Diagnosing Diabetes Type II Using a Soft Intelligent Binary Classification Model

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1 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r Danosn Das T II Usn a So Inlln Bnar lasscaon Modl Mhd Khash * Sad Ekhar Jamshd Parvzan 3 Darmn o Indusral Ennrn Isahan Unvrs o Tchnolo (IUT) Isahan Unvrs o Tchnolo (IUT) Isahan Iran * Khash@n.u.ac.r; s.khar@n.u.ac.r; 3 aa@cc.u.ac Asrac Das namd also sln kllr s a maolc dsas characrzd hh lood lucos lvls hch rsul rom od dos no roduc nouh nsuln or h od s rssan o h cs o nsuln. lasscaon modls ar on o h mos dl usd rous o daa mnn ools ha ral hl hscans o mrov hr ronoss danoss or ramn lannn rocdurs. lasscaon accurac s on o h mos moran aurs n ordr o choos h arora classcaon modl; hnc h rsarchs drcd a mrovn uon h cvnss o hs modls hav nvr sod. Noadas ds h numrous classcaon modls roosd n svral as dcads s dl rconzd ha das ar xrml dcul o class. In hs ar a hrd nar classcaon modl s roosd or das II classcaon asd on h asc concs o so comun and arcal nllnc chnus. Emrcal rsuls o Pma Indan das daa classcaon ndca ha hrd modl s nrall r han ohr lnar/nonlnar so/hard and classc/nlln classcaon modls rsnd or das classcaon. Thror our roosd modl ma a sual alrnav modl or mdcal classcaon o achv rar accurac and o mrov mdcal danoss. Kords Arcal Inllnc; So omun; lasscaon; Mdcal Danoss; Das Inroducon Das mllus has com a nral chronc dsas ha acs n % and 4% o h loal oulaon and s avodanc and cv ramn ar undoudl crucal ulc halh and halh conomcs ssus n h s cnur. Das s a maolc dsass characrzd hh lood lucos lvls hch rsul rom od dos no roduc nouh nsuln or h od s rssan o h cs o nsuln namd sln kllr. Th od nds nsuln o us suar a and ron rom h d or nr. Das s assocad h man comlcaons and can ncras h rsk o lndnss lood rssur har dsas kdn dsas and nrv dama (Tmuras al. 9). Das dsas s nrall caorzd n o caors das I and das II. Th mos usual orm o das s das II or das mllus. In das II h od s rssan o h cs o nsuln. Mllons o ol hav n danosd h das II and unorunal man mor unaar ha h ar a hh rsk. Ds rcn mdcal rorsss arl danoss o dsas has mrovd u aou hal o h ans o das II ar unaar o hr dsas and ma ak mor han n ars as h dla rom dsas ons o danoss hl arl danoss and ramn o hs dsas s val. lasscaon ssms hav n dl ulzd n mdcal doman o xlor an s daa and xrac a rdcv modl. Th hl hscans o mrov hr ronoss danoss or ramn lannn rocdurs. In rcn ars man suds hav n rormd n h danoss o dac dsas lraur. Svral drn mhods such as losc rrsson Nav Bas Sm Nav Bas mullar rcrons (MLPs) radal ass uncons (RBFs) nral rrsson nural norks (GRNNs) suor vcor machns (SVMs) Las suar suor vcor machns (LS SVMs) hav n usd n som o hs suds (hara al. ; Kaar & Yldrm 3; Bnn & Blu 998; Frdman al. 997). Dcson r chnus also hav n dl usd o uld classcaon modls as such modls closl rsml human rasonn and ar as o undrsand. Ton al. (6) consrucd a classcaon modl or das II usn anhroomrcal od surac scannn daa. Th ald our daa mnn aroachs ncludn arcal nural nork dcson r losc rrsson and rouh s o slc h rlvan aurs rom h daa o class 9

