Visualization of Navigation Patterns on a Web Site Using Model Based Clustering

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

stracbWet preents naewme htdology oof vrsualiizingn aivagtion apttresnon aebW itse.In ou rappraoch w,er stp atitrin sitoeus re inso ctlsture sscu that hnloy usrsew tih siilar navmgiaiont aphs ttrhouhg ht seti areeplaced i tnoth samee lcuster. henT f,o earchclu str, weedi play stheesp ahtsf o ruessr iwtihn tht aculste.rThe luctserignap roapchw emelpoy simode l baed sas(op psode t oditsacneb sade)a dnpar tition ssuersa ccoridg not ht oederr ni hwic hhtye equerstWe bpgeas I. naptrcilar, weucl usetru sresby l ernaign mixaure tofrst-order Mark ov mdeosl uisng teh EpextatconiM-xaimzaiiot nalogrthi. Omr ualogirth scmles alienarl yiwh tbto nhumeb rf ouses rna dnubme ro cluftess, rnadou ri pmleemnttionaea sly hindals melliino sofu ser sadn thuoands sfoc ustlers .I nhe tapper,w deseribe chet etdilasof o u trchenlooy agdna t olo bsad on iet alced WeblACNAS.V We illstrute ateh se ouf uor tecnology ho nsur-trae cdat arfom mnscbco..m

eKwyrosd:Mdoe-basedlc usltrengi,sequnec cluseterin,g atd aivsalizutaion, ntIenret,W eb1 IntodrcuiontrguAalyb noeof theg ert caalhelgesn fo corpmute srcenci eni het coingmce nuryt wlilb e th undeertsndain of ghmaunbe havio rni tehc notxte o\difitgal envrionmenst" uch ss ahteW e.bG ienv uro imitlde xeeripnce eotda te wih mtdoelng sich unevronientsm, htre erae reatilvley ew existfni theogiersor rs t-pirniplec to sguid aey naalnsyis o mrdoelingendea orsv .O nth oehterhand, no ecn areaild oybtia vnst quanatiite of dsta afom rscuh evnrionmens.t n Itih scntoet,xdat -dairve neplxoartoin of igdtal triaec ss(uch a servser-og lercodr) iss leacry anl miportnt atsartni pgonitfor fruhetrig nurounder tsandngiof\ igdtai lebhavor." Iint ishpap e,r w deescireba onve aplporahct o viualsiztioa ann dxpleoartryo naaylissof d yanim becahiovrof i dinidvalusvi sitngia artpiulcr Wae siteb.As a etstbed fo roru owr, wkeuse se vrr elog sof ndividual biorsiwn gerocrs fdrom nyat ouhsnds of aindviduias lro uesrsat th e mnscb.cm oist. Oeura pporca hs itrasigthorwafr.d iFsrt, w ert psrtaitin uosrs entoic ulsetrs scu thaht nly osuer wsth siimlairb eavhio or nhe tsiet are lacep dinott h eams ceusltre. heT, nfr eaoch clutsre w, edsilap yht beeaviohs rfo teh usre swithnith a ctlsute. Thre ocfuso fou r paer ip os the nivsualzatioinan dculsteirgnaspects o f scu dhaat,ra terht hn oanth veaiourse ningerien igssus ienovledv inp eprocesrings srvere-lo gdata( dinte ictain,o s\esisnioaztio,n" ect). At t.ish oinpt i, itssu c eitnto assmuea f iarlyab trast chacratcreiaztio nf theo datat|ahtis, a()th serevre-ogl eslh ave bee nonvertec idnt oaset o fs euences, qoens eueqce fnr oache seu serssoi, (bn) eac sheueqcn es iepresrneedt saa nrdeoer lidts ofdis rcete smbyols an,d c) (eahc ysmoblr peeserts onn of seveerl apsoislb ceaegtriesoo febWpa es greuesqtd bye te hsue. r1

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

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Fguire 1: Asam pe of ulsres equecnse .igurFe1 s hows a asple mf suoc sehquneesc .Thes rvere los frgo msmncbc.o morf a twetn-foyr-huor uerpod iypitalclypr oudec srougly hoen mliloi snchus quenecse T.h efcuo sfo ht eorwkd secried ib ntih spaper si hetpr bolme f oeplxroing v,iuasiziln, agd nodemiln gtish yte pfolarg deaa tst.eT eher are nuambr oe aspecftso ftheda a twihh makc tehep orlbmen on-rtvial.iFi rs,t het nfirmoaion ts iinerhetnl dynymica. tSticadispl ay ssuc( hsa ihsotragsm fo agesp eruesqte)dw illnot fulylca tupre te hdyamincnature of tehu dnerlyng isu rg nehavboir Th.su, ewi nvseigtae tdnayic mmodle (aslbie telrtivale symilp eaMkrvomo dels to) etxact rdnamiyc behavoirat l esat ot st rorde. Anrimpo tratnpoint nit is hontectx si htatt ehes dyamicnmo desl srve eprimailrya sveihlcs feo drta eaxplrotaio andn wedo n otas suemt htathe mod lesn cesesailr yrpereens tht erte uata-gdnereatingpro escs .nIfa tc t,erehis s om eevdenic ehtt aWb-eur ng beshviar moayb e fnudmaenallt nyo-nMrkov ai nntare (uHubrema,n Proill, Piiktow an, dLkoues 1997).No etnelhsse, jsu ts auniarivte ahstoiragms erse vsa a seufu l\dtaawin ow"df o gernrel aumlitarvitead aa atnlyasi,s oru ue sofM arov mkdoles i nhtsi appe carn b veiweeda sa emhcniam to sporvdie t alaetsa p raial (tna udsfuel) piturc ef odnyamc Wie bbhaevio.r Seoncd,d namiy becavhoriin hits gneerl acotnxtei shighly likel yt ob equiet hetreogeeous.n Aopulpatoino f userso fhtsi sie ziwl teld nt haoev asvlty ide rnte Wb-eur sgnp ttarne. Tso ddaresst his heteorgenety, we iiaginmet ahtd i reentu sesrli e ni id reet ncluster,s hwere eca cluhtserh as a d irent Maekrov mdeo. Speci lallcy,we m odel the ata das hvaig nebe gneernaedt ni hte flolowig fnahisno: (1 A)u esr rrivesaat th e eW sbie tad in asssigndeto aaprictualrc ulset rwit shomepr bobailiyt,an d()2 thebeh aiovr o tfaht sure is2

