Cluster Analysis Applied to the NSW Meat Processing Industry

The World’s Largest Open Access Agricultural & Applied Economics Digital Library This document is discoverable and free to researchers across the globe due to the work of AgEcon Search. Help ensure our sustainability. Give to AgEcon Search AgEcon Search http://ageconsearch.umn.edu aesearch@umn.edu Papers downloaded from AgEcon Search may be used for non-commercial purposes and personal study only. No other use, including posting to another Internet site, is permitted without permission from the copyright owner (not AgEcon Search), or as allowed under the provisions of Fair Use, U.S. Copyright Act, Title 17 U.S.C. Clu8terAnalysisApplie'd to the NSW Meat Processing lntlu$try Alison Sberidan-Nethery!' Kate oweIll 1 Department of Agricultural Economics & Business Management University ,ofNew England 2The Rural Development Centre University ofNew England A contributed paper to the 35th Annual Conference ortbe Australian Agricultural Economics Society, lIto 14 February 1991, University of New England Tbeauthorswould Uke tothatik Ray Cooksey of the.Psychology Department at UNB forbis valuable comments, 2 Inttodu¢tion With 1im~datvlIbcreng'o ~·yproductsefb'Aa1im indusUy, very little research has been directed lOW$'dS understandingtheJundattlental w()rkingsofth$ec~ Thi$as:mped~t by·products•. TheJarger$tudythat,prpmpted thisp~$ devl(Jpmnto,:Oh~Ucig 'specifically CQncentc:d with redsingthpoblmyJ,1-uac()~vC'SfM sector frOnt the fU'rtl·ev(abQi;)~ WithmQrethan400abattoirs andslfiughterb(>uses J)peratif1~'\jnAsl.w oot possible to examine each wOrk$tothendr{lw .~pclusion abouthe:lscr~ Foctlsing on a sample of .tums was the only vjableproc~ With lilllited'1esearehfunds8vailable, onlyth~wrks in 'NSWcouldbe considered. HQwto.setect theaproi~fms .to study in order to capture the:important feanrres of'tbeindustry is acritica1issuewhenuslng case..studiesas a researrb 'tool. In this case, the problem w8show tQselectabattoirs.in NSW that capture the irnPOrtant (eatures of the totill by-ptodJ,lctsse<;:tor. Whentllckling thisissuc" cluster .analysis seemed an appropriatetool.to use. Cluster analysis isa generictetm encolllpassingarange oftechnique$ thatse¢k ,tQcla~sify :8 set of entities into a number ofctassc$.such ,that the entities withnc~sa.ve :gteatetshnilarity to each otherlbantheybavetoentities in.otherclasses{Everitt, 19.81). ,Applyillgcluster :ana1ysis .to tbethe abnttoirsinNSWresultedin .soluUonswhich'initially·appeai'edro be railyobustndvepg~ However, during the Malysi's certainsu~.o light that were cf)t1sidered wortb.examiningintJlQre detail. These ,related·tQ the different fonnationrules that clustering algorithms apply ingeneratlJlg .clUSfers a.ndtlle concept of similarity. Both issues are discussed 1n ...lcjilperand possiblc·sotutioos.offered. TheClusterim: Concept There are essentially 5 steps involved lnany classification procedute ( Vogel, 1975). These are: *the selection of tbeparameters to be used for the classification • the choice of the· similarity ~su", * the choice of the cluster algorithm to employ . *.tbedeelsion as to 'tbeappropriatenurriberof clusters an evaluation ofthe usefulness of·the resulting classification (the clusters) * As noted in Bventt (1981,p.t03) ,;. iti$g¢neratiy lmpos$ibtc .prioritQanticipate what comhinatlQli of varibls,ntyme~d chtsterln:B t(:Chniques ~ .likely to leadto.interestingand Infonnativcclassifi¢atiol)s".;()(ten 'therl,anysi$~ i nvtllves