Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
DOI:10.5121/acii.2016.3204 35
A
UTOMATIC
U
NSUPERVISED
D
ATA
C
LASSIFICATION
USING
J
AYA
E
VOLUTIONARY
A
LGORITHM
Ramachand a Rao Ku ada
1
and D . Ka eeka Pa an Kanadam
2
1
Ass . P o ., Depa men o Compu e Science & Enginee ing, Sh i Vishnu Enginee ing
College o Women, Bhima a am
2
P o esso , Depa men o In o ma ion Technology, RVR & JC College o Enginee ing,
Gun u
A
BSTRACT
In his pape we a emp o sol e an au oma ic clus e ing p oblem by op imizing mul iple objec i es such as
au oma ic k-de e mina ion and a se o clus e alidi y indices concu en ly. The p oposed au oma ic
clus e ing echnique uses he mos ecen op imiza ion algo i hm Jaya as an unde lying op imiza ion
s a agem. This e olu iona y echnique always aims o a ain global bes solu ion a he han a local bes
solu ion in la ge da ase s. The explo a ions and exploi a ions imposed on he p oposed wo k esul s o
de ec he numbe o au oma ic clus e s, app op ia e pa i ioning p esen in da a se s and me e op imal
alues owa ds CVIs on ie s. Twel e da ase s o di e en in icacy a e used o endo se he pe o mance
o aimed algo i hm. The expe imen s lay ba e ha he conjec u al ad an ages o mul i objec i e clus e ing
op imized wi h e olu iona y app oaches deciphe in o ealis ic and scalable pe o mance paybacks.
K
EYWORDS
Mul i objec i e op imiza ion, e olu iona y clus e ing, au oma ic clus e ing, clus e alidi y indexes, Jaya
e olu iona y algo i hm.
1.
I
NTRODUCTION
Fo he pas h ee decades, majo i y o op imiza ion p oblems demands imp o emen issues wi h
mul iple objec i es and a e a ac ed owa ds e olu iona y compu a ion me hodologies due hei
simplici y o ans o ma i e calcula ion. The le e age o hese e olu iona y app oaches a e
lexible, o add, emo e, modi y any p e equisi e ega ding p oblem concep ualiza ion, gene a ion
o compa a i e Pa e o se and has abili y o ackle highe complexi ies han he mains eam
me hods. These obus and powe ul sea ch p ocedu es gene ally po ay a se o candida e
solu ions, selec ion p ocedu e o ma ing, segmen ing and e-assembling o se o se e al
solu ions o p oduce new solu ions. This is e lec ed by he speedily inc easing o in e es in he
ield o e olu iona y clus e ing wi h mul i objec i e op imiza ions [1].
Da a clus e ing is ecognized as he mos p ominen unsupe ised echnique in machine lea ning.
This echnique appo ions a gi en da ase in o homogeneous g oups in iew o some
likeness/dispa i y me ic. Con en ional clus e ing algo i hms egula ly make p e ious
assump ions abou g ouping a clus e s uc u e, and adop able wi h a sui able objec i e unc ion
so ha i can be op imized wi h classical o me aheu is ic echniques. These es ima ions g ade
inadequa ely when clus e ing p esump ions a e no hold in da a [2].
The na u al pa adigm o i he da a dis ibu ion in he en i e ea u e space, disco e ing exac
numbe o pa i ions is iola ed in single objec i e clus e ing algo i hm i dis inc i e locales o
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
36
he componen space con ain clus e s o di e ged space. Es ima ing a combined solu ion which is
s able, con iden and lowe sensi i i y o noise is una ainable by any single objec i e clus e ing
algo i hm. Mul i-objec i e clus e ing can be pe cei ed as a dis inc case o mul i-objec i e
op imiza ion, a ge ing o concu en ly op imize se e al ade-o wi h nume ous objec i es unde
speci ic limi a ions. The aim objec i e o mul i-objec i e clus e ing is o disin eg a e a da ase
in o compa able g oups, by exploi ing he mul iple objec i es analogously [3-4].
