Discovering Block-Structured Process Models From Event Logs Containing Infrequent Behaviour

Transcription

1 Disovring Blok-Strutur Pross Mols From Evnt Logs Contining Infrqunt Bhviour Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst Einhovn Univrsity of Thnology, th Nthrlns {s.j.j.lmns,.fhln, w.m.p.v..lst}@tu.nl Astrt Givn n vnt log sriing osrv hviour, pross isovry ims to fin pross mol tht st sris this hviour. A lrg vrity of pross isovry lgorithms hs n propos. Howvr, no xisting lgorithm rturns soun mol in ll ss (fr of loks n othr nomlis), hnls infrqunt hviour wll n finishs quikly. W prsnt thniqu l to op with infrqunt hviour n lrg vnt logs, whil nsuring sounnss. Th thniqu hs n implmnt in ProM n w ompr th thniqu with xisting pprohs in trms of qulity n prformn. Kywors: pross mining, pross isovry, lok-strutur pross mols, sounnss, fitnss, prision, gnrlistion Introution Pross mining thniqus im to support orgnistions in improving thir usinss prosss. Evnt logs of historil hviour n us to isovr pross mols of th rl prosss s prsnt in th orgnistion, s oppos to mnully rt mols tht rflt wishful thinking, shoul- or s-it-ws-two-yrs-go hviour. Auiting of isovr mols n prov omplin with orgnistionl n govrnmntl rgultions [3], n rply of historil hviour on th isovr mol n rvl soil ntworks n ottlnks [7,5,4]. Th hllng in pross isovry is to fin th st pross mol givn ror historil hviour. Whih pross mol is st is typilly vlut using svrl qulity ritri. Four importnt qulity ritri r fitnss, prision, gnrlistion n simpliity. An unfitting mol nnot rprou ll hviour ror in th log. An impris mol llows for too muh τ Figur : Unsoun pross mol. itionl hviour tht is not sri in th log. A non-gnrl mol only sris th hviour in th log n thrfor might isllow futur hviour snt in th log. A non-simpl mol ns lot of pls, trnsitions n rs to xprss its hviour n might hr to r. Anothr importnt qulity ritrion is sounnss: ll pross stps n xut n som stisftory n stt, th finl mrking, is lwys rhl. For instn, th f

2 Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst Ptri nt in Figur is not soun s it ontins lok from whih th finl mrking with only singl tokn in th finl pl n nvr rh. An unsoun pross mol n still usful, ut pplying tsks suh s vlution, uiting, fining soil ntworks n ottlnks n iffiult if not impossil. Thrfor, for most us ss n unsoun pross mol n isr without vn onsiring th vnt log it is suppos to rprsnt. Trs in log might follow mny iffrnt pths through th pross. In most rllif vnt logs, som pths r tkn infrquntly, or trs only iffr y ourrn of infrqunt tivitis. Suh logs ontin infrqunt hviour n hllng isovry lgorithms, s pross mol soring wll on ll qulity ritri might not xist. If infrqunt hviour is inlu in th mol, simpliity might srifi, if infrqunt hviour is xlu from th mol, fitnss might srifi. Fortuntly, th Prto prinipl (lso known s th 800 rul) oftn pplis to vnt logs. Typilly, 80% of th osrv hviour n xplin y mol tht is only 0% of th mol rquir to sri ll hviour. Th 80% mol shows th highwys in th pross. Hn, it is mor intuitiv, ut n lso us s strting point for outlir ttion. []. To otin n 80% mol, lssil pproh is to glolly filtr th log for isovring mol. This hs numrous isvntgs, s it is iffiult to intify infrqunt hviour, n vn whn infrqunt hviour is filtr out, isovry lgorithms (α [6], B [6], ILP []) might still prou unsirl mols. Othr pprohs wr sign to ignor infrqunt hviour n n prou n 80% mol ut my prform lss on othr qulity ritri: gnti pprohs [5,9] hv long run tims n huristi pproh [0] prous unsoun mols. As of toy, no thniqu hs n propos tht isovrs soun 80% mol, os tht fst n is l to filtr infrqunt hviour. Svrl xisting pprohs pply ivi-n-onqur thniqus [0,,6], in whih th vnt log is split n mol is onstrut rursivly. In this ppr w prsnt n xtnsion of suh n pproh, IM, ll Inutiv Minr - infrqunt (IMi), tht ims to isovr soun 80% mol fst. W introu infrqunt hviour filtrs in ll stps of IM, suh tht infrqunt hviour is filtr lolly. IMi is implmnt in th InutivMinr pkg of th ProM frmwork [4]. To vlut IMi, w ompr its prformn n its isovr mols to othr isovry lgorithms y mns of th qulity ritri using rl-lif logs. Th rminr of this ppr strts with sription of logs, pross trs n IM. In Stion 3, IMi is introu. In Stion 4 IMi is ompr to xisting mining lgorithms. Stion 5 onlus th ppr. Prliminris Evnt Logs. An vnt log is olltion of trs. Eh tr is squn of vnts tht rprsnt ourrns of tivitis of pross xution in th rsptiv orr. Not tht tr might ppr multipl tims in n vnt log. Th tr without vnts is not with ɛ.

3 Disovring Pross Mols Construtivly Without Infrqunt Bhviour 3 Pross trs. Th lok-strutur pross mols isovr y IM, ETM n IMi r pross trs. A pross tr is n strt rprsnttion of soun lok-strutur workflow nt [6]. A tr rprsnts lngug, lf sris th singlton lngug of n tivity, n non-lf no is n oprtor tht sris how th lngugs of its hilrn r omin. In this ppr, w will onsir four oprtors:,, n. Th oprtor nots th xlusiv hoi twn its hilrn, th squntil omposition n th intrlv prlll omposition. Th (m, m... m n ) hs two groups of hilrn: m is th loop oy n m... m n is th loop ro prt. A tr in th lngug of (m, m... m n ) strts with tr from m, follow y rptition of tr from ny m... m n n tr from m gin. For instn, th lngug of (,, ) is {,,,,,,,,,,,...}. Anothr xmpl of pross tr is ( (, ), (, ), (, f)), noting th lngug () () () ((f) ). For forml finition, pls rfr to [6]. Inutiv Minr In this ppr, w xtn n xisting ivi-n-onqur pproh to pross isovry. Divi-n-onqur hs n us in pross isovry for. For instn, [?] omins it with trnsition systms n rgions; [] omins it with tr lignmnts. In this ppr w xtn th Inutiv Minr (IM) [6], of whih w first giv its si lgorithmi i n illustrt it with running xmpl. IM works y rursivly ) slting th root oprtor tht st fits L, ) iviing th tivitis in log L into isjoint sts n ) splitting L using ths sts into sulogs. Ths sulogs r thn min rursivly, until sulog ontins just singl tivity. W first introu how IM slts n oprtor n n tivity ivision, n illustrt it with running xmpl. Consir log L: [,,,,,, f,,, f, 00,,, f 00,, f, 00 ]. In irtly-follows grph, h no rprsnts n tivity n n g from no to no is prsnt if n only if is irtly follow y somwhr in L. Th frquny of g (, ) is how oftn this hppns. Figur shows th irtly-follows grph of L. IM srhs for hrtristi ivision of tivitis into isjoint sts, ut, of th irtly-follows grph. Eh oprtor (,, or ) hs hrtristi ut of th irtly-follows grph. If suh hrtristi mths, IM slts th orrsponing oprtor. Othrwis, flowr mol, llowing for ll squns of tivitis, is rturn. Th sh lin in Figur is ut: ll gs rossing it go from lft to right. Using th ut {,,, }, {, f}, IM splits th log y splitting h tr orrsponing to th ut: L = [,,,,,, 00, 00 ] for th lft rnh, L = [, f, f, 00 ] for th right rnh. Thn, IM rurss. W first onsir L. Figur shows its irtly-follows grph, th sh lin nots n ut, s no g rosss th ut. Th log L is split in L 3 = [,,,,,, 00 ] n L 4 = [ 00 ]. L 4 onsists of only singl tivity, so for L 4 IM isovrs th lf. Th isovr pross tr up till now is ( (..., ),...). IM rurss furthr. Figur shows th irtly-follows grph of L with its ut, whih splits L into L 5 = [ 3 ] n L 6 = f 3 ]. Figur shows th irtlyfollows grph of L 3 with its ut. IM splits L 3 into L 7 = [, 00 ] n L 8 = [ ]. Th omplt pross tr isovr y IM is ( ( ( (, ), ), ), (, f)). Figur shows th orrsponing Ptri nt. For mor tils, s [6].

