Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 5
,
O
c
tob
e
r
201
5, p
p
. 1
045
~105
3
I
S
SN
: 208
8-8
7
0
8
1
045
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Multiple Feature Fuzzy c-mean
s Clustering Algorithm for
Segmentation of Microarray Images
J. Hari
ki
r
a
n
1
, P.V
.
La
k
s
hmi
2
, R.
Kir
a
n
K
u
mar
3
1,2
Department of
IT, GIT,
GITA
M University
, India
3
Department of CS,
Kris
hna University
, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 15, 2015
Rev
i
sed
Jun
3
,
2
015
Accepted
Jun 20, 2015
Microarray
tech
nolog
y
allows
the
simu
ltaneous
monitoring of thousands of
genes. Based on
the gen
e
expr
ession
measurements, micr
oarr
ay
technolo
g
y
have proven powerful in gene expre
ssion profiling for discovering new ty
pes
of diseases and for predicting th
e ty
p
e
of a disease. Gridding
, segmentation
and int
e
nsit
y ex
trac
tion ar
e th
e
three
im
portant
steps in m
i
croar
r
a
y
im
age
analy
s
is. Clustering algorithms have
been us
ed for m
i
croarra
y
im
ag
e
s
e
gm
entation wi
th an advan
t
age
that the
y
are n
o
t res
t
ric
t
ed to
a parti
c
ul
ar
s
h
ape and
s
i
z
e
for th
e s
pots
.
Ins
t
ead
of us
i
ng s
i
ngle
fe
atu
r
e c
l
us
terin
g
algorithm
,
th
is paper presen
ts m
u
ltipl
e
fea
t
ure c
l
u
s
tering algor
ith
m
with three
featur
es
for e
ach
pixel s
u
ch
as
pi
xel in
tens
it
y,
dis
t
anc
e
from
the
c
e
nter of
the
spot and median of surroundin
g
pixels
. In all the traditional clusterin
g
algorithms, number of clusters and init
ial
cen
tr
oids are random
ly
selected
and often s
p
ecif
i
ed b
y
th
e us
er.
In
this paper, a new algorith
m based on
em
pirical m
ode decom
position
algorithm
for the histogram
of the input
im
age will gen
e
rate th
e num
ber
of clusters and i
n
itia
l c
e
ntroids r
e
quired for
cluster
i
ng.
It ov
ercom
e
s the sho
r
tage of r
a
ndom
init
ial
i
zation
in
trad
ition
a
l
cluster
i
ng and achiev
es high co
mputati
onal speed b
y
r
e
ducing
the number of
iter
a
tions. The experim
e
nt
al
re
sults
show that m
u
ltiple fe
atur
e Fuzz
y C-
m
eans
has
s
e
gm
ented the m
i
c
r
oarra
y im
age
m
o
re accura
tel
y
than othe
r
algorithms.
Keyword:
Em
p
i
rical Mo
d
e
Deco
m
p
o
s
itio
n
Im
age Proce
ssing
Im
age Segm
entation
Microarray
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Jon
n
a
d
ul
a Ha
ri
ki
ra
n,
Depa
rt
em
ent
of I
n
fo
rm
ati
on
Tech
nol
ogy
,
GITAM
In
stitute o
f
Techno
log
y
,
GIT
A
M
Uni
v
e
r
sity
,
Visa
kha
p
a
tnam
.
Em
a
il: j
h
ari.k
i
ran
@
g
m
ail.co
m
1.
INTRODUCTION
Microarrays widely recogniz
ed as
th
e n
e
x
t
revo
lu
tion
in
m
o
lecu
lar b
i
o
l
o
g
y
th
at en
ab
l
e
scien
tists to
m
oni
t
o
r t
h
e ex
pressi
o
n
l
e
vel
s
of t
h
ousa
n
ds of g
e
nes i
n
pa
ral
l
e
l
[1]
.
A m
i
croar
r
ay
i
s
a
col
l
ect
i
on o
f
b
l
ocks
,
each of whic
h contains a number
of
ro
ws a
n
d col
u
m
n
s of spots. Each
of th
e spot contains
m
u
ltiple copi
es of
si
ngl
e
DN
A se
que
nce
[2]
.
T
h
e i
n
t
e
nsi
t
y
of e
ach s
pot
i
n
di
ca
t
e
s t
h
e ex
pres
s
i
on l
e
v
e
l
of
t
h
e
part
i
c
ul
a
r
ge
n
e
[3]
.
The proces
sing of the
m
i
croarray im
ag
es [4
]
u
s
ually co
n
s
ists o
f
th
e fo
llowin
g
th
ree step
s: (i) g
r
idd
i
ng
, wh
ich
is the proces
s
of se
gm
enting the
m
i
croarra
y im
age into com
p
artm
ents
, each c
o
m
p
artment havi
ng
only one
spot
a
n
d bac
k
g
r
o
u
nd
(i
i
)
Se
g
m
ent
a
t
i
on,
whi
c
h i
s
t
h
e
pr
oce
ss of
segm
ent
i
ng eac
h c
o
m
p
art
m
ent
i
n
t
o
on
e sp
ot
an
d its b
a
ckg
r
o
und
area (iii) In
ten
s
ity ex
tractio
n
,
wh
ic
h
calcu
lates red
an
d green
foreg
r
ou
nd
i
n
ten
s
ity p
a
irs
an
d b
a
ckg
r
ou
nd
in
ten
s
ities [5].