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

hte ngeneatedr for ma arMkv oomdelw ti hpaamerter spsce c ito tathclus ert W. epreetd tnhismod le egerntesat heWeb adat ew bseorve,ecexp wet don t goe tt soe tee actuahl lustcre sasgnminte.sW ethe usn ae tsnaadr leadrnng ietcnihuq,e he EtpexcatitonM{ximaiaziton E()M lgariothm t, loean rth eporortiop no uferss saignse tod eah ccluter ass ewllas t hep raamtees ofr eachM rkavom dol.e n sI doion, gw assige necha uer sto clautersor fra citnolaylto ht seeto f cluterss. Tisha prpocaht oc ulsetrign iss oemtmes cialelda model -ab

sedap rpacoh,na lidsei n cotnasrtw th imreoc mmonol uyse ddsiatnc-eabseda ppoacrehs.T ehcl suetirngmo el we dlerna i sosetmies mcllaeda mxiutremod le .B ysinu a mgoedl-bsea dparopahc t ocultseing, requescne sof ide rne tlegnht msa ybea sisgendt o hte saem lcusert(e.g,.s euqnce 1ea dn5 n Fiiurg 1 eam yeryvl ikely beg neeratde fom r aingls emodlec orrseopdinn to oge of nhe tluscters. )Thi sappraoh pcovrdes i natauar andlc onsitesn metchnaim sof ranhdilgn hetpr obeml o mfdeoing anl dlucsetirngs qeuecne sf doi reetn lngthes F.ul letaildso fthe moeld and htea sosictae dlustcerng aliorgtim hraed icssusde ni eSctoni3. The t ihrd on-trivianla pecsto ft eh dtaa isit ssi ez. hTu, is ist ritcical that nay alogrithic mectnihqu esalecin a reaonasbe lfashio (neg., l.neia rron aerlinea-r)a a fsuctnin oof teh unmebro f esquecesn Nnda th numbeer o cflsture Ks . his rTquiermeet nurle sout(e g.. any )dreci tappiclaiot nofs tnadrda herairhccia cllutsreingt ecnhiqus ehtta saleca O(sKN2 ) in obht ite andm psceaco plemxit.yA n eamxpl eo sfchua naproapch woudl e bgagoleramtie clvustriengu snig f,or eaxpmel,sme foor mf paoirw-si eeitdd-sitnce bateeew nsquences.e nI ocnrtat, suo rlaogirhmt forlear inng culstes rof arkoMvc hins (tha eE Magolitrhm )erqiuresmemor ytat hsi inlarein Nadn anKdhas a ru tnime pe rietration htt iasli nare niN nd K a. In eStcio n4, e iwnestivatg tee ohervall scailgn bheviaro ofo ru paropac, had ndmeostrant eyb eperxmiet tnht ate hottl arnuitemo tfe hlgarithmo (vor aell teiatirosn sc)ale lisnearyli nb to Nh adn .KT ehp apr erpoceed sa sfloolsw.In eSciton2,we illu straet hw theo Mraok vcustelrngiappro ch aan bc leveeargedto usport an piterantcveie pxloatrroy dat analasiys wihc hporvdes idrietc nsight iiton the ethrogeneoeu sadndy anmicna ute ofrt ihsty p oef eW dabat .Secitn 3ot he pnorived as umh more cdtaiele acdocntuo ftheu denlyringmi xtru emodel na dht aessocaitedE clMutsernig lgaorthim,inlcudni gotuo--sfmpal expereimentl aesrultsc omarpni gte quhalti yf otehM arko vodems lith morw ertadiiotaln hstiogamrappr aocehs.S ecitn 4 onaayzls teehsca ablliti oyf theo eralv clustelrnig parpaohc,us ni egxerpmeinta lersltu tso alvdaie the t(oftnea susemd )nae-rlnieritayo fMEb-saeda lgoirhmt.sS ctieon5 b irey su mmrazesi erltad woer akd Sneciot n6c ocnludes ht eppear wih tasum mryaan d opsisbe eltxnesions fothis w ro.k3