2 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr das. Th shod ha h accurac o h dcson r and rouh s as ound o suror o ha o losc rrsson and nural nork. Josh al. () usd h classcaon r or classcaon and rrsson rs h a nar ar and n arus ncludn a sx mrnc darmn vss oc vss comord ndx dsldma hrnson cardovascular dsas rnoah and nd sa rnal dsas. Pola al. (8) roosd a n cascad larnn ssm asd on nralzd dscrmnan analss and las suar suor vcor machn or classcaon o das dsas. Th xamnd h rousnss o hr roosd ssm usn classcaon accurac k old cross valdaon mhod and conuson marx. Huan al. (7) rs ald aur slcon mhods n ordr o dscovr k arus acn dac conrol and hn usd hr comlmnar classcaon chnus ncludn Nav Bas IB and 4.5 o class ho ll h ans condon as conrolld. Hun al. () roosd ssm ulzd h survsd classr o scrn h mor rsk acors or drn chronc llnsss and hn usd hs sncan rsk acors o mlmn h classcaon and o consruc h arl arnn crra. alsr and Doankn () nroducd an auomac danoss ssm nrad lnar dscrmnan analss (LDA) and Morl avl suor vcor machn (LDA MWSVM) or das classcaon. Pal al. () uld a hrd classcaon modl hch could accural class nl danosd ans (rnan omn) no hr rou ha s lkl o dvlo das or no a rou hch dos no dvlo h das n v ars rom h m o rs danoss. Zhao (7) roos a mul ocv nc rorammn aroach o dvlon Paro omal dcson rs and llusra s alcaon n h das classcaon. Rcnl uzz aroachs hav com on o h ll knon soluons or mrovn classcaon modls. Fuzz hor as ornall dvlod o dal h rolms nvolvn lnusc rms (Zadh 975a) and hav n succssull ald o h road ran o rolms. Fuzz loc (Zadh 975) mrovs classcaon and dcson suor ssms (DSS) allon h us o ovrlan class dnons and s orul caals o handl uncran and vaunss (Sh al. 999). Gan & Aadh () roosd an an colon asd classcaon ssm o xrac a s o uzz ruls or danoss o das dsas namd FS ANTMINER. Khash al. () roosd n hrd modl comnn arcal nllnc h uzz modls n ordr o n rom unu advanas o hs chnus o consruc an cn and accura hrd classr. Kahramanl and Allahvrd (8) rsnd a n mhod or classcaon o daa o a mdcal daaas and dvlod a hrd nural nork ha ncluds arcal nural norks and uzz nural norks (FNNs). In hs ar a o sa hrd classcaon modl o radonal mul lar rcrons s roosd n ordr o ld mor accura rsuls han ohr hos modls n das II classcaon. In h rs sa o roosd modl a mul lar rcron s usd o r rocss o ra daa and rovd ncssar ackround n ordr o al a uzz rrsson modl. In scond sa h oand aramrs o rs sa ar consdrd n h orm o uzz numrs and hn h omum valus o roosd modl aramrs ar calculad usn h asc conc o uzz rrsson. In ordr o sho h cvnss and aroranss o roosd modl s rormanc s comard h hos o som uzz and nonuzz lnar and nonlnar and nlln classcaon modls. Emrcal rsuls o Pma Indan das daa classcaon ndca ha h roosd modl s an cv a n ordr o mrov classcaon accurac. Th rs o h ar s oranzd as ollos. In h nx Scon h asc concs and modlln aroachs o h radonal mul lar rcrons (MLPs) and ohr usd classcaon modls n hs ar ar rl rvd. Th ormulaon o h hrd roosd modl o classcaon asks s rvd n Scon 3. In Scon 4 h usd daa s Pma Indan das daa s s rl nroducd. In Scon 5 h roosd modl s ald o Pma Indan das daa s classcaon. In Scon 6 h rormanc o h roosd modl s comard o som ohr classcaon modls rsnd n h lraur or das classcaon. Fnall h conclusons ar dscussd. lasscaon Aroachs In hs scon h asc concs and modlln aroachs o h mul lar rcrons (MLPs) suor vcor machns (SVMs) K nars nhour

3 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r (KNN) uadrac dscrmnan analss (QDA) and lnar dscrmnan analss (LDA) modls or classcaon ar rl rvd. Mul Lar Prcrons (MLPs) Arcal nural norks (ANNs) ar comur ssms dvlod o mmc h oraons o h human ran mahmacall modlln s nurohsolocal srucur. Arcal nural norks hav n shon o cv a aroxman comlx nonlnar uncons (Zhan ). For classcaon asks hs uncons rrsn h sha o h aron n classs. In arcal nural norks comuaonal uns calld nurons rlac h nrv clls and h srnhs o h nrconncons ar rrsnd hs n hch h larnd normaon s sord. Ths unu arranmn can acur som o h nurolocal rocssn al o h olocal ran such as larnn and dran conclusons rom xrnc. Arcal nural norks comn h lxl o h oundar sha ound n K nars nhour h h cnc and lo sora rurmns o dscrmnan uncons. Lk h K nars nhour arcal nural norks ar daa drvn; hr ar no assumd modl characrscs or dsruons as s h cas h dscrmnan analss (Brard & Zhan 999). Mul lar rcrons (MLPs) ar on o h mos moran and dl usd orms o arcal nural norks or modlln orcasn and classcaon (Slva 8). Ths modls ar characrzd h nork o hr lars o sml rocssn uns conncd acclc lnks (F. ). Th rlaonsh n h ouu ( ) and h nus ( x x... x ) has h ollon mahmacal rrsnaon: ( x ) hr and... ar modl aramrs on calld conncon hs; s h hddn ransr uncon; s h h nos m ; s h numr o nu nods; and s h numr o hddn nods. Daa nrs h nork hrouh h nu lar movs hrouh hddn lar and xs hrouh h ouu lar. Each hddn lar and ouu lar nod collcs daa rom h nods aov (hr h nu lar or hddn lar) and () als an acvaon uncon. Acvaon uncons can ak svral orms. Th o acvaon uncon s ndcad h suaon o h nuron hn h nork. In h maor o cass nu lar nurons do no hav an acvaon uncon as hr rol s o ransr h nus o h hddn lar. Th losc and hrolc uncons ar on usd as hddn lar and ouu ransr uncons or classcaon rolms ha ar shon n E. and E. 3 rscvl. Ohr ransr uncons can also usd such as lnar and uadrac ach h a var o modlln alcaons. S Tanh x( x ) x. x( x ) x( x ) x. Th sml nork vn () s surrsnl orul n ha s al o aroxma h arrar uncon as h numr o hddn nods hn s sucnl lar. In racc sml nork srucur ha has a small numr o hddn nods on orks ll n ou o saml orcasn. Ths ma du o h ovr n c call ound n h nural nork modlln rocss. An ovr d modl has a ood o h saml usd or modl uldn u has oor nralzal o daa ou o h saml. 3 Inu lar Bas un Hddn ransr Fun. Hddn lar Bas un Ouu lar FIG. MULTI LAYER PEREPTRON STRUTURE (N (--) ) Thr xs man drn aroachs such as h runn alorhm h olnomal m alorhm h canoncal dcomoson chnu and h nork normaon crron or ndn h omal archcur o an arcal nural nork. Ths aroachs can nrall caorzd as ollos (Khash & Bar ): () Emrcal or sascal mhods ha ar usd o sud h c o nrnal aramrs and choos arora valus or hm asd on h rormanc o modl. Th mos Ouu ransr Fun. () (3)

