Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
23
,
No.
3
,
Septem
ber
2021
, pp.
1602
~
1610
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
23
.i
3
.
pp
1602
-
1610
1602
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
Develop
a dynam
ic DBS
CAN
algorith
m f
or solvin
g in
itial
paramet
er sele
ction p
roblem
of
th
e DBSC
AN algo
rithm
Md. Z
ak
ir
H
ossain,
Md.
Ja
kirul
Islam
, Md.
W
aliur R
ah
m
an
Mi
ah
,
Jahid H
asan
Rony,
Momo
ta
z
Beg
um
Depa
rtment
o
f
C
om
pute
r
Scie
n
ce a
nd
Engi
n
ee
rin
g,
Dhak
a
Unive
r
sit
y
of Engin
e
ering a
nd
Technol
o
g
y
,
Ga
zi
pur,
Bangl
ad
esh
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
1
4
,
2020
Re
vised
Ju
l
1
1
,
2021
Accepte
d
J
ul
1
8
,
2021
The
amount
of
d
at
a
has
be
en
inc
r
ea
sing
expon
ent
i
al
l
y
in
eve
r
y
sec
tor
such
as
banki
ng
sec
ur
it
i
es,
he
al
th
ca
r
e,
educ
a
ti
on,
m
anuf
ac
tur
ing,
consum
er
-
tra
d
e
,
tra
nsporta
ti
on,
a
nd
ene
rg
y
.
Mos
t
of
the
se
dat
a
ar
e
noise,
diff
ere
n
t
in
shape
s,
and
outl
i
ers.
In
such
ca
ses,
it
is
cha
l
le
nging
to
f
i
nd
the
desire
d
d
at
a
c
luste
rs
using
conve
n
ti
o
nal
cl
uster
ing
algorithms
.
DBS
CAN
is
a
popu
la
r
cl
ust
eri
ng
al
gorit
hm
whi
ch
is
widely
used
for
nois
y
,
arb
it
r
ar
y
shape
,
and
outl
ie
r
data.
How
eve
r,
i
ts
pe
rform
anc
e
high
l
y
d
epe
nds
on
th
e
prope
r
se
le
c
ti
o
n
of
cl
uster
rad
ius
(
Eps
)
and
the
m
ini
m
um
n
um
ber
of
point
s
(
MinP
ts
)
tha
t
are
req
uir
e
d
for
form
ing
cl
usters
for
the
giv
e
n
dat
ase
t
.
In
the
ca
se
of
re
al
-
worl
d
cl
usteri
ng
proble
m
s,
it
is
a
diffi
cult
ta
sk
to
sele
ct
th
e
exact
val
ue
of
Eps
an
d
MinP
ts
to
per
form
the
cl
u
steri
ng
on
unknown
dat
ase
ts.
T
o
addr
ess
the
se,
thi
s
pape
r
prop
oses
a
d
y
n
a
m
ic
DBS
CAN
al
gorit
hm
tha
t
ca
l
c
ula
t
es
the
suit
able
val
u
e
for
Eps
and
MinP
ts
d
y
namic
al
l
y
b
y
which
t
he
cl
ust
eri
ng
qual
i
t
y
of
the
give
n
proble
m
will
b
e
inc
r
ea
sed
.
T
h
is
pape
r
evalua
t
es
the
p
erf
orm
a
nce
of
the
d
y
nami
c
DBS
CAN
al
gorit
h
m
over
seve
n
cha
l
le
nging
dat
ase
ts.
Th
e
expe
riment
al
r
e
sults
conf
irm
th
e
eff
ec
t
ive
ness
of
the
d
y
n
amic
DBS
CA
N
al
gorit
hm
ov
er t
he
wel
l
-
known clusteri
ng
al
gor
ithm
s.
Ke
yw
or
ds:
Arbit
rar
y s
ha
pe
DBSCA
N
Eps
In
it
ia
l pa
ram
eter
Mi
nP
ts
Ou
tl
ie
r
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
:
Md.
Ja
kir
ul Isl
a
m
Dep
a
rtm
ent o
f C
om
pu
te
r
Scie
nce a
nd E
ng
i
ne
erin
g
Dh
a
ka U
niv
e
rs
it
y of
E
ng
i
neeri
ng
a
nd Tec
hn
o
lo
gy, Gazi
pur
, Ban
glades
h
Em
a
il
:
j
akirdu
et
@duet.ac.
bd
1.
INTROD
U
CTION
In
t
he
la
st
dec
ades,
c
om
pu
te
r
an
d
in
form
at
i
on
te
c
hnol
og
y
hav
e
bee
n
devel
op
e
d
ra
pid
ly
.
As
a
res
ult,
the
data
volum
e
has
bee
n
incr
eased
m
assively
in
sci
ence
an
d
en
gin
ee
rin
g,
and
it
will
be
increase
d
c
on
st
antly
on
a
la
r
ge
sc
a
le
[1]
.
The
in
crease
of
data
from
te
rab
yt
es
to
pet
byte
s
cha
ng
es
sci
e
nce
a
nd
en
gi
ne
erin
g,
trans
for
ms
diff
eren
t
or
gan
iz
at
ion
f
ro
m
data
-
poor
to
increa
s
ing
ly
data
-
rich
.
This
cause
to d
evel
op
a
si
gn
i
ficant
nu
m
ber
of alg
ori
thm
s in
the f
i
el
d
of
data
cl
us
te
ring.
Cl
us
te
rin
g
is
the
key
to
fi
nd
accurate
data
pa
tt
ern
s
of
la
r
ge
dataset
s
[
2]
.
C
lusterin
g
has
be
en
us
ed
in
m
any
app
li
cat
ion
s
,
inclu
ding
m
ark
et
i
ng
,
ne
twork
i
ng
,
i
m
age
proce
ssin
g,
bio
l
og
y,
geogr
a
phic
obser
va
ti
on
,
web
a
naly
sis
,
and
m
edical
-
ba
sed
ap
plica
ti
ons
[
3
]
.
C
luster
ing
play
s
a
sign
ific
ant
r
ole
in
al
lowing
auto
m
at
ic
identific
at
ion o
f un
la
beled rec
ords by
gro
up
i
ng them
into
cl
us
te
rs
b
ase
d o
n si
m
il
arit
y
m
ea
su
rem
ents
[
4]
.
Re
centl
y,
sev
eral
resea
rche
rs
hav
e
bee
n
fo
c
us
i
ng
on
the
dev
el
opm
ent
of
dif
fe
ren
t
cl
us
te
rin
g
al
gorithm
s,
suc
h
as
BIRC
H
[
5]
,
D
B
SCA
N
[6]
,
k
-
nea
r
est
neig
hbor
[7]
,
m
ini
-
batc
h
k
-
m
eans
[7
]
,
[
8]
,
k
-
m
eans
[7
]
,
[
9]
,
OP
T
ICS
[
10
]
,
a
nd
GM
M
[11]
.
T
hese
cl
us
te
rin
g
al
gorithm
s
are
reco
gniz
ed
i
n
di
ff
e
ren
t
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
Develo
p a dyn
am
ic
DB
SCAN
a
lg
or
it
hm f
or
so
lv
in
g
init
ial
pa
r
amet
er sele
ct
ion
…
(
Md
. Zakir
Ho
ss
ai
n
)
1603
cat
egories:
centr
oid
-
base
d
c
lusterin
g,
gr
a
ph
-
base
d
cl
us
te
rin
g,
par
ti
ti
on
i
ng
cl
us
te
rin
g
and
de
ns
it
y
-
base
d
cl
us
te
rin
g [12].