In his pape , we p o ide an clus e ing algo i hms unde played wi h Jaya e olu iona y algo i hm
[15] o sol e la ge se o objec i es, o a ica ing ac ual au oma ic k de e mina ion, ha a e
in e es ing, sui able de achmen p omp ed in da a se s, and op imizing a se o clus e alidi y
indices (CVIs) simul aneously o encou aging mos a ou able con e gence a inal solu ions.
Fo conque ing high in a-clus e likeness and low in e -clus e likeness, his algo i hm uses CVIs
as objec i e unc ions as men ioned in [5]. The se o in e nal and ex e nal alidi y indices used as
i ness unc ions in his pape a e Rand, Adjus ed Rand, Silou e, Chou Be, Da ies–Bouldin and
Xie–Beni indexs [6].
The emainde o his pape is o ganized as ollows. Sec ion II p esen s a e iew o ecen
au oma ic clus e ing algo i hms. In Sec ion III, desc ibes he scalabili y o he p oposed
Au oJAYA algo i hm and o iginal Jaya e olu iona y algo i hm. The e ec i eness o ou scheme
is discussed in Sec ion IV. Finally, Sec ion V concludes his pape .
2.
L
ITERATURE
R
EVIEW
The su ey published by Mukhopadhyay, Maulik and Bandyopadhyay, S. in 2015 a gue he
impo ance o using mul iobjec i e clus e ing in he domains o image segmen a ion,
bioin o ma ics, web mining wi h eal ime applica ions. The su ey u ges he impo ance o
Mul iobjec i e clus e ing o op imizing mul iple objec i e unc ions simul aneously. The au ho s
highligh s he echniques o encoding, selec ion o objec i e unc ions, e olu iona y ope a o s,
schemes o main aining non-domina ed solu ions and asso ing an end solu ion [7].
In o de o imp o e sea ching skills, in 2015, Abadi, & Rezaei combined o con inuous an
colony op imiza ion and pa icle swa m op imiza ion and p oposed a s a egy which is a
combina ion o hese wo algo i hms wi h gene ic algo i hm, he esul s demons a ed we e o
high capaci y and esis ance [8].
In 2015, Oz u k, Hance and Ka aboga used a i icial bee colony algo i hm in dynamic
(au oma ic) clus e ing disc e e a i icial bee colony as a simila i y measu e be ween he bina y
ec o s h ough Jacca d coe icien [9]. In 2014, Kuma and Chhab a, g a i a ional sea ch
algo i hm in eal li e p oblems, whe e p io in o ma ion abou he numbe o clus e s is no
known in image segmen a ion domain o a ain au oma ic segmen a ion o bo h g ay scale and
colou images [10].
In 2014, Kuo, Huang, Lin, Wu and Zul ia de e mined he app op ia e numbe o clus e s and
assigns da a poin s o co ec clus e s, wi h ke nel unc ion o inc ease clus e ing capabili y, in
his s udy hey ha e used wi h bee colony op imiza ion o a aining s able and accu a e esul s
[11]. In 2014, Wikaisuksakul p esen ed a mul i-objec i e gene ic algo i hm o da a clus e ing
me hods, o handle he o e lapping clus e s wi h mul iple objec i es, using he uzzy c-means
me hod. The eal-coded alues a e encoded in a s ing o ep esen clus e cen e s and Pa e o
solu ions co esponding o a ade-o be ween he wo objec i es a e inally p oduced [12].
In 2014, Mukhopadhyay, Maulik,Bandyopadhyay, and CoelloCoello, published wo su ey’s
wi h Pa I and Pa II on mul iobjec i e e olu iona y algo i hms o da a mining wi h
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
37
E olu iona y Compu a ion [13-14]. Pa I su ey holds li e a u e o basic concep s ela ed o
mul i-objec i e op imiza ion in da a mining and e olu iona y app oaches o ea u e selec ion and
classi ica ion. In pa II he au ho s p esen he ules o associa ion, clus e ing and o he da a
mining asks ela ed o di e en mul i-objec i e e olu iona y algo i hms.