4 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr ssmac and nral o hs mhods ulzs h rncls rom Tauch s dsn o xrmns. () Hrd mhods such as uzz nrnc hr h arcal nural nork can nrrd as an adav uzz ssm or can ora on uzz nsad o ral numrs. () onsrucv and/or runn alorhms ha rscvl add and/or rmov nurons rom an nal archcur usn a rvousl scd crron o ndca ho arcal nural nork rormanc s acd h chans. Th asc ruls ar ha nurons ar addd hn rann s slo or hn h man suard rror s larr han a scd valu. In oos nurons ar rmovd hn a chan n a nuron s valu dos no corrsond o a chan n h nork s rsons or hn h h valus ha ar assocad h hs nuron rman consan or a lar numr o rann ochs. (v). Evoluonar sras ha sarch ovr oolo sac varn h numr o hddn lars and hddn nurons hrouh alcaon o nc oraors and valuaon o h drn archcurs accordn o an ocv uncon (Bnardos al. 7). Alhouh man drn aroachs xs n ordr o nd h omal archcur o an arcal nural nork hs mhods ar usuall u comlx n naur and ar dcul o mlmn (Zhan & Pauo 998). Furhrmor non o hs mhods can uaran h omal soluon or all ral orcasn rolms. To da hr s no sml clarcu mhod or drmnaon o hs aramrs and h usual rocdur s o s numrous norks h varn numrs o hddn uns sma nralzaon rror or ach and slc h nork h h los nralzaon rror (Hossn al. 6). Onc a nork srucur s scd h nork s rad or rann a rocss o aramr smaon. Th aramrs ar smad such ha h cos uncon o nural nork s mnmzd. os uncon s an ovrall accurac crron such as h ollon man suard rror: N E N n N ( ) N n hr N s h numr o rror rms. Ths mnmzaon s don h som cn nonlnar omzaon alorhms ohr han h asc ack (4) roaaon rann alorhm (Rumlhar & Mcllland 986) n hch h aramrs o h nural nork ar chand an amoun accordn o h ollon ormula: E hr h aramr s h larnn ra and E s h aral drvav o h uncon E h rsc o h h (5). Ths drvav s commonl comud n o asss. In h orard ass an nu vcor rom h rann s s ald o h nu uns o h nork and s roaad hrouh h nork lar lar roducn h nal ouu. Durn h ackard ass h ouu o h nork s comard h h dsrd ouu and h rsuln rror s hn roaad ackard hrouh h nork adusn h hs accordnl. To sd u h larnn rocss hl avodn h nsal o h alorhm Rumlhar and Mcllland (986) nroducd a momnum rm n E. (5) hus oann h ollon larnn rul: E Th momnum rm ma also hlul o rvn h larnn rocss rom n rad no oor local mnma and s usuall chosn n h nrval [; ]. Fnall h smad modl s valuad usn a sara hold ou saml ha s no xosd o h rann rocss. Lnar Dscrmnan Analss (LDA) Lnar dscrmnan analss (LDA) s a vr sml and cv survsd classcaon mhod h d alcaons. Th asc hor o lnar dscrmnan analss s o class comounds dvdn an n dmnsonal dscror sac no o rons ha ar sarad a hr lan ha s dnd a lnar dscrmnan uncon. Dscrmnan analss nrall ransorms classcaon rolms no uncons ha aron daa no classs hus rducn h rolm o h dncaon o a uncon. Th ocus o dscrmnan analss s on drmnn hs unconal orm and sman s cocns. In h lnar dscrmnan (6)

5 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r analss hs uncon s assumd o lnar. Ronald Almr Fshr (936) rs nroducd h lnar dscrmnan uncon. Fshr s lnar dscrmnan uncon orks ndn h man o h s o arus or ach class and usn h man o hs mans as h oundar. Th uncon achvs hs rocn h aru ons ono h vcor ha maxmall saras hr class mans and mnmzs hr hn class varanc. Th Fshr s lnar dscrmnan uncon can rn as ollos: X X X X S X X c X S hr X s h vcor o h osrvd valus X s h man o valus or ach rou S s h saml covaranc marx o all varals and c s h cos uncon. I h msclasscaon cos o ach rou s consdrd ual c s s o zro. A mmr s classd no on rou h rsul o h uaon s rar han c (or zro) and no h ohr lss han c (or zro). A rsul ual o c ndcas ha a saml canno classd no hr class asd on h aurs usd n h analss. Th lnar dscrmnan uncon dsnushs n o classs. I a daa s has mor han o classs h rocss mus rokn don no mull o class rolms. Th lnar dscrmnan uncon as ound or ach class vrsus all samls ha r no o ha class (on vrsus all). Fnal class mmrsh or ach saml as drmnd h lnar dscrmnan uncon ha roducd h hhs valu. Lnar dscrmnan analss s omal hn h varals ar normall dsrud h ual covaranc marcs. In hs cas h lnar dscrmnan uncon s n h sam drcon as h Bas omal classr (Bllns & L ). Th lnar dscrmnan s knon o rorm ll on modra saml szs hn comard o mor comlx mhods (Ghass & Burnl ). As a srahorard mahmacal uncon rurn nohn mor comlcad han marx arhmc h lnar dscrmnan s rlavl sml o rorm. Th assumon o lnar n h class oundar hovr lms h sco o alcaon or lnar dscrmnan analss. Ral orld daa runl canno sarad a lnar oundar. Whn oundars ar nonlnar h rormanc o h lnar dscrmnan ma nror o ohr classcaon mhods. (7) Quadrac Dscrmnan Analss (QDA) Quadrac dscrmnan analss (QDA) rs nroducd Smh (947) s anohr dsanc asd classr hch s vr smlar o h lnar dscrmnan uncon classr. In ac uadrac dscrmnan analss s an xndd o h lnar dscrmnan uncon. Boh dscrmnan uncons assum ha h valus o ach aru n ach class ar normall dsrud hovr h dscrmnan scor n ach saml and ach class s calculad usn h saml varanc covaranc marx o ach class saral rahr han h ovrall oold marx and so s a mhod ha aks no accoun h drn varanc o ach class. On h ohr hand n lnar dscrmnan analss s assumd ha h covaranc marcs o h rous ar ual hras uadrac dscrmnan analss maks no such assumon. Whn h covaranc marcs ar no ual h oundar n h classs ll a hr conc and n hor h us o uadrac dscrmnan analss ll rsul n r dscrmnaon and classcaon ras. Hovr du o h ncrasd numr o addonal aramrs ha nd o smad s u ossl ha h classcaon uadrac dscrmnan analss s ors han ha o lnar dscrmnan analss (Malhora al. 999). Th uadrac dscrmnan s ound valuan h uaon: X ' ' S S X X S X S X ' S X X ' S X S Ln X S c Th sam condons al o h naur o c and classcaon n h cas ha h rsul s ual o c or zro. As h h lnar dscrmnan h uadrac dscrmnan uncon dsnushs n o classs. For mull class daa ss hs as handld h sam as or lnar dscrmnan analss. Th sz o h drncs n varancs drmns ho much r h uadrac dscrmnan uncon ll rorm han h lnar dscrmnan. For lar varanc drncs h uadrac dscrmnan xcls hn comard o h lnar dscrmnan. Addonall o h o onl h uadrac dscrmnan can usd hn oulaon mans ar ual. Alhouh mor roadl alcal han h lnar dscrmnan h uadrac dscrmnan s lss rsln undr non omal condons. Th uadrac (8) 3