In
this
researc
h,
we
f
ocu
s
on
the
de
ns
it
y
-
ba
sed
cl
us
te
rin
g
al
gorithm
,
wh
ic
h
m
ai
nly
dep
ends
on
th
e
no
ti
on
of
de
nsi
ty
.
In
th
e
li
te
r
at
ur
e,
t
he
de
nsi
ty
-
based
cl
us
te
rin
g
m
et
ho
d
descr
i
bes
cl
ust
ers
acco
r
ding
to
th
e
high
-
de
ns
it
y
reg
io
ns
w
hich
are
sepa
rated
f
ro
m
the
low
-
de
ns
it
y
reg
io
ns
[1]
.
T
he
cl
us
te
rs
co
ntin
ue
gr
ow
i
ng
un
ti
l
the
de
ns
it
y
exceeds
a
certai
n
thres
hold
[13]
.
Accor
din
g
to
that
,
the
densi
ty
-
base
d
cl
us
te
rin
g
al
go
rithm
has
a
n
a
dvanta
ge
in
creati
ng
gro
up
s
w
it
h
ar
bitrary s
ha
pes.
The
DB
SCA
N
is
a
popu
la
r
de
ns
it
y
-
base
d
cl
ust
ering
al
gorith
m
that
go
al
at
i
den
ti
fyi
ng
the h
ig
h
de
nse
reg
i
on
to
for
m
cl
us
te
rs
and
low
a
reas
to
sepa
rate
the
m
.
The
DBS
CAN
al
gorit
hm
m
a
inly
fo
cuses
on
m
ini
m
iz
ing
th
e
num
ber
of
input
par
am
et
e
rs.
It
disc
ov
e
r
s
cl
us
te
rs
e
ff
ic
ie
ntly
without
us
in
g
s
pecify
ing
t
he
nu
m
ber
o
f
cl
ust
ers
[
14]
.
It h
as
bee
n
s
uccess
f
ully
app
li
e
d
in d
iffe
re
nt
fiel
ds
inclu
ding
m
edical
i
m
ages,
sa
te
ll
it
e
i
m
ages,
an
oma
ly
detect
ion
in
te
m
per
at
ur
e
data,
a
nd
G
P
S
data
[15].
Howe
ver,
the
perform
ance
of
this
al
gorithm
is
hi
gh
ly
de
pe
nd
e
nt
on
tw
o
us
er
-
de
fine
d
pa
ram
eter
s
as
s
how
n
in
Fig
ure
1,
na
m
el
y
Eps
and
Mi
nPts
.
Fo
r
e
xam
ple,
if
the
la
rg
e
val
ue
is
ch
os
en
for
Eps
,
the
n
DB
SCAN
form
s
t
he
cl
us
te
rs
with
dissim
il
ar
data.
On
the
ot
her
ha
nd,
if
a
sm
al
l
value
is
ch
os
e
n
for
E
ps
,
t
he
n
this
te
ch
nique
form
s
the
cl
ust
ers
ha
ving
a
sm
a
ll
a
m
ou
nt
of
sim
il
ar
data.
I
n
s
uc
h
cases
,
t
he
s
el
ect
ion
of
Ep
s
an
d
Mi
nPts
i
s
a
c
halle
ng
i
ng
ta
s
k
for
perf
or
m
ing
cl
us
te
rin
g
on
r
eal
-
w
or
ld
data
set
s,
wh
ic
h
is
the
m
ai
n
con
c
ern
of
t
his
res
earch
.
Alth
ough,
m
any
research
er
s
hav
e
bee
n
f
oc
us
in
g
on
im
pr
ov
i
ng
t
he
pe
rfor
m
ance
of
t
he
DBSCA
N
al
gorithm
us
ing
ei
ther
sel
ect
ing
t
he
init
ia
l
value
of
Eps
or
Mi
nP
ts
dynam
ic
al
l
y
[16
]
-
[
21]
.
The
li
te
ratur
e
sho
ws
that,
the
re
is
no
re
searc
h
works
hav
e
bee
n
ta
ke
n
init
ia
ti
ve
to
sel
ect
the
init
ia
l
value
of
both
Eps
an
d
Mi
nPts
dynam
ic
al
ly
.
Ther
ef
ore,
t
his
pap
e
r
propose
s
a
dynam
ic
DBSCA
N
al
gorithm
that
sel
ect
s
the
init
ia
l
value
of
both
E
ps
a
nd
Mi
nPts
dynam
ic
al
l
y, hopi
ng that
good
qu
al
it
y cl
us
te
rs wit
h bett
er a
c
cur
acy
will
b
e
foun
d
at
the
e
nd of t
he
r
un.
Figure
1. I
niti
al
p
aram
et
er
E
ps
an
d
Mi
nPt
s
The
orga
nizat
ion
of
t
his
pa
pe
r
is
as
f
ollo
ws.
I
n
Sect
io
n
2
,
the
detai
l
of
DBSC
AN
al
gori
thm
is
pr
ese
nted
.
In
Sect
ion
3
,
the
w
orks
relat
ed
to
this
resea
r
ch
a
re
descr
i
be
d.
I
n
Sect
io
n
4
,
the
detai
l
of
the
pro
po
se
d
dynam
ic
DBSCA
N
a
lg
ori
thm
i
s
desc
ribe
d.
Sect
ion
5
de
m
on
strat
es
the
ex
per
im
ental
res
ults
pro
vid
e
d
by
th
e
pro
po
se
d
a
nd
the
well
-
kn
own
dat
a
cl
us
te
rin
g
m
et
ho
ds
.
Sect
ion
6
desc
ribes
th
e
co
ncl
us
io
n
and f
uture
wo
r
k of t
his
resear
ch.
2.
RELATE
D
W
ORK
Cl
us
te
rin
g
is
c
on
si
der
e
d
f
or
pr
e
par
i
ng
a
n
e
ff
ic
ie
nt
unsupe
rv
ise
d
a
naly
sis
thr
ough
t
he
da
ta
.
I
n
t
his
reg
a
rd,
se
ve
ra
l
cl
us
te
rin
g
al
gorithm
s
hav
e
de
velo
pe
d
in
the
la
st
deca
des.
I
n=t
ca
n
be
see
n
that,
thes
e
al
gorithm
s
have
ex
per
ie
nced
diff
ic
ulti
es
w
he
n
the
dataset
s
are
un
st
ru
ct
ured,
noise
,
different
in
sha
pe
s
an
d
siz
es,
an
d
de
nsi
ti
es.
The
DBS
CAN
al
gorith
m
is
recog
nized
as
a
popula
r
densi
ty
-
base
d
cl
us
te
rin
g
al
gorithm
s
wh
ic
h
can
pe
rfor
m
cl
us
te
ring
on
t
he
dataset
s
with
di
ff
e
ren
t
siz
es
and
s
ha
pes
[
7].
H
owe
ver,
it
s
perfor
m
ance
highly
d
e
pends
on th
e
v
al
ue o
f
E
ps
a
nd the
val
ue
of
Mi
nPts
.
Seve
ral
researc
her
s
hav
e
bee
n
condu
ct
e
d
f
or
the
i
m
pr
ovem
e
nt
of
DBSCA
N
al
gorithm
.
Fo
r
e
xam
ple,
in
[
16
]
,
a
ne
w
heurist
ic
is
pro
po
s
ed
a
s
a d
ist
ance
m
e
asur
in
g
m
et
ho
d
t
o
pe
rfor
m
the
cl
us
t
erin
g
in
m
ulti
-
densi
ty
dataset
s.