3.
AUTOMATIC
CLUSTERING
ALGORITHM
-
A
UTOJAYA
This pape a emp s o cons ella e exac numbe o p ope de achmen in da ase s au oma ically
wi hou any human in e en ion du ing he algo i hm execu ion. The objec i e unc ions o
asso ing an end solu ion is pos u ed as a mul i-objec i e op imiza ion p oblem, by op imizing a
cus oma y o clus e alidi y indices concu en ly. The p oposed mul i-objec i e clus e ing
echnique uses a mos ecen ly de eloped e olu iona y algo i hm Jaya [15], based on mul i-
objec i e op imiza ion me hod as he unde lying op imiza ion s a egy. The poin s a e assigned
andomly o selec ed clus e cen es based on Euclidean dis ance. The Rand, Adjus ed Rand,
Silhoue e, Chou Be, Da ies–Bouldin and Xie–Beni CVIs a e op imized simul aneously o
endo se he alidi y o aimed algo i hm. De e mina ely, he aimed algo i hm is able o pe cei e
bo h he bes possible numbe o clus e s and p ope appo ioning in he da ase . The e iciency o
he p oposed algo i hm is shown o wel e eal- ime da a se s o a ying complexi ies. The
esul s o his mul i objec i e clus e ing echniques p esen ed in Table 1, Table 2.
3.1.
I
NITIALIZATION
To ini ialize he candida e solu ions, he clus e cen es a e encoded as ch omosomes. The
popula ion α o numbe o candida e solu ions a e ini ialized andomly wi h n ows and m
columns. The se o solu ions a e ep esen ed as α
,
0= α
+ and1 ∗ α
− α
and
each solu ion con ains Max
numbe o selec ed clus e cen e s, whe e Max
is andomly chosen
ac i a ion h esholds in [0, 1].
3.2.
O
BJECTIVE
/
F
ITNESS
F
UNCTIONS
A s aigh o wa d way o pose clus e ing as an op imiza ion p oblem is o op imize some CVIs
ha e lec he goodness o he clus e ing solu ions. The co ec ness o accu acy o any
op imiza ion me hod depends on i s objec i e o i ness unc ion being used in he algo i hm [2-
3]. In his manne , i is egula o ins an aneously ad ance wi h nume ous o such measu es o
op imizing dis inc i e a ibu es o da a. To compu e he dis ance be ween he cen oid and
candida e solu ions Euclidean dis ance measu e is used, along wi h i he o he objec i e unc ions
op imized simul aneously a e he RI, ARI, DB, CS, XI, SIL CVIs [6].
.
3.3.
J
AYA
E
VOLUTIONARY
A
LGORITHM
Jaya is a simple, powe ul op imiza ion algo i hm p oposed by R Venka a Rao in 2015 o sol ing
he cons ained and uncons ained op imiza ion p oblems [15]. This algo i hm is p edica ed on he
idea ha he ou come ob ained o a gi en p oblem should mo e owa ds he bes solu ion and
e ade he wo s solu ion. This e olu iona y app oach does no equi e any pa icula algo i hm-
speci ic con ol pa ame e , a he manda es common con ol pa ame e s. The wo king p ocedu e
o his e olu iona y me hod is as ollows:
Le α is he objec i e unc ion o be minimized o maximized. A any i e a ion , assume ha
he e a e ′m′ numbe o design a iables i.ej = 1,2,…m, ′n′ numbe o candida e solu ions (i.e.