6 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr dscrmnan can hav ors han h lnar dscrmnan or small saml szs. Addonall daa ha s no normall dsrud rsuls n a oorr rormanc h uadrac dscrmnan hn comard o h lnar dscrmnan. Marks and Dunn (974) ound h rormanc o h uadrac dscrmnan uncon o mor snsv o h dmnsons o h daa han h lnar dscrmnan mrovn as h numr o arus ncrass o a cran omal numr hn radl dclnn. Lnar and nonlnar dscrmnan uncons ar h mos dl usd classcaon mhods. Ths road accanc s du o hr as o us and h d avalal o ools. Boh hovr assum h orm o h class oundar s knon and s a scc sha. Ths sha s assumd o smooh and dscrd a knon uncon. Ths assumons ma al n man cass. In ordr o rorm classcaon or a dr ran o ral orld daa a mhod mus al o dscr oundars o unknon and ossl dsconnuous shas. K-Nars Nhour (KNN) Th K nars nhour (KNN) modl s a llknon survsd larnn alorhm or arn rconon ha rs nroducd Fx and Hods n 95 and s sll on o h mos oular nonaramrc modls or classcaon rolms (Fx & Hods 95; 95). K nars nhour assums ha osrvaons hch ar clos ohr ar lkl o hav h sam classcaon. Th roal ha a on x lons o a class can smad h rooron o rann ons n a scd nhourhood o x ha lon o ha class. Th on ma hr classd maor vo or a smlar dr sum o h scd numr (k) o nars ons. In maor von h numr o ons n h nhourhood lonn o ach class s cound and h class o hch h hhs rooron o ons lons s h mos lkl classcaon o x. Th smlar dr sum calculas a smlar scor or ach class asd on h K nars ons and classs x no h class h h hhs smlar scor. Du o s lor snsv o oulrs maor von s mor commonl usd han h smlar dr sum (haovalons 7). In hs ar maor von s usd or h daa ss. In ordr o drmn hch ons lon n h nhourhood h dsancs rom x o all ons n h rann s mus calculad. An dsanc uncon ha scs hch o o ons s closr o h saml on could mlod (Fx & Hods 95. Th mos common dsanc mrc usd n K nars nhour s h Eucldan dsanc (Van ). Th Eucldan dsanc n ach s on and rann s on s ach h n arus s calculad usn h uaon: d s s... n sn In nral h ollon ss ar rormd or h K nars nhour modl (Yldz al. 8): ) hosn o k valu. ) Dsanc calculaon. ) Dsanc sor n ascndn ordr. v) Fndn k class valus. v) Fndn domnan class. On challn o us h K nars nhour s o drmn h omal sz o k hch acs as a smoohn aramr. A small k ll no sucn o accural sma h oulaon roorons around h s on. A larr k ll rsul n lss varanc n roal smas u h rsk o nroducn mor as. K should lar nouh o mnmz h roal o a non Bas dcson u small nouh ha h ons ncludd v an accura sma o h ru class. Enas and ho (986) ound ha h omal valu o k dnds uon h saml sz and covaranc srucurs n ach oulaon as ll as h roorons or ach oulaon n h oal saml. For cass n hch h drncs n h covaranc marcs and h drnc n saml roorons r hr oh small or oh lar Enas and ho (986) ound ha h omal k o 3 8 N hr N s h numr o samls n h rann s. Whn hr as a lar drnc n covaranc marcs and a small drnc n saml roorons or vc vrsa h 8 drmnd N o h omal valu o k. Ths modl rsns svral advanas (Brrua al. 7): () Is mahmacal smlc hch dos no rvn rom achvn classcaon rsuls as ood as (or vn r han) ohr mor comlx arn rconon chnus. (9) 4