4 4 Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst f 00 () L with ut f () L with ut () L with ut τ () L3 with ut τ τ f τ () Disovr Ptri nt Figur : Dirtly-follows grphs. Dsh lins not uts. Egs hv thir frqunis not. () is th min Ptri nt. 3 Extning IM In this stion, w introu Inutiv Minr - infrqunt (IMi) y ing infrqunt hviour filtrs to ll stps of IM. For h of th oprtionl stps of IM it is sri how infrqunt hviour ffts th stp n how istinguishing frqunt n infrqunt hviour n us to improv isovry of th 80% mol. In h rursion stp, IMi first pplis th stps of IM unltr. Only if this fils n IM woul rturn flowr mol, th filtrs r ppli. Frqunis of trs n vnts r ignor y IM ut r tkn into ount y IMi in orr to istinguish frqunt n infrqunt hviour. In th oprtor n ut sltion stps, two thniqus r ppli: filtring th irtly-follows grph for infrqunt gs n using vrint of th irtly-follows grph for sltion of. Filtrs r to s s ttion to filtr umult rtifts of filtring ovr rursions. In th following, k nots usr-fin thrshol vlu twn 0 n to sprt frqunt n infrqunt hviour. Filtrs on th oprtor n ut sltion stps r sri first, follow y filtrs on s ss, n filtrs on log splitting. 3. Filtrs on Oprtor & Cut Sltion In th oprtor n ut sltion stps, huristis-styl filtr is ppli y IMi. In s of, vrition of th irtly-follows grph n us. Huristis-styl Filtring. Consir log L : [h,,,,,, f i, h,, f, i00, h,, f i00, h, f, i00, h,,, f i ], whih is th log us in Stion xtn with n infrqunt tr h,,, f i. Figur 3 shows its irtly-follows grph. Compr to Figur, th infrqunt tr introus th g (, ), n thrfor th sh lin is not ut. Similr to th thniqu us in HM, IMi filtrs th irtly-follows grph to only ontin th most frqunt gs. Th g (, ) is rltivly infrqunt ompr to th othr outgoing gs of. An outgoing g of no is too infrqunt if it hs frquny of lss thn k tims th frquny of th strongst outgoing g of tht no. All too infrqunt gs r filtr out in IMi for uts of, n r tt.