In
[
17]
,
an
im
pr
oved
DBSC
AN
al
gorithm
cal
le
d
so
ft
DBSCA
N
wh
e
re
fu
zzy
se
t
theo
ry
is
ap
pl
ie
d
t
o
perform
the
clu
ste
rin
g
on
suc
h
dataset
s.
I
n
[1
8],
a
ne
w
DBSA
C
N
cl
ust
ering
al
gorith
m
is
pr
op
os
e
d
f
or
norm
al
iz
ed
dat
aset
s
wh
ic
h
ar
e
pr
ove
n
to
be
an
eff
ic
ie
nt
cl
ust
ering
a
ppr
oa
ch.
H
oweve
r,
this
m
et
ho
d
un
able
to
reso
l
ve
the
pro
blem
of
sel
ect
ing
in
pu
t
par
a
m
et
ers
as
in
th
e
DBSC
AN
al
gorithm
.
In
[19],
an
othe
r
DB
SC
A
N
al
gorithm
based
on
grap
h
-
bas
ed
inde
x
str
uct
ur
e
is
pro
pose
d
f
or
perform
i
ng
cl
ust
erin
g
on
high
-
dim
ension
al
.
In
[20],
the
D
BSC
AN
al
gorithm
is
i
m
ple
mented
in
a
distr
ibu
te
d
syst
em
.
The
distri
bu
te
d
syst
e
m
s
app
ly
in
big
dataset
s
to
pro
cess
the
data
in
a
ver
y
fast
-
gro
wing
way.
P
arall
el
iz
at
ion
al
so
us
es
in
the
distrib
uted
syst
e
m
.
In
[21],
an
im
pr
ov
e
d
DB
SCA
N
al
gorithm
i
s
propose
d
to
reduce
the
com
pu
ta
ti
on
al
tim
e
of
the
existi
ng
DBSCA
N
al
go
rithm
.
This
al
go
rithm
can
divi
de
data
s
pace
into
gri
de
a
nd
then
op
ti
m
iz
es
the
com
pu
ta
ti
on
a
l
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.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
16
02
-
16
10
1604
cost
by
re
du
c
ing
unnece
ssa
r
y
query
oper
at
ion
s
of
the
DBSCA
N
al
gorithm
s.
I
n
[
22]
,
the
pa
rtit
ion
i
ng
te
chn
iq
ue
is
com
bin
aed
with
DBSC
AN
t
o
sel
ect
the
su
it
able
value
of
the
use
r
-
de
fine
d
par
am
eter
s
of
DBSCA
N
al
gorithm
.
Howe
ver,
this
m
et
ho
d
has
not
eva
luate
d
a
gainst
the
dataset
s
with
dif
f
ere
nt
de
ns
it
ie
s.
The
aut
hors
of
[
23
]
ha
ve
in
corp
or
at
ed
t
he
gau
s
sia
n
-
m
eans
into
t
he
D
BSC
AN
al
gorithm
to
i
m
pr
ove
the
sel
ect
ion
of
t
he
value
of
D
BSC
AN
pa
ra
m
et
ers.
H
ow
e
ver,
this
m
et
ho
d
co
uld
not
sh
ow
bette
r
cl
us
te
rin
g
perform
ance
against
de
ns
e
da
ta
set
s.
In
[24
]
,
the
bi
nar
y
di
f
fer
e
ntial
evalu
at
ion
co
nce
pt
is
inco
rpor
at
e
i
nto
the
DBSCA
N
al
gorithm
to
eff
ect
ively
deter
m
ine
the
value
of
DB
SCA
N
par
am
et
ers.
In
[2
5],
a
n
i
m
pr
ove
d
DBSCA
N
cl
ust
ering
al
gorit
hm
nam
e
ly
DBSCA
N
-
KNN
-
GA
is
pro
po
s
ed
by
a
doptin
g
t
he
k
-
near
est
neig
hborh
ood con
ce
pt (KNN
)
and
genet
ic
algorit
hm
(
GA
)
into D
BSC
AN
al
gorithm
s w
hich
fin
ds
the v
a
lue o
f
Eps
a
nd
Mi
nPt
s
dynam
ic
al
l
y.
It
ca
n
be
obs
erv
e
d
that
al
l
of
t
hese
al
gorithm
s
hav
e
di
ffi
culti
es
to
sel
ect
th
e
us
er
-
def
ine
d
pa
ram
et
ers
of
DBSCA
N
al
gorithm
.
Ther
e
fore,
this
stu
dy
pr
op
os
es
a
dynam
ic
DBSCAN
al
gorithm
f
or
non
-
s
ph
e
rical
clusterin
g.
T
he p
rop
os
ed
te
c
hn
i
qu
e
does not re
ly
o
n
any pre
de
fine
d
pa
ram
eter
s as
the
or
i
gin
al
D
BSC
AN
te
c
hniqu
e.
T
he
pro
po
s
ed
m
et
ho
d
cal
culat
es
the
best
Eps
a
nd
Mi
nP
ts
dyna
m
ic
al
l
y,
wh
ic
h
im
pr
ove
s the cl
us
te
r q
ua
li
ty
.
3.
THE
D
BS
CAN CLUSTE
RI
NG ALG
ORIT
HM
The
DBSCA
N
al
gorithm
aim
s
to
ide
ntify
the
hi
gh
de
ns
e
reg
i
on
cl
us
te
rs
by
sepa
rati
ng
them
fr
om
low
de
ns
e
reg
i
on
s
.
It
ha
s
tw
o
us
e
r
-
def
i
ned
pa
ram
et
ers
nam
el
y
Eps
a
nd
Mi
nPts
wh
ic
h
a
re
re
qu
ire
d
t
o
fin
d
the
cl
us
te
rs
of
dataset
s
.
The
m
ain
idea
of
t
he
DBSCA
N
is
th
at
each
point
i
n
the
dataset
is
scan
ned
t
o
det
erm
ine
the
nea
rest
nei
ghbors
within
a
par
ti
cular
dis
ta
nce
[
1
7
]
.
T
o
determ
ine
a
cor
e
-
po
i
nt,
the
num
ber
of
neig
hbors
sh
oul
d
excee
d
the
thre
shold
.
Othe
rw
ise
,
it
m
igh
t
be
a
bor
der
-
point
or
a
no
ise
.
Be
f
or
e
pro
vid
in
g
the
idea
of
the D
B
SCA
N al
gorithm
, s
ome
noti
ons
need
to b
e
d
e
fine
d fi
rst. T
he n
otions are
,
Directly
den
sit
y
-
reac
habl
e
:
A
po
i
nt
q
is
s
ai
d
to
be
di
rec
tl
y
den
sit
y
-
rea
chab
le
f
ro
m
a
po
i
nt
p
,
i
f
a
nd
on
ly
if
the
poin
t
q
is i
n
the
E
ps
nei
ghbor
hood
of point
p
,
as
shown i
n
Fi
gu
re
2
(a
)
.
D
e
n
s
i
t
y
-
r
e
a
c
h
a
b
l
e
:
A
p
o
i
n
t
q
i
s
d
e
n
s
i
t
y
-
r
e
a
c
h
a
b
l
e
f
r
o
m
p
o
i
n
t
p
b
e
c
a
u
s
e
t
h
e
r
e
e
x
i
s
t
s
a
s
e
q
u
e
n
c
e
q
1
,
q
2,
,
.
.
.
,
q
n
w
i
t
h
q
1=
p
,
q
2=
p
,
.
.
.
.
q
n=
q
.