7 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r () I s r rom sascal assumons such as h normal dsruon o h varals. () Is cvnss dos no dnd on h sac dsruon o h classs. In addonal hn h oundars n classs canno dscrd as hr lnar or hr conc K nars nhour rorms r han h lnar and uadrac dscrmnan uncons. Enas and ho (986) ound ha h lnar dscrmnan rorms slhl r han K nars nhour hn oulaon covaranc marcs ar ual a condon ha suss a lnar oundar. As h drncs n h covaranc marcs ncrass K nars nhour rorms ncrasnl r han h lnar dscrmnan uncon. Hovr ds o h all advanas cd or h K nars nhour modls h also hav som dsadvanas. K nars nhour modl canno ork ll lar drncs ar rsn n h numr o samls n ach class. K nars nhour rovds oor normaon aou h srucur o h classs and o h rlav moranc o ach varal n h classcaon. Furhrmor dos no allo a rahcal rrsnaon o h rsuls and n h cas o lar numr o samls h comuaon can com xcssvl slo. In addon K nars nhour modl much hhr mmor and rocssn rurmns han ohr mhods. All roos n h rann s mus sord n mmor and usd o calcula h Eucldan dsanc rom vr s saml. Th comuaonal comlx ros xonnall as h numr o roos ncrass (Muzznolu & Zurada 6). Suor Vcor Machns (SVMs) Suor vcor machns (SVMs) ar a n arn rconon ool horcall oundd on Vank s sascal larnn hor (Vank 998). Suor vcor machns ornall dsnd or nar classcaon mlos survsd larnn o nd h omal saran hr lan n h o rous o daa. Havn ound such a lan suor vcor machns can hn rdc h classcaon o an unlald xaml askn on hch sd o h saran lan h xaml ls. Suor vcor machn acs as a lnar classr n a hh dmnsonal aur sac ornad a rocon o h ornal nu sac h rsuln classr s n nral non lnar n h nu sac and achvs ood nralzaon rormancs maxmzn h marn n h o classs. In h ollon v a shor ouln o consrucon o suor vcor machn. onsdr a s o rann xamls as ollos: n x x R ;... m () hr h x ar ral n dmnsonal arn vcors and h ar dchoomous lals. Suor vcor n machn mas h arn vcors x R no a ossl hhr dmnsonal aur sac ( z x ) and consruc an omal hr lan z n aur sac o sara xamls rom h o classs. For suor vcor machn h L somarn ormulaon hs s don solvn h rmal omzaon rolm as ollos: Mn s.. m z... m () hr s a rularzaon aramr usd o dcd a rad o n h rann rror and h marn and...m ar slack varals. Th aov rolm s comuaonall solvd usn h soluon o s dual orm: Max s.. m m ; m hr kx x x x k x x...m () s h krnl uncon ha mlcl dn a man. Th rsuln dcson uncon s: m x sn kx x (3) All krnl uncons hav o ull Mrcr horm; hovr h mos commonl usd krnl uncons ar olnomal krnl and radal ass uncon krnl rscvl (Son & Tan 5). k x x ax x d (4) 5

8 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr k x x x x x (5) Suor vcor machns dr rom dscrmnan analss n o sncan as. Frs h aur sac o a classcaon rolm s no assumd o lnarl saral. Rahr a nonlnar man uncon (also calld a krnl uncon) s usd o rrsn h daa n hhr dmnsons hr h oundar n classs s assumd o lnar (Duda al. ). Scond h oundar s rrsnd suor vcor machns nsad o a snl oundar. Suor vcors run hrouh h saml arns hch ar h mos dcul o class hus h saml arns ha ar closs o h acual oundar. Ovr n s rvnd scn a maxmum marn ha saras h hr lan rom h classs. Samls hch vola hs marn ar nalzd. Th sz o h nal s a aramr on rrrd o as (Bron al. ; hrsann & Talor ). Formulaon h Hrd Proosd Modl Mul lar rcrons (MLPs) ar lxl comun ramorks and unvrsal aroxmaors ha can ald o a d ran o classcaon rolms h a hh dr o accurac (Khash al. ). Svral dsnushn aurs o mul lar rcrons mak hm valual and aracv or classcaon asks. Th mos moran o hs s ha MLPs as oosd o h radonal modl asd chnus ar daa drvn sl adav mhods n ha hr ar a ror assumons aou h modls or rolms undr sud (Khash al. 9). Th aramr o MLP modls (hs and ass) ar crs ( ). In roosd modl nsad o usn crs uzz aramrs n h orm o ranular uzz numrs ar usd or rlad aramrs o lars ( ~ ~... ). Th modl s dscrd usn a uzz uncon h a uzz aramr (Khash al. ): ~ ( ~ ~ ( ~ ~ Whr )) (6) ar osrvaons ~ ~... ar uzz numrs. E. (6) s modd as ollos: ~ ( ~ ~ X ~ ) ( ~ X ~ ) (7) hr X ~ ( ~ ~ ). Fuzz aramrs n h orm o ranular uzz numrs ~ a c ar usd: ~ Whr a c a c a ohrs c (8 ) ~ s h mmrsh uncon o h uzz s ha rrsns aramr. B aln h xnson rncl coms clar ha h mmrsh o X ~ ~ ( ~ ) n E. (7) s vn as (Khash al. 8): x X ~ X a a X c c ohrs a X X c (9) 6

9 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r 7 hr......k and...k. onsdrn ranular uzz numrs X ~ h mmrsh uncon E. (9) and ranular uzz aramrs ~ ll as ollos: () ohrs d d d ~ Th mmrsh uncon o ) X ~ ~ ( ) X ~ ~ ~ ( ~ s vn as (). No consdrn a hrshold lvl h or all mmrsh uncon valus o osrvaons h nonlnar rorammn s vn as (). As a scal cas and o rsn h smlc and cnc o h modl h ranular uzz numrs ar consdrd smmrc ouu nuron ransr uncon s consdrd o lnar and conncd hs n nu and hddn lar ar consdrd o o a crs orm. Th mmrsh uncon o n h scal cas mnond s ransormd as ollos: (3) ohrs X or X c X ~ Smulanousl rrsns h h osrvaon and h lvl s h hrshold valu rrsnn h dr o hch h modl should sasd all h daa ons k.... A choc o h h valu nluncs h dhs o h uzz aramrs: (4)...k or h ) ( ~ () ohrs A A B A B A A B A B 3 3 Y ~ hr d a a d B a d A c c B c A 3 c a d