severa1stages:atwbith .ther~ mayirttcxV¢netQ makc~gt$o variblC$,.sect'~1my tQcusoo4ifrerent'sub-sctsOfentiti.;s.and 'make othertllinot; ~justn1er. ,tQ the 'C1us~gtQ,enr.habcl$ inu$CM groups. It isin)portant then. ,lhatc~begnis¢ur ofcluster .anlysi$~ ~ydoing $O.nth~user iSfarless li(e~yt) make tbeJllisWce oi:tCfYng~ cl~tesouin" ,(Aldendetfer ,&;alashfield, :1984,p.t 4). TheCIJoiceand ;MeasurementQf Variables The initial choice of variables to include in clustes:analys!s isajud~ntbyhe researcherastQ whicatrbues,ond~ important (orthepllrp(>Sesot.classification. AsstJch, thefinalcs~ovdr1! in :asense,arbitraryasthe classe$ prod~ bytheclusringpQCd~a natunPly. greatly influenced 'hythe ·Variablesemploy¢<t Theclustrbod,f'()nyv~wipJ" and US¢s" (Man, 1989,p.27). 'Irtthisstudy, t1eprimayQbj~v r..ticlust¢nn,g·wasto id~nfy classesofabauoirsinwhicbthemelllbers ·~rela.tivy ,a1ikentbrPQduco~C$. The infonnation available concerning dle61licensed abattPirseummtlyopenttingin NSW was fairly limited asproductinfOl.S~ comi11efCiallysensitive. cot theinfonnationlliatcouldbe attained relating to the works"thefli~g vari~les were c()nsideredrelevant for sorting abattoirs 'into 'relatively homogeneous groups. YARIA'BLE Volume of throughput Type of license STATE high medium loW Export Class 1 ClasS 2 Rendrig~cts Presence Absence Species Slaughtered Part or a Company Cattle Sheep Other Yes No 4 'I'he'Qataconcelllingthesevariablcs forthe,abAttQirsin 'NSW~ obtaitledCrom' perS()nlllcQtnmllmcation with staff ofthe !NewSouthWales Meatlnd.ustry ,Authority w.eU 'asinformanon (NSWMIA.)andteJ~prmofP,byus:iEg Plbised;nth~ 'NSWMIA,'s Anlluat'Repon,(l989). 1tedrmiOl;oa¢hf~vbs isgenenllly se1f~xplJUt()'.Wih respect to the type ofUcensesheld"tbe ,sen~ distinction betwec:nthe three 'licenses isconcerow With ~ :healtndbygi~s littit :th¢ WQrksbave to m~t, 1berqu~mhts for the :'axpon li~n$C.a1' roorestringentthan for the Class 1 Ucense, wblch in. tum are mQrestrlngentthan fortheCtas,s.Z liceJ~. The'othel' species slaughtered'arepigs and goats. AU :thevariables w~tead· di¢hotmus,$1:S(W~e ~'lQtOpin4caJe the presenccQr·a,I)$enc¢' QfUle fcatllr¢, respectively. For the Yariabte$"tvQlurneof thrOOghput" 'and "'type ofUcensetJasQUtlined abov¢,the~ were .more· ,thantwC)states possible. However, byincl1l4ingpnly ~ostae for ~ch variable, then if bptll W~ coded O,by implication the 'variable must ~·in the third state. Fotinstante,byinc1llgmg.onJy high ~d mediuM as:the states possible for "volume .ofthroughput".andifboth.are cod~'O, theabattoirrnu$thavea lowtbrol1ghput Similarly, byinclU;dingonlytbe;$tates,JlxPQtt and' ·Class 1for tb~ variable "type of1icens~'.adbtu()y illlplicab"p ,the abattOir has a Class 2 License. Ifa works proCesses Ii lowyolume of.thrOugpasl'CI~ rendering.(acilitics. ~laughters tattle IUldShePtbunpors~i to I company, then it WQu]d be coded-as follows: 1 U~nseild SJKtd~sl\()beo wbereH=Higb throughput M~'C(iumthrogp X =E'gpottUc¢n$e Cb=Class 1 Ucense RF:endrigtlC~ ;flndFie(198,p.?)rovau~hckst CA=Cattle$laughten:d SH=Sheepslaughtered OT= Othetspecies slaughten:d Co=Part of·,acQmpany :&ch ofthe61abattotrs werec.oded in this manner 10 create. the data set. 'Tabachnick the researcher should folIowwben :s c.tat.. ~t ~in'l 'an1lY8es~ t()"~nsu¢ ther~, Catrying:~,heck$ 61abtoirs~npve()ul:$ ,~y n()proble$With'd~a WiUQtdy~lY'af ,fQr~batid$C.hc scxei'dng~t '2of,~ •.. At;.