T
h
e
p
o
i
n
t
’
s
q
i
+
1
i
s
d
i
r
e
c
t
l
y
d
e
n
s
i
t
y
-
r
e
a
c
h
a
b
l
e
f
r
o
m
q
i
,
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
2
(b)
.
Densit
y
c
onne
cted
:
A
po
i
nt
q
is
de
ns
it
y
co
nn
ect
e
d
t
o
a
point
p
with
res
pect
to
Ep
s
a
nd
Mi
nPts
if
the
re
is
a
po
int
f
bel
ongs
to
a
dataset
su
ch
that
bo
th
q
an
d
p
a
re
densi
ty
-
reacha
ble
from
f
with
resp
ect
to
E
ps
and
Mi
nPts
, as
shown i
n
Fi
gu
re
2(
c
)
.
Co
re
p
oint
:
A data
point
p
is
a cor
e
point if
the
nu
m
ber
of
points in
it
s
Eps
neig
hborh
ood
is gr
eat
er
tha
n
or eq
ual to
the
Mi
nPts
, as
s
hown in Fi
gure
2
(d)
.
Border
p
oint
:
A
point
is
cal
le
d
bor
der
po
i
nt
if
it
is
a
par
t
of
a
cl
us
te
r
and
not
dense
them
sel
ves,
as
sh
ow
n
in
Fi
gur
e 2
(d)
.
No
ise
po
i
nt
:
A
point is cal
le
d
no
ise
point if
it
does
not bel
ong
to
an
y cl
us
te
r
,
as s
how
n
i
n
F
igur
e
2
(
d)
.
Clust
er
:
A
cl
ust
er
C
is a
non
-
e
m
pty sub
set
of the
d
at
a set
,
a
s sho
wn in Fi
gure
2
(d)
.
Figure
2
.
D
BS
CAN
al
gorith
m
n
otion
s
(
E
ps =
2, Mi
nPts
=
4
),
(a) directl
y
d
e
ns
it
y
-
reac
ha
ble,
(b) d
en
sit
y
reacha
ble,
(c)
densi
ty
co
nnec
te
d,
a
nd (d) c
or
e,
bo
rd
e
r,
nois
e point a
nd clu
ste
r
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
Develo
p a dyn
am
ic
DB
SCAN
a
lg
or
it
hm f
or
so
lv
in
g
init
ial
pa
r
amet
er sele
ct
ion
…
(
Md
. Zakir
Ho
ss
ai
n
)
1605
In
DBSC
A
N
al
gorithm
,
the
co
re
po
i
nt
is
us
e
d
t
o
m
ake
pri
m
ary
cl
us
te
rs.
If
al
l
co
r
e
points
are
densi
ty
-
connec
te
d
from
on
e
a
no
t
her,
the
n
al
l
pr
im
ary
cl
us
te
rs
m
erg
ed
to
t
he
sam
e
c
luster.
Af
te
r
form
at
io
n
of
the
pr
im
ary
cl
u
ste
rs,
the
rst
of
the
data
po
int wil
l
be
trat
ed
as
ei
ther
bord
e
r
po
i
nts
or
n
oise
po
ints.
T
hee
xisti
ng
DBSCA
N
al
gorithm
is d
em
on
strat
ed
in
A
l
gorithm
1
.
Algorithm 1
Psodocode of DBSCAN (
X
,
eps
,
minpts
)
Input:
X
-
a
se
t
of
un
vi
si
te
d
po
in
ts
,
eps
-
th
e
di
st
an
ce
th
re
sh
ol
d,
an
d
minpts
-
th
e
mi
ni
mu
m
number of points
Output:
A set of clusters.
1.
for
each
x
in
do
2.
x :
=
MarkedAsVisited(
True
);
3.
←
ℎ
(
,
)
;
4.
if
(
|
|
<
)
then
5.
x :
=
MarkedAsNoise(
True
);
6.
Else
7.
←
{
}
;
8.
for
each
′
do
9.
:
=
\
′
;
10.
if
(
!
Vis
ited
(
′
)
)
then
11.
x :
=
MarkedAsVisited(
True
);
12.
′
←
ℎ
(
′
,
)
;
13.
if
(
|
′
|
≥
)
then
←
∪
′
;
e
nd if
16.
if
(
′
not
in
C
)
then
←
∪
{
′
}
;
e
nd if
19.
e
nd if
20.
end foreach
22.
e
nd if
23.
end foreach
4.
THE
PROPO
SED
ALGO
R
ITHM
The
m
ai
n
pu
r
pose
of
the
rese
arch
is
to
dete
r
m
ining
the
bes
t
value
for
E
ps
and
Mi
nP
ts
dy
nam
ic
al
l
y
wh
ic
h
will
i
m
pro
ve
the
cl
us
t
er
qual
it
y.
For
the
ex
pla
natio
n
purpose
,
we
co
ns
ide
r
the
i
nput
data
poin
ts
are
sp
rea
d
in
a
tw
o
-
dim
ension
al
(
x
,
y
)
sea
rch
spa
ce
with
the
uni
form
distribu
ti
on. I
n
the
first
stage,
we
cal
cu
la
te
a
distance m
at
rix
D
us
i
ng these
po
ints, as
sho
wn
in Figu
re
3.
nn
n
n
n
n
n
d
d
d
d
d
d
d
d
d
d
d
d
D
3
2
1
2
14
22
21
1
13
12
11
Figure
3. Ma
trix calc
ulate
d
f
r
om
assu
m
ed
data p
oi
nts
Each
el
em
ent
jk
d
(e
uclidia
n
dis
ta
nce
from
data
po
int
j
to
da
ta
po
int
k
)
of
this
m
at
rix
can
be
cal
culat
ed usin
g (1).
2
1
)
(
i
i
jk
P
P
d
(1)
I
n
t
h
e
s
e
c
o
n
d
s
t
a
g
e
,
w
e
c
a
l
c
u
l
a
t
e
t
h
e
m
e
a
n
d
i
s
t
a
n
c
e
M
f
o
r
e
a
c
h
r
o
w
o
f
d
i
s
t
a
n
c
e
m
a
t
r
i
x
D
u
s
i
n
g
t
h
e
(
2
)
.
n
i
jk
i
d
m
1
(2)
The
m
ean
dista
nce
M
is cal
c
ul
at
edas follo
ws,
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.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
16
02
-
16
10
1606
n
m
m
m
M
2
1
In
the
thi
rd
st
age,
we
fin
d
the
m
ini
m
u
m
m
ean
value
f
r
om
M
us
in
g
the
f
ollow
i
ng
(3).
This
f
ound
m
ini
m
u
m
m
ea
n value is
cons
idere
d
to
b
e
th
e closest
near
e
st neig
hborh
oo
d po
i
nt of t
he
th
i
da
ta
p
oi
nt.
n
i
m
m
i
w
h
e
r
e
)
m
i
n
(
m
i
n
(3)
Her
e
,
the
th
i
data
point
is
t
he
highest
den
sit
y
point
wh
ic
h
i
s
de
note
d
by
)
,
(
y
x
h
.
In
this
pap
e
r,
t
he
highest
den
sit
y p
oin
t
)
,
(
y
x
h
is t
he ke
y t
o
sel
ect
the
best
value of
E
ps
a
nd
Mi
nP
ts
,
r
es
pecti
vely
.
In
the
fou
rth
s
ta
ge,
we
cal
c
ul
at
e
Ma
nh
at
ta
n
distance
f
ro
m
the
highest
de
ns
it
y
po
int
h
to
ot
her
data
po
i
nt
P
by t
he fol
lowing
(
4)
.