5 Disovring Pross Mols Construtivly Without Infrqunt Bhviour 5 Evntully-follows Grph. Dspit huristis-styl filtring, infrqunt gs might rmin in th irtly-follows grph. Consir log L = [,,,,,,,,,,,,,,,,,,,, ]. Th son tr is th only tr ontining two s: th son is infrqunt. Figur 3 shows th irtly-follows grph of L. Th sh lin in Figur 3 is not squn ut s g (, ), introu y th infrqunt, rosss it in th wrong irtion. As ll outgoing gs of hv frquny, no vlu of k oul filtr g (, ). Similr to thniqu us in [9] ( wk orr rltion ), IMi uss th vntullyfollows grph, whih is th trnsitiv losur of th irtly-follows rltion: n g (, ) is prsnt if n only if is follow y somwhr in th log. Th vntully-follows grph of L is shown in Figur 3. In this grph, ll outgoing gs of r mplifi, xpt th infrqunt g (, ), whih n thn filtr out. In this xmpl, using th vntully-follows grph llows IMi to l with infrqunt hviour. An infrqunt ourrn of n tivity still inrss frquny of infrqunt gs, ut s t most to h of thm. Th vntully-follows grph mplifis ll othr hviour, so using th vntully-follows grph for ut ttion inrss roustnss ginst infrqunt hviour. IMi uss filtr vntully-follows grph to tt uts n if it fins on, slts s oprtor f 00 () Dirtly-follows grph with n infrqunt g. Th sh lin is not ut s (, ) rosss it in th wrong irtion. () irtly-follows grph Figur 3: Dirtly n vntully follows grphs. 5 () vntully-follows grph 3. Filtrs on Bs Css In ition to th singl-tivity s s in IM, s n rtift of filtring it is possil tht trs without vnts, ɛ, rmin. On oth s ss filtrs r introu. Singl Ativitis. Assum th following two logs: L = [ɛ 00, 00,, 00,,, 00 ] L = [ɛ, 00,,,,, ] Both L n L onsist of singl tivity, nnot split furthr n r s ss. Givn th rprsnttionl is of IMi, for oth logs ithr flowr mol or singl

6 6 Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst tivity n isovr. In L, ll trs r frqunt n flowr mol is oviously th st hoi. In L howvr, only is frqunt n st rprsnts th frqunt hviour. Choosing ithr option influns qulity imnsions: isovring for L srifis fitnss, whil isovring flowr mol for L srifis prision. is only isovr y IMi if th vrg numr of ourrns pr tr of in th log is los nough to, pnnt on th rltiv thrshol k. Empty Trs. Assum th following log: L = [,, 00,,, 00,, ]. In th first rursion, IMi slts th oprtor n splits L into L = [ 0 ], L = [ɛ, 00, 00 ] n L 3 = [ 0 ]. Consir L. A fitting solution for th mpty tr in L woul to min (τ,...) n rurs on L \{ɛ}. For L, ɛ is infrqunt n isovring (τ,...) woul srifi simpliity. This is troff, ut for L lrly (τ,...) is prfrr. To ovrom this prolm, IMi only isovrs (τ,...) if ɛ is frqunt nough ompr to th numr of trs in th log n with rspt to k. If ɛ is not frqunt nough, IMi filtrs ɛ from L n rurss on L \ {ɛ}. 3.3 Filtrs on Log Splitting Assuming th oprtor n ut hv n slt, som infrqunt hviour in th log might not fit th hosn oprtor n ut. If not filtr out, this unfitting hviour might umult ovr rursions n osur frqunt hviour. This stion sris how infrqunt hviour n filtr uring log splitting. It is ssum tht th oprtor n ut r orrtly slt n tht ny hviour tht violts this sltion is infrqunt. For h oprtor, w sri th typs of violtions tht n tt n how thy r filtr y IMi, illustrt y n xmpl. In ths xmpls, Σ = {}, Σ = {} is th hosn ut n L, L r th sulogs to--rt. Bhviour