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

Dat VisaauliatizoAs nweh avejust d isucsesd, uor appraohc toexpl ortoaryd ta anaaylis is tsocl utse urses rand tenhv suiailz tee hbeahvio or fsuesr i naeh clcsuetr. e Whaevi plemenmtde aootlf r toese tahkss, aclle WedCAbVNAS Web Clus(ternig AaNlysisa d VnsuiAilazitno of equSneces.) nIt hs seciion,t weil lstuarte het isuvlaizatoinc opomnnteo f WbeCANAS Vo ndat from a alrageW b setie T.h daet acoem srofmInter et Innfroamion teSverr I(I)Sl osg of msnbrccom a.ndn werelatsed potiros onf msn.co fmor th enetir dea yf Sopteebem, r28, 991 9(Pcia SctadnrdaTi m).eE ca shquenceei nt heda aset tcoresropnsdto paegvi ws eof

a sue drruni gtah tday .I npratcilaru t,h behaveirs oofu ses rrae ont rboke nodw innto en rssesonsi .aEch veent i tne shqeunececorr spenod tsoa u ers' resquets orf a age.pR questes ae rno rtceored dat the nes tlvee ol fdetai|thal its,at the lev el f oRL, bUturat er,h thye aerre crdoed t aht leveel ofp ag ectegary. oheTcate goreis,eveldpeodby one fo s u(.W.S,)ar enfiormatvei etysma l inln umer (bevseteenn). hT eatcegrieso ra feornptage,n wse, echt lo,ac,l pinoion,on- ar,im ic, swetaeh, rhaelt, lihing,vbu inesss, sopts, rsmmaury, bsb(bu lelit nboardse vicer),ratelv,snm-nws, enadm sn-psots.rAl hotghu ht etmie of eah rceueqt issk own, wn modee lnlyo hte rdoerin whi ch te hequrses treare qeuted. sFruthemrore an,yr qeeussts rvee vdiaa achicn gechmnaism ra neo rtceodrde The.fu ll dtaaestcon sstsio fpaprxioatmlye oe nmilloni esqeuncs (esues)r,w ti hn aavraege of 57 events pe. sequenrce .fAte ar btio efxpeirentmaitn, oew fuodntha t ara donm asmpleo f0100,0 s0qeeunce wass mroet hn adequate afro urpopsse f bouidilgn lcsuert ssufelufor isualivzatino .Th cleutersswe sow hhree wee grenratede suni theg etmohd sedsrciebdin ectioSn ap3liepd to schu ausbaspmel .Oneh nuder dcultess rewe grneraetd.e Fgiur 2esh wosWe CANVbASs'in italid iplas yo ftentyw oufr fo theone h udner cdusltres .Noramly,lt ehc usterls ra oederedrl fe-tto-righ tand otp-t-bottom oi nescdedinngorder yb he ntmuerbof user isneac hlcutesr.F r ohtisdi psaly h,wover,e theor de ofr thec lstuer ars sercmbledaso a sntoto evealr otpneiatlyl ensitsiv ienfomrtioana outb ht esmbcn.oc msiet. Ech wianodw orrcepsods tnoa cluters. Te whidnos awer tlid end eaac chna bee sial movey adnd esizre.d acE how of rsuareq ins caustle corrrseondp ts o usare squenece. Each suqae ri anr wo nceode sapage req uetsin a artpculair atecorgye cnoeddby t heco lorof het quasr. (Aec aegtoy releng ind hswn inoth e ower-lirgthc oner rf othescr en.e F)or xemapel,th seeonc udsr ei then sceon dcuslte rhsathe r qeeus tseuencq eensw o,n-ai,ron -ar,i locla,oipnio,no pniion on,-air,o pnion, ienws .n ourI epxreenicewit WhbCeNVASA,a ise atdmiinstraor cta inendtify useflu adn unxpecteed inorfmtaoi afntre oln ayfew mo entsm f lookingo t aidplsysa usch s ahteo eni n4

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

iFgre 2u: Iintil aidpsal yf msonbccom d.ta ausnig ebCWANASV E.ch wiadownc roerpsnosdt ao clustr. eEca hrw on i awidno cworerposds no tth paeh tf o sanige lsuer trhuog hhets tie. Eahcp thai s cloorco ed dy bactegory .Teh caetgor leygne di at sthel oew rrihgt oft h escern.eN OE:TTHI SFI GUREA D TNH EFOLLWING TOW SHOULD OB ERIPTED NI CNLOR.O5

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

igureF 2 I. this ncsa, the eise adtinmsitarot (rS.W. )dscoverei desevrali nteertsnigf cts: (a) 1teher re aisgn icnaly latrg georusp ofp epol eneetirn http://www.77cn.com.cno mo ntech (lcutsrse 1 1an d13) nadloca l (lcstuer 2)2 pgas e()2t ehe rs a siigi cnnaly latge group ro pfopleena igvaingtfrom on-ar io ltcola clu(str 12) ean (d)3there i ssrupiringsl lyttleina igation betwven eech and btuisnes sesctions E.ach f ohtsee dsioc