1
w
h
e
r
e
n
i
P
h
md
i
i
i
(4)
I
n
t
h
e
f
i
f
t
h
s
t
a
g
e
,
w
e
s
e
t
t
h
e
v
a
l
u
e
o
f
E
p
s
=
0
.
5
a
n
d
t
h
e
n
c
o
u
n
t
t
h
e
n
um
b
e
r
o
f
d
a
t
a
p
o
i
n
t
s
t
h
a
t
l
i
e
s
w
i
t
h
i
n
E
p
s
.
A
f
t
e
r
t
h
a
t
w
e
i
n
c
r
e
a
s
e
t
h
e
v
a
l
u
e
o
f
E
p
s
b
y
0
.
5
a
n
d
t
h
e
n
a
g
a
i
n
c
o
u
n
t
t
h
e
n
um
be
r
o
f
d
a
t
a
p
o
i
nt
s
w
i
t
h
i
n
E
p
s
.
T
h
i
s
p
r
o
c
e
s
s
c
o
n
t
i
n
u
e
s
u
n
t
i
l
a
l
o
c
a
l
m
a
x
i
m
um
i
s
r
e
a
c
h
e
d
.
T
h
e
w
h
o
l
e
i
d
e
a
i
s
p
r
e
s
e
n
t
e
d
i
n
F
i
g
u
r
e
4
wh
e
r
e
the
val
ue
of
E
ps
1,
Eps
2,
Ep
s
3
an
d
E
ps
4
is
0.5
,
1.0,
1.5,
a
nd
2.0,
res
pecti
vely
.
I
t
can
be
obse
rved
that
E
ps1
,
E
ps
2
,
Eps3
a
nd
E
ps4
c
onta
in
th
re
e,
f
our
,
five
a
nd
th
ree
data
po
i
nts,
res
pecti
vely
.
He
re,
th
e
Ep
s3
is
the
loca
l
m
axi
m
u
m
,
as
sh
ow
n
in
Fig
ure
5.
I
n
t
he
sixth
sta
ge,
we
sel
ect
Eps
4
as
the
desire
d
Ep
s
and
co
rr
es
po
nd
i
ng
nu
m
ber
of d
at
a
points as
the
de
sired
Mi
nPts
of the
pro
pose
d DBSCA
N
al
gorithm
sh
ows
in
Fi
gure
5.
Figure
4. Data
densi
ty
in
the
di
ff
ere
nt E
ps
Figure
5
.
Rel
at
ion
s
hip
bet
wee
n
E
ps
a
nd
Mi
nP
ts
In
t
he
final
st
age,
we
cal
c
ulate
Ma
nh
at
ta
n
distance
f
ro
m
the
high
-
de
nsi
ty
po
int
h
to
ot
her
data
po
i
nts
P
of
t
he
dataset
.
Af
te
r
that
we
fi
nd
the
c
or
e
poi
nts
a
nd
bo
undar
y
points
ba
sed
on
the
f
ound
Eps
a
nd
Mi
nPts
.
This
proc
ess
will
con
ti
nue
for
al
l
the
unvisit
ed
data
po
i
nts.
T
he
pr
opos
e
d
al
gorit
hm
i
s
dem
on
strat
ed
in Alg
or
it
hm
2
.
5.
RESU
LT
A
N
D ANALY
SIS
5
.
1.
Data se
ts
a
n
d e
xp
eri
me
nt
al
set
u
p
F
o
r
t
h
e
e
x
p
e
r
i
m
e
nt
a
l
p
u
r
p
o
s
e
,
s
e
v
e
n
2
D
a
r
t
i
f
i
c
i
a
l
d
a
t
a
s
e
t
s
a
r
e
c
o
n
s
i
d
e
r
e
d
.
T
h
e
s
e
d
a
t
a
s
e
t
s
a
r
e
h
a
l
f
R
i
n
g
,
t
h
r
e
e
s
pi
r
a
l
s
,
c
o
r
n
e
r
s
,
s
e
m
i
c
i
r
c
u
l
a
r
,
h
a
l
f
m
oo
n
,
h
a
l
f
k
e
r
n
e
l
,
a
n
d
a
g
g
r
e
g
a
t
i
o
n
.
T
h
e
s
e
d
a
t
a
s
e
t
s
h
a
v
e
di
f
f
e
r
e
n
t
d
e
n
s
i
t
i
e
s
i
n
c
l
u
di
n
g
c
l
u
s
t
e
r
s
i
n
s
i
d
e
c
l
u
s
t
e
r
s
,
m
ul
t
i
-
d
e
n
s
i
t
y
,
c
o
n
n
e
c
t
e
d
c
l
u
s
t
e
r
s
,
a
n
d
w
e
l
l
-
s
e
p
a
r
a
t
e
d
d
e
n
s
i
t
i
e
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
Develo
p a dyn
am
ic
DB
SCAN
a
lg
or
it
hm f
or
so
lv
in
g
init
ial
pa
r
amet
er sele
ct
ion
…
(
Md
. Zakir
Ho
ss
ai
n
)
1607
Algorithm 2
The Proposed DDBSCAN Clustering Algorithm
1.
Calculate Euclidean distance matrix
D
from the dataset;
2.
Calculate
the
mean
of
e
ach
row
of
D
.
Fi
nd
th
e
mi
ni
mu
m
me
a
n
va
lu
e
am
on
g
al
l
th
e
me
an
of
ro
w
of
D
.
Th
is
m
in
im
um
me
an
is
th
e
hi
gh
-
density
point
which
is
c
onsidered
to the center point
P
center
;
3.
Set
r
= 0.5;
4.
Set
P
count
[0] = 0;
5.
for
i
:
=1 to
N
do
6.
for
j
:
= 1 to
N
do
7.
calculating the Manhattan distance
d
from
P
center
to
P
i
;
8.
if
(
d
<
r
)
then
P
count
[i] := count the number of points within
r
;
end if
9.
end for
10.
if
(
P
count
[i]>
P
count
[i
-
1])
then
r
:=
r
+0.5;
continue;
11.
E
lse
12.
calculate
diff
i
:=
]
1
[
]
[
i
P
i
P
c
o
u
n
t
c
o
u
n
t
;
13.
end if
14.
MinPts
:=
diff
i
;
;
15.
Eps
:=
r
;
16.
e
nd for
17.
Repeat
18.
for
i
:=1 to
N
do
19.
for
j:
=1 to
N
do
20.
calculate distance
d
ij
;
21.
i
f
(
d
ij
<=
Eps
)
then
22.
if
(
d
ij
=
Eps
)
then
this is the boundary point and count
C;
23.
E
lse
24.
this is not the boundary point and count
C
;
25.
end if
26.
end if end for
27.
end for
28.
if
(
MinPts
<=
C
)
then
29.
th
is
is
th
e
co
re
po
in
t
P
core
.
Calculate
another
core
point
Pcore
an
d
ma
ke
cl
us
te
r
with
boundary point and mark visited;
30.
Else
31.
c
ontinue;
32.
end if
33.
until
all the data points are not visited.
These
dataset
s
al
low
exam
ine
the
pe
rfor
m
ance
of
the
dy
nam
ic
DBSCA
N
al
gorithm
ov
er
the
well
-
known
de
ns
it
y
-
base
d
cl
ust
ering
al
gorithm
s.
The
prop
e
rtie
s
of
t
hese
dataset
s
are
su
m
m
arized
in
Table
1.
All
the
exp
e
rim
ents
wer
e
pe
rform
ed
on
I
ntel
Core
i5
2.4
GH
z
process
or
with
4GBR
AM
on
th
e
pl
at
fo
rm
Mi
cro
s
of
t
Win
dows
10.