tht violts th oprtor is th prsn of tivitis from mor thn on sutr in singl tr. For instn, th tr t =,,,,,,,, ontins tivitis from oth Σ n Σ. Σ xplins th most tivitis, is most frqunt. All tivitis not from Σ r onsir infrqunt n r isr:,,,,,,, L. Bhviour tht violts th oprtor is th prsn of vnts out of orr oring to th sutrs. For instn, in th tr t =,,,,,,,,,, th lst ours ftr, whih violts th. Filtring infrqunt hviour is n optimistion prolm: th tr is to split in th lst-vnts-rmoving wy. In t, th split,,, L,,,,, L isrs th lst vnts. A prlll oprtor llows for ny squn of hviour of its sutrs. Thrfor, no hviour violts n infrqunt hviour n nithr tt nor filtr whil splitting th log. Bhviour tht violts th oprtor is whn tr os not strt or n with th loop oy: For instn, (, ), is violt y ll trs tht o not strt n n with n. For h suh invli strt or n of tr, n mpty tr is to

7 Disovring Pross Mols Construtivly Without Infrqunt Bhviour 7 L to inrs fitnss of th rsulting mol. Consiring th tr t 3 =,,, thn [ɛ, ] L n [ ] L. In h rursion stp, first th oprtor n ut sltion stps of IM r prform y IMi. If tht woul rsult in th flowr mol, th prour is ppli gin, with th infrqunt hviour filtrs in oprtor n ut sltion, s ss n log splitting, suh tht in ll stps of IM filtrs r ppli y IMi. In th nxt stion, IMi is ompr to xisting pross isovry mining thniqus. 4 Comprison to Othr Disovry Algorithms In this stion, w ompr IMi to xisting mining lgorithms on prformn n qulity ritri of isovr mols, using is from [8,]. W first sri th xprimntl stup n th us logs, n finish with isussion of th rsults. 4. Exprimntl stup W ompr th mining lgorithms IM, IMi, HM, ILP n ETM using th following qulity ritri: w ompr prformn n msur sounnss, fitnss, prision, gnrlistion n simpliity. To provi slin, w inlu flowr mol (FM), llowing for ll squns of tivitis. n tr mol (TM). Figur 4 givs n ovrviw of th xprimntl stup. prpross log pply minr onvrt to Ptri nt msur fitnss, prision, gnrlistion trmin simpliity trmin sounnss mining tim Figur 4: Exprimntl stup Prprossing. As prprossing stp, w rtifiil strt n n vnts to th logs. Mining lgorithms might rquir singl strt n n vnts, n ths vnts hlp to trmin sounnss. Mining. Sonly, th minrs r ppli: IM IMi, ILP, HM, ETM, FM n TM. W ompr ll mining lgorithms using thir fult sttings. Lik in [], prmtr optimistion is outsi th sop of this ppr. HM n ETM o not prou Ptri nt. Thrfor th output of h of ths minrs is onvrt to Ptri nt, msur mining tim inlus this onvrsion. W rport n initiv mining tim on ul Intl Xon E5-630 hxor, hving 64GB of RAM, running 64-it Winows 7. As w wnt to min mols fst, w st mximum mining tim of two hours. ILP is stopp ruptly ftr this oun, ETM is llow to finish its roun of gnti stps. A tr mol llows for ll trs in th vnt log, ut no othr hviour.

8 8 Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst Msuring. W r prmissiv in th sounnss hk: w ovious finl mrkings to th isovr mols if th mining lgorithm os not provi it, n h rsonl finl mrking in th isovr mols is onsir to vli finl mrking to rh y th pross. To msur fitnss [7], prision [8] n gnrlistion [] of th min mols w us th PNtRplyr pkg in th ProM frmwork [4]. For ths msurs, first projtion of th log on th isovr mol is omput, n lignmnt. Th thniqu sri in [7] provis n lignmnt tht shows th