veier susggse tctaonis o tb tekae nto ipmrve toe hist. eEcah lcutesrwindo wc nabe s rocled solt aht aste adiinmstiarotrc an,in rpiniplec v,iew eervyuser in achec ustle.rAnot eh rfetaue of rWbeCNAVS, Ahwoeer,vpro vdis the siet eadmnistratoi wirh t suammray f otehc otenns of etca chulstre .nIpar itcluar,w eh na ndminaitsatrr oigrhtcli kc os n alcustre,t ehco rerponsidgnrst ord-re Mrkoav omeld of rtath lcutser sis isdpaled.y Fgure 3 isowhs te hisdlaypw hn ehe tuse rclcis okncl sture8 . Prbobaiitiel sn iht deislpya re encodae dy ibnetnitys hi(ghrepr babiliotes iare bigrhert) .Te hrst column dspiayl tshema giran lisdributiont f octegaoryr queets.sT ah its t,e hsrtc lounsm hsows,f roe ch caateoryg, ht probeabiiltyt ha ta usre ni teh lcsturew il relqeust a apeg n tiathca egort. Thy eseond ccoumnl diplayssthe rpobbaliit ydsitirbutinoo ev crtaegoy rrequses tfor he trsteven t .Te himddel lbco kdisplyasthe tr asnitoi prnobbiliatei s(ip )j|het robapblity thatia ues wirl leqruet satcegro iy follwod ebycate goy jr|fro allp ira s ind a .j Noe thtt, aalthouhg Makor vomedl sar eotfen neodced b yocdntionila rpbobiliaiets (j pji, w) eahe fvoud ntahtjoin tpr bobaiitleis (p ij)= pj (jip()) iraem oe irfnoramivte,bcease theyu iclund ehteli kleihoodof str erueqtinsgca etgroyi . Therst-o rerd arkovMmo el dhswnoin F gurei3 i s straghitfowrrd ta ontirpert. Useresin the lcsutr esartt o nfornpage tadnt he mna ypocree do almtostany oher catetgroy. nce Oi anc aetgro,yus rse my braose wof a wrile, hbut etrurnt o rfotnpgea efbre movong iot anthor ecaegtoyr. Uers stednt o eave tlehsi tef ro mrfotnpage adn ubsneiss F.nilly, athree ill bwes iuattios nwehrea si t ademnistriatr oodesn o tcra eaout bhte rdero i whinhcr queets aserma e. Idnthis ca s, we elcuster seus uring samode lt aht ree tscthis l cka o intfrestenam|ely,a mi xurteo fze rohtord-r eaMrkvomod els( see Secton i)3. Figur e 4sowhs eWbACNAV'sS diplsyaof clus tes creraet id nhtsiwa y.Twent yfou rfo te hno eundhrd cluseers tgneeatrd areesh own.T e chontetn sofse vearl lustecs hriglihhgtt eh lcutersng mideo'slin i drenec eo reqtust eoderr F.o eramplex,c lutse 8rc onainstro ughlyeq ualnumb res f ono-ari ot umsamr anyds umarym o to-anr tirasinionst an dlcuser 9 cotntins aorugly hquae lnmburse ofnew sto fortnagpeand f ronptge atone wstran sitoins

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

Figue r:3Thi sdsiply ahsosw he rtsuletof rightcl icikg on nlcutser 8. WbeCANAS sVhos twe cohresprndongi rtsor-erdM akor movdl.

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

gireu 4:he Tamsed aa tlcstuerd usine agm itxre uo fzeothr-rdeor aMrov kmdeos.

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

lsturing AelgriohtmsIn htiss ecitn,o w prevodie ekydetai s lo for moued-blaeds cuslteinr gppaorcha In. gneerla,luscetirgn ist e ghrupion ogf ismilr eatitiens(e. g,. usrs)e on hetb sais of tatibrteusof the etinitse.T ehes tatibutesr an bce ordnil, caateogicarl or,cnotiuoun savuel. We ddnote teh eset f ottairutbes b Xy nda avlesu fothe se of tatrtibutesby x1, x2 a,dns oo n.In istandceb-asd clesuertnig on edene s pasueo-ddsitnce aetrmi bec

tweenu ses, rorm oerp ecisely, brtweene het attibrtue alvus efor wo dt ereni ustes,rd si(xi xtj) . Thi sisdantc metric eecnode sht netioon of ismlairty bitweeen seru sndais the bas s for iiednitfyni gcustlrs.e hus, tTh cenotrsutcon of ai istadcn eemtri ic tseh mthoe dy wbhic had omia enxpret can necodet e rheatliv eimporatcen f otaritbute asdn/rocomb intaon oi attfrbites utaht rae mpirotntain ed ing snmiliairy.t oCsnruttcni gdsitane mcetris,c owevher,ca nbe d i uctl fo rsmo eomadni. sFo rinstacne,ocnsied thr proelbe mf de oinng ad istncaemetric fo rsqeueces onf he tyte psowhn inF guri e.1M dol-baseed lcutsriengi s teahncque iin hichw oen uses a collecion otfsta isticta moledsl togr oup ht useesr o infterste .Wenow e amixent hsia pporac ahndsom ef ios advtantgea oversthe disancetb-sad aepporch.a.3 1odMleBase-dC ulsternignIthe m oeldbased a-propch toa lcstuerng,iwe as sme ouu draat i sgeenarted i thne follwoig fnasihno 1:.A usr earrivs at teheWeb s tieand i sssiange tdo one fo K luctses witrhs me proobablitiy,na d2.Gi ev ntha atuse r i is anc lutsr, ehis or her beahivro sig eneratedfro m osm esttaisicalt odme slecp cit otha tclsuer.tSta titsiianc sreef rot sucha model a simtuxre omdle wit Kh compnonte. snitiallI, yofcou ser,ewd on othave the mdoel ew hve aolynthe dat .a Nnetoehelss, e cwn aappl ytsnadra dsattsitcil aethcnqiesu t our dato ao telran or modulena|mly,e(1 )th e nmbeu rfo omcopnets, (2) thenp roabibily dittsriutionb used ota signs suers t otehv aroui slucsetsr,ad n() 3he ptaraemtres foea chmo delcompo ennt .One cth emoed li sealrnd,e wecan ue it to sssigan ach useer o a tlcsutr or ferctaoniall yt the soe tfo custlrs.eF omarll, yew edscibr eam itxue mrdelow tihK c mpononest sa floolsw.L t X eeb amutilvaiarteran dom arivbal taeikg on valuesncor rsepnoidg to tne bhehaivr of oidniviuadlu sers.Le tCbe aisdrcte-eavule variabdel tkinago nva ules 1c: ::K .c Teh vale ou C f