In d
i
g
ital i
m
a
g
e seg
m
en
tati
o
n
app
licatio
ns, clu
s
te
ri
n
g
t
echni
que
i
s
u
s
ed t
o
se
gm
ent
re
gi
o
n
s
o
f
in
terest an
d to d
e
tect
b
o
rd
ers of
ob
jects
in an im
age. Clustering algori
th
m
s
are base
d
on
t
h
e
si
m
ilari
t
y
o
r
di
ssi
m
i
l
a
ri
t
y
inde
x bet
w
ee
n pai
r
s of pi
xel
s
.
It
i
s
an
iterativ
e p
r
o
cess
wh
ich
is term
in
ated
wh
en
all
clu
s
ters
co
n
t
ain
similar
d
a
ta. In
o
r
d
e
r to
seg
m
en
t th
e i
m
ag
e, th
e lo
catio
n
of
each
sp
o
t
m
u
st b
e
id
en
tif
ied
t
h
r
ough
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
104
5
–
10
53
1
046
gri
ddi
ng
pr
oce
ss. A
n
a
u
t
o
m
a
t
i
c
gri
d
di
n
g
m
e
t
h
o
d
by
usi
n
g t
h
e
h
o
ri
zo
nt
al
and
vert
i
cal
pr
ofi
l
e
si
g
n
al
of t
h
e
i
m
ag
e p
r
esen
ted
in
[6
] is u
s
ed
to
perform
the im
age gridding.
The al
gori
th
m
can
satisfy th
e requ
irem
en
ts of
micro
a
rray imag
e seg
m
en
tatio
n. In
th
e clu
s
terin
g
al
g
o
rithm
s
, p
a
ra
m
e
ters su
ch
as clu
s
t
e
r nu
m
b
er and in
itia
l
cen
tro
i
d
po
sitio
n
s
are cho
s
en rando
m
l
y an
d
o
f
ten
sp
ecified
b
y
th
e
u
s
er.
Instead
o
f
rand
o
m
ly in
itial
i
z
i
n
g
t
h
e
p
a
ram
e
ters in
th
e clu
s
tering
algo
rith
m
s
, th
e ECNC (Esti
m
at
io
n
of
Cen
t
ro
i
d
s and Nu
m
b
er of
Clu
s
ters)
alg
o
rith
m
u
s
in
g
Em
p
i
rical
Mo
d
e
Deco
mp
o
s
ition
on
th
e h
i
stog
ram
o
f
inp
u
t
im
ag
e will au
to
m
a
tically
d
e
term
in
e th
e clu
s
ter
cen
ters an
d th
e num
b
e
r o
f
cl
u
s
t
e
rs in th
e imag
e.
Usi
n
g ECNC algo
rithm
as a
p
r
elim
in
ary sta
g
e with
clu
s
terin
g
algo
rith
m
s
redu
ces th
e num
b
e
r o
f
iterati
o
n
s
for seg
m
en
tatio
n
and
costs less
ex
ecu
tion ti
m
e
. Th
is al
g
o
rithm
is an
ex
tended
v
e
rsi
o
n
for
th
e Hill clim
b
i
n
g
algo
rith
m
presen
ted
i
n
[17] for
est
i
m
a
ti
on
of
c
l
ust
e
ri
n
g
para
m
e
t
e
rs and
w
o
rks
eve
n
t
h
e i
m
age c
ont
ai
ns l
o
w l
e
vel
n
o
i
s
e.
Man
y
m
i
cro
a
rray i
m
ag
e seg
m
en
tatio
n
appro
a
ch
es h
a
v
e
b
een
p
r
op
o
s
ed in
literatu
re. Fix
e
d
circle
segm
ent
a
t
i
on [
7
]
,
A
d
a
p
t
i
v
e c
i
rcl
e
Segm
ent
a
t
i
on Tec
hni
q
u
e [
8
]
,
See
d
e
d
re
gi
o
n
gr
ow
i
ng m
e
t
hods
[
9
]
an
d
cl
ust
e
ri
n
g
al
g
o
r
i
t
h
m
s
[10]
are
t
h
e m
e
t
hods t
h
at
deal
wi
t
h
m
i
croarray
i
m
age segm
ent
a
t
i
on p
r
o
b
l
e
m
.
Thi
s
pape
r
main
ly fo
cu
ses o
n
clu
s
teri
ng
alg
o
rith
m
s
. These algorit
hm
s
have the a
d
vantages
that they are not restricted to
a p
a
rticu
l
ar spo
t
size and
shap
e,
d
o
e
s no
t
requ
ire an
in
itial state o
f
p
i
xels an
d
no
n
e
ed
of
p
o
s
t
p
r
o
c
essin
g
.
Th
ese al
g
o
rithm
s
h
a
v
e
b
e
en
d
e
v
e
l
o
p
e
d
b
a
sed
o
n
th
e i
n
fo
rmatio
n
abo
u
t
t
h
e in
ten
s
ities of th
e p
i
x
e
ls on
l
y
(one
feature
)
. B
u
t in the microarray im
ag
e seg
m
en
tatio
n
prob
lem
,
n
o
t
o
n
l
y th
e
p
i
x
e
l in
ten
s
ity, bu
t also
th
e
d
i
stan
ce
of
pi
xel
f
r
om
t
h
e cent
e
r
of t
h
e sp
ot
an
d
m
e
di
an of i
n
t
e
nsi
t
y
of a ce
rt
ai
n n
u
m
b
er of s
u
r
r
o
u
n
d
i
n
g
pi
xel
s
in
flu
e
n
ces t
h
e resu
lt o
f
cl
u
s
terin
g
. In
th
is p
a
p
e
r, m
u
ltip
le featu
r
e fu
zzy c-m
ean
s clu
s
terin
g
algo
rit
h
m
is
p
r
op
o
s
ed
,
wh
ich
u
tilizes m
o
re th
an
on
e
featu
r
e.