~ .2ab~tQirs,lughe[ncf ,popU}atlonthC:Wget,$tu4yiscoficerQtdwiili. ,~$Ower was roadcupof S9 abattQh-s wblr9clichototnQ\l$ VAtiJlb~$. wcrenotP~ Tbe dam :set~aing ot~P del~trA entinC$,;lS sinPlator dissitllUar is the,b!lSis fot ~lpSsifcaton To ~gtU Simlartyhowev~.cnbd,¢(L'pQ1fsJ$ whether entities are ,alikcQrnot atikerbuns~ and implentd"J'~b ,tjew~y!fbscop$ (Alder1t~,6G ,81e¢xl'ressed Blashfield, 1984~ p~17).n<Uom panicularcircgmstallCes with wbichpne isd~b1g, tbeexptessions iorstnla~cvy greatly. As ,clus~ringha l>e(:ome increasglypou~,dJPt n.:~h" number oftecbniqushavm,dlp~Wyw: to reflect particular cireumstan~, A Vital.issue to'~adresWbn;.cl)1mgCupw analysis,tben,is what.simil{Ujty mea$~bold beu,~togahdrQflikncs$ betW~J'lh.nisw which the r¢seachi$.~ng div~felso . Wben Ute data are dicnotQlT14)u$, .sin'lilarlt)'and .dissimilaritybetwetQ'tWo cases .i$ repsn~itb 'fpresnc·tQ1"ab~ .orJ)~met· depi¢,~jntb folwingt~ way rss&:ietiooiable: CASE 1 __~l~+- CASE.2 1 a b __ .a+b wh~a o =joint.presence ofafeatllre b =~bsenc?f f~ture .for Case 1 and presence ;offeature for Case 2 c=presenceof feature Car ease 1 and absence pf feature for Qu;e. 2 d= jointabsenceof.a feature p:;a+btctd A numbetQr~a.ivsA1': avilb~t()re"Psngh cndties on sim1$tybc:w~n when 'dJeatricboQf)(usWl$1987~Hwv,I ·are$ltnpy~.iQs ~bl$ic measu~.of association: td.n:apl¢matdling a+d/a+p"f1:+d a/a+b+c b+c:/a+btc+<l. Ja~crd binary . euclidean aoth &irnple matcbin8dl~resyf$QCP ~omtnQUiybews. ~ydiferonl) ~ltQfhej9in,absp 2ulattnbute.Wilh sirnPlernatcbing, joint absences tndica~sblry. Ja¢~'scoefint. which 19noresth~ joint absen~ of features, 'was devl~pt()mcsI'Ciaryn 9Qe$ wbereitisinapPJ'()priate, t() con$idertw~lsamhJ.b¢u :1x>mlttck MtUtrlbute. Binary eltUd~is adistnce~mf.("roU,ly tIultit focuses on .thenumOOrof Jltrib~haw() .entities (lQnot :haveinC>fJ1l'(~Wtr the res~h 'wisbes to focus on sbl11'ed ornon-sltaredattriPllfesd*nds(){l tb~ natUtePf.lhe problen~ig aQdressed. Fortlwpm:PO$es()fhi.a~ thesimpMng·~cwado:q all variables sil'llilarity WflS lrnpUclt inJointapsences. In chQi~ofalgrJm,te selecting representa!ivetirms sJ"etdwohigHly~rabcu sbould.peF~t,ahmi$nry distance.(lr:y)bwgQup$~Fom proposiijc:m thatclustenpg·PtQvidesan aYentJcfQf tbatana!gpritbm between entiticswidtin gro,upsandUte thabden~y thelarg~myof .to find :tighbypel'$rc~us we~ ~S6rUbmsavAletQ CPllsidercdthe Dl()St .$;ls$imllar.aspPS$ibleoyer appropriate. ThenatlrCQf:~ clgsterjmpih.an~ all dimensions (variables). 1bis.tendencyhas beencriticiSC!d 'inSQn)e .discp1~$:f«t persi$tanc.3Plygh~b n!gfU'<Uess ()f meutldel'lyjngshape' (Everit,p~957) For tXQJll»le,hypeJ."Spheres .may be considered inappropriate where entities can have a WicJe :rnnge pVcr one.()t .more dimensions but $~UbeCQnsid¢ml-.That b,real.cl\l$terstnay be~l()fptdnhr tha,nypmericJ.WbU:$~ is ~nsiprote this$wdy iim4 indeed conceivably lnmany econonUc applications, itroaY' ~ con$id~re inappropriate in some instances. 7 'The $~Qnd, ·~m<)re.in1ly,atbu$ ~lu,tg!"Qjhrs sbou1dgelrJtCpima$c>~ 'WbU~a:JulmcrQf (Bverit~).wcly·b ~$Qritbave@'dy¢lop applie4rodi.chotOJll()US '~ .di~ve .~ ,~.Jijng:techmqls'(avb¢ ;TWQ.,e~«:pnloUtc Wi$luu:t(1987)suito:of.pro,nuns)" ..,orit.hms~·plbu 'In th~inlW.Sagofmy$sbeQ w.ith (idler$uQ;po~1wm $Olllti()ns we~At()ds dn>pe.c:ltiQrh~·;a1ys :nemotb~icdvhQu(W$Jr, p~790) anlUy,is whe,rHb~fint data. :~ntedm As ·... ~tClT3iveo whict~ ~IAluinth dle·.ijnal ~tiQn •.9f,thepa~wuUC4 .JO . ~, optimngalQrdu1,S~"9J. ~PQS ~ ~lp$B;staeY ~lQtions('.MPI$gJ1rhTeu"pA M4sqbject tbe~ :JQCAl.Qpgmum only~ 'T()incretl$ethe lU<el!boPdtluttaglpbilloppqlumhas'*n ~h«I'requStcpmJon Jrom a nurbe()fs~gpomt ($¢lec~itb.nud)Qyfx>mp thrOugh·otb¢r '~gQrithl$). lt1iaS9uonJsB·grhm.