lst vition twn log n mol. For omputtion of th lignmnt, th finl mrking to rh is rlvnt. On th mols isovr y minrs tht o not provi finl mrking, w omput th lignmnt ssuming tht vry mrking is finl mrking. For fitnss, this yils n uppr oun. Exprimnts show tht th uppr oun is not nssrily tight: w foun iffrns of 0.3 in fitnss twn msur with n without finl mrking. In th rsults, w not ths uppr oun fitnss vlus using itlis. From th lignmnt, grph of rh n rhl mrkings, n gs twn thm is omput. On th mrkings in this grph, th numr of gs tht is nvr us in th lignmnt is msur for prision [8], whil th frquny of th gs us in th lignmnt is msur for gnrlistion. Th vlus of prision n gnrlistion highly pn on th hosn optiml lignmnt. Thrfor, th rsults with n without finl mrking shoul not ompr for prision n gnrlistion. Exprimnts show tht th vlus r quit los: w foun iffrns with mximum of out 0. in prision whn thr is no finl mrking, n for gnrlistion. W not vlus otin without finl mrking in itlis. W ssss simpliity y msuring th numr of rs, pls n trnsitions in th Ptri nts. 4. Logs To ompr th mining lgorithms, w us rl-lif vnt logs. Tl hrtriss th iffrnt logs. A pross from th gynology prtmnt of n mi hospitl is logg in th BPIC log []. Th BPIC log [3] origints from n pplition pross for prsonl lon or ovrrft within glol finnil orgnistion. Furthrmor, w us non-puli logs of uiling prmit pprovl pross in fiv muniiplitis, rsulting from th CoSLog projt 3. W inlu ths fiv oth untouh, WABO through 5, n filtr to ontin only tivitis ommon to ll fiv, WABO through Rsults Tl shows th rsults. inits n unsoun mol, soun. A sh (-) inits tht th minr i not prou rsult, n mpty sp inits tht msurmnt oul not otin on our mhin u to mmory rstritions. For som xprimnts, W pt th fitnss omputtion in th PNtRplyr pkg to hiv this. 3 S

9 Disovring Pross Mols Construtivly Without Infrqunt Bhviour 9 mining took longr thn two hours. This is not with (). Th xprimnts for whih finl mrking h to guss r not with (). A mol with lok is not with (0). () nots tht th mol ontins trnsition, () tht th mol ontins ithr n unoun or n unrhl trnsition. Tl : Log sizs n rsults. BPIC BPIC WABO WABO WABO trs vnts tivitis IM IMi HM () () () () () () () () () () () () ILP () () () () () ETM FM TM () () IM IMi HM - () (0) () (0) () () () () () () () ILP - () - () () () () ETM FM TM - - IM IMi HM ILP ETM FM TM IM IMi HM ILP ETM FM TM IM IMi HM ILP ETM FM TM IM IMi HM ILP ETM FM TM rmrks sounnss mining tim (s) fitnss prision gnrlistion WABO WABO 3 WABO 3 WABO 4 WABO 4 WABO 5 WABO Disussion First osrvtion is tht for ll logs mol ws isovr within two hours y IM, IMi, FM n ETM. IMi ws for ll logs it slowr thn IM, whil tking lot lss tim

10 0 Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst Tl : Simpliity (#rs,#pls,#trnsitions). IM IMi HM ILP ETM FM TM BPIC 56,5,68 90,7, ,7,8 56,3,68 - BPIC 80,7,40 66,4, ,76, ,88,38,, 80,3,40 - WABO 368,,84 474,97,37 07,3,496-3,5,6 354,3,77 958,953,979 WABO 96,5,48,37,6 49,9, 80,73,46 7,3,35 96,3, ,890,308 WABO 336,8,68 406,43,0 870,34, ,5,6 56,8,6 38,3, ,8454,8670 WABO 0,6,60,5,56 35,9,6 770,6,46 44,, 96,3, ,766,877 WABO 3 378,8,89 358,4,79 946,344,459 -,4,3 348,3,74 08,983,0064 WABO 3,5,6 6,3,58 79,9,35-4,,8 96,3, ,56,530 WABO 4 304,3,5 90,,45 764,70,36-34,6,7 74,3,37 