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

orcrsponde to ths enkunon wculter asssgimnentf o ar seru A .mixurt moeed for lX iwhtK co mopnentshas t e fohr:pm(

= xX )j

=

k== 1KK pXC (= cj p )X(=jC x=c k kk )k

X

=1kk pk (=X jxC= c kk)

whreek= p( C= k c j )sith e mrganalip orabilbity fo ht etk hlcuset (r kk= 1, )k p(xjkc k )si he statistictl aodme ldsecibinr tge dhisrtbiuitnoof t heat tirbtuse or uferss n the kthi culser,t and= f 1::: k:1:: Kg ar eteh apramtees rofth emdoel.For th e wok redsciber idnthis apep, rewco nsdeir teh spciel acase werh Xe=(X1 ::: XL )sia n aribtarily rlong esuqnceeo fv aiarlesbde cribsni thg uese'r path strohuh gteh ist.eT ehv riaabel Xi tkea sno osm veaue xli rfmoam nogthe p osibsel pgea catgoeiesr hta tht eseurcould avh reeuestqd.eThu s,for eamxpe,lt h sequeecen( 1 x2x:::xL )i dncatesit ahtthe usr ers rteuqste xs1, th ne 2x a,n sd on.o oFro u raalysisn, wea ls onilcue ad n\nde"tast etoind cate ithta onad iditnal opgae sewe rrqeeuste (odn hat tdya) I.n one apprach toom dolengi tihs dtaa, ew assmeu tah taeh cmdoe clomp

onentis a r sto-der rMrkav modol:ep (k

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Ti;i1k ): TI Iwh eerk= f k k g, ke cnode tshe prbaboliitydi tribstiounove r ht eintiailpag ec-atgeroyT eruqse tmaognu ses rn ilcustrek,na d ekcndose,orfe cha atcgero,y he tonditcinaol prboaibliytd itsribtuio nverot h nexte ctageroy reuesqtde yba use r n cilusetrk. T hi sodel cmatureps(t soomede gree) te orhdero f he tsur'e seqruetss S.peci cllya,ti catprus ete uherss'i niialt equrset,t he epdneedcn beywetn ewto onsceuctive requesst an,|dbyvir tu efot he iclunsion fot h eends tate|tehla ts atecgor reqyesteu. Id oun wror,k eac vahraibelXi I Ts idicretes,p(x1j k ) i sa umtliomnali ditsibrtionu,adnp (i jxix1; k) s iase tofmu tlinomaildistri btuiosn.Ther e aer amy varnations if ohts iismpe lmoed.l Fr oxample, ueisg nigher orhdre aMkovrm deol sof reca homponecn, wet anc capture epdnedenciesb yone tdoshe nico necstivu ereuqets. snoAhet rariavtio cnnab e ued shwn ehets teiad mnistirtaro deos nt careo abot thue odrr ei nwich hther questseare amde. nI hts icas, foe raeh componect on tfe homedl,w cen uase asmile zeprto-orhdreMark ov omdl (aleos clald e UnigaarmM del)o:pk(

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1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

he prbobailiiet s(pC= ckj x)a erso emimest caledl embersmihp rpbobaliitis.eOn ecw e avhe comptud ethse eporbaibltiis, we ecn eather iassignthe u esr to teh cusltr witehhig hes tpobabilirt|ayh rad saisngemn|otra signs th esur efactronaliy tl toh eetsof cultser sccaodringt this disotirbutoi|an ofsta ssginenmt Th. ecurrntei plememnatton of WibCeNVAASu ess har dssignament.s

M were hk ncedoesthe mrainga diltsirubitnoov r ecteagoy reruesqt fors asur ine lucster k. AMgia,np (ixj )kis malutnomiiladi stirbuitn.o We nto ehat,tby uingsa mod elba-eds parpach,o i tsis rtagihtofrardwfo ra sit edamiinsrttao ro td ne aleetrnatve piartitoni sfothe ser uppuloatin. Thereo s io nc\rrocet"mode lofrc ulsterngiea{hc modl ceatpresu i deret aspncestof th deta.aA omaind xepectc an onsidecr i edenrt ricertaiof inteestr ofrpar ititnoing suers,tarnsalt etesehcri etiar ota terlntive maoeds, lna edavulat eeahcm oedli termn sf ohe tsefulneus os ifnigstsh agned. Ais ew salhl descibr seohtlyr, w cae learn anmi turxe moeld (K na dte mhdol eaparetmer)sgi ev onr udaa.t ncOe hetm oeldis le anedr, w cea nseu t it oasisgn usre to csustels ar follsows.G vient e bheavhiroof auer x,swe ancc oputem th eprboabiitlydi trisbutoni oerv hte idden vahiarbe l Ccrresopnodig ton tehc ustleras isnmgnte of he utersb y aBys'erul e:kp k(X= xj C=c k k )p(C=kc x j )= K P1()j=1 jjp(X= xjC= c j )

j3. 2eLrnian gMxiuretM oedsletLus be ginb yocsidnrineg emthdosf o lerranignt h pearametrs oe f miaturex odel mwih tknon wnuber omfco mpoentsn, Kigenvt rinaignd ata Dtrai n=( x 1::: x N). On epos sbil crieterin foord iong so sito dinetfy tihse paormaterev alusef rotha tma imizexth elkeiilhod ofothe t raniignd aa:t L M=agmax rp(Dtrainj The)separa

meter sra efoen rtfereerd ot saa m axiumml ieklihood r oLMe tisamt. Aelteratnvilye,o en may ahev pirr onkoledgewab ot uteh doainm nad acn neode thic snifrmoatinoin tehform f o arior prpbaobliitydi striubiot onvre tehp raaemtrse, ednotedp( ). I tnhsi stuaiiot, an crietiron fr loarneig tnhep raaemtresis t oientifdyt hsoe parmaeers ttat maximhze iteh opsetrir oprbaoilibtyof g vei nurot arniig ndta:MaPA=ragmax (p Djtria n= )rgmax ap(traDin )jp(=p)Dtrai(n