W
e
im
ple
m
ent
the
pro
po
se
d
dyna
m
ic
DBSCAN
al
gorithm
us
ing
C+
+
a
nd
ar
ti
fici
al
data set
s
us
in
g M
ATLA
B
.
Table
1.
Su
m
m
ary o
f use
d datase
ts
Da
ta
Set
S
ize
Cla
ss
es
Co
rners
1000
4
Three
Sp
ir
als
312
3
Half
Rin
g
373
2
Se
m
i Ci
rcular
1000
2
Half
M
o
o
n
1000
2
Half
Ker
n
el
1000
2
Ag
g
regatio
n
788
7
5
.
2.
Per
fo
r
m
an
ce
metric
In
this
researc
h,
we
e
val
uate
the
acc
ur
acy
of
the
dynam
i
c
DBSC
AN
al
gorithm
ov
e
r
t
he
dataset
s
i
n
Table
1 usin
g Pur
it
y crit
eri
on, as
s
how
n
i
n (
5). T
he purit
y m
et
ric evaluates t
he q
ualit
y of f
or
m
ed
cl
us
te
r
s.
k
q
j
q
l
j
n
n
P
u
r
i
t
y
1
1
m
a
x
1
(5)
W
h
e
r
e
n
i
s
t
h
e
t
o
t
a
l
n
um
b
e
r
o
f
s
a
m
p
l
e
s
;
l
i
s
t
he
n
u
m
b
e
r
o
f
c
a
t
e
g
o
r
i
e
s
,
j
q
n
i
s
t
h
e
n
u
m
b
e
r
o
f
s
a
m
p
l
e
s
i
n
c
l
u
s
t
e
r
q
t
h
a
t
be
l
o
n
g
s
t
o
t
h
e
o
r
i
g
i
n
a
l
c
l
a
s
s
)
1
(
l
j
j
.
A
c
l
u
s
t
e
r
q
u
a
l
i
t
y
i
s
h
i
g
h
i
f
t
h
e
p
u
r
i
t
y
c
l
o
s
e
t
o
1
0
0
%
.
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.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
16
02
-
16
10
1608
5
.
3
.
Result
analys
is
The
res
ult
of
this
stud
y
is
ob
t
ai
ned
to
exam
i
ne
the
perf
or
m
ance
of
the
pro
po
s
ed
al
gorith
m
and
oth
e
r
well
-
kn
own
al
gorithm
s
su
ch
as
DBSC
AN
[
7],
BD
EDBSC
AN
[
24]
,
an
d
DBSCA
N
-
KNN
-
GA
[
25]
ov
er
these
dataset
s.
W
e
a
pp
ly
the
Dy
na
m
ic
DBSCAN
al
gorithm
on
the
dif
fer
e
nt
sha
pe
dataset
s
in
order
to
visu
al
iz
e
the
sh
a
pes
of
the
c
lusters
.
It
is
i
m
po
rtant
to
c
he
ck
if
the
pro
pose
d
al
gorit
hm
can
pro
duce
c
lusters
with
a
r
bitrary
sh
a
pes
si
nce
it
is
one
of
t
he
prim
ary
req
ui
re
m
ents
of
de
ns
i
ty
-
based
cl
us
te
rin
g
al
gorit
hms.
Fi
gure
6
s
ho
ws
t
he
cl
us
te
r for the
Corner
d
at
aset
wh
e
re t
he pr
opos
e
d
al
gorithm
selec
ts
Eps
=
2.5 a
nd
Mi
nPts
= 12
dynam
icall
y.
A
f
t
e
r
t
h
a
t
,
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
t
h
e
p
r
o
p
o
s
e
d
d
y
n
a
m
i
c
D
B
S
C
A
N
a
l
g
o
r
i
t
hm
i
s
e
v
a
l
u
a
t
e
d
o
v
e
r
t
h
e
t
h
r
e
e
s
p
i
r
a
l
s
d
a
t
a
s
e
t
.
F
o
r
t
h
e
s
e
d
a
t
a
s
e
t
s
,
t
h
e
p
r
o
p
o
s
e
d
a
l
g
o
r
i
t
hm
s
e
l
e
c
t
s
E
p
s
=
1.
5
a
n
d
M
i
n
P
t
s
=
2
d
y
n
a
m
i
c
a
l
l
y
a
n
d
c
r
e
a
t
e
s
c
l
u
s
t
e
r
s
,
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
7
.
T
h
e
f
o
r
m
a
t
i
o
n
o
f
t
h
e
c
l
u
s
t
e
r
s
b
y
t
h
e
pr
o
p
o
s
e
d
a
l
g
o
r
i
t
hm
f
o
r
t
h
e
r
e
s
t
o
f
t
h
e
d
a
t
a
s
e
t
s
i
s
s
h
ow
n
i
n
F
i
g
u
r
e
8
.
E
x
p
e
r
i
m
e
nt
a
l
r
e
s
u
l
t
s
o
f
f
o
u
r
d
i
f
f
e
r
e
n
t
D
B
S
C
A
N
a
l
g
o
r
i
t
hm
s
s
h
o
w
n
i
n
T
a
b
l
e
2
.
Figure
6. Co
rners
dataset
cl
ust
ering res
ult
Figure
7. Th
re
e sp
iral
s
datase
t
cl
us
te
rin
g res
ult
Figure
8. The
re
su
lt
s of
perf
orm
ing
cluste
rin
g usin
g
t
he pr
opose
d DBSC
A
N
al
go
rithm
o
n
half
rin
g, sem
i
ci
rcu
la
r, h
al
f
m
oon, hal
f k
er
ne
l, an
d
a
ggre
gation datase
ts
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
Develo
p a dyn
am
ic
DB
SCAN
a
lg
or
it
hm f
or
so
lv
in
g
init
ial
pa
r
amet
er sele
ct
ion
…
(
Md
. Zakir
Ho
ss
ai
n
)
1609
Table
2.
E
xper
i
m
ental
r
esults
of f
our dif
fer
e
nt D
BSC
A
N
al
gorithm
s
Data Set
DDBSC
AN
DBSC
AN
BDEDBSC
N
DBSC
AN
-
KNN
-
GA
Pu
rity
(%)
Pu
rity
(%)
Pu
rity
(%)
Pu
rity
(%)
Co
rners
100
9
1
.33
100
100
Three
Sp
ir
als
100
9
2
.14
9
9
.52
9
9
.33
Half
Rin
g
9
9
.97
9
0
.26
9
9
.21
9
9
.37
Se
m
i Ci
rcular
100
9
0
.04
9
9
.10
9
9
.61
Half
M
o
o
n
9
9
.98
9
1
.46
9
9
.75
9
9
.75
Half
Ker
n
el
9
9
.5
9
1
.12
9
9
.01
9
9
.31
Ag
g
regatio
n
9
2
.61
7
1
.42
9
2
.51
8
1
.42
6.
CONCL
US
I
O
N
In
this
resea
rc
h,
we
are
m
oti
vated
to
el
i
m
i
nate
the
dr
a
wbacks
of
the
or
i
gin
al
DBSC
A
N
al
gorithm
.
The
sel
ect
ion
of
E
ps
an
d
Mi
nPts
in
the
D
BSC
AN
al
go
rithm
is
a
chall
e
ng
i
ng
ta
s
k
in
the
real
w
or
l
d.
If
th
e
DBSA
C
N
has
chosen
a
la
rg
e
value
for
E
ps
t
hen
DBSC
AN
form
s
the
cl
us
te
rs
ha
vi
ng
diss
i
m
i
la
r
data.