86,5907,6093 WABO 4 00,7, 08,33,54 30,9,4 39,80,46 78,35,3 96,3,48 474,55,37 WABO 5 368,8,84 39,30,96 90,356, ,33,78 46,, 360,3,80 68,636,634 WABO 5 96,5,48 6,36,58 54,9, 786,60,46 64,3,7 96,3,48 5,48,56 thn ILP, ETM n TM. A notil iffrn xists twn ETM n IMi; ETM took muh longr for h log. Son osrvtion is tht, not onsiring FM n TM, no minr hs log on whih it prforms st on ll fitnss, prision n gnrlistion. Troffs hv to m. IM n ILP i not mng to isovr goo 80% mol: to hiv prft fitnss, IM srifis prision, whil ILP srifis prision n simpliity. An 80% mol ws isovr for most logs y HM, ut wr lss simpl, not soun, n for som logs isovry took long tim. ETM, with its fult sttings s tst, fouss on prision n thrfor hivs lowr fitnss. Morovr, isovry took long tim. IMi isovr soun 80% mols quikly in ll ss. Rgring prision, two groups of vnt logs n intifi: BPIC n WABO to WABO 5. On ths logs, IMi prous 80% mols with ttr prision thn IM n th slin FM. Fitnss of IMi on ll ths logs is, s xpt for 80% mols, highr thn ETM, ut lowr thn IM. A mnul insption of th rsulting mols shows tht IMi rturns squn of tivitis, whrs IM rturns flowr mol. Still, som squntil lmnts r flowr mols, using th low prision. Figur 5 shows prt of th mol isovr y IMi for WABO 4. BPIC n WABO to WABO 5. On ths logs, IMi isovrs goo 80% mols tht n kp up with othr minrs. Figur 5 shows th rsults of thr minrs on th WABO log. Th mol isovr y ETM ontins th lst numr of trnsitions n is oviously th simplst mol, ut its fitnss (0.6) is onsirly lowr thn of IMi (0.946). Th min iffrn is tht IMi s two flowr sumols not isovr y ETM, giving prision of for IMi n for ETM. For gnrlistion, oth mols hv th prft sor. Of th 44 tivitis in WABO, 3 r not in th mol isovr y ETM n only r not in th mol isovr y IMi. Thrfor, futur tr is mor likly to pt y th IMi-mol thn y th ETM-mol. Also, not tht IMi rturn mol in 0. sons n ETM n 4 minuts, showing tht IMi n hiv ttr rsults in signifintly lss tim.

11 Disovring Pross Mols Construtivly Without Infrqunt Bhviour () IMi on WABO () IMi on WABO 4 (prt of). () ILP on WABO (prt of) 5 Conlusion () ETM on WABO Figur 5: Rsults of isovry. In this ppr, w prsnt th Inutiv Minr - infrqunt (IMi), n xtnsion of th Inutiv Minr (IM, ll B in [6]) tht filtrs infrqunt hviour lolly in h lgorithmi stp of IM: slting n oprtor n ut, splitting th log n th s ss of th rursion. Unlik othr pprohs, IMi n rt th so-ll 80% mol using th Prto prinipl whil gurnting to rturn soun pross mol in short tim. W ompr IMi to svrl xisting thniqus using prformn n sounnss, fitnss, prision, gnrlistion n simpliity of th isovr mols. IM, HM, ILP n ETM wr ppli to twlv rl-lif logs. Compr with IM, mols isovr y IMi hv lowr fitnss, highr prision, qul gnrlistion n omprl simpliity. IMi lwys rturn soun 80% mol fst, n on ll logs sors goo on ll qulity ritri xpt prision. Rsults for prision r twofol: on hlf of th logs, IMi isovr soun 80% mols fst, hving lowr prision u to isovry of flowr mols rly in th rursion. Not tht for mny logs, mol soring wll on ll qulity ritri osn t xist: pross isovry is troff. On th othr hlf of th logs, IMi isovr ttr 80% mols fstr thn ny othr isovry thniqu, showing th potntil of th onstrutiv pproh. Futur Work. Th prlll oprtor rmins prolmti in oprtor n ut sltion, s non of th fturs propos in this ppr n filtr infrqunt hviour n inompltnss rlt to this onstrut. Effiint ttion of non-omplt prlll logs rmins sujt of furthr rsrh. Rfrns. vn r Alst, W., Arinsyh, A., vn Dongn, B.: Rplying history on pross mols for onformn hking n prformn nlysis. Wily Intrisiplinry Rviws: Dt Mining n Knowlg Disovry (), 8 9 (0). vn r Alst, W.M.P., t l.: Pross mining mnifsto. In: Businss Pross Mngmnt Workshops (). Ltur Nots in Businss Informtion Prossing, vol. 99, pp Springr (0)