Th
e
qu
alitativ
e an
d
quan
titativ
e resu
l
t
s sh
ow th
at m
u
ltip
le
feature
fuzzy
C-m
eans clustering algo
rit
h
m
h
a
s seg
m
en
ted
th
e im
ag
e b
e
tter th
an
o
t
h
e
r cl
usterin
g
algo
rithm
s
.
The pa
per
i
s
o
r
ga
ni
zed
as f
o
l
l
o
ws:
Sect
i
o
n
2 prese
n
t
s
Em
pi
ri
cal
M
o
de Decom
posi
t
i
o
n
,
Sect
i
o
n 3 p
r
esent
s
ECNC Algo
rith
m
,
Sectio
n
4
p
r
esen
ts fu
zzy c-m
ean
s
clu
s
tering
algo
rit
h
m
,
Sectio
n 5 presen
ts m
u
ltip
le feature
cl
ust
e
ri
n
g
al
go
ri
t
h
m
,
Sect
i
on
6
prese
n
t
s
E
x
p
e
ri
m
e
nt
al
resul
t
s
an
d fi
nal
l
y
Sect
i
on
7
rep
o
rt
concl
u
si
o
n
s.
2.
EMPI
RIC
A
L MO
DE DEC
O
MP
OSITIO
N
Th
e Em
p
i
rical Mo
d
e
Deco
mp
o
s
ition
(EMD) propo
sed
b
y
Norden
Hu
ang
[11
]
,
was
a
tech
n
i
q
u
e
fo
r
anal
y
z
i
ng
n
onl
i
n
ear a
n
d n
o
n
-
s
t
a
t
i
onary
si
gn
al
s. It
se
rves
as
an al
t
e
r
n
at
i
v
e
t
o
m
e
t
hods s
u
c
h
as
wa
vel
e
t
an
al
y
s
i
s
an
d
sho
r
t-tim
e
Fou
r
ier tran
sform
.
It d
eco
m
p
o
s
es an
y co
m
p
licated
sig
n
a
l in
to
a fin
ite and o
f
ten
sm
all n
u
m
b
e
r
o
f
In
trin
sic M
o
d
e
Fu
n
c
tion
s
(IMF). Th
e
IM
F is symmetric
with
res
p
ect to local ze
ro mean a
n
d satisfi
es the
fo
llowing
t
w
o
co
nd
itio
ns.
1.
The
num
b
er of extrem
a and the
num
ber
of z
e
ro cro
ssi
n
g
s
m
u
st
ei
t
h
er
be equal
o
r
di
ffe
r by
o
n
e.
2.
At
any
p
o
i
n
t
,
t
h
e m
ean val
u
e
of t
h
e e
n
v
e
l
ope
de
fi
ne
d
by
l
o
cal
m
a
xi
m
a
and l
o
cal
m
i
nim
a
i
s
zero,
in
d
i
cating
th
e fu
n
c
tion
is lo
cal
ly sy
mmetric.
The dec
o
m
pos
i
t
i
on m
e
t
hod i
n
EM
D i
s
cal
l
e
d Shi
f
t
i
ng P
r
ocess [
1
3]
. Th
e shi
f
t
i
n
g pr
oc
ess of t
h
e
1-
di
m
e
nsi
onal
si
gnal
ca
n
be
ad
apt
e
d a
s
f
o
l
l
o
w
s
.
1.
Let Io
ri
g
i
n
a
l
b
e
th
e orig
in
al sig
n
a
l to
b
e
d
eco
m
p
o
s
ed
.
Let j
=
1
(i
n
d
e
x n
u
m
b
e
r of IMF), In
itially,
I=
Io
riginal.
2.
Ide
n
t
i
f
y
t
h
e l
o
c
a
l
m
a
xim
a
and
l
o
cal
m
i
nim
a
poi
nt
s i
n
I
.
3.
B
y
usi
n
g i
n
t
e
r
pol
at
i
o
n, c
r
eat
e t
h
e
up
pe
r e
n
vel
o
pe E
u
p
of
l
o
cal
m
a
xim
a
and
t
h
e l
o
we
r
envel
ope
El
w
of
local m
i
nima.
4.
Com
pute the
mean of the
upper
en
vel
o
pe a
n
d
l
o
wer
en
vel
ope
.
Em
ean= [Eup
+ Elw]
/2
5.
Iim
f
= I- Em
ean.
6.
Rep
eat step
s 2-5
u
n
til Iim
f
can
b
e
co
nsid
ered
as an IMF.
7.
IMF(
j)=
Iim
f
, j=j+1,
I =
I-
Iim
f
,
8.
Rep
eat step
s 2
-
7
un
til, th
e stan
d
a
rd
d
e
v
i
atio
n
o
f
two
con
s
ecu
tiv
e IMFs is less th
an
a p
r
ed
efi
n
ed
thresho
l
d
o
r
th
e
nu
m
b
er o
f
ex
trem
a in
I is less th
an
t
w
o
.
