A New Clustering Validity Index for Fuzzy C Means Algorithm Based on Measure Of Disparity.

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1 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr A Nw Clusr Valy Ix for Fuzzy C Mas Alorm Bas o Masur Of Dspary ADEKUNE YA, AAO OD, EBIESUA SEUN, SARUMI JERRY, AINAM JEAN-PAU,,, Compur S Dparm, Babok Uvrsy, Ilsa-Rmo, Ou Sa, Nra Compur S Dparm, aos Sa Poly, Ikorou, aos Sa, Nra ABSTRACT Clusr valy xs av b us o valua fss of paros prou by lusr alorms Ts papr prss a w valy x for fuzzy lusr all r-lusr a ra-lusr sparao (ICS) x Trfor, w propos fuo of spary w ombs ra a r-lusr sparao xs bw lusrs T rsuls of omparav suy sow a propos ICS x as ably prou a oo lusr umbr sma Ts prforma s av by ak o osrao xs spary bw lusrs To assss w valao x, wo aa ss (Fsr s IRIS a Burfly aa s) wr us a rsuls sow a ICS ouprforms or lusr valao x for fuzzy -mas Ky wors: lusr valy x, fuzzy lusr, a fuzzy -mas, fuzzy - paros INTRODUCTION Fuzzy lo s a form of may-valu lo or probabls lo w als w raso T rm fuzzy lo was frs rou by A Za [] as a w way o rprs vauss vryay lf Fuzzy lo as b x o al op of paral ru, wr ru valu may ra bw omplly ru a omplly fals [] Clusr [,,,, ] s a usuprvs lassfao mo w oly aa avalabl ar ulabl, a o sruural formao abou s avalabl T objv of lusr s o f aa sruur a also paro aa s o roups w smlar vuals [] Amos varous fuzzy lusr alorms, fuzzy -mas ISSN: All Rs Rsrv IJARCET

2 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr (FCM) [] s bas o S as som rawbaks, svral alorms av b vlop o mprov prforma Alou, svral fuzzy lusr valy s av b propos o valua fuzzy lusr, y all suffr from lak of omb ra-lusr, rlusr a omry asp of lusr or Ts papr fouss o vlop a ovl valao x for fuzzy lusr alorm by ak aou spary amo lusrs Ts rsar s oraz as follow Frs, a ovrvw o rla works s prs (I), x, w brfly srb fuzzy -mas alorms (II) I r par of our papr, w prs propos x by xb valao rra a FCM valao alorm Fally, wo aa ss wr us o assss propos x a xprmal rsuls ompar w a umbr of kow valao s suss [,,,, ] I REATED ORKS M Ramz Rza al, [] rou a w valy x w asssss avra ompass a sparao of fuzzy paros ra by fuzzy - mas alorm Us wo aa ss, y ompar prforma of r x w a umbr of kow valao s [,,, a ] T rsuls of s suy sus a w valao x a av opmal rsul for ay possbl aa s By w umral rprsao os o srb ffr obj faurs o o proprly srma bw ffr lasss, valao x may fal Also, Eula orm (us s mol) may b urlabl for a spf aa s Fally, y appl FCM by ak oly a fw sampls of w xpo (m = ), s paramr os o f a arful aalyss V CB rqur vry lar valus of m Mara Halk al, [] rvw approas a prs lusr valy k approas bas o ral, xral a rlav rra Ty suss rsuls of a xprmal suy bas o wly kow valy s a fally llusra ssus a ar urarss by r approas a propos rsar ros fl Tou, o lusr valy x was sus, our work s bas o s rsar for y po ou a qualy masurs a assss qualy of paro o b vlop a ra-lusr qualy, r-lusr ISSN: All Rs Rsrv IJARCET