popula ion size, k = 1,2,…n. Le he bes candida e bes ob ains he bes alue o
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
38
αi.e. α
'()*
in he en i e candida e solu ions and he wo s candida e wo s ob ains he
wo s alue o αi.e. α
-./)*
in he en i e candida e solu ions. I α
,,
is he alue o he j
*0
a iable o he k
*0
candida e du ing he i
*0
i e a ion, hen his alue is modi ied as pe he
ollowing equa ion
α
,,
′
= α
,,
+
1,,
2α
,'()*,
−3α
,,
34 −
5,,
2α
,-./)*,
−3α
,,
34.1
whe eα
,'()*,
is he alue o he a iable o he bes candida e and α
,-./)*,
is he alue o he
a iable j o he wo s candida e. α
,,
′
is upda ed alue o α
,,
and
1,,
and
5,,
a e he wo
andom numbe s o he j
*0
a iable du ing he i
*0
i e a ion in he ange [0,1]. The e m
1,,
2α
,'()*,
−3α
,,
34 indica es he endency o he solu ion o mo e close o he bes solu ion
and he e m
5,,
2α
,-./)*,
− 3α
,,
34 indica es he endency o he solu ion o a oid he wo s
solu ion. α
,,
′
is accep ed i i gi es be e unc ion alue. All he accep ed unc ion alues a he
end o he e mina ion a e main ained and hese alues become he inpu o he nex i e a ion. A
he end o each i e a ion all he accep ed unc ion alues a e e ained and a e ed as inpu s o he
nex i e a ion. This algo i hm in ends o each bes solu ion and ies o a oid wo s solu ion.
The s eps in Jaya algo i hm a e as ollows:
1. Ini ialize popula ion size, numbe o design a iables and e mina ion condi ion
2. Iden i y bes and wo s solu ion in he popula ion
3. Modi y he solu ions based on bes and wo s solu ions using (1)
4. Is he solu ion co esponding o α
,,
6
be e han he co esponding o α
,,
a. accep and eplace he p e ious solu ion
5. Else keep he p e ious solu ion
6. Is he e mina ion c i e ion sa is ied
a. epo as op imum solu ion
7. Else go o S ep 2
3.4.
P
ROPOSED
A
UTOJAYA
A
LGORITHM
The wo king p ocedu e o he aimed algo i hm Au oJAYA is as ollows:
1. Ini ialize he numbe o candida e solu ions andomly as , in 7 ows and m columns.
2. The se o solu ions a e ep esen ed as and
each solu ion con ain numbe o selec ed clus e cen e s, whe e is andomly
chosen ac i a ion h esholds in [0, 1].
3. The i ness unc ion o be maximized by de aul is Rand Index, and he solu ion
o a cu en gene a ion wi h design a iables is ep esen ed as
4. Spo he ac i e clus e cen e s wi h alue g ea e han 0.5 as bes candida es,
solu ions and less han 0.5 as wo s candida es, solu ions
5. Fo do
a. Fo each da a ec o , calcula e i s dis ance om all ac i e clus e cen e s using
Euclidean dis ance
b. Assign o closes clus e
c. E alua e each candida e solu ion quali y using he i ness unc ions and ind
solu ions
d. Modi y he solu ions based on bes and wo s solu ions using (1)
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
39
6. I he solu ion co esponding o be e han he co esponding o accep and
eplace he p e ious solu ion else keep he p e ious solu ion
4.
E
XPERIMENTAL
A
NALYSIS
A
ND
D
ISCUSSION
In his sec ion, we epo on expe imen s ha use mul i-objec i e clus e ing o iden i y pa i ions
in di e ged se o da ase s. The enac men o he aimed algo i hm is p agma ic om he esul s
conque ed by he ollowing c i e ia elec ed, i.e. au oma ic k-de ec ion, minimal consump ion o
CPU ime, low pe cen age o e o a e and ideal alues in CVIs.The numbe o i e a ions is
es ic ed o 30 independen uns o all he da ase s. Table 1, Table 2 demons a es he esul s o
Au oJAYA algo i hm used o e eal- ime da ase s. These eal- ime da ase s a e ex ac ed om
UCI Machine Lea ning Reposi o y [18].The bes esul s a e shown as bold ace.