On
the
oth
e
r
hand,
if
a
sm
all
value
is chosen
f
or
Ep
s
,
the
n
this
te
ch
nique f
orm
s
the
cl
u
ste
rs
ha
vi
ng
a
sm
al
l
a
m
o
un
t o
f
si
m
il
ar
data.
I
n
this
researc
h,
we
a
ddress
the
init
ia
l
value
sel
ect
ion
probl
e
m
of
the
DBSCAN
al
gorith
m
an
d
pro
po
se
a
dynam
ic
DBSCA
N
al
gorithm
t
o
rem
ov
e
init
ia
l
par
am
et
er
s
ensiti
vity
.
The
pro
posed
te
c
hn
i
que
cal
culat
es
the
best
E
ps
a
nd
Mi
nPts
dy
nam
ic
al
ly
,
wh
ic
h
i
m
pr
ov
es
t
he
cl
us
te
r
qual
it
y.
The
e
xp
e
rim
ent
al
resu
lt
s
evaluate
d
the
pe
rfor
m
ance
of
the
dynam
ic
D
BSC
AN
al
gori
thm
fo
r
va
rio
us
2D
data
set
s
and
c
om
par
ed
it
with
the
DBSC
AN,
BDEDBSC
A
N
,
an
d
DBSC
A
N
-
KNN
-
G
A
al
gorithm
s.
The
resu
l
t
s
hows
th
e
bette
r
pe
rform
ance
of
the
pro
po
se
d
Dynam
ic
DBSCAN
al
go
rithm
ov
er
the
ot
her
existi
ng
al
gorithm
s
on
seven
var
i
ou
s
da
ta
set
s
.
Fu
tu
re
researc
h
on
D
DBSC
AN
sho
uld
c
onside
r
the
f
ollow
i
ng
iss
ues
.
In
t
he
D
DBSC
AN
al
gorithm
,
we
us
e
pair
-
wise
Eucl
idian
distance
,
so
wh
e
n
the
data
set
is
la
rge,
it
s
per
form
a
nce
is
red
uc
ed
.
If
the
inter
-
c
luster
distance is l
ow, the D
DBSCA
N
al
go
rithm
p
erfor
m
ance w
il
l be
dec
reased
.
REFERE
NCE
S
[1]
C.
Cassisi,
A.
Ferro,
R.
Giugn
o,
G.
Pigol
a,
an
d
A.
Pulvire
nt
i,
"Enha
nci
ng
de
nsit
y
-
b
ase
d
c
luste
ring:
Para
m
ete
r
red
uction
and
outl
ie
r
detec
ti
on,
"
Information
Syste
ms
,
vol.
38,
no.
3,
pp.
317
-
330,
2013,
doi:
10.
1016/j.is.
201
2.
09.
0
01
.
[2]
S.
Sharm
a,
J.
Agrawal
,
S.
Ag
ar
wal,
and
S.
Sha
r
m
a,
“
Mac
hine
l
e
arn
ing
t
ec
hniqu
e
s
for
dat
a
m
ini
n
g:
A
surve
y
,
”
in
2013
IEE
E
Int
ernati
onal
Conf
ere
nce
on
Comput
ati
onal
Int
el
l
igence
and
Computing
Re
search
,
pp.
1
-
6,
Dec
.
201
3,
doi:
10
.
1109/IC
CIC.
2013.
67241
49.
[3]
S.
Agarwal
,
“
Da
ta
m
ini
ng:
Dat
a
m
ini
ng
concept
s
and
te
chn
ique
s,
”
in
2013
Int
ernati
onal
Con
fe
re
nce
on
Mac
hin
e
Inte
lligen
ce and Re
search Advan
ce
ment
,
De
c. 20
13,
pp
.
203
-
207
,
doi: 10.
1109
/IC
MIRA
.
2013.
45.
[4]
Q.
Li
u
,
M.
Den
g,
Y.
Shi
,
and
J.
W
ang,
"A
de
nsit
y
-
b
ase
d
spa
t
ia
l
cl
ust
eri
ng
algorithm
considering
both
sp
at
i
a
l
proximit
y
and
at
tr
ibut
e
sim
il
arit
y
,
"
Comp
ute
rs
&
Geos
ci
en
ce
s
,
vo
l.
46,
pp.
296
-
3
09,
2012,
doi
:
10.
1016/j.c
age
o.
2011.
12.
017
.
[5]
T.
Zh
ang,
R
.
Ra
m
akr
ishnan,
and
M.
Li
vn
y
,
"BIRCH
:
an
eff
i
cient
dat
a
cl
uster
in
g
m
et
hod
for
ver
y
la
rge
d
ataba
ses,
"
ACM
Sigmod
Record
,
vol
.
25
,
no
.
2
,
pp
.
103
-
114
,
1996,
doi: 10.
11
45/235968.
2333
24.
[6]
M.
Este
r
,
H.
-
P.
Krieg
el,
J.
Sand
er,
and
X.
Xu,
“
A
density
-
base
d
al
gor
it
hm
for
d
i
scove
ring
cl
uste
rs
in
l
arg
e
spatia
l
dat
ab
ase
s with
n
oise,
”
ser.
KDD
’
96
,
AA
AI Press,
1996,
pp.
226
-
2
31,
[7]
P.
Berkhi
n,
“
A
s
urve
y
of
cl
ust
ering
dat
a
m
ini
ng
te
chni
qu
es,
”
in
Gr
ouping
multi
dimensional
data
.
Springer,
2006,
pp.
25
-
71
,
doi
:
1
0.
1007/3
-
540
-
28
349
-
8_2.
[8]
C.
C.
L
iu,
S.
W
.
Chu,
Y.
K.
Cha
n,
and
S.
S.
Yu,
“
A
m
odi
fie
d
K
-
m
ea
ns
al
gorit
hm
-
two
-
lay
er
K
-
m
ea
ns
al
gorit
hm
,
”
in
2014
Tenth
I
nte
rnational
Co
nfe
renc
e
on
In
t
el
li
g
ent
Information
Hiding
and
Mult
imed
ia
Sig
nal
Proc
essing
,
2014,
pp
.
447
-
4
50.
[9]
M.
Hos
sain,
M.
Akhtar
,
R
.
Ahm
ad,
and
M.
R
ah
m
an,
“
A
d
y
nami
c
k
-
m
ea
ns
c
lustering
for
da
ta
m
i
ning,
”
Indone
sia
n
Journal
of
Elec
t
rical
Engi
n
ee
rin
g
and
Computer
Sci
ence
(
IJE
EC
S)
,
vol.
13,
no.
2,
pp.
521
-
526,
Feb.
2019,
doi:
10.
11591/ijeecs.
v13.
i2.
pp521
-
52
6.
[10]
D.
S
cul
ley
,
“
W
eb
-
sca
le
k
-
m
ea
ns
cl
uster
ing,”
in
Proce
ed
ings
of
t
he
19th
In
te
rnat
ional
Conf
ere
nc
e
on
World
Wi
d
e
We
b,
ser.
WW
W
’10.
New
Y
o
rk,
N
Y
,
USA:
A
ss
oci
ati
on
for
Computing
Mac
hi
nery
,
2010,
pp
.
1177
-
1178,
doi:
10.
1145/177269
0.
1772862.
[11]
G.
Yu,
G.
Sapi
ro,
and
S
.
Mallat,
“
Solving
inv
erse
proble
m
s
with
pie
c
ewise
li
ne
ar
esti
m
at
or
s:
From
gaus
sian
m
ixt
ure
m
odel
s
to
struct
ur
ed
sparsit
y
,
”
IE
EE
Tr
ansacti
ons
on
I
mage
Proce
ss
in
g
,
vol.