3 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr sparao a omry of lusrs o b ak o aou Cuu Za al, [] propos a ovl valy x for fuzzy-possbls -mas (FPCM) alorm I ombs x paro ropy a r lass smlary w s alula from fuzzy s po of vw T propos x oly rqurs mmbrsp marx a possbls (ypaly) marx, a s fr from avy sa ompu Ty fally ompar r x w [, ] a rsuls sow s ffvss Howvr, y o osr smlary bw fuzzy ss a mor or suaos wr bavor of propos x may la o wors rsul Yuaa Ta al, [] propos a w valao x for fuzzy lusr orr o lma moooally ras y as umbr of lusrs approas o umbr of aa pos a avo umral sably of valao x w fuzzy w xpo rass Two umral xampls av b prs o sow ffvss of propos valao x Y, propos valao suffrs from lak of masurs a assss qualy of paro a a al, [] rou fuamal ops of lusr valy, a prs a rvw of fuzzy lusr valy s avalabl lraur Ty also ou xsv omparsos of mo s ojuo w Fuzzy C-Mas lusr alorm o a umbr of wly us aa ss, a ma a smpl aalyss of xprmal rsuls No ovl valao x s propos o r work Moum El-Mly al, [] sou a aswr o quso o ow wll lusr valy xs a auomaally rm appropra umbr of lusrs a rprs aa T papr survy svral ky xs soluos for lusr valy oma of ma smao a sus wo w xs Tr ovls xs ar oly vo o oma of ma roo a rfor ao b asly appl o or omas ulss w ajusms Tr ar may ors publaos, arls a joural o prss or fuzzy lusr valao x [,,,, a ] amo ors Mos of s valy s usually assum aly a aa pos av osa sy o lusrs; owvr s o sur of ral problms so far; r s o valao x ISSN: All Rs Rsrv IJARCET

4 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr for fuzzy -mas lusr alorm w aks aou a sam m r fuamal asp of lusrs: omry of lusrs, r-lusr a ra-lusr sparao II FUZZY C-MEAN AGORITHM Fuzzy -ma (FCM) alorm s a usuprvs lusr alorm w a aa po blos o a lusr w a r spf by s mmbrsp ra T srpo of oral alorm as bak o [, ], rvavs av b srb w mof fo for orm a prooyps for lusr ros [,, ] To f ro a lusr a ra of mmbrsp for a obj lusrs, FCM mmzs a objv fuo Jm, w s w sum of squar rrors w roups a s f as follows: J m U, V = m u j j = = x j v () < m < r U s mmbrsp marx a s allow o av o oly a bu also lms w ay valus bw a Ts marx sasfs osra: = u j =, j =,, N () v s lusr r of fuzzy roup, a paramr m s a w xpo o a fuzzy mmbrsp ( our mplmao, w s o, wl mos of prvw paprs s o ) v s f by: v = j = m j = u j u j m x j () A u j (bw a ) sasfs osra: u j = II k= x j v x j v k m () NE VAIDATION INDEX FOR FUZZY C-MEAN (ICS) a Valao rra T FCM a f a paro of aa for a fx umbr of lusrs kow as objs O objv of lusr valy s o rm auomaally opmal umbr of lusrs [] Tr s a umbr of lusr ISSN: All Rs Rsrv IJARCET

5 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr valaos avalabl [,,,, a ] Som valy mos us oly mmbrsp valus of a fuzzy paro of aa Amo or fuoal, su s ar paro off V PC, paro ropy V PE, proporo xpo a uform aa fuoal Tabl lss a umbr of lusr valao s, w ar valua our suy a Valao alorm ε = u k + u k () () Fuzzy -ma alorm: Sp : Coos a umbr of lusr w rfrs o a umbr of lusr o Sp : Raomly alz lusr r Sp : Rpa ul proram as ovr, a s wr Ɛ Sp : Compur ro of a lusr us formula q () Sp : For a po, ompu s off of b lusr us formula q () C Sp : Gra w ro for a lusr us formula q () Sp : Compur Ɛ by us formula q (), f Ɛ >, o o sp E loop E alorm w a ollo of ros ( ) b Propos valao x Alou may valao x as b propos, a rlabl valao fuoal for FCM mus osr bo r a ralusr sparao of a fuzzy -paro If oly r-lusr sparao s osr by valao, paro oba osr a aa as a spara lusr a l ra-lusr sparao; a s, sa bw a obj of lusr a r Trfor a valao x w ombs bo rra wll av a opmal valu for a paro av s s valao x a all Ir- Clusr a Ira-Clusr Sparao (ICS) x ICS s f as follow: VP IC S Ira-lusr sa ar mmz U, V = αir + βira () Ir-lusr sa ar maxmz Fur : Ira a Ir-lusr rprsao ISSN: All Rs Rsrv IJARCET

6 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr I orr o a rlabl a fuoal valao x for FCM, valu of β quao () soul b as small as possbl β s o (β ), ra-lusr sa s also mmz A lassfao s rfor av by oos α su as α s o sas vara of populao Cro of a lusr s rm by = k = u k () T ro s (ypally) ma of pos lusr T ra a r-lusr sparao ar ompu as follow: For o lusr r: Dr = x x j j () Or Dr = r x x For k lusr, k = k r= Dr r T r-lusr sa s f by: If (umbr of lusr = ) Els () a ra = x = x + () r s rprss umbr of obj lusrs x + A x rprs wo objs lusr a rao III ANAYSIS AND RESUTS Two aa ss ar us o assss our propos x a prforma s ompar w fv wll-kow valao s a Daa ss T frs aa s us o assss our x s all Fsr s IRIS aa T full aa s osss of ss from a of r sps of Irs (Irs Sosa, Irs Vra a Irs vrsolor) Four faurs wr masur from a sampl: l l a w of spals a pals mrs Howvr, r s o o pl up sampl umbrs for our xprms T frs wy ss of masurms for a sps wll suff Ts ar rprou Tabl T so aa s us o assss x s all burfly aas from [] ISSN: All Rs Rsrv IJARCET