The fi
rst
fe
w I
M
Fs obt
ai
ne
d
fr
om
EM
D cont
ai
n t
h
e hi
gh
fre
que
ncy
com
p
o
n
e
n
t
s
w
h
i
c
h
corre
sp
o
n
d
to
salien
t
feat
ures in
orig
in
al
i
m
age and the
residue re
prese
n
ts low fr
e
que
ncy com
p
onent in the im
age. The
ori
g
inal
im
age
can be recove
red by
inverse
EMD
as follows:
I = RE
S+
j
j
IMF
)
(
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
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SN
:
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8-8
7
0
8
Mu
ltip
le Fea
t
ure Fuzzy c-mean
s Clu
s
teri
n
g
Alg
o
r
ithm f
o
r
S
e
gmen
ta
tion
o
f
…
(Jo
nna
du
l
a
H
a
rikira
n
)
1
047
3.
ESTIMATI
O
N
O
F
CENTR
O
IDS
A
N
D
N
U
MBE
R
O
F
CLUSTE
RS (
E
CN
C)
1.
Let
h(
k)
be t
h
e hi
st
o
g
ram
fo
r t
h
e i
n
p
u
t
i
m
age I
wi
t
h
k=
0 ,…
.,
G a
nd
G bei
ng t
h
e m
a
xi
m
u
m
i
n
t
e
nsi
t
y
value i
n
the image
2.
Di
vi
de
t
h
e
hi
s
t
og
ram
h(k
)
i
n
t
o
IM
F
s
usi
n
g
em
pi
ri
cal
m
ode
dec
o
m
posi
t
i
on.
T
h
e
fi
rst
IM
F ca
rri
es t
h
e
h
i
stog
ram
n
o
i
se, irreg
u
l
arities an
d
sh
arp
d
e
tails o
f
th
e
h
i
stog
ram
,
wh
ile the last IMF and
residu
e d
e
scribe
th
e trend
of the h
i
sto
g
ram
.
On
th
e o
t
h
e
r
h
a
nd
, th
e in
term
ed
iate IMFs d
e
scrib
e
th
e in
itial h
i
stog
ram
with
si
m
p
le an
d un
i
f
or
m
p
u
l
ses.
3.
Co
n
s
i
d
er th
e su
mmatio
n
of i
n
term
ed
iate IMFs as
fo
llows:
II
NT
=
1
2
n
j
j
I
MF
(2
)
whe
r
e n
i
s
t
h
e num
ber of
IM
Fs.
4.
Determ
in
e all l
o
cal m
i
n
i
m
a
in
IINT.
0
*m
i
n
INT
TG
I
IT
(3
)
I*
is th
e
v
ector carrying
all l
o
cal
m
i
n
i
m
a
. All th
o
s
e
l
o
cal
m
i
nim
a
coul
d e
x
press
i
m
age cl
ust
e
rs
,
but
m
o
st
of them
are very close to each othe
r and some of them
lie
too high to
be
a cluster. So, truncate the loc
a
l
min
i
m
a
to
th
e im
p
o
r
tan
t
on
es
th
at
could
express an im
age cluster.
5.
Th
e t
r
un
cation pro
cess is carried
ou
t in two
step
s.
In
t
h
e first
step
, th
e algo
rith
m
trun
cates all lo
cal
m
i
nim
a
t
h
at
have a val
u
e l
a
rg
er t
h
a
n
t
h
e t
h
r
e
sh
ol
d,
whe
r
e
t
h
res
hol
d i
s
eq
ual
t
o
ave
r
a
g
e of t
h
e
val
u
es
o
f
lo
cal m
i
n
i
ma. Th
e trun
cation
step
is ex
pressed
as fo
llo
ws:
**
*
*
1
2
i
i
II
I
th
r
I
N
(4
)
whe
r
e
*
I
N
is th
e
nu
m
b
er of lo
cal
min
i
m
a
b
e
lo
ng
ing
to
*
I
and
*
i
I
i
s
t
h
e l
o
cal
m
i
ni
m
a
bel
ongi
n
g
t
o
vector
*
I
.
*
{}
t
i
I
I
, if
*
i
I
< thr a
n
d
*
i
I
*
I
(5
)
Whe
r
e
t
I
con
s
ist
s
of all lo
cal m
i
n
i
m
a
wh
ich
ar
e less th
an
the
esti
m
a
ted
th
resh
o
l
d
thr.
6.
In t
h
e second truncation st
ep
, th
e alg
o
rith
m
ap
p
lies an
iterativ
e p
r
o
c
ed
ure th
at calcu
lates th
e nu
m
b
er
of
im
age pixels
belonging t
o
ea
ch ca
nd
id
ate i
m
ag
e clu
s
ter an
d pru
n
e
s th
e
clu
s
ter
with
smallest n
u
m
b
e
r
o
f
i
m
ag
e p
i
x
e
ls (less th
an
2
p
e
rcen
t of to
tal nu
m
b
er o
f
im
age pixels). The pruned ca
ndidate clusters are
merged with their closest im
a
g
e clusters.
7.
The
num
b
er of ele
m
ents in
final vect
or
t
I
re
prese
n
t
s
t
h
e
nu
m
b
er of cl
ust
e
r
s
de
n
o
t
e
d
by
N
C
.
8.
Determ
in
e th
e
lo
cal m
a
x
i
m
a
i
n
IINT.
