
Co
ns
ide
r
a
d
a
ta
set
D
, give
n
as sho
wn
in
T
a
ble 3
:
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
IPO
C
: an ef
fi
ci
ent appro
ac
h
f
or
dy
namic
as
s
ociatio
n
r
ule
ge
ner
ation
us
i
ng inc
reme
nta
l
…
(
P. Na
res
h
)
1087
Table
3
.
T
ra
nsa
ct
ion
database
w
it
h o
rd
e
red it
e
m
s o
f
m
in_
s
up
2
Tr
an
sactio
n
I
D
Ite
m
s
Ordered I
te
m
s
T20
0
I1,I6,I7
I1,I6
T20
1
I1,I2,I3,
I5
I2,I3,I5,
I1
T20
2
I2,I3,I5,
I9
I2,I3,I5
T20
3
I2,I3,I5,
I8
I2,I3,I5,
T20
4
I2,I3,I4,
I5,I6
I2,I3,I5,
I6
This
T
able
3
c
on
ta
in
s
trans
ac
ti
on
id’
s,
it
em
s
resp
ect
to
ea
ch
tran
sact
ion
and
orde
red
it
e
m
s
der
ive
d
by
a
pp
ly
in
g
m
i
n_
s
uppo
rt(
2)
.
I
4
,
I
7,
I
8
a
nd
I
9
are
el
i
m
inate
d
f
or
m
order
e
d
it
e
m
s
li
st
becau
se,
their
s
upport
is
le
ss
than
m
in_
su
pp
or
t.
By
usi
ng
t
he
rest
or
it
e
m
s
a
PO
C
tr
ee
is
goin
g
to
be
gen
e
rated
a
s
sho
wn
i
n
Fi
gure
1.
So
i
n nex
t
ste
p, ge
ne
rate a P
O
C t
ree for gi
ve
n data D
.
Figure
1.
P
OC
t
ree
A
ne
w
data
d1
is
add
ed
to
D
,
and
the
n
the
P
OC
will
becom
e
IP
OC
by
m
aking
up
date.
Af
te
r
a
dd
i
ng
new
dataset
d1
to
D
in
Ta
ble
4,
s
om
e
it
e
m
s
su
pp
or
t
sat
isfie
s
the
m
in_
sup
crit
eria.
S
o
I
7
and
I
8
will
be
adde
d
to
existi
ng
tree
and
al
so
ne
w
fr
e
qu
e
nt
it
e
m
s
will
be
gen
e
rat
ed
inclu
ding
ne
w
data.
Dep
e
nd
s
on
the
f
requenc
y
count
of
eac
h
it
e
m
the
it
e
m
s
order
will
change
in
orde
red
it
e
m
s
li
st.
So
it
is
no
t
need
e
d
to
m
ine
fr
om
sc
ratc
h
(ex
ist
in
g
data).
In
ste
a
d
of
t
hat
new
it
e
m
s
count
is
update
d
i
n
tree
str
uct
ur
e
,
by
seei
ng
c
ou
nt
it
is
easy
to
m
ine
fr
e
qu
e
nt it
em
s.
Th
e
foll
ow
i
ng tree
descr
i
bes t
he
I
PO
C
struc
ture.
Table
4
.
Orde
r
ed
it
em
s o
f
ori
gin
al
(D) a
nd new tra
ns
act
io
n database
(d1)
Tr
an
sactio
n
I
D
Ite
m
s
Ordered I
te
m
s
Origin
al Data
-
D
T20
0
I1,I6,I7
I1,I6,I7
T20
1
I2,I3,I5
I2,I3,I5
T20
2
I2,I3,I5,
I9
I2,I3,I5
T20
3
I2,I3,I5,
I8
I2,I3,I5,
I8
T20
4
I2,I3,I4,
I5,I6
I2,I3,I5,
I6
New data
-
d1
T20
5
I1,I6,I7,
I8
I1,I6,I8,
I7
T20
6
I1,I2,I3,
I8
I2,I3,I1,
I8
T20
7
I1
I1
In
the
Fi
gure 2,
root nod
e is e
m
pt
y no
de
a
nd h
ad
chil
d’
s
. Each
nod
e
repre
sents one item
li
ke
I1
, I2
…
al
ong
with
it
s
fr
eq
ue
ncy
coun
t.
Ou
tsi
de
the
e
ach
node
the
it
e
m
s
pr
eo
rd
e
r
is
rep
r
esente
d.