7 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr ISSN: All Rs Rsrv IJARCET Tabl : Frs wy spms from a sps lu Fsr () Irs aa Irs Sosa Irs vrsolor Irs Vra Pal Spal Pal Spal Pal Spal M M a x M a M a

8 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr V ar a S D v Commo valao x for fuzzy -ma: Tabl : Four valao fuoal for fuzzy -ma from [] Vala o Ix Paro off Paro ropy Fukuyam a a Suo X a B CB, M Ramz al ICS Fuoal Dsrpo V PC U = V PE U = k= = k= = V FS,m U, V; X = u k m k= = u k u k lo a u k x k v v v A V XB U, V; X m = k= u k x k v = m v v j V CB U, V = Sa + Ds() VP ICS U, V = αir + βira () Opmal lusr umbr Max ( V PC (U,, m)) M V PE U,, m M V FS U,, m M V XB U,, m M V CB U,, m M (U,, m)) (VP ICS CB = Compos a bw sar CONCUSION AND FURTHER STUDIES All rou s rsar, w mosra ssy of propos a w lusr valao x for fuzzy -mas alorm by ak o aou spary bw a obj of lusr Nx, by rv a fuo of spary a omb w w lusr valao x, w ar sur a our mol wll ovr fasr o valu of so-fx Ɛ Howvr, fuzzy -mas lusr a smlar alorms av problms w msoal aa ss a a lar umbr of prooyps [], our propos mol a suffr from s Mor sus mus b o s ara orr o ovrom msoal aa ss ass Furrmor, sa of oos β raomly as propos s mol (β small mpls a los ralusr sparao), som a f a mamaal formula abl a mor aura ompuao of β r Sa = = σ(x) σ(v ) a Ds = D max D m k= [] z v k v z ISSN: All Rs Rsrv IJARCET

9 Iraoal Joural of Ava Rsar Compur Er & Toloy (IJARCET) Volum Issu, Spmbr REFERENCES [] Za, A () Fuzzy ss, Iformao a Corol (), pp [] Novak, V, Prflva, I a Mokor, J () Mamaal prpls of fuzzy lo Dor: Kluwr Aam ISBN --- [] MR Arbr, Clusr Aalyss for Applao, Aam Prss, Nw York, [] PA Dvjvr, J Klr, Par Roo: A Sasal approa, Pr-Hall, oo, [] JA Hara, Clusr Alorms, ly, Nw York, [] AK Ja, RC Dubs, Alorms for Clusr Daa, Pr-Hall, Elwoo Clffs, NJ, [] Y G Ta, FC Su, ZQ Su, Improv valao x for fuzzy lusr, : Amra Corol Cof, Ju,, Porla, OR, USA Tras Par Aal Ma Ill (),, Au [] Bzk, JC, Clusr valy w fuzzy ss J Cybr (), [] Bzk, JC, Mamaal mols for sysmas a axoomy I: Esabrook, G (E), Pro Ira Cof Numral Taxoomy Frma, Sa Fraso, CA, pp [] Fukuyama, Y, Suo, M, A w mo of oos umbr of lusrs for fuzzy -mas mo I: Pro Fuzzy Sys Symp, pp [] Clusr Valy Ck Mos: Par II, Mara Halk, Yas Basaks, Mals Vazras [] A Valy Ix for Fuzzy a Possbls C-mas Alorms, Cuu Za, Ym Zou, Trvor Mar [] Improv Valao Ix for fuzzy lusr, Yuaa Ta, Fuu Su, [] Fuzzy lusr alorms for mx faur varabls, M-S Ya, P- Yua Hwa, D-ua C, Fbruary [] Za, A al Fuzzy Ss, Fuzzy o, Fuzzy Sysms, orl Sf Prss, ISBN --- [] A w lusr valy x for fuzzy -ma, M Ramz Rza, BPF lvl, JHC Rbr, [] X, X, B, GA, A valy masur for fuzzy lusr IEEE ISSN: All Rs Rsrv IJARCET