On the Representational Bias in Process Mining

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1 On t Rprsnttionl Bis in Pross Minin W.M.P. vn r Alst Dprtmnt of Mtmtis n Computr Sin Einovn Univrsity of Tnoloy, Einovn, T Ntrlns Emil: WWW: vlst.om Astrt Pross minin srvs ri twn t minin n usinss pross molin. T ol is to xtrt prossrlt knowl from vnt t stor in informtion systms. On of t most llnin pross minin tsks is pross isovry, i.., t utomti onstrution of pross mols from rw vnt los. Toy tr r ozns of pross isovry tniqus nrtin pross mols usin iffrnt nottions (Ptri nts, EPCs, BPMN, uristi nts, t.). Tis ppr fouss on t rprsnttionl is us y ts tniqus. W will sow tt t oi of trt mol is vry importnt for t isovry pross itslf. T rprsnttionl is soul not rivn y t sir rpil rprsnttion ut y t rtristis of t unrlyin prosss n pross isovry tniqus. Trfor, w nlyz t rol of t rprsnttionl is in pross minin. I. INTRODUCTION Pross minin is n mrin isiplin proviin omprnsiv sts of tools to provi ft-s insits n to support pross improvmnts [1]. Tis nw isiplin uils on pross mol-rivn ppros n t minin. Howvr, pross minin is mu mor tn n mlmtion of xistin ppros. For xmpl, xistin t minin tniqus r too t-ntri to provi omprnsiv unrstnin of t n-to-n prosss in n orniztion. Businss Intllin (BI) tools tn to fous on simpl sors n rportin rtr tn lr-ut usinss pross insits. Businss Pross Mnmnt (BPM) suits vily rly on xprts molin iliz to- prosss n o not lp t stkolrs to unrstn t s-is prosss s on ftul t. Pross minin provis nw mns to improv prosss in vrity of pplition omins. Tr r two min rivrs for tis nw tnoloy. On t on n, mor n mor vnts r in ror tus proviin til informtion out t istory of prosss. Som fiurs illustrtin t rowt of vnt t n foun in [2]. Stor sp rw from 2.6 optimlly omprss xyts ( yts) in 1986 to 295 omprss xyts in Not tt tis inlus ppr, potos, r-isks, CDs, t. In 2007, 94 prnt of ll informtion stor pity on Ert ws iitl. T otr 6 prnt rsi in ooks, mzins n otr non-iitl formts. Tis is in strk ontrst wit 1986 wn only 0.8 prnt of ll informtion stor pity ws iitl. Ts numrs illustrt t xponntil rowt of t. In morn orniztions mny vnts r ror n tis will only inrs furtr, tus nlin pross minin tniqus. On t otr n, orniztions v prolms lin wit t omniprsn of vnt t. Most orniztions inos prolms s on fition (Powrpoint slis, Visio irms, t.) rtr tn fts (vnt t). Trfor, it is vitl to turn t mssiv mounts of vnt t into rlvnt knowl n insits. Evnt los n us to onut tr typs of pross minin: () isovry, () onformn, n () nnmnt [1]. T ol of isovry is to xtrt mols from rw vnt t in informtion systms (trnstion los, t ss, uit trils, t.). A isovry tniqu tks n vnt lo n prous mol witout usin ny -priori informtion. An xmpl is t α-loritm [3] tt tks n vnt lo n prous Ptri nt xplinin t vior ror in t lo. T son typ of pross minin is onformn. Hr, n xistin pross mol is ompr wit n vnt lo of t sm pross. Conformn kin n us to k wtr rlity, s ror in t lo, onforms to t mol n vi vrs. Tniqus s prsnt in [4] my us to tt, lot n xplin vitions, n to msur t svrity of ts vitions. T tir typ of pross minin is nnmnt. Hr, t i is to xtn or improv n xistin pross mol usin informtion out t tul pross ror in som vnt lo. Wrs onformn kin msurs t linmnt twn