I
t
sh
ows
the
or
der
in
wh
ic
h
al
l
the
t
ran
sact
io
nal
it
em
s
wer
e
m
ined
to
obta
in
f
re
qu
e
nt
it
e
m
s.
Fo
rm
the
ob
ta
in
ed
it
e
m
s,
it
is
need
e
d
to
dr
a
w
valid
a
sso
ci
at
ion
r
ules
wh
ic
h
gi
ve
r
el
at
ion
sh
i
p
am
ong
al
l
it
e
m
s
a
nd
te
ll
s
the
an
al
yst
wh
ic
h
it
em
s
are
m
os
t
fr
equ
e
nt.
By
us
ing
IPOC
tree
str
uctur
e
,
m
or
e
tim
e
need
e
d
for
m
ining
will
s
ave
an
d
m
ining
fast,
eff
ic
ie
ncy is i
m
pr
ov
e
d.
T
hes
e are t
he
m
os
t fr
e
qu
e
nt ass
oci
at
ion
ru
le
s
dra
wn from
D
a
nd d1 wit
h 4 item
s
:
{I1
I6
I8
I7
}
, {I2
I3
I5
I
8}, {I
2
I3
I5
I
6}
a
nd {
I2
I3
I1
I
8}
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
24
, N
o.
2
,
N
ove
m
ber
2
02
1
:
108
4
-
10
9
0
1088
Fig
ure
2.
IPOC
tree
f
or
old
da
ta
(
D
)
a
nd n
e
w
d
at
a
(d1)
3.
RESU
LT
S
AND DI
SCUS
S
ION
Ex
per
im
ental
backg
rou
nd
:
Pyt
hon
3.6
.4
was
use
d
for
i
m
ple
m
entin
g
the
need
e
d
al
go
rit
hm
s.
The
j
upyt
er
la
b
us
ed
as
inte
grat
ed
devel
op
m
ent
env
i
ronm
ent
(I
DE
)
wh
e
r
e
source
co
de
i
s
wr
it
te
n
an
d
s
uitable
dataset
s w
e
re uplo
a
ded. T
he
da
ta
set
s
m
ay
f
ilt
ered
t
o
gi
ve
m
or
e e
ff
ic
ie
nt in
form
ation
, a
nd h
ere it
is possi
ble t
o
analy
ze
the
da
ta
set
s
and
outc
om
es
by
m
eans
of
grap
hs
a
nd
scat
te
r
plo
ts.
To
ac
hieve
t
hi
s
it
is
m
and
at
or
y
t
o
us
e
buil
t
-
in li
braries
w
hich
s
uppo
rt addit
ion
a
l functi
onal
it
ies.
Dataset
s
us
e
d:
To
a
naly
ze
an
d
disco
ver
t
he
fr
e
qu
e
nt
it
em
s
so
m
e
sta
nd
ar
d
dataset
s
we
r
e
nee
ded.
I
n
this
im
ple
m
ent
at
ion
m
us
hro
om
,
con
nect,
ch
ess
an
d
onli
ne
retai
l
dataset
s
wer
e
use
d.
M
ush
r
oom
,
conne
ct
an
d
chess
da
ta
set
s
wer
e
do
wn
l
oa
ded
f
r
om
fr
equent
it
e
m
set
m
i
ning
i
m
ple
m
entat
ion
s
(
F
IMI
)
re
posit
ory
and
on
li
ne
retai
l
dataset
was
ta
ke
n
fro
m
UCI
m
achine
le
ar
ning
re
po
sit
or
y
[
34]
.
The
fo
ll
owin
g
T
able
5
disp
l
ay
s
the
dataset
s
with
their
instance
s,
at
tribu
te
s,
siz
e
and
no
of
it
e
m
s
pr
esent.
All
the
dataset
s
wer
e
tran
sac
ti
on
al
dataset
s
m
or
e
su
it
able
f
or
m
i
ning
of
fr
e
que
nt
it
e
m
s.
Table
6,
il
lust
rates
the
c
om
par
at
ive
stud
y
(stat
ist
ic
s)
of
existi
ng and
propose
d
al
gorithm
s b
y m
eans o
f
tim
e and
m
em
oy co
ns
u
m
ption
s
for dif
fer
e
nt d
at
aset
s.
Table
5
.