0
*m
i
n
MI
N
T
TG
I
IT
(6
)
IM* is t
h
e
vect
or carrying all local m
a
xim
a
.
9.
Thre
sh
ol
di
ng:
Fi
nd t
h
e
peak
s (l
ocal
m
a
xima) w
hose
val
u
e i
s
hi
ghe
r t
h
a
n
o
n
e pe
rce
n
t
of t
h
e m
a
xim
u
m
p
eak in
h(
k)
.
10
.
R
e
m
ove t
h
e pe
aks w
h
i
c
h are
very
cl
ose. T
h
i
s
i
s
done
by
ch
ecki
n
g t
h
e di
f
f
e
rence
bet
w
ee
n t
h
e gr
ey
l
e
vel
s
of
t
h
e t
w
o
i
n
di
vi
d
u
al
pea
k
s
.
I
f
t
h
e
di
f
f
ere
n
ce
i
s
l
e
ss
th
an
20
,
th
en
th
e p
e
ak
with
lowest v
a
l
u
e
is rem
o
v
e
d
.
11
.
Nei
g
hb
o
r
i
n
g
pi
xel
s
t
h
at
l
e
a
d
t
o
t
h
e
sam
e
peak a
r
e
gr
ou
pe
d t
oget
h
er
.
12
.
Th
e
v
a
lu
es of t
h
e id
en
tified peak
s
represen
t
th
e in
itial cen
tro
i
d
s
of th
e inpu
t im
ag
e.
End
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
JECE Vo
l. 5
,
N
o
. 5
,
O
c
tob
e
r
20
15
:
104
5
–
10
53
1
048
4.
FUZ
Z
Y
C-M
E
ANS
CL
US
TERING
AL
GOR
ITHM
The Fuzzy C-means [12] is an uns
up
erv
i
sed
clu
s
tering
alg
o
rith
m
.
Th
e
m
a
in
id
ea o
f
in
trod
u
c
i
n
g
fuzzy c
once
p
t
in the Fuzzy C-m
eans al
gori
t
hm
i
s
t
h
at
an o
b
ject
ca
n bel
o
ng si
m
u
l
t
a
neo
u
sl
y
t
o
m
o
re t
h
an
o
n
e
cl
ass and
doe
s so by
va
ry
i
ng
deg
r
ees ca
l
l
e
d
m
e
m
b
ershi
p
s
.
It
di
st
ri
but
es t
h
e m
e
m
b
ershi
p
val
u
es i
n
a
n
o
rm
alized
fash
ion
.
It
d
o
e
s no
t requ
ire
p
r
i
o
r kn
owledg
e ab
ou
t th
e
d
a
ta to
b
e
classified
. It can
b
e
u
s
ed with
any
n
u
m
b
er o
f
feat
ures a
n
d
num
ber
of cl
asses. T
h
e f
u
z
z
y
C
-
m
eans i
s
an i
t
e
rat
i
v
e
m
e
t
hod
w
h
i
c
h
t
r
i
e
s t
o
sep
a
rate t
h
e set o
f
d
a
ta in
to a n
u
m
b
e
r
o
f
com
p
act clu
s
ters. It im
p
r
o
v
e
s t
h
e p
a
rtitio
n p
e
rfo
r
m
a
n
ce and
rev
eals
the classification of
objects
m
o
re r
easona
b
le. The
pre
d
efined
pa
ram
e
te
rs s
u
c
h
as
num
ber of cluste
rs a
n
d
in
itial clu
s
tering
cen
t
ers are
prov
id
ed
b
y
EC
NC algo
rith
m
.
Th
e Fu
zzy C-mean
s algo
rithm
is su
mmarized
as
fo
llows:
A
l
go
r
ith
m
Fu
zzy C-
M
eans
(x, N, c, m
)
Beg
i
n
1.
In
itialize th
e me
m
b
ersh
i
p
m
a
t
r
ix
u
ij is a v
a
l
u
e in
(0,1) and
t
h
e
fu
zzi
n
e
ss param
e
ter
m
(
m
=2
). Th
e su
m
of
al
l
m
e
m
b
ershi
p
val
u
e
s
of a
pi
xel
bel
o
n
g
i
n
g t
o
cl
ust
e
rs sh
ou
ld
satisfy th
e con
s
train
t
ex
pressed
in
th
e
fo
llowing
.
1
1
c
ij
j
U
(7
)
fo
r al
l
i
=
1,2,
…….
N, w
h
e
r
e
c i
s
t
h
e num
ber o
f
cl
ust
e
rs
and
N i
s
t
h
e n
u
m
b
er of
pi
xe
l
s
i
n
m
i
croarra
y
im
age
2.
C
o
m
put
e t
h
e c
e
nt
r
o
i
d
val
u
es
fo
r eac
h cl
u
s
t
e
r c
j
. Eac
h
pi
xel
sh
oul
d
have
a
deg
r
ee
of
m
e
mbers
h
i
p
t
o
t
hos
e
designated cl
usters. So the
goal is to fi
nd t
h
e
m
e
m
b
er
ship
values
of pi
xels belonging to
each cluste
r. T
h
e
alg
o
rith
m
is an
iterativ
e op
timizatio
n
th
at m
i
n
i
mizes th
e cost fun
c
tion
d
e
fi
n
e
d as
fo
llows:
F=
c
i
N
j
1
1
u
i
j
m
||
x
j
-c
i
||
2
(8
)
where
u
ij
rep
r
esen
ts t
h
e
me
m
b
ersh
ip
of p
i
x
e
l
xj
in th
e
ith
clu
s
ter
and
m
is th
e fu
zzi
n
e
ss
p
a
ram
e
ter
.