mol n rlity, tis tir typ of pross minin ims t nin or xtnin t -priori mol,.., in nw prsptiv to t pross mol y ross-orrltin it wit t lo. An xmpl is t xtnsion of pross mol wit prformn t. For instn, y ominin t timstmps in t vnt lo wit t isovr pross mol it is possil to sow ottlnks, srvi lvls, trouput tims, n frqunis. Pross minin is not rstrit to t ontrol-flow prsptiv n my inlu otr prsptivs su s t rsour/orniztionl imnsion, t tim/prformn imnsion, n t ojt/t imnsion. Howvr, in tis ppr w fous on t most llnin pross minin tsk: pross isovry. Altou tis tsk ily pns on t rprsnttionl is osn, lion s sr of ttntion is vot to possil minin loritms rtr tn sltin suitl trt rprsnttion. Tis ppr monstrts tt t rprsnttionl is plys ruil rol wn isovrin prosss. II. PROCESS DISCOVERY: A CHALLENGING PROBLEM In orr to xplin t rol of t rprsnttionl is in pross isovry, w strt off wit n xmpl. T xmpl

2 strt strt strt ristr ristr ristr xmin sully xmin sully xmin torouly xmin torouly xmin sully k tikt i k tikt f i k tikt rinitit i rinitit py ompnstion py ompnstion rjt rjt N 1 : fitnss = +, prision = +, nrliztion = +, simpliity = + rjt N 2 : fitnss = -, prision = +, nrliztion = -, simpliity = + N 3 : fitnss = +, prision = -, nrliztion = +, simpliity = + f n n n strt ristr ristr ristr ristr k tikt xmin sully k tikt xmin sully (ll xmin sully k tikt xmin sully k tikt ristr ristr ristr xmin torouly k tikt xmin torouly k tikt i i i i rjt rjt N 4 : fitnss = +, prision = +, nrliztion = -, simpliity = - 21 vrints sn in t lo) k tikt xmin torouly i i i py ompnstion py ompnstion py ompnstion rjt rjt n Fi. 1. Four ltrntiv pross mols for t sm lo is us to isuss qulity ritri n llns. A. Disovrin Pross Mols: An Exmpl Tl I sows n strtion of som vnt lo. T lo ontins informtion out 1391 ss (pross instns). E s orrspons to for ompnstion. W us sinl lttrs to sri tivitis,.., = ristr. 455 ss follow t pt,,,,, 191 ss follow t pt,,,,, t. T vnt lo ontins in totl 7539 vnts. Not tt Tl I only sows tivity nms. In rl-lif vnt los, vnts v timstmps, ssoit rsours (.. t prson xutin t tivity), trnstionl informtion (.., strt, omplt, or suspn), t ttriuts (.., mount or typ of ustomr). Sin w fous on ontrolflow isovry, w strt from su itionl informtion. Fiur 1 sows four mols tt oul isovr usin xistin pross minin tniqus. If w pply t α- loritm [3] to vnt lo L, w otin mol N 1 sown in Fi. 1. N 2 is mol tt only llows for ss vin tr,,,,, i.., only t most frqunt vior is ptur. N 3 sows vrint of t t so-ll flowr mol : ny tr is llow s lon s it strts wit n ns wit or. N 4 is t mol tt simply numrts t 21 iffrnt trs sn in t vnt lo. Fiur 1 illustrts tt iffrnt pross minin loritms my prou iffrnt rsults. E mol is rprsnt y workflow nt (WF-nt). WF-nts r sulss of Ptri nts tilor towrs t molin of usinss prosss. E WF-nt s sour pl (strt) n sink pl (n). Pross instns flow from strt to n. Intuitivly, mol TABLE I EVENT LOG L: = ristr, = xmin torouly, = xmin sully, = k tikt, = i, f = rinitit, = py ompnstion, AND = rjt frquny rfrn tr 455 σ 1,,,, 191 σ 2,,,, 177 σ 3,,,, 144 σ 4,,,, 111 σ 5,,,, 82 σ 6,,,, 56 σ 7,,,, 47 σ 8,,,, f,,,, 38 σ 9,,,, 33 σ 10,,,, f,,,, 14 σ 11,,,, f,,,, 11 σ 12,,,, f,,,, 9 σ 13,,,, f,,,, 8 σ 14,,,, f,,,, 5 σ 15,,,, f,,,, 3 σ 16,,,, f,,,, f,,,, 2 σ 17,,,, f,,,, 2 σ 18,,,, f,,,, f,,,, 1 σ 19,,,, f,,,, f,,,, 1 σ 20,,,, f,,,, f,,,, 1 σ 21,,,, f,,,, f,,,, f,,,, N 1 sown in Fi. 1 sms to ptur t vior sn in t vnt lo in Tl I wll. B. Qulity Critri for Pross Disovry Dtrminin t qulity of pross minin rsult is iffiult n is rtriz y mny imnsions. As isuss in [1], vnt los my inomplt n ontin nois. Nois rfrs to rr n infrqunt vior not rprsnttiv for t typil vior of t pross. Inompltnss rfrs to t