)were hte hescno iddentiy follotwsby ayes' Buler .hTee pasraemters aeroften ref rere do ta samimxm uaosperitor io MrAPestim aet.W enhuse in dconujncton witi hagveuor non-nifrmoatvei ripor,s APM stimetas eae rsmoohtd e(i..e,l ssee tremxe)ve sroin sf oML1 1

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

estmaits. Ien uo workr elatrde toth si paer,p e wlarne AMPe stimtae sfo rhte aprmetaer suisn gnnoinf-romtiveaDi ichletrp roisr. W eearnl he tarpametes rsingu ht eM algoEriht,m a nitearivetal orgithsmt hta ds lnoaclo tipa imn MPA a(dnM ) eLstmites.aT he aglrotih has mn Expaecattin or E osept,i wnihhc ew uset hec ruert netsimtea o ftoa sign seac uhser f(ractoinalyl) to eac hclsutr,eand a M aimxzaitoi onrM stpei n whic he ndwa n e wAP Mestimtae or bfy reptndeni thatg hets erfaciotanla ssingmnetsa r erel data. aW eitreae tth E enda Mstpes, utnl iuscecsisveMA Psetiamet ase rsatlb (seeeSe cito n4. To)i itinlizeat ehEM algo irth,m wesim lp chyoos some evect(o) raluve for . Inth werk odecrised in tbhisp aepr,we hcooesthe praaemerts 1::: tK beoe uqal .W eintiiailze het arpaetemrs ofour c opomnetnm oeld s bkye tisamtnig teh aparmteersfor as inlg-eomponentcc lsuert omdl ead tnhe randonmy lperutbrngit h earpmetera avule syb asmla lmoanu tto obain K tses of taprmatere ss(e Theeissn, oMeke, Chikcreig, nan decHerkmna 1,99 fo9 drteilsa). Fnaliy, lwhnel eraning a arpitcual rodel,mw e rn utewny tets sof nitiilapa ametrrs et coovergence, nan tdeh nuse th veale uor fhta tahst e highehst ospteiorr rpbabolitiy.W eh aev fundo hatt uchs\r staetirn" gyelisdrou gly 0:2h% mirovepmntesin th eogl ospertorsiof he partaetmrs. Ien tehE s eptof th elgaortih, givenma crrunt vealeu f the oparamteesr,wef arctionaly lsaisg a nser uiwt hbhaveorix t ocultserc uksngi te mhmberesip prhbaoblitieis given b Equyatino1. I nth eM tspeo fht algoreihtm, e prewtendth ta htse feartcioan lassignenmtsc orersopdn to rae ldat, aad neasrisn got e the MAbP stiemte giave tnih sctiitus dotaa I. nparitcular,o terassign he taparetems r( 1::: K) w,e coutn te numbhe ofr usesras sgnie dtoe ac hcultse bry suminm ghtem ebershipmpro abblitiei fos reahc custerl We .combni etehse cunts withoo urD richlet ipiorrto obta inou rMAPes imatt.eT or aessig thn peaametersrof thez eroh-toredrMa rkovmod le,we ouct thnen umebr f oimtseu esr isnclus ert rekuesq teac chaetgory. aEch equestrfor a catego y byr a user ncireemnt ths eount cfrotha cttegaoyrby t ehu sers 'mebmrseih prpobbalitiy or fhttac ustel. re Whtn eomcbin teihsco ntuwit hthe prir otoo tain thb MeAPes tmiaet .Smiilarly,of trhe tkh srt-odrr eMakrvo modle I,w eeasrsig nht paraeemetr csrorspondengito tehi nitia paleg-catgoeryreque stk a d ntehT rtasinion ptorabbliiiet sk y bocuntni, regspetcveiyl,t he nmueb of rtimse ac teaogyr s ite ihnitai lapgea d nthenu bmre foti me as tranistonifr o onemc aetgoryto naohert s imade W. cemobne tihsee conts aud nuo prirr too obtai nuor MA Pestmates.i B iterayitveyl palypni ghteE st epa d M sten,p w eomnootinallc impyorevt he etsiamtes o fhet modlep raametesr, ens uring oncvreengc e(nued friray genelra colnidtoni) tsoa lcalo maimxumof the psteroiro istrdibuiontfo r. T ehe rrea sevrel aeraonsbalec hicose fro canvoregneecc rietron. in ouIrim lempntatien, we soa thatyth eal gortih ham scovneger dwenh to wocsencuive itetratoisnpr duco elogli elkhiodsoo tneh tairnni dgta athta d ir eyb1

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

2less than0 0:%1.No w le,t s ucnsodire hwo t idenotif ayg odo vlua eforK . I npirnipcl,e wesh olu cdhooe sthen muber ofclu sers byth vinga as tei amdinitrstoa roloka t mdeosl hvani gK= 1,=K, an2d o so,nand c oose dhiertlcy .f Ocorsue,th i issim parcitca.lI oun wrok,rwe c ohseot e humbern o cfustelsrby n idn gth eodel mtah tbste repdict sen testwda atDte ts. That si,ew hoosc ethe moeld iwt Khclust rs thatem nimiizs thee uo-to-fsmpal seorc: elog pX ( xj=j K ) sc or(eKDtest=);j=1 2 P leNgth(nixi=)1