~ gent1il:p~ ,,1.,$' $QftW~1ilaons p~ltJde4 $Cttle4 ,pponfor thi~$udy theJlsof,mi$ra~gy ~tb.apfUl W.MtQlJa1y$Cde~Sing cltJseriga()m~Toh ,ft nPmbet ot.$uiUb~hm'cl1 seJienlted $imU~SQlt( d~lh"'tbaSQim lev~rcqu,th :re~ulting W{IS .,~dl ctllstcrs<»u1d, be~gardsJ'Qutloh ,dJ~1gbtno CQtlsPu~anpir. 'lbe~ngtU$cQsi()r ,b,'Uu; .hasO\lUinedWocb~rupt autbon;to ~higlydbe inv~sjgatc:)Q 'Th~ wJUQhn~adresig 'inclustqinSa!gQriwrns anr;l·.~theS1bj iS$uc$a5sociated with mesatriblp~noJ)' ifc11)stering is to b~ 'fruitDlJ~noUca.\Iy$C Witbnh~:eracCl;$1.ymodfv .~ 'tecbniqpcs .~in pfongomJJ lew·oftho$e geneflll u~. (opr ofthese Wf,i'C consi4er.d,Th~a: CctmRJeu; )jnk,a" method, whi«:bcluste1'$by ·tbcnJlcthat amy entityto.beincluded intoM e~i.sdnglJWh\S tQbe;··wlthin '.a cenainlevel ()f:~imb.uty tQ ~ lllernber$pfUmt ,cJuster'(A:fn4~adBlhi ,p~4()thai varince.Thsmt()Cb~ clustef$>mad~.P of v~ry shown.tohave atendcy()firomp,b~h¢U similar (:as¢s. itUes()mn~ tbeintrtlrcla$s W0;4'§metb<>4 >is desi~tomlh" th~ vari~wthn Clu$t¢rnB,J).~fio(aISsbp .whQS~ ofcluster$ i$fl$$Cs$t;d im,~tbe increase inth¢ v~an ~combine<fvrt.p9l) wbi¢h .~1'Qqgbly·eat iJl~Z)Wd. unjoJlI~$·tQhes W~sl1¢th04_gne"Ay clu$teJl.At each sblg.,'jn .gevlQP$·cust~ twc> .c~$'et hyPetsp(:rica1.nb~ ~aV¢u:e Jinqt~meb9d Openltes1>),deriVlrlg'¢r) average, value foritbe sitPilArity waUcas¢$ ,in·tb¢ ¢xistinS clU$ter,Ai~ Qf.~ca$ebingo"sdrltv ~joil)$ ifa.level ofsitnlladty :i$lllWn¢dU$inBtblS :avergJu~ clUst~r panicPl~yuserJ i~ This !~S()rithm$ insq>fU'atjngoUtIieJ'$. The penqoi 4m;w94 depictshlurn~ fonne4tl1ey .~tePIaCdbylcO>rinsQh centrQid. .are. then fused~ 1li.s~thOd$npouarbecQ simple (l.4mce &, WjlU~, distance~w.:hro space~nrvig aIld·JS~custer$ .an4is ~lativ¢y iNoollctechmqUe is considen:<i$up¢rior tQ t~ However, only twO, WArd's and completnk~g. '.~ Th~grQupswit lbesn:u~.t it 'ls 1967). othet$ in ltU~in;umsJace$. llkelyto sati$fyb,~ ~uiremnt of tj.gbypersh~ Widlbienu:thical.clusteringtwbniqllcs, -the res.~h,mutdci clustering.}$ mQ$tsignifiCAAtThaJ ls, 'wh~t n~mberofclusJS;$t¢apQ1·i gro1,Jpin~sf tbe~a()ir$. natunU VariOtlS stop.iJlrueh~vbn mi(l fast .anc1few .llI'eappUcable ~saU .clusterssh()uld ~. wbatlevel p( noe~ :h~ clustering ·a]g()ritbms. BQwever,atdlc'n)inhnutn c(mteJ(tofthed1\ta. ilt~JCm1>ewhn Apracul~thodfing:wbe toJernliacus~h'$d,pm isplottingtbeclassifi9aticmcriterionagainstllie number pfclusfet$ .tu)d.· ..asharp nurober of.claset~(Owr, 1975)~aQwe"r,' ,this method ac~ptne, .stepinhJdca~ is reco$ni~u being subjecriYan1h~fod studies ltmust:\)epse<i cautl()s'~Wh!1eringqm twod~sivep to '~inplcabe we~aplidtoh w~reapClfot Thefinalst~p: ·.three· ,andtbe four~lpstin1'd ~onebtwh the Qtber belWe¢ntl}escvenandeight c1usl~r discunglthepmbaSQC~ ina numberQf sol"tpJ$(~eni .Apendi,(1)~ flch$~eringpQCdut.Vaobs1Ev¢,m witbjpdgingtbevalidityQf clustmSp~$haQi1.e m~$()fYalidt.1ghe clpstCll formedisd:tat of:runningavanety .of~lustc;riagJh1$ ba#d·on :diffetentMsumpti()fls, artd"onlycU$ef()m.bhji~ datA rned19s:b~ptf "averit,p.7S)~1b$JPQc: algoritunsv~ wM~¢Il,andtheusg 'lincage,dtrow~ WtU'd's JIld'~mp¢ tQ yJWdate'~ liOkagcsolud9ns. The reS\lIting ~lJstC"$difre4onwha;\,#!:gQu' l.owlevcls,()f,fusiQll buteonv~,g Atbi shcrleve1.$. ThefQPr·clJst~uion for tbeWQnf'~ ~I}t«)id a1gcdtlunswe~ identical. ~dtbc:r \W~ ()Jlly .dfer~,btwQCnJlhUs·o ,tIu'ee abattoiQ by .Jbe~ ,lllgcritlun$'andtlleaVenls¢.JinQgc8Jl4complete linkagc$Ql\luQn$(tne three ~.irswbatdleh1fnUy"m¢c ,oftheJa~i1.w Alg~). As th~rels$ucbamdifn"w.o1Q, ,tbe ~lustef$nabyWm clusterif1g,p'QC$\V~jdo be ,ftUpyrobUst. 