3 l to rply vnt lo fitnss nrliztion not ovrfittin t lo pross isovry Om s rzor simpliity prision not unrfittin t lo Fi. 2. Blnin t four qulity imnsions: fitnss, simpliity, prision, n nrliztion prolm tt on typilly ss only frtion of ll possil viors. Suppos tt on woul only v sn 1000 of t 1391 ss sown in Tl I; it woul likly tt som of t 21 trs woul not ppr in t vnt lo. Tis os not mn tt ts tr r impossil. Typilly, w only s positiv xmpls n no ntiv xmpls. Pross minin loritms n to l to l wit nois n inompltnss. Gnrlly, w us four min qulity imnsions for juin t qulity of t isovr pross mol: fitnss, simpliity, prision, n nrliztion. Fiur 2 ivs i-lvl rtriztion of ts four qulity imnsions. A mol wit oo fitnss llows for t vior sn in t vnt lo. A mol s prft fitnss if ll trs in t lo n rply y t mol from innin to n. Tr r vrious wys of finin fitnss [1]. It n fin t t s lvl,.., t frtion of trs in t lo tt n fully rply. It n lso fin t t vnt lvl,.., t frtion of vnts in t lo tt r in possil orin to t mol. WF-nts N 1, N 3, n N 4 v oo fitnss, i.., in of ts mols it is possil to rply ll of t 1391 ss sown in Tl I. WF-nt N 2 s poor fitnss (ot t t s n vnt lvl), us most of t ss/vnts nnot rply. T simpliity imnsion rfrs to Om s Rzor; t simplst mol tt n xplin t vior sn in t lo, is t st mol. T omplxity of t mol oul fin y t numr of nos n rs in t unrlyin rp. Also mor sopistit mtris n us,.., mtris tt tk t struturnss or ntropy of t mol into ount. Clrly, WF-nts N 1, N 2, n N 3 r simplr tn WF-nt N 4. Fitnss n simpliity lon r not qut. Tis is illustrt y WF-nt N 3. T flowr mol llows for ny squn strtin wit n nin wit or. T rsultin mol is simpl n s prft fitnss. Bs on t first two qulity imnsions tis mol is ptl. Tis sows tt t fitnss n simpliity ritri r nssry, ut not suffiint. If t flowr mol N 3 is on on n of t sptrum, tn t numrtin mol N 4 is on t otr n of t sptrum. T numrtin mol of lo simply lists ll t squns possil, i.., tr is sprt squntil pross frmnt for tr in t mol. At t strt tr is on i XOR split sltin on of t squns n t t n ts squns r join usin on i XOR join. Extrm mols su s t flowr mol (nytin is possil) n t numrtin mol (only t lo is possil) sow t n for two itionl imnsions. A mol is pris if it os not llow for too mu vior. Clrly, t flowr mol lks prision. A mol tt is not pris is unrfittin. Unrfittin is t prolm tt t mol ovr-nrlizs t xmpl vior in t lo, i.., t mol llows for viors vry iffrnt from wt ws sn in t lo. A mol soul nrliz n not rstrit vior to t xmpls sn in t lo (lik t numrtin mol N 4 ). A mol tt os not nrliz is ovrfittin. Ovrfittin is t prolm tt vry spifi mol is nrt wrs it is ovious tt t lo only ols xmpl vior, i.., t mol xplins t prtiulr smpl lo, ut nxt smpl lo of t sm pross my prou ompltly iffrnt pross mol. Bs on t four ritri it is ovious tt