3.
C
o
m
put
e t
h
e updat
e
d m
e
m
b
ershi
p
val
u
es
ui
j bel
o
n
g
i
n
g t
o
cl
ust
e
rs f
o
r ea
ch pi
xel
an
d cl
ust
e
r cent
r
oi
ds
according t
o
the give
n
form
ula.
(9
)
4
.
Rep
eat step
s 2-3
u
n
til th
e
co
st
fu
n
c
tion
is m
i
n
i
mized
.
End.
5.
MULTIPLE FEATURE CLUSTERING
The cluste
ring algorithm
s
used for m
i
croarray im
age segmentation are
base
d
on
th
e i
n
fo
rm
atio
n
ab
ou
t th
e i
n
tensities o
f
th
e
p
i
x
e
ls on
ly. Bu
t
in
m
i
cro
a
rray imag
e seg
m
en
tatio
n
,
t
h
e po
sit
i
o
n
o
f
t
h
e
p
i
x
e
l an
d
m
e
di
an val
u
e
of s
u
rr
ou
n
d
i
n
g
pi
xel
s
al
s
o
i
n
fl
ue
nces t
h
e
re
sul
t
o
f
cl
ust
e
ri
ng a
n
d s
u
b
s
eq
uent
l
y
t
h
at
l
e
a
d
s t
o
seg
m
en
tatio
n
.
Based
on
th
is o
b
s
erv
a
tio
n, mu
ltip
le featu
r
e
clu
s
tering
alg
o
rith
m
is d
e
v
e
lop
e
d
for seg
m
en
tatio
n
of m
i
croarray
im
ages. To apply fuzzy
c-m
eans cl
ust
e
ri
ng
al
gori
t
h
m
on
a si
ngl
e sp
ot
,
we t
a
ke al
l
t
h
e pi
xel
s
t
h
at
are c
o
nt
ai
ned
i
n
t
h
e s
pot
are,
w
h
i
c
h i
s
obt
ai
ne
d a
f
t
e
r
gri
ddi
ng
p
r
oce
ss, a
n
d
creat
e
a dat
a
set
D =
{x
1
, x
2
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mu
ltip
le Fea
t
ure Fuzzy c-mean
s Clu
s
teri
n
g
Alg
o
r
ithm f
o
r
S
e
gmen
ta
tion
o
f
…
(Jo
nna
du
l
a
H
a
rikira
n
)
1
049
x
3
, x
4
, x
5
,…
…,x
n
}, whe
r
e x
i
= [
x
i
(1)
, x
i
(2)
, x
i
(3)
] is a th
ree
d
i
men
s
io
n
a
l
v
ect
o
r
t
h
at represen
ts th
e ith
p
i
x
e
l in
th
e
spot
re
gi
o
n
.
W
e
use
t
h
ree
feat
ures
,
defi
ned
a
s
f
o
l
l
o
ws
x
i
(1)
: Represents th
e
p
i
x
e
l in
ten
s
ity v
a
lu
e.
x
i
(2)
:Repres
e
nt
s the
distance
from
pixel to the center of t
h
e
spot
re
gion.
Th
e spo
t
cen
ter is calcu
lated
as fo
llo
ws:
1.
Ap
pl
y
ed
ge
det
ect
i
on t
o
t
h
e
sp
ot
re
gi
o
n
i
m
age usi
n
g
can
ny
m
e
t
hod.
2.
Perform
flood-fill ope
ration
on the
edge im
age
using im
fill
m
e
thod.
3.
Ob
tain lab
e
l m
a
trix
th
at con
t
ain
lab
e
ls
for t
h
e 8-conn
eted
ob
j
ects u
s
i
n
g bwlab
e
l
fun
c
tion
.
4.
C
a
l
c
ul
at
e t
h
e c
e
nt
r
o
i
d
of
eac
h
l
a
bel
e
d
re
gi
o
n
(c
on
nect
ed
co
m
ponent
)
usi
n
g
regi
on
pr
o
p
s
m
e
t
hod.
x
i
(3)
:
R
epres
e
nt
s t
h
e m
e
di
an
of
t
h
e i
n
t
e
nsi
t
y
o
f
s
u
r
r
o
u
ndi
ng
pi
xel
s
.
For each
pixel
in the s
pot
re
gion,
once
the
feature
s
ar
e obtained form
ing
the data
set D, the
n
the fuzzy c-
m
eans cl
ust
e
ri
ng al
go
ri
t
h
m
is appl
i
e
d. T
h
e
cent
r
oi
ds
a
n
d num
ber of cl
usters in t
h
e dataset are calculated
usi
n
g EC
NC
al
go
ri
t
h
m
.
6.
E
X
PERI
MEN
T
AL RES
U
L
T
S
Qu
alitativ
e Analysis:
The p
r
o
p
o
se
d cl
ust
e
ri
n
g
al
g
o
r
i
t
h
m
i
s
perf
or
m
e
d on t
w
o m
i
croa
rray
i
m
ages dra
w
n
fr
om
the st
an
dar
d
m
i
croarray
dat
a
base c
o
rres
p
o
nds
t
o
b
r
east
c
a
t
e
go
ry
aC
G
H
tu
m
o
r tissu
e.