'Thefour.clostell:Siven 'by Wani's ,~ pre lis~nApeQdx MtlIysisQfabattoirswillolllybe ~lev8Jtfor tbi$stydyif tbecl"$J~,Qi{nmo ~he principalcQaracteristics.ThedistblgWsbipg c~trh;q9fe ,~AJ;l$ter of ~lust$·,are4i :~h)w. The (lI'St .gro\lP is mll4epp()f 14 }abl1tQirswhC~v aXpOn.licellSC$.Theworlcs:in thi$cafe~u. ~$lausb catl~(wib :~td$lauberig. on~ieJ)ad dley Jill have ~ndrigftes. nere,a,e afew~ wodcs:.~tJla\ghernIy ... fcmturenot fO\lJldirtanywotlc$ just se.rvicin ~ :tl\e localma.rkct. The .ciisUngliisbingfeatme of the second group,iJU\llt cacbof .thO· five wQdc$only s1.au~hter$p '1breeof the five ;wQrk$hllve·an export1i~nldbIQgJ>a:ms. FOUfof lhe w9tkshandle alow yolunte ofthrC)ughpllt .. dleexpol1 WQ~ h~dlirg.a volume ,prtbPJlShuasony'«e~ complet¢daniSfr9C$O~,bQ t,he .()ther wQJ'kii. n.e~ ·.~18(lbatoirsgneh4 clu$~, ISo! wbicb,bavea ~la$ t 1icn~ " lbethreewOricSwith a Class .~ Ucen~ .prelncludetl ind.tsca~g()1y:U$elYhr ·a· medium volume Qftbrougbput aJl;l\lyPlcalfeatJ,irefor Class 2. wotics.()nlytlu'ee gf the worb,hl.tbt·S cat~orybelJg'Q .CQmp~yandt1l; barp!le.slJlughtet,aU species. .'!' ,wt! largest and is .rna4e,. lPoft~reuUnig2 The final c.~oryis ~lWQrk$haO only ~srntv()lue Clas$2 woncs~ .Qfthro\lghpytand does .noflx:1Qngto a cprnpany, The Vil$troajQriJyQf thc~laugberp¢i .thQ~genly '" ., Wbil~ Thj$8J'OUP~sent:,il ;,$Crvi~blgUtejJ. . ·~four .b¢nceth¢lQw VQl~9f.t:Im>ugbp ·onal.~et!> clustersolpti<>n$4Usn«l1»th;tlle tpWytical.1IDd n:~ that n~4 of lhe 'wiqersttldy, t1US:$QhlriOWn()op~ ~ilJnt"cge'$axsmhd. l~ in UteclJs~hrm-)' iJ)$Ulbn~ofsutQ"_w:d investg~o, Inthex~o lh~ The in$tabllity Qf clust~ .. bignU~ .tbeprvious~n WQrQ clust~agorihm;d undeyigca$tof~ tc;qglre~ns nOtfCprc~l,he probable J\$S\lclt .ilQoptimal$Olutlonwoulc,Jc,qst at • :l()w~r :lovel$ Wtl118nted ln$tabiUty .~gi$CQ mebrsipat.lQw~odc\SO meniloneg .in anUrtl~QfpobeSPsciAwhu., AJl4. appUcatiQnof:sirrUhnity clu~tering.sAadwb1o to dichotomous da~ Two SOllJ'Ce$ of instability were jdenti.f,ThmQ~ SOQrCe lies in tbe QiffCl'entJQinins rulesdtrit 9b~«=rQ!jU1tn$plyi Unl~$ ~m ,cQIltaindisUnctgrQups()f ~nti?mO¢aopf.rgc can vary 8C¢ordingtqme ~8oriUlt'emp(»d.F) elongat~scUr 9£ enti:~s$g1¢ lingge «)n~(f ,nearestne,iahbQurtulewUl PJDbal)'prodg~$in,e hl1nd. ~k$to ,minbsetra~lu'vc ,ntQrctight clusters. While this problem h;t$I)e(.1invga4bymr~, ,CQtn1llQn ··J!n4·disruptlve fQilng~ps. J~ ~bienuchal 'loscJu$~¢r and would m~r.tendOpoPC lnJ~eQits siven .•u~latv¢JywPrQm famlly),'wbi<:h jQin$.pn W1P'ds,on '~Ol :t\Voor applicable ruleS·AS to wne#.pAJticuar1sQhmoldb'v~ gcm~'Jty devlo~ The~ond$OUfc·()jstlbiyWSu to "~ties lnmC$im.ilfbity<:oefficients. Tie$occurwh¢n tWo enti~s :haveiQenucal. $hniJaritytoa ~thirdenpy but(!iffet,fromeacb ()m~. ToiU\lstrlltt;,. tt"te simiJarif¥l>etween the fQltowinS·~. enudes' w~s ~culaU!dsin simplematcbing. Variables ~! ,CaseS .r... : ..... '~ i.•·.· .•~.· .•· :.•. ~ .•. i.·. ·i.·•.·. :. .•.• 10 .100 1 DO 1 11 1 ,77.$ ;2 3 1 ana. 3 ,;U-¢ ~t .8$. $q)tu1leC"s~,y .it .1$ lmp9SsUjl¢ t() distn~lh with which .cluslCr entity2sn9pldjoill, Thispr.edicamenf is .n<>t .ur4que to $implematching. 'Sinc¢ mt binary f1S$QCi~tnm ·~.mputedfrQJb, ·tw~W,a)' 3sSQCiatiQrltab)e"t\C$ .(:~, Q¢Clr.eg~d,sfWhic#4Pt1'\ ti~.are v~ .rewme problem may not be sev~bptwhnd ma.trixh$nubeQf~ cluster.$Od,on~y be<:<>me bishly.