WF-nt N 1 is t st mol for t vnt lo in Tl I C. Wt Mks Pross Disovry Diffiult? Fiur 3 illustrts t prolm of lnin tr of t four qulity ritri: fitnss, prision, n nrliztion. (T fourt ritrion, simpliity, is not irtly rlt to t linmnt of trs n mol.) E lk ot rprsnts tr (i.., squn of tivitis) orrsponin to on or mor ss in t vnt lo. (Rll tt multipl ss my v t sm orrsponin tr.) An vnt lo typilly ontins only frtion of t possil vior, i.., t ots soul only sn s smpls of mu lrr st of possil viors. Morovr, on is typilly primrily intrst in frqunt vior n not in ll possil vior, i.., on wnts to strt from nois n trfor not ll ots n to rlvnt for t pross mol to onstrut. Rll tt w fin nois s infrqunt or xptionl vior. It is intrstin to nlyz su noisy viors, owvr, wn onstrutin t ovrll pross mol, t inlusion of infrqunt or xptionl vior ls to omplx irms. Morovr, it is typilly impossil to mk rlil sttmnts out noisy vior ivn t smll st of osrvtions. Fiur 3 istinuiss twn frqunt vior (soli rtnl wit roun ornrs) n ll vior (s rtnl), i.., norml n noisy vior. T iffrn twn norml n noisy vior is mttr of finition,.., norml vior oul fin s t 80% most frquntly ourrin trs. Lt us ssum tt t two rtnls wit roun ornrs n trmin y osrvin t pross infinitly lon wil t pross is in sty-stt (i.., no onpt rift). Bs on ts ssumptions, Fi. 3 skts four isovr mols pit y s rtnls. Ts isovr mols r s on t xmpl trs in t lo, i.., t lk ots. T il pross mol llows for t vior oiniin wit t frqunt vior sn wn t pross

4 frqunt vior tr in vnt lo ll vior (inluin nois) trt mol () τ strt p1 p2 n () non-fittin mol ovrfittin mol strt p1 p2 n () strt p1 p2 n unrfittin mol Fi. 4. Tr WF-nts for t vnt lo L 1 = [,, 20,, 30 ] Fi. 3. Ovrviw of t llns tt pross isovry tniqus n to rss woul osrv infinitum. T non-fittin mol in Fi. 3 is unl to rtriz t pross wll s it is not vn l to ptur t xmpls in t vnt lo us to lrn t mol. T ovrfittin mol os not nrliz n only sys somtin out t xmpls in t urrnt vnt lo. Nw xmpls will most likly not fit into tis mol. T unrfittin mol lks prision n llows for vior tt woul nvr sn if t pross woul osrv infinitum. Fiur 3 illustrts t llns pross isovry tniqus n to rss: How to xtrt simpl trt mol tt is not unrfittin, ovrfittin, nor non-fittin? III. REPRESENTATIONAL BIAS Fiur 1 sows four xmpl mols tt my isovr s on t vnt lo in Tl I. Not tt ts r only xmpls,.., t α-loritm will nrt WF-nt N 1. T α-loritm [3] ssums tt t unrlyin pross n qutly sri y WF-nt. Any isovry tniqu rquirs su rprsnttionl is. T notion of rprsnttionl is n (mtporilly) illustrt usin Fi. 3. If w ssum upfront tt t trt mol is irl or trinl wil t frqunt vior forms rtnl, tn it woul iffiult to fin suitl pross mol. Tis stion will sow tt tis rprsnttionl is is of ruil importn. Wrs most popl fous on unrstnility of t rprsnttion, w mpsiz t importn of t impliit sr sp impli y t rprsnttionl is. A. Exmpl: T Rprsnttionl Bis of t α-aloritm T α-loritm ssums tt t unrlyin pross n sri y WF-nt wr trnsition rs uniqu n visil ll. In su WF-nt it is not possil to v two trnsitions wit t sm ll or trnsitions wos ourrns rmin invisil (i.., it is not possil to v so-ll silnt trnsition τ). Ts ssumptions my sm rmlss, ut, s sown nxt, v notil fft on t lss of pross mols tt n isovr. Lt us onsir, for