Datas
et
s d
esc
riptio
n
Dataset
No
of
I
n
stan
ces
No
of
Attr
ib
u
tes
Size
Ite
m
s
Ch
ess
3196
36
3
4
9
KB
76
Mus
h
roo
m
8124
22
3
6
5
KB
119
Co
n
n
ect
6
7
5
5
7
42
5
8
2
9
KB
129
On
lin
e
Retail
5
4
1
9
0
9
8
2
3
1
6
0
KB
2603
Table
6
.
C
om
par
iso
n of al
l d
a
ta
set
s
Alg
o
rith
m
/Dataset
Mus
h
roo
m
Co
n
n
ect
Ch
ess
On
lin
e r
etail
Ti
m
e
(sec)
Me
m
o
r
y
(M
B)
Ti
m
e
(sec)
Me
m
o
r
y
(M
B)
Ti
m
e
(sec)
Me
m
o
r
y
(M
B)
Ti
m
e
(sec)
Me
m
o
r
y
(M
B)
FP
0
.45
2
7
.29
1
9
.89
4
7
.85
0
.27
1
7
.95
5
6
.29
7
6
.25
sPOC
0
.77
1
9
.29
2
0
.47
4
4
.28
0
.36
1
5
.46
5
8
.65
7
4
.62
IPOC
(
Prop
o
sed
)
2
.24
1
8
.87
2
1
.21
5
3
.49
0
.48
1
5
.93
6
1
.87
8
3
.54
The
F
ig
ur
e
3
il
lustrate
s
tim
e
t
aken
by
FP,
P
OC,
PPC
an
d
I
PO
C
al
gorithm
s
fo
r
m
us
hro
om
dataset
,
in
3(
a
)
a
nd
c
onne
ct
dataset
in
3(
b)
.
The
IPOC
sh
owe
d
bette
r
pe
rfor
m
ance
whil
e
m
ining
fr
e
quent
it
e
m
s.
Figu
re 4
il
lustrate
s
tim
e
ta
ken
by
FP,
PO
C,
PPC
a
nd
IP
OC
al
gorith
m
s
fo
r
ches
s
da
ta
set
,
in
4(
a)
and
retai
l
dataset
in
4(b)
. T
he IP
O
C sh
ow
e
d bett
er
perform
ance whil
e m
ining f
reque
nt it
e
m
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
IPO
C
: an ef
fi
ci
ent appro
ac
h
f
or
dy
namic
as
s
ociatio
n
r
ule
ge
ner
ation
us
i
ng inc
reme
nta
l
…
(
P. Na
res
h
)
1089
(a)
(b)
Figure
3.
Tim
e
com
par
iso
ns
of
dataset
s
;
(a)
m
us
hr
oom
(
b)
connect
d
at
aset
s
(a)
(b)
Figure
4.
Tim
e
co
m
par
iso
ns
of
dataset
s
;
(a) c
hess (
b
) o
nline
retai
l
dataset
s
4.
CONCL
US
I
O
N
I
n
t
h
i
s
p
a
p
e
r
,
f
i
n
d
i
n
g
f
r
e
q
u
e
n
t
i
t
e
m
s
e
t
s
a
n
d
a
s
s
o
c
i
a
t
i
o
n
r
u
l
e
m
i
n
i
n
g
f
o
r
v
a
r
i
o
u
s
d
a
t
a
s
e
t
s
w
e
r
e
a
n
a
l
y
z
e
d
.
W
h
i
l
e
w
o
r
k
i
n
g
w
i
t
h
s
t
a
t
i
c
d
a
t
s
s
e
t
s
t
h
e
r
e
i
s
n
o
i
s
s
u
e
s
i
n
c
o
m
p
l
e
x
i
t
y
i
n
m
i
n
i
n
g
a
n
d
t
i
m
e
c
o
n
s
u
m
p
t
i
o
n
.
W
h
e
n
d
e
a
l
i
n
g
w
i
t
h
d
y
n
a
m
i
c
d
a
t
s
e
t
s
i
t
i
s
s
u
b
j
e
c
t
t
o
c
o
n
t
i
n
u
o
u
s
u
p
d
a
t
e
s
a
n
d
m
i
n
i
n
g
b
e
c
o
m
e
d
i
f
f
i
c
u
l
t
a
s
d
a
t
a
s
e
t
v
a
r
i
e
s
i
n
s
i
z
e
a
n
d
t
r
a
n
s
a
c
t
i
o
n
c
o
u
n
t
.