12 Snr J.J. Lmns, Dirk Fhln, n Wil M.P. vn r Alst 3. vn Alst, W.M., vn H, K.M., vn Wrf, J.M., Vronk, M.: Auiting.0: Using pross mining to support tomorrow s uitor. Computr 43(3), (00) 4. Vn r Alst, W.M., Song, M.: Mining soil ntworks: Unovring intrtion pttrns in usinss prosss. In: Businss Pross Mngmnt, LNCS, vol. 3080, pp Springr (004) 5. vn r Alst, W., Miros, A., Wijtrs, A.: Gnti pross mining. Applitions n Thory of Ptri Nts , (005) 6. vn r Alst, W., Wijtrs, T., Mrustr, L.: Workflow mining: Disovring pross mols from vnt logs. Knowlg n Dt Enginring, IEEE Trnstions on 6(9), 8 4 (004) 7. Arinsyh, A., vn Dongn, B., vn r Alst, W.: Conformn hking using ost-s fitnss nlysis. In: Entrpris Distriut Ojt Computing Confrn (EDOC), 0 5th IEEE Intrntionl. pp IEEE (0) 8. Arinsyh, A., Munoz-Gm, J., Crmon, J., vn Dongn, B.F., vn r Alst, W.M.: Alignmnt s prision hking. In: Businss Pross Mngmnt Workshops. pp Springr (03) 9. Buijs, J., vn Dongn, B., vn r Alst, W.: A gnti lgorithm for isovring pross trs. In: Evolutionry Computtion (CEC), 0 IEEE Congrss on. pp. 8. IEEE (0) 0. Crmon, J.: Projtion pprohs to pross mining using rgion-s thniqus. Dt Mining n Knowlg Disovry 4(), 8 46 (0). D Wrt, J., D Bkr, M., Vnthinn, J., Bsns, B.: A multi-imnsionl qulity ssssmnt of stt-of-th-rt pross isovry lgorithms using rl-lif vnt logs. Informtion Systms 37, (0). vn Dongn, B.: BPI Chllng 0 Dtst (0), 3. vn Dongn, B.: BPI Chllng 0 Dtst (0), 4. vn Dongn, B., Miros, A., Vrk, H., Wijtrs, A., vn r Alst, W.: Th ProM frmwork: A nw r in pross mining tool support. Applitions n Thory of Ptri Nts , (005) 5. vn Dongn, B.F., Arinsyh, A.: Pross mining: fuzzy lustring n prformn visuliztion. In: Businss Pross Mngmnt Workshops. pp Springr (00) 6. Lmns, S.J.J., Fhln, D., vn r Alst, W.M.P.: Disovring lok-strutur pross mols from vnt logs - onstrutiv pproh. In: Ptri Nts. Ltur Nots in Computr Sin, vol. 797, pp Springr (03) 7. Mns, R., Shonnrg, M., Song, M., Vn r Alst, W., Bkkr, P.: Applition of pross mining in hlthr s stuy in uth hospitl. In: Biomil Enginring Systms n Thnologis, pp Springr (009) 8. Miros, A., Wijtrs, A., vn r Alst, W.: Gnti pross mining: n xprimntl vlution. Dt Mining n Knowlg Disovry 4(), (007) 9. Smirnov, S., Wilih, M., Mnling, J.: Businss pross mol strtion s on synthsis from wll-strutur hviorl profils. Intrntionl Journl of Cooprtiv Informtion Systms (0), (0) 0. Wijtrs, A., vn r Alst, W., Miros, A.: Pross mining with th huristis minrlgorithm. Thnish Univrsitit Einhovn, Th. Rp. WP 66 (006). vn r Wrf, J., vn Dongn, B., Hurkns, C., Srrnik, A.: Pross isovry using intgr linr progrmming. Funmnt Informti 94, 3874 (00). Yzquiro-Hrrr, R., Silvrio-Cstro, R., Lzo-Cortés, M.: Su-pross isovry: Opportunitis for pross ignostis. In: Entrpris Informtion Systms of th Futur, pp Springr (03)