Imag
e 1 con
s
ist
s
of a to
tal
o
f
3
880
8
pi
xel
s
a
n
d
Im
age
2 c
o
n
s
i
s
t
s
o
f
64
8
8
0
pi
x
e
l
s
.
Gri
d
di
n
g
i
s
pe
rf
orm
e
d
on
t
h
e i
n
p
u
t
i
m
ages by
t
h
e
m
e
t
hod
p
r
op
o
s
ed
in [13
]
, to
seg
m
en
t th
e im
ag
e in
to
co
m
p
art
m
ents, whe
r
e eac
h c
o
m
p
artm
ent
is h
a
v
i
ng
on
ly on
e spo
t
reg
i
o
n
an
d
b
a
ck
gro
und
. Th
e
g
r
i
d
d
i
n
g
o
u
t
p
u
t is sh
o
w
n
in
Fig
u
re 1. Mu
ltip
le featu
r
e cl
u
s
tering
algo
ri
th
m is
ap
p
lied to
each co
m
p
ar
tm
en
t
f
o
r
seg
m
en
tin
g th
e for
e
gr
ound
an
d b
a
ckg
r
ou
nd
r
e
g
i
on
. The ECN
C
al
g
o
r
ith
m
is
ex
ecu
ted
on
the h
i
stog
ram
o
f
in
pu
t im
ag
es fo
r id
en
tificatio
n
o
f
nu
m
b
er
o
f
clu
s
ters and
i
n
itial cen
tro
i
d
s
wh
ich
i
s
req
u
i
r
e
d
f
o
r
cl
ust
e
ri
n
g
al
go
ri
t
h
m
.
The
o
u
t
put
o
f
t
h
e
pr
op
ose
d
m
e
t
hod
o
n
a
com
p
art
m
ent
f
r
om
im
age
1 a
n
d
i
m
ag
e 2
is show
n in
Figu
r
e
1.
I
m
age 1
Gridded I
m
age
Co
m
p
a
r
t
m
ent
No
1
Histogr
am
IMF1
IMF2
IMF3
IMF4
IMF5
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o
. 5
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O
c
tob
e
r
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15
:
104
5
–
10
53
1
050
IMF6
Co
m
b
ined I
M
F
Local Mini
m
a
Local M
a
xi
m
a
Centroids
Seg
m
ented I
m
age
using Multiple features
No of clusters :2
Centroids are
4, 145
I
m
age 2
Gridded I
m
age
Co
m
p
a
r
t
m
ent
No
8
Histo
g
r
a
m
IMF1
IMF2
IMF3
IMF4
IMF5
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7
0
8
Mu
ltip
le Fea
t
ure Fuzzy c-mean
s Clu
s
teri
n
g
Alg
o
r
ithm f
o
r
S
e
gmen
ta
tion
o
f
…
(Jo
nna
du
l
a
H
a
rikira
n
)
1
051
IMF6
Co
m
b
ined I
M
F
Local Mini
m
a
Local M
a
xi
m
a
Centroids
Seg
m
ente
d I
m
age
using Multiple features
No of clusters :2
Centroids are
4, 181
Fi
gu
re 1.
Se
gm
ent
a
t
i
on res
u
l
t
Qu
an
titativ
e An
alysis:
Qu
an
titativ
e an
alysis is a
n
u
m
erically o
r
ien
t
ed pro
c
edu
r
e to
figu
re ou
t th
e
p
e
rfo
r
m
a
n
ce of
alg
o
r
ith
m
s
w
i
t
h
ou
t an
y
hu
m
a
n
err
o
r
.
Th
e M
ean
Sq
u
a
re Erro
r
(MSE) [1
4,
1
5
]
is sign
ifican
t m
e
tric
to
v
a
lid
ate
th
e q
u
a
lity o
f
imag
e. It
m
easu
r
es th
e squ
a
re
erro
r
b
e
twee
n
p
i
x
e
ls of th
e orig
in
al and
th
e resu
ltan
t
i
m
ag
es. The
MSE is m
a
th
ematical
ly d
e
fined
as
MSE =
ଵ
ே
k
j
1
j
c
i
||v
i
-c
j
||
2
(1
0)
Wh
ere
N is the to
tal n
u
m
b
e
r o
f
p
i
x
e
ls i
n
an
im
ag
e an
d
xi is th
e p
i
x
e
l
wh
ich
b
e
l
o
ng
s to
th
e
j
t
h
clu
s
ter. Th
e
lowe
r diffe
re
nce between the resultant and the ori
g
inal
im
age reflects that all the data in the region are
lo
cated
n
ear t
o
its cen
tre. Tab
l
e 1
shows
th
e qu
an
tita
tiv
e ev
alu
a
tion
s
o
f
t
h
ree cl
u
s
tering
algo
rith
m
s
. The
resu
lts co
nfirm
th
at m
u
ltip
le featu
r
e
fu
zzy c-mean
s al
go
rithm
p
r
o
d
u
ces t
h
e lo
west M
S
E
valu
e fo
r seg
m
en
tin
g
th
e m
i
cro
a
rray i
m
ag
e. As the in
itial cen
troid
s
req
u
i
red
for clu
s
teri
n
g
al
g
o
rith
m
s
are determin
ed
b
y
ECNC
alg
o
rith
m
,
th
e nu
m
b
er of iterativ
e steps req
u
i
red fo
r classifyin
g th
e
o
b
j
ects is
red
u
ced
.