Table 1. Resul s o Au oma ic Clus e ing algo i hms Real- ime da ase s
Da ase s (size*dim, k)
No. o
au o
clus e s
CPU
ime
(sec)
% o
e o
a e
Mean alue o CVIs
ARI RI HIM SIL CS DB
I is (150*4, 3) 3.01 19.45 10.11 0.9815 0.9987 0.0922 0.9214 0.8416 0.7152
Wine (178*13, 3) 3.00 105.32 40.64 0.8414 0.7912 0.4910 0.6048 0.6417 0.8915
Glass (214*9, 6) 6.00 114.23 30.78 0.8000 0.9000 0.6018 0.6980 0.5297 1.0050
Ionosphe e (351*3, 4) 2.00 30.12 8.01 0.9580 0.9877 0.9632 1.2580 1.0470 0.9784
Ecoil (336*7, 8) 8.00 45.12 11.48 0.9587 1.0145 0.9964 1.0258 0.9478 0.7859
Rocks (208*60, 2) 2.01 74.20 12.45 0.9971 0.9999 1.0000 1.0001 0.9478 0.9481
Pa kinson (195*22, 2) 2.10 42.14 12.08 0.9240 0.9920 0.9974 0.9608 0.9814 1.0040
Diabe ic (768*9, 2) 2.00 74.25 10.45 0.9871 0.9997 1.0024 0.9999 0.8478 0.8481
Segmen (1500*20, 2) 3.01 1041.02 14.12 0.9631 0.9941 0.0786 0.9740 0.8994 0.4448
Weigh ing (500*8, 2) 5.99 110.29 15.23 1.0019 0.9663 0.0222 1.0025 0.9648 0.2560
Sona
(208*60, 2)
1.98
67.20
24.23
0.9988
1.0205
0.9635
0.9845
0.8458
0.8932
Ripplese (250*3, 2) 2.00 10.23 5.48 1.2800 1.0200 0.9874 1.0000 0.9990 0.9011
The Au oJAYA ende s exac numbe o au oma ic clus e s in Wine, Glass, Ionosphe e, Ecoil,
Diabe ic, Sona , Ripplese , when compa ed o ac ual numbe o clus e s (k) shown in column 1
o Table 1. The Ripplese da ase is he only da ase whe e Au oJAYA consumes minimum
amoun o CPU ime among all he da ase s o a ying size and complexi y. In gene al, he CPU
ime consumed by all he compa ing da ase s is be ween 5.48 sec o 1041.12 sec, which is pu ely
dependen on he olume and complexi y o he da ase . Likewise, minimal pe cen age o e o
a e is logged o he aimed algo i hm in I is and Wine da ase s and he o he likening da ase s
egis e s he e o a e be ween 5.48 % and 40.64%.
The CVIs in RI in I is, DB in Wine, DB in Glass, CS in Ionosphe e, RI in Ecoil and HIM in
Rocks and mines da ase egis e s op imal mean alue, by endo sing he alidi y o he algo i hm.
The CVIs DB in Pa kinson, RI in Diabe ic, RI in Segmen , ARI in Weigh ing, RI in Sona and
SIL Ripplese also ollow he same endency by submi ing op imal mean alue owa ds he
on ie s o CVIs. All hese implica ions ele a e he sup emacy o p oposed algo i hm in
ob aining a ou able esul s. The au oma ic clus e s gene a ed by Au oJAYA algo i hm a e
shown in Figu e 1.
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
40
Figu e 1. Au oma ic clus e s p oduced by Au oJAYA in Glass and Weigh ing da ase s
Table 2. Values o F-measu e, ROC and SSE in eal- ime da ase s using Au oJAYA algo i hm
Da ase s F-Measu e ROC SSE
I is 0.940 0.955 7.81
Wine 1.115 1.132 9.25
Glass 0.186 0.472 52.18
Ionosphe e 0.501 0.485 726.10
Ecoil
0.479
0.464
695.10
Rocks 0.171 0.420 49.812
Pa kinson 1.180 0.459 50.22
Diabe ic 0.513 0.497 149.51
Segmen 0.043 0.496 532.78
Weigh ing 0.893 0.941 520.9
Sona 0.153 0.464 21.71
Ripplese 0.441 0.421 44.81
The esul s o F-measu e, ROC a ea and Sum o Squa ed E o (SSE) o he p oposed algo i hm
on each eal- ime da ase a e included in Table 2. The alue de ia ions o F-measu e, ROC a ea
and SSE amongs all he da ase s is shown in Fig. 2. I is obse ed om bo h Table 1 and Figu e 2
ha he aimed algo i hm has ob ained be e esul in mos o he cases o all he eal- ime
da ase s.