NP()2whre K ei stehMAP setmiat efo he patameretrso tabnidefrom the rtiainngd ta, ana denglht(xi)is the elgtn ohft e seqheunecfo user ir Not. teat this shocerr e ets cht eveaarg eunbem rfo btisr eqired ut encode o actagoreyre quet mase db thy euse.rI nhe tenxt esciot,n e use wthi asprpaoc to chhoose Kfr oor umnscb.co mdata. I istin tresetng iot ntoeth t tahe emtoh fodrse ecltngith en uberm fo clsturs eadn chooisgn omedl arpmeaertsw ehn aplipedt rots-rdeo Mrakor vomdlseca nela dota m ixtreumo dl ei wnhci twho o mrorecl steru sacnb e ncoede by ads ngile mdole ocmponen.t Forin tsnaec c,onsdie tro wclsuetr:s a clsutr ef ouess rhwo intiaillyr qeuset cteagroya na dthnec ohoe beswtee cantgoeres b ina dc, nada luscte rf osuesrwh oi niitalyl reueqtscat geoyrd an dtehn coohse beteewn catgerios ee nd f a.T hse teowc lsuter sacnbe e codne dni a singe clmponentoo fthem xtireum deo, lbeacse utehs qeencesuf o trehs perate acultesr dos nt ocontianc ommnoele enmst I.n fct, an ior uappilatioc onfth eM algorEtimhto t hems http://www.77cn.com.cnmo ata, mdan such cyopmoentnsa r leaerne. dTeh persenceo f ultim-lusctr coepoments dnos eno at et thecpred ictve poiew rfoa omel. Ndoentheelss, wen ushd en conjunctioi nithw uo viruasilaziot noto,l teh xeitsenc ef souc choponenmts ar erpbleoatmi.c Spec icall,y ht behavioer so fseus frrom morethan one cl suet rraep reesned intth esa em iwnod, ofwen tcnfusoing ro isdtarctnig hetsi e adtmniistrtaor. onCseueqntyl,th ere s ia een dtopro dcu modelsewit ouhtm lti-ucuslet rcompoents.nOne me hot fod dros ois tor unth eME laogritmh adn ten posh prtcoesst he reslutin mgoed, lespartaign an ymltui-lcsutre coponenmt sfo

un. dA secnd moehodt i tos allwoo nly oen state (actgoey)r otha e v aon-nerz poobariliby tofb ieng te inhitia ltstae n iaech o fth rse-trode rMarovk moelsd U.snigt e hecondsm etohdc a have nthe nforuunate ctonseqenceu tha atc lsteu ofr user thats hvead ieent riitianl tsats ebtus milia ratph aftes rhet niitials ate trea ivddie idtonsep artaec ultsesr A. sw ese en itehne xt ecstoi,nho ewver, his totpnetali rpoleb ampepra tosb iesngnii cntaf ormsnb .cocm dta.a13

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

3.3App lciatino t oMnsc.cbmWeo applei dhe leartinngt chnieuqe wse aveh ustjde sciber dot smpale sfoo u rmnsbc.co mdta. Fao varrous mioeldty pe snd aarivos clusuerts izes, Kwe elrnad modele ssiugn a raitnnigs e otf100, 032se uenceq ssamlepdfrom heto irigan ole nmilion. We thel enalvatue tdh eodems lsinu tgeho utof-sa-mle psoce irnE uqtiaon 2on a d ieenr stapmel of 89,687 sqeuecne drsawnf orm teh roignilada ta Al. lurs, ninculdng itosehd screbiedi tnhe nxt seeticn,ower eprferomde n oa dektsp PCo wiht aentiuPm IIIXeon rpcessoo rurningn t 500MaHz wtih noegu mhemoyr t oavoidpa ing. In guo lragertsruns wth i= 2N0 0000and K 20=,0on y l115.bMof mem roy ewe used.r Fgiur 5es ohw tshe utoof-s-mpal escros efo rsrt- nadz rote-hrdoreMar kvom oelsd for vairos uvaues lf toehn umbe of crultses r K. Wes eet athth ebe t rss-toredrmodel byo r uritecirnois a modl wieht K=0 4compnoets.nI cnntroat,st h zeertho-rdor emdoes lcontnie to du oebter tasK icnraese. Of cosrseu w,en h rKeches same voalu eessl hantN, te hnumbre ofm oel dcompoentnswill ecexd eth enmuerbof idtisctno bsrevtiaos.n tA tih sponi, thteou -tfo-samlpesc oercan not nciraes enyaf utrer hwthi K .On leasto servbtainoab ot theuset o wcurevsis that fo, rvauesl fo K ofpra ctcai ilterestn(K <3000),he best tezrohtor-ed mroed liswo re as tredpcting iuoto-f-ampls eata dtahnth weost rK(= 1 r)t-sodrremod e.lWe also le anrde imturxseo frtsorde- Mrrakov omeds in whlchius es rni eah cocpomennt ewr ceosnraitne dtoh va teeh same rtsre quets. s Aw entode in ht peerviuo secston, itihs contrasnitg urantaeest ath a signe lmxtuie rocmopnnte ilw lncodee xaetcl yno elcsteu.rFr o miFguer5,wes eet ah ttesh coensrtaiend odemlsha ve pradeiticevp worea mlsot quealto hatt foth eu nconsrtiande omeds. lhTs oibseravitn ouggestssth at oru imsle apprpoac foh guararteninegon ec uster perlc ompneot nwrksow lle fr in theo mnsb.coc mdomian.O fco rse,uw hn entiorucdin tghis consrtiat,n orme ocmonentp asr needee to drpresenett ehda tat han i tne hnucnosrained tace. Fors tish arptciuarld taa,a c nosrtaine mdoed wlthi 100c moponntse ah slmastot ehp rdeictivepo wreo f a nncountraisedn odemlwi h t04 copmneonts F.roo urvisu aliaztoini n eStcion,2 w esuedt hecon trsaind meodl ewihtK 10= 0o tsaisnguse s to clustersr.4Sca lbiliaytsAno edtin t he itnordctionu, no ofe ht eihneenrtd iulcitsei nt h enaaylsiso fhet ersev-lrogd ta as in iis stiez.I ntihss eciont,w exeamni theescal baliiy tf otheEM a lgrithom aplied po tour tskaof cluste rni sgequnce daet