\ntae,J~ next$eCUQn.tm ~tenau":Uod for Q~culatin,bry Ifenti~s " ' ' , \ shnUarityC)efc¢jpo~'Wb!.l: - , , ov~spe$ InUle preceding$CCtionequivalent difet1~, cases w~oneftbcdiQl1s :idertfc.l~,ausng otie~ in, the .$lrnUait)'~w ins~bUty incblster m.e~hip 'The likelihood ofthisCQnditionoccuring isbiglleJ' .for·dichotoroous MUitban fQI c(mtinuQ\lsot mUlti-state data .as dicho{QffiOus da~.re limitedw two state va1u~. Con~Qtly, iustabilityin loweronfer hienm::mca.lclustcrsPhltions c~be,d toOCC\li' nt<>re frequently when similarity i$calut~ .fm,mdichotomousdata. lntb$~"o anew npproJIChtoclllculatingSimilcu;tyfrombinary d~whicb$ designtQ.ruc~b li.kelihqQd of ties, is .,:ported. (1982) and others haveexplQrrA lb~ aplic~ton iofalgebraic ~opl()gy. in the . anlysi~ofthe'Ucur ofsccialreladons within a groupo(individualS.ThedilUl tllatare the .spbject ofanalysi$ indlis contt?te ar¢Qrtert .<JiCho~!1lO$Fr .exlIlllp1e. the data ~maybe inthefoM·of.an inC,jdec~ma\'}Qg e~h ind;ru~s plU'ticipation ,in .·l~ries Qf ·Jlcpvi.tes~Thaon of a1g~bri¢ topcllogy Involves.analy$is of.dle~pQnc m~tri" wbichis formed by the ptoduc~f the in(;idencernatrix .anditS trans~e(Pobl, ~J;m p.219;~)ThecQ-Consd¢matrix& indlvu1sjomtyprcJ>a~ 'simplicial ~ple?t'{U1dC9rs - ~. . the .frequency wbh wbichany two urtacivy~ A toW (or column) ofthis matrix is termed a the fre.q\lency With Which an individualjointlY,pardCipateP 12 inactivities Witb ~;tch ()ftb~· individuals. the ·groupinvQlvc$ 'analysis ofthe ipetwod~ of~i,mpUcalCQeX$ ·Th~:identca1o()r.l $'p~tnl:o£ !&c:>manotbr~l'Speiy",hfkJCA· . .interp~dasmqQfl el~nt()f., $itnlmy~wo 'simplicial comple,~n:ts the frequency with wbi¢bdlcy jomtlypanic~he,vJs 'l~\viduas.In9WPr$tch 'tbesinl~y.) twQimlividl.UlJ.sln .~tm$·()f Another.PQssibility t which does ,nmappear.tc) baYel>e¢n cxplOJ'ed. J$ .t()rea,h~ s.implcaoe~;nt am~ure·of similarity. .In otherw<mJs,iW; panem of.~ c~dnew eacb :jndivu~ and .llll othc:i,ndvjua1$~mesb of similarity..lf .two inQividllalS possess identical Simplicial cQfnple~sth similarity between dto~ two individuals is exact, Therno~ ·the :simplicialcpmplexesdiffet:, ·lhe.P1Qfe dissimilar are two individuals. The employn~f the simplicial cornplex;asa Jlletl$\lfeofsimih\rity wbel.~ta are dichQtol1l()1,ls has the ~fecl of diminishing the :likelihpod of .tie$inshnilllrity~ Th~ reduction int~arse from two source~Fit, the value.$of ~simp1cale"Mut$ rather than dichotomous. Second, use ofthec()mpl~x involves,implicitly,comparisolls between entities .acrossattributes'anda(:tOss all entities in the data. CQnvepoa1<~urs of sirnilarityinvolve. comparisionsbetween entities acrostibu~pnly, simlartyh~ To operationalise. the uSCQf the simplicial complex as a·basiformcun~ followingsirnilarity measure was developed: i,j,k = l, ••••• ,n Where» is the number of individulllS Of cases, and thf'l :"IJ denote¢lernent Jor simplicial complex i,nor.maUsed by the primary simplex for case 1, Algebraicallyt "ij =wij I wii Where WiJ is element Jofsimplicial complex i. 13 Thelt$r.mg~uJ'C is.~ dissirniJarityCoefficient.pOs&e$sil1g,b()th ~p;and bounds,the.c()mi~ .canbc int¢rpfe~ .asnrasuring.the ¢ucUd~rtis simplicialcomplexe$ (Everitt, p.l7), When the coefficiealtwas etnployedto .meas~;i#ltrybwn()'$ lower ,betwetmtwo the nutnberof deswaignfcJltIY~U1h$mpQ matCblng¢Qfieh~r ·'were 37 IS ties present ill the 'Illatrhc_ In ton)paris.he'w~ 43desp~ntih.marx when the proposedcoefftcicntwa&'adopted ....TedQCtion,8pr~. ntc ¢qefficient clearlY' offers 'pronuseasa means ofreduclngthe effect·()fties.OIl clustttinstability. To ~stwbehrcpoPQdmau 'irnprovesstabiUty .