Table 2 shows he co esponding alues o F-Measu e, ROC a ea and SSE o all compa ing eal-
ime da ase s. A signi ican ema k on Table 2 is all he da ase s ende be e alues o F-
measu e and ROC a ea. The SSE alue is e y nominal o I is and Wine da ase s and ela i ely
me e op imal alues o emaining da ase s.
The culmina ing ema ks a e examining he applicabili y o Au oJAYA algo i hm o e eal- ime
is he aimed algo i hm lodges be e in mos o he da ase s in iden i ying he exac numbe o
au oma ic pa i ions, wi h minimum consump ion o CPU and ela i ely low pe cen age o e o
a e.. Hence hese expe imen s specula e ac ha Au oJAYA algo i hm lay ba e he ad an ages
o mul iobjec i e clus e ing op imized wi h e olu iona y app oaches deciphe in o ealis ic and
scalable pe o mance paybacks.
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
41
Figu e 2. Values o F-Measu e, ROC and SSE ende ed by Au oJAYA in eal- ime da ase s
5.
C
ONCLUSIONS
In his a icle, a no el mul i-objec i e clus e ing echnique Au oJAYA based on he newly
de eloped Jaya E olu iona y algo i hm is p oposed. The explo a ions and exploi a ions en o ced
on he echnique, au oma ically de e mine he p ope numbe o clus e s, p ope pa i ioning om
a gi en da ase and me e op imal alues owa ds CVIs on ie s, by op imizing i ness unc ions
simul aneously.
Fu he mo e, i is obse ed ha he aimed algo i hm exhibi s be e pe o mance in mos o he
conside ed eal- ime da ase s and is able o clus e app op ia e pa i ions. Much u he wo k is
needed o in es iga e he p o ound algo i hm using di e en and mo e objec i es, compa e wi h
well es ablished au oma ic clus e ing algo i hm and o es he app oach s ill mo e ex ensi ely
o e di e si ied domains o enginee ing.
R
EFERENCES
[1] Zi zle , Ecka , Ma co Laumanns, and S e an Bleule . "A u o ial on e olu iona y mul iobjec i e
op imiza ion." Me aheu is ics o mul iobjec i eop imisa ion. Sp inge Be lin Heidelbe g, 2004. 3-37.
[2] S ipa naSaha, Sanghami aBandyopadhyay,"A new poin symme y based uzzy gene ic clus e ing
echnique o au oma ic e olu ion o clus e s",In o ma ion Sciences 179, 2009, pp. 3230–3246,
doi:10.1016/j.ins.2009.06.013
[3] S ipa naSaha, Sanghami aBandyopadhyay,"A symme y based mul iobjec i e clus e ing echnique
o au oma ic e olu ion o clus e s", Pa e n Recogni ions 43, 2010, pp. 738-751,
doi:10.1016/j.pa cog.2009.07.004
[4] Edua do Raul H uschka, Rica do J. G. B. Campello, Alex A. F ei as, and And ´e C. Ponce Leon F. de
Ca alho, "A Su ey o E olu iona y Algo i hms o Clus e ing", IEEE ansac ions on sys ems, man,
and cybe ne ics—pa c: applica ions and e iews, Vol. 39-2, 2009, pp. 133-155.