S
o
m
e
p
r
e
v
i
o
u
s
a
l
g
o
r
i
t
h
m
s
r
e
f
e
r
r
e
d
i
n
s
u
r
v
e
y
w
e
r
e
u
n
a
w
a
r
e
o
f
d
y
n
a
m
i
c
d
a
t
a
h
a
n
d
l
i
n
g
a
n
d
s
o
m
e
w
e
r
e
d
o
i
n
g
u
n
w
a
n
t
e
d
t
a
s
k
s
w
h
i
c
h
d
e
t
e
r
i
o
r
a
t
e
t
h
e
m
i
n
i
n
g
p
r
o
c
e
s
s
b
y
w
a
s
t
i
n
g
t
i
m
e
.
S
o
t
h
o
s
e
i
s
s
u
e
s
w
e
r
e
h
a
n
d
l
e
d
i
n
t
h
i
s
p
a
p
e
r
b
y
a
d
o
p
t
i
n
g
t
r
e
e
s
t
r
u
c
t
u
r
e
s
a
n
d
F
I
M
a
l
g
o
r
i
t
h
m
s
w
h
i
c
h
i
n
t
e
r
n
s
e
n
h
a
n
c
e
d
t
o
w
o
r
k
w
i
t
h
d
y
n
a
m
i
c
d
a
t
a
b
a
s
e
.
P
r
o
p
o
s
e
d
I
P
O
C
t
r
e
e
w
i
t
h
n
o
d
e
s
e
t
c
o
n
s
i
d
e
r
s
p
r
e
o
r
d
e
r
o
f
a
l
l
t
r
a
n
s
a
c
t
i
o
n
a
l
i
t
e
m
s
a
n
d
i
n
c
r
e
m
e
n
t
a
l
l
y
u
p
d
a
t
e
t
h
e
t
r
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e
w
h
e
n
e
v
e
r
n
e
w
d
a
t
a
i
t
e
m
s
w
e
r
e
a
d
d
e
d
.
F
I
N
a
l
g
o
r
i
t
h
m
p
a
r
a
l
l
e
l
l
y
a
n
d
c
o
n
t
i
n
u
o
u
s
l
y
w
o
r
k
s
o
n
t
r
e
e
t
o
m
i
n
e
f
r
e
q
u
e
n
t
i
t
e
m
s
a
n
d
r
e
d
u
c
e
n
u
m
b
e
r
o
f
c
a
n
d
i
d
a
t
e
s
i
n
t
h
e
p
r
o
c
e
s
s
o
f
c
o
n
s
t
r
u
c
t
i
n
g
t
r
e
e
s
.
F
o
u
r
d
a
t
a
s
e
t
s
w
e
r
e
c
o
n
s
i
d
e
r
e
d
t
o
a
n
a
l
y
z
e
t
i
m
e
a
n
d
m
e
m
o
r
y
p
a
r
a
m
e
t
e
r
s
o
f
e
x
i
s
t
i
n
g
a
n
d
p
r
o
p
o
s
e
d
.
T
h
e
p
r
o
p
o
s
e
d
a
p
p
r
o
a
c
h
p
r
o
v
e
d
r
e
d
u
c
e
d
t
i
m
e
c
o
n
s
u
m
p
t
i
o
n
,
t
o
o
k
l
e
s
s
m
e
m
o
r
y
a
n
d
e
f
f
i
c
i
e
n
t
f
o
r
d
y
n
a
m
i
c
d
a
t
a
s
e
t
s
.
REFERE
NCE
S
[1]
J.
Sun,
Y.
Xun,
J.
Zha
ng,
and
J.
Li
,
“
Inc
remen
ta
l
Freque
nt
Ite
m
se
ts
Miningwit
h
FC
FP
Tre
e
,
”
IE
E
E
Ac
c
ess
,
vol.
7
,
pp.
136511
-
136
524,
20
19
,
doi
:
1
0.
1109/ACCESS
.
2019.
2943015
.
[2]
P.
S.
Yu,
and
Y.
Chi,
"
As
socia
t
i
on
Rule
Mining
o
n
Strea
m
s,"
In:
LIU
L.,
ÖZ
SU
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S
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e
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m
s
e
t
m
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n
i
n
g
:
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h
n
i
q
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e
t
o
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l
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t
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s
e
d
a
l
g
o
r
i
t
h
m
,”
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n
t
e
r
n
a
t
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n
a
l
J
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u
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l
o
f
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e
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r
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c
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l
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n
d
C
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m
p
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r
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(
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