~tw¢en:a1gorihmsc simihlrity mamceswere used to fonclist~'ug W~ntsiloda .completinkg~ Instability, measured intenns OfCOOll1lOllClassification ·()fCtlSeS, was'improvedtU~ siX cluster solution but reduced at .the fouticblser;SQn~ Atthesix cluster sotution.73 .~ cent of cases were ,placed in thesameclassificanQn.using the proposee coefficient while 69 per cent ofcase$ wercplaccd in "he sante classlncatiQn when botbalgorithms w~ap1ied tQtbesimpletnatcbin,g coefficient. At the (Pur clustersoluuonthe results Were '61 :and78 percent for theprosdanDlcig~f:uvy. The decrease instabilityofclllster ,SOllltionsat' ·broaderclassmcation levelsusirtgthe proposed coefficient probably arises frotntWo $Ouree5.. ·First,thc; lower the level of :the hieran:hica1 solution,thernoreimportant istheroleplay¢4 ~y nessince differences in joining rules (that is, clllstering atgonthms) are ,tllQte likely to generate dj.f~nC$,i cluster membership. Second,the range ofstatcvalues pfconverttionalbinarysimilarity coefficients is limited to the number of variables. In conU'ast .the range rorthe proposed.coefficient isa . function of: the number orvaibles~ the number oreases a14thediv~y of simplicial complexes. Therefore. when a conventional coeffickentisUsed different clustering ·algoritbmsarelikely·toconvergemore quicklytohesamrng.~ levels in the hierarchy• This behaviour emphasises .the importanceofchoosint; the C()rrect level!'n the hierarchy as the appropriate c)u$terlngsolution. Ittil$OhighUght$ .the need for more robust optimisil1g clus~ng algorithms. to be developed toassistreseatcbers in .tnJOOngthis choice. .By way ofexamplet the optimising procedure ": 'monothenc divisive clus~ng (mentiod~1r) was ctllployed()Ilthe data. The treatment ot the data by UUs,procedure mostclosclyresembles. ofall the Clustering ·procedures. 'the 'manner in wbicb datr~ treatedbyilieproposedcoefficient.Thisproceduregenetated anoptin'lum .solution of.seven clusters 8i1d 90 per centofcases. were placed in the same classifications that are obtaine4in a seven cluster solution usingWani's·metbod.For .complete linlcage. a70percent agreement 14 with th~$Cve.clusr()ijo1d, whiJe',tconCOIabW~.8d ,cQmplet$Oudons.a~Wrw 76petcm.Thi$o~Wa:rn agreement betw~n Want's and.complete WheJl '·$Cvcn.clustet$OllltiOtt'ls .g~neratdJsi tbe sinlple.tn;ltching coefficient Th~sirnlatyuepod $hows.pruUea:~( :filt.MUringsimUaritywhcm na~ ,art)dicho(lU~Fune work iStJ~yofneh conceptS pre$Cnteqhere .andto cxpalldtheiJPpliclitl(:m .Qf,Jhetoeffici¢nt. AdditionalwQ[k .is being undenaken todevelqpan optimising clusterinJ:a1gQbmfo;~ witb~. ~ficten. Thepurposc ,of~pIYi"g(luster'anyhNSWm.dw ·to establish some· meansotcategorising ·abattoirs into relatively 'hQnlg~JOqsroupF ~ach ofthes¢gtoupsasarnplefinn could'ilien.bednlwnwbich would capturc thtmng¢.of workscUITentlyoperadng.Jnso fat .~th¢ cl\lste1:'S,genetatedinthemidalanalysis ~ tairlymbustand. inlerptab~ this objective wassatlsfied. :Whiletbe four·clu$tet' $Olption satisfied . bo~the;ma1yicnd·,sOur'q\ of.theWidc:r .study, ·.UUSSOlutionwas not optitnalmtbafitdiCl ootrepre$¢nt'lhe probable tnaturaltclusterstllatexist in the .data. As ,sllchanoptimPl soJutionwoUld existatalbwer level in .