[5] NobukazuMa ake, Tomoyuki Hi oyasu, Mi suno i Miki, Tomoha uSenda, "Mul iobjec i e Clus e ing
wi h Au oma ic k-de e mina ion o La ge-scale Da a", GECCO’07, July 7–11, 2007, London,
England, Uni ed Kingdom, ACM 978-1-59593-697-4/07/0007
[6] E éndi aRendón, I zel Abundez, Alejand a A izmendi and El ia M. Qui oz., "In e nal e sus Ex e nal
clus e alida ion indexes", In e na ional jou nal o compu e s and communica ions, 1(5), 2011.
[7] Mukhopadhyay, A., Maulik, U., &Bandyopadhyay, S. (2015). A Su ey o Mul iobjec i e
E olu iona y Clus e ing. ACM Compu ing Su eys (CSUR),47(4), 61.
Ad anced Compu a ional In elligence: An In e na ional Jou nal (ACII), Vol.3, No.2, Ap il 2016
42
[8] Abadi, M. F. H., &Rezaei, H. (2015). Da a Clus e ing Using Hyb idiza ion S a egies o Con inuous
An Colony Op imiza ion, Pa icle Swa m Op imiza ion and Gene ic Algo i hm. B i ish Jou nal o
Ma hema ics & Compu e Science, 6(4), 336.
[9] Oz u k, C., Hance , E., &Ka aboga, D. (2015). Dynamic clus e ing wi h imp o ed bina y a i icial
bee colony algo i hm. Applied So Compu ing, 28, 69-80.
[10] Kuma , V., Chhab a, J. K., & Kuma , D. (2014). Au oma ic clus e e olu ion using g a i a ional
sea ch algo i hm and i s applica ion on image segmen a ion. Enginee ing Applica ions o A i icial
In elligence, 29, 93-103.
[11] Kuo, R. J., Huang, Y. D., Lin, C. C., Wu, Y. H., &Zul ia, F. E. (2014). Au oma ic ke nel clus e ing
wi h bee colony op imiza ion algo i hm.In o ma ion Sciences, 283, 107-122.
[12] Wikaisuksakul, S. (2014). A mul i-objec i e gene ic algo i hm wi h uzzy c-means o au oma ic da a
clus e ing. Applied So Compu ing, 24, 679-691.
[13] Mukhopadhyay, A., Maulik, U., Bandyopadhyay, S., &CoelloCoello, C. (2014). A su ey o
mul iobjec i e e olu iona y algo i hms o da a mining: Pa I. E olu iona y Compu a ion, IEEE
T ansac ions on, 18(1), 4-19.
[14] Mukhopadhyay, A., Maulik, U., Bandyopadhyay, S., &Coello, C. (2014). Su ey o mul iobjec i e
e olu iona y algo i hms o da a mining: Pa II.E olu iona y Compu a ion, IEEE T ansac ions on,
18(1), 20-35.
[15] R. Venka a Rao, "Jaya: A simple and new op imiza ion algo i hm o sol ing cons ained and
uncons ained op imiza ion p oblems",In e na ional Jou nal o Indus ial Enginee ing Compu a ions,
7, 2016, doi: 10.5267/j.ijiec.2015.8.004
[16] Ramachand a Rao Ku ada, KanadamKa eekaPa an, AllamAppaRao,"Au oma ic Teaching–
Lea ning-Based Op imiza ion-A No el Clus e ing Me hod o Gene Func ional
En ichmen s",Compu a ional In elligence Techniques o Compa a i e Genomics, Sp inge B ie s in
Applied Sciences and Technology.2015. 10.1007/978-981-287-338-5.
[17] Ramachand a Rao Ku ada, Ka eekaPa anKanadam, "A gene alized au oma ic clus e ing algo i hm
using imp o ed TLBO amewo k", In . Jou nal o Applied Sciences and Enginee ing Resea ch, Vol.
4, Issue 4, 2015, ISSN 2277 – 9442.
[18] Lichman, M. (2013). UCI Machine Lea ning Reposi o y [h p://a chi e.ics.uci.edu/ml]. I ine, CA:
Uni e si y o Cali o nia, School o In o ma ion and Compu e Science.