21,
no
.
5
,
pp.
2481
-
2499
,
2012,
doi
:
10
.
11
09/T
IP.2011.
217
6743.
[12]
V.
W
.
Ajin
and
L.
D.
Kum
ar,
“Bi
g
dat
a
and
c
lu
steri
ng
al
gor
it
h
m
s,”
in
2016
Int
ernati
onal
Conf
ere
nce
on
Re
sea
rch
Adv
anc
es
in
Integr
ate
d
Nav
igat
io
n
Syste
ms
(
RA
IN
S
),
2016
,
pp
.
1
-
5.
[13]
A.
Saxena
et
al
.
,
“
A
rev
ie
w
of
c
luste
ring
te
chn
iq
ues
and
dev
el
op
m
ent
s,”
Neuroc
omputing
,
vol
.
2
67,
pp.
664
-
681
,
2017,
doi
:
10
.
10
16/j
.
n
euc
om
.
201
7.
06.
053
.
[14]
M.
Parimala
,
D.
Lope
z
,
and
N.
Senthi
lkumar,
"
A
surve
y
on
de
nsit
y
b
ase
d
cl
ust
eri
ng
al
gor
it
hm
s
for
m
ini
ng
la
rge
spati
al datab
ase
s,"
Int
ernati
onal
Journal
of
Ad
va
nce
d
S
cienc
e
an
d
Technol
og
y
,
v
ol.
31
,
no
.
1
,
p
p
.
59
-
66,
2011
.
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.
23
, N
o.
3
,
Se
ptem
ber
2
02
1
:
16
02
-
16
10
1610
[15]
J.
Sander
,
M.
Este
r,
H.
-
P.
Kri
ege
l
,
and
X.
Xu,
“
Densit
y
-
bas
ed
c
luste
ring
in
spatial
d
ataba
s
es:
Th
e
al
gori
thm
gdbsca
n
and
it
s
appl
icati
ons,
”
Data
mining
and
knowl
edge
di
scov
ery
,
vol
.
2,
no.
2,
pp.
169
-
194,
1998,
doi
:
10.
1023/A:1009
745219419
.
[16]
T.
Cheng
,
"A
n
improved
DBSCAN
cl
usteri
ng
al
gorit
hm
for
m
ult
i
-
density
da
ta
sets,
"
in
Proc
ee
dings
of
th
e
2
nd
Inte
rnational
Co
nfe
renc
e
on
Intel
li
gent Inf
orm
ati
o
n
Proce
ss
ing
,
20
17,
pp
.
1
-
5.
[17]
A.
Sm
it
i
and
Z
.
El
oudi
,
“
Soft
d
bsca
n:
Im
provin
g
dbsca
n
cl
uster
ing
m
et
hod
usin
g
fuz
z
y
s
et
the
o
r
y
,
”
in
2013
6
th
Inte
rnational
Confe
renc
e
on
Hum
an
Syste
m
Inte
ract
ion
s
(
HSI
)
,
Aug
.
2013,
pp
.
380
-
385,
do
i:
10.
1109/HSI.20
13.
6577851.
[18]
Nidhi
and
K
.
A.
Pate
l
,
“
An
ef
f
icient
and
sc
al
ab
le
density
-
b
ase
d
c
l
usteri
ng
al
gori
th
m
for
norm
al
iz
e
dat
a
,
”
Proce
d
ia
Computer
Sci
e
nce
,
vol.
92,
pp.
136
-
141,
2
016,
2nd
Int
er
nat
ion
al
Conf
er
enc
e
on
Int
el
l
i
gent
Com
puti
n
g,
Com
m
unic
at
ion
Converge
n
ce,
ICCC
2016,
24
-
25
Janua
r
y
2016
,
Bhu
bane
sw
ar
,
Odi
sha,
Indi
a,
do
i:
10.
1016/j.proc
s.
2016.
07.
336
.
[19]
K.
Mahe
sh
Kum
ar
and
A.
Ra
m
a
Mohan
Redd
y
,
“
A
fast
dbsca
n
c
luste
ring
a
lgori
thm
b
y
acc
el
er
at
ing
n
ei
ghb
or
sea
rch
ing
using
groups m
et
hod,
”
Pattern
R
ec
ogn
i
ti
on
,
vol. 58
,
pp
.
39
-
48,
2016,
do
i:
10
.
1016/j.pa
tcog.2
016.
03
.
008.
[20]
A.
Merk,
P.
Cal,
and
M.
W
oźni
ak,
"D
istri
bute
d
DBS
CAN
Algor
it
hm
–
Conce
pt
a
nd
Expe
rimental
Eva
luation,
"
in
Inte
rnational
Co
nfe
renc
e
on
Computer
Re
cogn
ition
Syste
ms
,
201
7,
pp.
472
-
480:
Springer
,
doi
:
10.
1007/978
-
3
-
319
-
59162
-
9_49
.
[21]
L.
Meng
'
Ao,
M
.
Dongxue,
G
.
Song
y
uan
,
and
L.
Shufen
,
"Re
sea
rch
and
improvem
ent
of
D
BS
CAN
cl
uster
al
gorit
hm
,
"
in
2
015
7th
Inte
rnat
ional
Confe
ren
c
e
on
Informatio
n
Technol
ogy
in
Me
dic
in
e
and
E
ducat
ion
(
ITME)
,
2015,
pp
.
537
-
5
40:
IE
EE
,
doi
:
1
0.
1109/IT
ME
.
20
15.
100
.
[22]
H.
Darong
and
W
.
Peng,
"G
rid
-
base
d
DBS
CAN
al
gorit
hm
with
ref
ere
n
tial
par
a
m
et
ers,
"
Phy
sics
Proce
dia
,
vo
l.
24,
pp.
1166
-
1170
,
2012
,
doi
:
10
.
10
16/j
.
phpro
.
2012.
02.
174
.
[23]
A.
Sm
it
i
and
Z.
El
ouedi,
“
Dbs
ca
n
-
gm
:
An
imp
rove
d
cl
uster
ing
m
et
hod
base
d
on
gaussian
m
ea
ns
and
dbsca
n
te
chn
ique
s,”
in
2012
IEE
E
16th
Inte
rnational
C
onfe
renc
e
on
Inte
lligent
Engi
ne
ering
Syste
ms
(
I
NES)
,
2012,
pp.
573
-
578
,
doi
:
10
.
1109/INES.
201
2.
6249802
.
[24]
A.
Kara
m
i
and
R.
Johanss
on,
"Choos
ing
D
BS
CAN
par
am
et
ers
au
tomatic
al
l
y
using
di
ffe
ren
tial
ev
o
lut
io
n,
"
Inte
rnational
Jo
urnal
of
Comput
er
Applications
,
vol.
91
,
no
.
7
,
pp
.
1
-
11
,
2014
,
doi
:
10.
5120
/15890
-
5059
.
[25]
B.
Mu,
M
.
Dai
,
and
S.
Yuan
,
“
DBS
CAN
-
K
NN
-
GA
:
a
m
ult
i
den
sit
y
-
le
v
el
p
ara
m
et
er
-
fr
ee
cl
ust
ering
al
gor
it
hm
,
”
i
n
IOP
Confe
ren
ce
Serie
s: Mat
erials
Sci
en
ce and En
gine
ering
,
vol
.
7
15,
no
.
1
.
IOP
Publishing, 2020,
pp.
012023
.
Evaluation Warning : The document was created with Spire.PDF for Python.