~clu$tering .hienuchy,the instabilityofsOlutl.c)nsat Jowetfuslonlevels. warranted ,iny~stglo.Twurce 'of .instability were identified.thcdlfferences injoining.ndesthat clusteratgoritbms apply in 'fonnil'lgclusters,andtbe presence ·pftie$ .i!'l'tbe data. Thefonner source has been thefoc,s:mur~abli1 ofthe issuesmvQlved ,jsunUlcely for$Ome time. It is, therefore, largely left tothereseareher toheuristicalJ'Y justify their cooice()f.atgorithm. Withrespcomaungbywd~()l, 'a, 'new:approach l()cauting$r~ was presented. The attributes Qf theprPPosed simiJaritycoefficient largely Qve~m the problem 'wjthties.Use oftllecoeffieieotis the subjectofnil,graChp~ ,it may be of value in;lddressinganumber Qt other iSsues con~rjgim1aty De$pit~hQsorcml1gS ;greatpondliqu~v t~hniqle conep,tsflq$~y discuSS¢(J intlttspapetthe<authors feel cll,lsfet .analysis has economic lUla1ysis. .Apparent,lhopgh.is the ~toaplyhe witbcaudonand an urgent need ,for furtberinvestigatiQn.intotheproblemsand apply :in economic analyses. .IS WAR]) '.8 CO:E;FFICIEN"r CENTROIDCOEF.FICIENT ~o. O~1·-r .......-.~tIi' -+-'"!""P_-_ _____--,.-_ -r---,. .-....-- ----r-- .----r- -r--..- .,....-I .0 12 Cluste-rs 16 CLUSTER! 1.Blaynf!yJ\battOir P/L 2.Cudgegollg (Abattoir) County Council '3~GunedahSirCocl 4.Metro Meat (Moss Vale) S:R.J,(]ilbertsQn PIL ~WiflgharnAbtoPIL 7.T11eMidCoastMeat eoI'lL 8:NorthWestExpotts ,P/L 9. NorthemC()o!opMeat CQ Ltd .10. The' Aberdeen Jleef Ct) 11.(Jgyra M~tPacldng I'lL 12.Riverstone Metit ·CQPIL P/L 14.MetroMeat(Wagga)Ltd 13.Lacht~y,Me$ CLUSTER 2 1S.AustralianSuperiorMeatPackersPIL 16.Australian Specialsd~ MeatProductsPIL 17~Fletchr IntemationalBxportsP/L 27~StadmnPlL S9.SlPayMeatCo. CLUSTER 3 18 Beers Butcheries :P/L 19.A.l. Bush &SonsP/L 20~Castlergh Regional Abauoir 21.F.ONicbols,(Abattoir} Z2.Tamworth .City Abattoir 23. T.& J.Wadland :P/L. 24.CowraAbattoir Ltd 2S.PJP'rish Mcmt Supplies 26.G.M.ScQUPIL 28.S.Motrow &. Sons 29.Griffith Abattoir 30~BurtaJ18ong Abattoirs ..~ 17 '3.l . R.NTaylorP~ '32~\1ndra Abattoir PIt., ,~3JI!l$tingMeaS\py 34~I.RB\lrnt 3S.EJenMelts P/L 39.WoUandillyO:nttJ!l. :Killing,O>-Qp, CLUSTER 4 36.()llJUblgaiKillingCentre 37.WandaeIPas,tora} Company 38.~yPorah & Sons ,40.Swans Butchery 41~).& S~Af1ick 42~DeringuaMts 43.Wyalong Meatwotics '4.F~ericktOn Meat Servi<:e 4S~YoP 46.BablaraaJ'/L 47,.MurwU1im~J\bat()P/L 48.Moore l/iLatimore 49.CunnynghliJl1Btos SO.Tancred &. Conslllble Sl.SPulbernJUverina 'M~tSuply S2.R.G.Uat1oW S3!C.p.Ba}1 Butchery & Co 54.C.0. Perry&Cp S~R.&N Stenhouse S6.'P.R.& R.N~Andrews ,57.MorgtUlsllulchery 58.Macleay Valley MeatS .P/L 18 ~Retrnf!$ Alden~r.MS,&Bashfi RJ<:.(1984), quslerAnalxsis.$agePiJ1)licatlQns. . . J1evetlyHills. Clifford,a:r. &. 'Stephenson,W•.(1915), ,An IntrqduQtipl1 TQN\lmerical Classification, Academi.c l:'re~s,NwYok. .. .' . ,. 'Donen, p~ (1982)~ 'Orlthe J)elineationof 'Sm;tU GroupS~ct' ,in Hud$On;H.& J)aJ8. JQ$ey..;SClS$inc, ·San. PnmCisco Associate.s. CJasifyl~oR, Everitt, ,B. (1981),Clu$ter AJla1)!sj,2nde.tPrNwYok~ Oower,l~C. (1911),A Gen~CoficJ Gren.PE~, J3iQmFtrC$.')7,8S~2 ofSimilarity and SOm¢ofjtsPr~e, TuU, D.$~&Albau,G(98) Prenti~.;HalmoEc: Res_FQrMykc;tin~ New York.. . . .,. " .. pWi§ions. ..., 1arcUnc,N.&SibSQn, R. (1968), The ConstructiQn QfaiertU'Chcnlo~Hb¢ Classifications,C9'UpUl$!rloumaJ. 11, l17...184 Rum~l,Dl 'R,.J. (t970), 'AppJiesJFacto[ AnaJysi~.Notl\Ve¢,rUvCf$P;Q ... ' ., .................. SJl~tbP,H.A& Sokal R.R •.(1973),HumedcalTxQnoDy"W:~Ftr . Fra~i Tabchni:k,B~G.&FldetLS(98)J1sMvjyrgC2 QfSl J\ndJews.Edinburgh . 4 CO,SJ\1l ...............................' ..... RpwPDblishers,New York. Wishm,]). (l987).ChJ~tanUr '. . . ' . ' ... . . . «lb.·a(U'p:t~ Mannal. 4th Edition, ComputingybQratc>ry, Univ~qst)'· ,