10 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr Mn k c d a Suc.o B B A A A B B A A A h h 3 3 or or...k...k () Th ndx rrs o h numr o non uzz daa usd or consrucn h modl. On h ohr hand h uzznss S ncludd n h modl s dnd : k S c X (5) Whr s h conncon h n ouu nuron and h nuron o h hddn lar; x s h ouu valu o h nuron o h hddn lar n h m. Nx h rolm o ndn h aramrs n h roosd mhod s ormulad as a lnar rorammn rolm as ollos: Mnmz k S c X X h c X suc.o X h c X c or.....k..k (6) Thn h daa around h ur and lor ound o h roosd modl hn modl has oulrs h a d srad ar dld n accordanc h Ishuch s rcommndaons. In ordr o mak h modl o nclud all ossl condons c has a d srad hn h daa s ncluds a sncan drnc or ouln cas. Ishuch and Tanaka (988) sus ha h daa around h modlʹs ur and lor oundars dld so ha h uzz rrsson modl can rormulad. Fnal on s ha h ouu o h roosd modl s uzz and connuous hl our classcaon rolm drs n ha s ouu s dscr and nonuzz. Thror n ordr o al h roosd modl o classcaon cran modcaons o h modl ndd o mad. For hs uros ach class s rsl assnd a numrc valu and hn h mmrsh roal o h ouu n ach class s calculad as ollos: P A P hr B m P A and ( x )dx ( x )dx m ( x )dx ( x )dx (7) P B ar h mmrsh roal o h class A and class B rscvl and m s h man o h class valus. Fnall h saml s u n h class h hch s ouu has h lars roal. In roosd modl du o hs ac ha ouu s uzz ma r o al h lar class valus. Th larr class valus xand small drncs n h ouu hln h modl o com mor snsv o varaons n h nu. For xaml nsad o usn h or h or ar r o usd as class valus (Khash al. ). Pma Indan Das Daa S Th Pma Indan Das daa s s collcd h Naonal Insu o Das and Dsv and Kdn Dsass and consss o das danoss (osv or nav) and arus o mal ans ho ar a las ars old and o Pma Indan hra (Golu al. 999). Th h arus rrsn ) h numr o ms rnan ) h rsuls o an oral lucos olranc s 3) dasolc lood rssur (mm H) 4) rcs skn old hcknss (mm) 5) h srum nsuln (mcro U/ml) 6) od mass ndx (h n k/(hh n m)^) 7) das dr uncon and 8) a (ar). Th odmnsonal dsruon o hs o classs aans 8

11 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r FIG. THE TWO DIMENSIONAL DISTRIBUTION OF PIMA INDIAN DIABETES LASSES TABLE BRIEF STATISTIAL INFORMATION OF ATTRIBUTES No. Aru Nam Man Numr o ms rnan Sandard Dvaon Plasma lucos ( Hours) Dasolc lood rssur Trcs skn old hcknss To hour srum nsuln Bod mass ndx Das dr uncon A h (X X3) (X6 X7) (X X6) (X3 X7) (X X7) and (X3 X6) as xaml s shon n F.. Som sascal normaon o arus s vn n Tal. Th daa s consss o 768 samls aou o hrd o hch hav a nav das danoss and on hrd h a osv danoss. Th daa s s randoml sl no ual sz o rann and s ss o 384 samls ach. Alcaon o h Hrd Proosd Modl o Das lasscaon In ordr o oan h omum nork archcur o h roosd modl asd on h concs o mullar rcrons dsn (Khash & Bar ) and usn runn alorhms n MATLAB 7 acka soar drn nork archcurs ar valuad o comar h MLPs rormanc. 9

12 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr Th s d nork hch s slcd and hror h archcur hch rsnd h s accurac h h s daa s comosd o h nus v hddn and on ouu nurons (n arvad orm N (8 5 ) ). Thn h mnmal uzznss o h uzz aramrs s drmnd usn E. () h h=. As mnond rvousl h h lvl valu nluncs h dhs o h uzz aramrs. In hs cas consdr h= n ordr o ld aramrs h mnmum o dh. Th msclasscaon ra o ach modl and mrovmn rcnas o h roosd modl n comarson h hos o ohr classcaon modls or h Pma Indan das daa n oh rann and s daa ss ar summarzd n Tal and Tal 3 rscvl. Th msclasscaon ra and mrovmn rcna o h modl (B) aans h modl (A) ar rscvl calculad as ollos: Msclasscaon Ra Imrovmn No.o ncorrc danoss MR No.o saml s A MR - Prcna MR MR B A omarson h Ohr Modls % (8) (9) Accordn o h oand rsuls (Tals & 3) our roosd modl has h los rror on h s oron o h daa s n comarson o ohr hos usd modls or h Pma Indan Das daa s h a msclasscaon ra o 8.8%. Svral drn archcurs o arcal nural nork ar dsnd and xamnd. Th s rormn archcur or a radonal mul lar rcron roducs a 5.3% rror ra hch roosd modl mrovs 5.69%. Lnar dscrmnan analss rorms scond s h an rror ra o.9% a classcaon ra 4.6% ors han h roosd modl. Quadrac dscrmnan analss msclasss 8.% o h s samls hch s also a 33.% ors han h roosd modl. As K nars nhour scors can snsv o h rlav manud o drn arus all arus ar scald hr z scors or usn K nars nhour modl (Anal al. 3). Th s K nars nhour h a K=3 has rror ras o 4.7%ha s a 3.89% hhr han h roosd modl rror. Th suor vcor machn modl h = roducs an rror ra o 3.%. Th roosd modl mrovs uon hs 37.33% or h suor vcor machn. TABLE PIMA INDIAN DIABETES DATA SET LASSIFIATION RESULTS Modl lasscaon rror Trann Daa Ts Daa Lnar Dscrmnan Analss (LDA) %6.6 %.9 Quadrac Dscrmnan Analss (QDA) %3.7 %8. K Nars Nhour (KNN) [K=3] %3.4 %4.7 Suor Vcor Machns (SVM) [=] %9.9 %3. Arcal Nural Norks (ANN) [N (8 5 ) ] %8.8 %5.3 Hrd roosd modl %7.6 %8.8 TABLE 3 IMPROVEMENT OF THE PROPOSED MODEL IN OMPARISON WITH THOSE OF OTHER LASSIFIATION MODELS Modl Imrovmn (%) Trann Daa Ts Daa Lnar Dscrmnan Analss (LDA) Quadrac Dscrmnan Analss (QDA) K Nars Nhour (KNN) Suor Vcor Machns (SVM) Arcal Nural Norks (ANN) onclusons Das s a maolc dsass characrzd hh lood lucos lvls hch rsul rom od dos no roduc nouh nsuln or h od s rssan o h cs o nsuln namd sln kllr. lasscaon chnus hav rcvd consdral anon n olocal and mdcal alcaons ha ral hl hscans o mrov hr ronoss danoss or ramn lannn rocdurs. Boh horcal and mrcal ndns hav ndcad ha usn hrd modls or comnn svral modls has com a common racc o rduc uon hr msclasscaon ra scall hn h modls n comnaon ar u drn. In hs ar a hrd modl o mul lar rcrons s roosd as an alrnav classcaon modl usn h unu so comun advanas o h uzz loc. Th roosd modl nrall consss o v hass as ollos: ) Trann h nural nork usn h avalal normaon rom osrvaons