a.As w eh av eemtioned,nt h eemmoyrr euireqents of tmehE Ma loright mra lieeanrin th nembeurof sequnees Nc ad nte nhuber mo fluscers tK . uFrthrmeoe,rthe run tie 14m

1 We present a new methodology for visualizing navigation patterns on a Web site. In our approach, we rst partition site users into clusters such that only users with similar navigation paths through the site are placed into the same cluster. Then, for eac

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aiZen,X ni, ad Hann 1(98)9,Spiloopuoul, ohPel,na dFaultisc, h19(99, C)oole,y Ta,na n Sdrviastvaa (199)9 as,ewlla snum rouesc mmerocil assyetms. I nterm so thf epecs cip rblomeof c lsueting rsues barsde n oheir Webt avingatoi napttens, thre noyl piro rwrokth tawe aer aawe rofi sb Fy,uSan hdu,and S hi h(1999. )T

he apypiel BIRCH da scalabl( edsiantcbased eluctesirng lgoriathm)to clusetirgn ser sessions, uherwe eachs essoi ni reprsesneedta sa v cteor f otmiessp etn yb th usee or eanchp aeg{taht s,i staaict eprerentastiono ufserbe havoir The.rei s asol ar elatveiy lsmal blod yo frpor iwrk tohat idrcelytus e sengeatrveipr bobilaitsicm doeslto cha arcteirze Websi t nevigaaitonp atetrn.sBe tsarovs (991)6 na Zukedram,nA brlceth ndaNichol so n19(9) 9nivetigased tav aiert yo Mfrkavomod les t pordecit uess' rftuuer age rpqueetssc odinitneodo pnsatpage vssitied Bor.es agdnLeve n (19e99)a ls oedcribs the use ef otk-hoder raMrok vmoedls (ni he tfrmo o pforabblisiti chpyerettx rammargs)t och raatcreize ebWn vigatioa npaterns.t hTse appeoachers shaer wih thts piper atheu ndelyingr sueof a Ma krovr perseentaion tfo dynarimc ebhviao,rbu tfouc sona si gne lmoeldf ro gagregate opulatpoi charnatceritscs, irtaer hhat nelrnanig clsuetrs of ebhavoir of drie rnt greopsu ofu sers.I n ag eneral(non-Web) cntoet,x hteu s oe mfdeol-absedp rbabioislti cclsutrine gor fmutliaviare tectorv daat i swel lnkwon na widedylused .orF egenrl raeievsws e Tetitrengtoin, miSth ad naMkvo( 915)8 M,Lcaclhna nd aasBfod r(188), Ba9ne d aldn aftRrey(1 939),Cheseemn aan Stutd z(1959) a,nd ralFeya ndR atery f(9198.)I adniditno,htre have ebeenn uemrou susccsesfluappl caiionsto this apfproach i nreaas a disvesre ocnusme mrakreitng Wedel(an damakKrau 199,)8an d tmasophericscie ce (nSmyt,h dI, anedGh il, 199)9. oneNheltes, shtree s rieatliely vltitle owr onk porabbilistc miodle-baed clssuering tf oesqeucen. saRinerb, Le,e Jaun, agn dWilop (19n9)8pro idvean ea ry llaorgtihm or clusftrien gi dreet nspeechu ttrancee ussng mixitres ufo ihden daMkov mordlse .oPuslen(199 ) i0ntordued c partaciularf om or Mfrakv oixmuters orf odemingl hetrogeeeonus ebahviro incon smure purhcsiagn data. roKhg 1994() metionns teh ossipbliity fous ingmi xtreus f ohdiend arMkvo modlsef or cultserignse qences. uMroe egeralnve rsios of Marnov kmxiuterswe r independeenty ldevlepoe bydbot h Syth (m917, 1999)9a dnR idewga (y997)1 i,cludingna g neearl MEfr meaowk for lrarning. eMoerr ecenlty, aCezd nadS yth (199m9 )have sowhnt htaa l ofl htseea glorthmi sca bn eviwede sa secpia lcaes sofa egnrale Byeasian hireacrhcialm delo .oTour knowl deeg the,orkw rperote here di sht retsap plcaitin oo sefqencue-asbd perbabolistiic culstring eo tWeb avnigtaoin ada.tI nte ms ro vfisuailztaon iof avngaiitnop tatenrs,t hree ar neumroesu omcercmail(an doftn erporpietra) yysstmse hat atlolw oen tovie wu er snaivagion tapternts t a apartculir Wea bstie T.hsee sysetmsd ont opaepa rotus erobapibliticsdyna icm cusltr emdoels In a.17

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