Wh
ile t
h
e in
itial
cent
r
oi
ds
o
b
t
a
i
n
ed
by
EC
NC
are
uni
que
, t
h
e se
gm
ent
e
d
resu
lt is m
o
re stab
le co
m
p
ared
with
trad
it
io
n
a
l
algorithm
s
. Ta
ble 2 shows t
h
e com
p
arison of iterative
steps num
b
ers for clusteri
ng
alg
o
rith
m
s
with
an
d
with
ou
t EC
NC
.
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. 5
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e
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5
–
10
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1
052
Tabl
e 1.
M
S
E val
u
es
M
e
thod
M
S
E
Values
(
C
o
m
par
t
m
e
nt
No 1)
In i
m
age 1
MSE Valu
es
(
C
o
m
par
t
m
e
nt
No 8)
In i
m
age 2
K-m
e
ans
282.
78
1
346.
47
Fuzzy
c-m
e
ans
216.
39
2
228.
69
Multiple feature F
u
zzy C-
me
a
n
s
198.
32
7
186.
276
Tabl
e
2. C
o
m
p
ari
s
o
n
of
i
t
e
rat
i
v
e st
e
p
num
ber
s
Cluster
i
ng
algor
ithm
Iterative st
eps
(
w
ithout E
C
NC)
Iterative st
eps
(with
ECNC)
(
C
om
pa
r
t
m
e
n
t
N
o
1
)
In i
m
age 1
K-m
e
ans 10
4
Fuzzy C-
m
e
ans
14
6
Multiple feature F
u
zzy C-
m
eans
17
9
Cluster
i
ng
algor
ithm
Iterative st
eps
(
w
ithout E
C
NC)
Iterative st
eps
(with ECNC
)
(
C
om
pa
r
t
m
e
n
t
N
o
8
)
In i
m
age 2
K-m
e
ans 11
6
Fuzzy C-
m
e
ans
16
12
Multiple feature F
u
zzy C-
m
eans
19
11
7.
CO
NCL
USI
O
N
Th
is p
a
p
e
r presen
ts m
u
lt
ip
le
feature fuzz
y c-
m
eans clustering algorit
h
m
for
m
i
croarray im
age
segm
ent
a
t
i
on.
Inst
ea
d
of
usi
n
g si
ngl
e
feat
u
r
e i
.
e.,
pi
xel
i
n
t
e
nsi
t
y
, t
w
o
ot
h
e
r
feat
ure
s
s
u
c
h
as
di
st
ance
o
f
t
h
e
p
i
x
e
l
fro
m
th
e sp
o
t
cen
ter and m
e
d
i
an
v
a
lu
e
o
f
surrou
nd
ing p
i
x
e
ls are
u
s
ed
for seg
m
en
tatio
n
.
Th
e qu
alitativ
e
an
d
q
u
an
titativ
e an
alysis d
one p
r
o
v
e
d
th
at
m
u
l
tip
le featu
r
e Fu
zzy C-m
e
an
s h
a
s
h
i
gh
er seg
m
en
tatio
n
q
u
a
lity
t
h
an
ot
her cl
us
t
e
ri
ng al
g
o
r
i
t
h
m
s
wi
t
h
si
ngl
e
feat
ure
.
C
l
ust
e
ri
n
g
al
go
ri
t
h
m
co
m
b
i
n
ed w
i
t
h
EC
NC
ove
rcom
es
th
e p
r
ob
lem
o
f
rand
o
m
select
io
n
of nu
m
b
er o
f
clu
s
te
rs and in
itializa
tio
n
o
f
cen
t
ro
id
s. Th
e propo
sed
m
e
th
od
redu
ces t
h
e
n
u
m
b
er o
f
iterati
o
n
s
fo
r seg
m
en
tatio
n
of m
i
croarray im
ag
e and
co
sts less ex
ecu
tio
n tim
e.
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0.
BIOGRAP
HI
ES OF
AUTH
ORS
J.
Ha
rik
i
ran
r
eceived B
.
Tech
and M.Tech
degr
ee from JNTU H
y
der
a
bad and Andhra
University
in the
y
ear 2005 and 2008 respectively
.
He is currently
workin
g as Assistant
profes
s
o
r in the
Departm
e
nt of
I
T
, GIT
,
Git
a
m
Univers
i
t
y
.
His
res
earch
int
e
res
t
includ
e Im
age
S
e
gm
entation
,
M
i
croarra
y Im
a
g
e
P
r
oces
ing et
c.
Curr
ently
he is persuing ph
d from JNTU
Kakinada.
Dr.
P.
V.
Lakshmi
receiv
ed M.Tech
and PhD degrees
from Andhra University
. Her research
inter
e
st in
clude
Cr
y
p
togr
aph
y
,
Algorithm
s
in Bioi
nform
a
ti
cs
et
c..
Current
l
y
S
h
e is
working
as
Professor and H
ead, Depar
t
ment of Inform
ation
Techno
log
y
, GIT, GITAM Univ
ersity
.
Dr.
R.
Kiran Kumar
receiv
e
d
MCA, M.Tech a
nd Phd degrees from
Andhra Un
iversit
y
, JNTU
kakinad
a
and Achar
y
a Nagar
j
una
Univers
i
t
y
. His
res
earch
inter
e
s
t
include im
ag
e proces
s
i
ng and
bioinformatics.
Currently
he
is working as assist
ant Professor, Department
of Co
mputer science,
krishna Universi
t
y
, Ma
chil
ipa
t
na
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.