13 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r ) Drmnn h mnmal uzznss usn h oand hs and sam crron ) Dln h oulrs accordanc h Ishuch s rcommndaons v) alculan h mmrsh roal o h ouu n ach class v) Assnn h ouu o arora class h lars roal Fv ll knon sascal and nlln classcaon modls lnar dscrmnan analss uadrac dscrmnan analss K nars nhour suor vcor machns and mul lar rcrons ar usd n hs ar n ordr o sho h aroranss and cvnss o h roosd modl or das classcaon. Th oand rsuls ndca ha h roosd modl o suror o all alrnav modls. For nar classcaon o h Pma Indan Das nchmark daa s roosd modl rorms r han h radonal mul lar rcrons. Th mrovmn vars rom 6.38% o 5.69% n comarson o h mul lar rcrons or h rann and s daa ss. In addon h rormanc o h hrd roosd modl s ovrall r han suor vcor machn and also ohr radonal classcaon modls such as lnar dscrmnan analss and uadrac dscrmnan analss. Our roosd modl dos no assum h sha o h aron unlk h lnar and uadrac dscrmnan analss. In conras o h K nars nhour modl h roosd modl dos no rur sora o rann daa. Onc h modl has n rand rorms much asr han K nars nhour dos caus dos no nd o ra hrouh ndvdual rann samls. Th roosd modl dos no rur xrmnaon and nal slcon o a krnl uncon and a nal aramr as s rurd h suor vcor machns. Our roosd modl soll rls on a rann rocss n ordr o dn h nal classr modl. Fnall h roosd modl dos no nd lar amoun o daa n ordr o ld accura rsuls as radonal mul lar rcrons. AKNOWLEDGEMENTS Th auhors sh o xrss hr raud o anonmous rvrs and Gh. A. Rass Ardal ndusral nnrn darmn Isahan Unvrs o Tchnolo ho ral hld us o mrov hs ar. REFERENES Anal P. Fanns G. Tmmrman D. Morau Y. and Moor B.D. Basan alcaons o l norks and mullar rcrons or ovaran umor classcaon h rcon Arcal Inllnc n Mdcn Vol Bnardos P.G. and Vosnakos G.. Omzn dorard arcal nural nork archcur Ennrn Alcaons o Arcal Inllnc Vol Bnn K. P. and Blu J. A. A suor vcor machn aroach o dcson rs IEEE World onrss on omuaonal Inllnc Brard V. and Zhan G. P. Th c o msclasscaon coss on nural nork classrs Dcson Scncs Vol Brrua L. Alonso Salcs R. Hrr K. Survsd arn rconon n ood analss Journal o hromaorah A Bllns S. and L K. Nonlnar Fshr dscrmnan analss usn a mnmum suard rror cos uncon and h orhoonal las suars alorhm Nural Norks Vol Braul J. L. Goodall. R. and Fos P. J. Daa mnn a dac daa arhous Arcal Inllnc n Mdcn Vol Bron M. Grund W. Ln D. rsann N. Sun. Fur T. Ars M. and Hausslr D. Knold asd analss o mcroarra n xrsson daa usn suor vcor machns Procdns o h Naonal Acadm o Scncs o h Und Sas o Amrca Vol alsr D. and Doankn E. An auomac das danoss ssm asd on LDA Wavl Suor Vcor Machn lassr Exr Ssms h Alcaons Vol haovalons W. On h m srs k nars nhor classcaon o anormal ran acv IEEE Transacons on Ssms Man and rncs Par A: Ssms and Humans Vol hara S. Oddra D. Samana S. and Vdarh S. omuaonal Inllnc n Earl Das Danoss:

14 .su.or/r Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr A Rv Th Rv o Das Suds Vol hrsann N.and Sha Talor J. An nroducon o suor vcor machns amrd Unvrs Prss. Duda R. Har P. and Sork D. Parn classcaon N York: John Wl & Sons Inc.. Enas G. and ho S. hoc o h smoohn aramr and cnc o k nars nhor omurs and Mahmacs h Alcaons Vol Fshr R. A. Th us o mull masurmns n axonomc rolms Annals o Euncs Vol Fx E. and Hods J. Dscrmnaor analss Nonaramrc dscrmnaon: onssnc rors Proc No Ror No. 4 onrac No. AF 4(8) 3 USAF School o Avaon Randolh Fld Txas 95. Fx E. and Hods J. Dscrmnaor analss Nonaramrc dscrmnaon: Small saml rormanc. Proc No Ror No. onrac No. AF 4(9) 3 USAF School o Avaon Randolh Fld Txas 95. Frdman N. Gr D. and Goldszm M. Basan norks classrs Machn Larnn Vol Gan M. F. and Aadh M. S. A uzz classcaon ssm asd on An olon Omzaon or das dsas danoss Exr Ssms h Alcaons Vol Ghass M. and Burnl. Masurn cvnss o a dnamc arcal nural nork alorhm or classcaon rolms Exr Ssms h Alcaons Vol Golu T.R. Slonm D.K. Tamao P. Huard. Gaasnk M. Msrov J.P. ollr H. Loh M.L. Donn J.R. alur M.A. Bloomld.D. and Landr E.S. Molcular classcaon o cancr: class dscovr and class rdcon n xrsson monorn Scnc Vol Hossn H. Luo D. and Rnolds K.J. Th comarson o drn d orard nural nork archcurs or EG snal danoss Mdcal Ennrn & Phscs Vol Huan Y. Mcullah P. Black N. and Harr R. Faur slcon and classcaon modl consrucon on dac ansʹ daa Arcal Inllnc n Mdcn Vol Ishuch H. and Tanaka H. Inrval rrsson analss asd on mxd nr rorammn rolm J. Jaan Soc. Ind. En. Vol Jn. H. Wan.. Jan B.. hu Y. H. and hn M. S. Alcaon o classcaon chnus on dvlomn an arl arnn ssm or chronc llnsss Exr Ssms h Alcaons Vol Kahramanl H. and Allahvrd N. Dsn o a hrd ssm or h das and har dsass Exr Ssms h Alcaons Vol Kaar K. and Yldrm T. Mdcal danoss on ma Indan das usn nral rrsson nural norks arcal nural norks and nural normaon rocssn (IANN/IONIP) Isanul Turk Khash M. and Bar M. A novl hrdzaon o arcal nural norks and ARIMA modls or m srs orcasn Ald So omun Vol Khash M. and Bar M. An arcal nural nork ( d ) modl or m srs orcasn Exr Ssms h Alcaons Vol Khash M. Bar M. and Haz S. R. omnn sasonal ARIMA modls h comuaonal nllnc chnus or m srs orcasn So omun Vol Khash M. Bar M. and Rass GH A. Imrovmn o Auo Rrssv Inrad Movn Avra modls usn uzz loc and arcal nural norks (ANNs) Nurocomun Vol Khash M. Hamadan A. Z. and Bar M. A uzz nlln aroach o h classcaon rolm n n xrsson daa analss Knold Basd Ssms Vol Khash M. Haz S. R. Bar M. A n hrd arcal nural norks and uzz rrsson modl or m

15 Rv o Bonormacs and Bomrcs (RBB) Volum Issu Dcmr.su.or/r srs orcasn Fuzz Ss and Ssms Vol Khash M. Znal Hamadan A. Bar M. A novl hrd classcaon modl o arcal nural norks and mull lnar rrsson modls Exr Ssms h Alcaons Vol Malhora M. Sharma S. and Nar S. Dcson makn usn mull modls Euroan Journal o Oraonal Rsarch Vol Marks S. and Dunn O. Dscrmnan uncons hn covaranc marcs ar unual Journal o h Amrcan Sascal Assocaon Vol Muzznolu M. and Zurada J. RBF asd nurodnamc nars nhor classcaon n ral arn sac Parn Rconon Vol Pal B. M. Josh R.. and Toshnal D. Hrd rdcon modl or T dac ans Exr Ssms h Alcaons Vol Pola K. Guns S. and Arslan A. A cascad larnn ssm or classcaon o das dsas: Gnralzd dscrmna analss and las suar suor vcor machn Exr Ssms h Alcaons Vol Rumlhar D. and Mcllland J. ʺParalll dsrud rocssnʺ amrd MA: MIT Prss 986. Sh Y. Erhar R. and hn Y. Imlmnaon o voluonar uzz ssms IEEE Transacons on Fuzz Ssms Vol Slva L. Marus J. and Alxandr L. A. Daa classcaon h mullar rcrons usn a nralzd rror uncon Nural Norks Vol Smh. A. Som xamls o dscrmnaon Annals o Euncs Vol Son J. and Tan H. Suor vcor machns or classcaon o homo olomrc rons ncororan susunc dsruons Journal o Molcular Srucur: THEOHEM Su. T. Yan. H. Hsu K. H. and hu W. K. Daa mnn or h danoss o II das rom hrdmnsonal od surac anhroomrcal scannn daa omurs & Mahmacs h Alcaons Vol Tmuras H. Yumusak N. and Tmuras F. A comarav sud on das dsas danoss usn nural norks Exr Ssms h Alcaons Vol Vank V. Sascal larnn hor Wl N York 998. Van S. Drr R. Basns B. and Dadn G. A comarson o sa o h ar classcaon chnus or xr auomol nsuranc clam raud dcon Th Journal o Rsk and Insuranc Vol Yldz T. Yldrm S. Allar D. Sam lrn h aralllzd KNN alorhm Akadmk Blsm 8. Zadh L.A. Th conc o a lnusc varal and s alcaon o aroxma rasonn I Inormaon Scncs Vol Zadh L.A. Th conc o a lnusc varal and s alcaon o aroxma rasonn II Inormaon Scncs Vol Zhan G. P. An nvsaon o nural norks or lnar m srs orcasn omurs and Oraons Rsarch Vol Zhan G. Pauo B. E. and Hu M. Y. Forcasn h arcal nural norks: Th sa o h ar Inrnaonal Journal o Forcasn Vol Zhao H. A mul ocv nc rorammn aroach o dvlon Paro omal dcson rs Dcson Suor Ssms Vol