xmpl, vnt lo L 1 = [,, 20,, 30 ]. Fiur 4() sris t unrlyin pross wll: tivity n skipp y xutin t τ trnsition. (Not tt t τ trnsition orrspons to so-ll silnt stp of t pross, i.., it is not ror.) Fiur 4() sows n ltrntiv WF-nt usin two trnsitions n no τ trnsition. Ts two mols r tr quivlnt. Howvr, it is not possil to onstrut WF-nt witout uplit n τ lls tt is tr quivlnt to ts two mols. Fiur 4() sows t mol prou y t α-loritm; us of t rprsnttionl is, t loritm is stin to fil for tis lo. T WF-nt in Fi. 4() n only rprou tr,, n not,. Evnt los L 1 illustrts t fft rprsnttionl is n v. From t viwpoint of t α-loritm, t oi to not onsir uplit lls n τ trnsitions is snsil. τ trnsitions r not ror in t lo n n ny loritm will v prolms ronstrutin tir vior. Multipl trnsitions wit t sm ll r unistinuisl in t vnt lo. Trfor, ny loritm will v prolms ssoitin t orrsponin vnts to on of ts trnsitions. Fiur 5 sows notr xmpl illustrtin t fft rprsnttionl is n v. T WF-nt in Fi. 5() s so-ll non-fr-oi onstrut. T onpt of froi nts is wll-fin in t Ptri nt omin [5]. A Ptri nt is fr oi if ny two trnsitions srin n input pl v intil input sts. Trnsitions n sr n input

5 () () () Fi. 5. Two WF-nts n on BPMN mol for t vnt los L 2 = [,, 20,,, 30 ] n L 3 = [,, 20,,, 30,,, 1,,, 2 ] pl, ut v iffrnt input sts. For xmpl, pl p 1 is n input pl of, ut not of. Pls p 1 n p 2 ontrol t oi followin. Trfor, t WF-nt in Fi. 5() llows for only two possil trs:,, n,,. T WF-nt in Fi. 5() is fr-oi nt us t oi twn n is no lonr ontroll y p 1 n p 2. Now tr r four possil trs. For xmpl,,, is lso possil. Fi. 5() sows t orrsponin BPMN nottion. T BPMN nottion os not llow for t non-froi onstrut sown in t first WF-nt. Most pross minin loritms o not llow for non-fr-oi onstruts us of tir rprsnttionl is. Now onsir two vnt los: L 2 = [,, 20,,, 30 ] n L 3 = [,, 20,,, 30,,, 1,,, 2 ]. T WF-nt in Fi. 5() n t BPMN mol in Fi. 5() n rply ot los, i.., fitnss is oo wit rspt to L 2 n L 3. T WF-nt in Fi. 5() n rply L 2 ut not L 3. Howvr, t fitnss wit rspt to L 3 is rsonl s 50 out of 53 ss n rply. On oul ru tt t WF-nt in Fi. 5() n t BPMN mol in Fi. 5() r unrfittin ot los. In ft, for L 2, t non-fr-oi WF-nt in Fi. 5() is lrly t st mol. Howvr, mny pross molin lnus r inrntly fr-oi, tus mkin it impossil to isovr p 1 n p 2. T non-fr-oi onstrut is just on of mny onstruts tt xistin pross minin loritms v prolms wit. Otr xmpls r ritrry nst loops, nltion, unln splits n joins, n prtil synroniztion. In tis ontxt it is importnt to osrv tt pross isovry is, y finition, rstrit y t xprssiv powr of t trt lnu, i.., t rprsnttionl is. B. Typil rprsnttionl limittions T wll-know workflow pttrns [6], [7] srv s oo sis for isussin t limittions impos y t rprsnttionl is of pross minin loritm. T Workflow p 1 p 2 Pttrns Inititiv ws stlis wit t im of lintin t funmntl rquirmnts tt ris urin usinss pross molin on rurrin sis n sri tm in n imprtiv wy. T pttrns vlop in tis ontxt lp to isuss n intify t rprsnttionl is of lnu. Hr, w o not isuss t mor tn 40 ontrol-flow pttrns [7]. Inst, w mntion som typil rprsnttionl limittions impos y pross isovry loritms: Inility to rprsnt onurrny. Low-lvl mols, su s Mrkov mols, flow rts, n trnsition systms, o not llow for t molin of onurrny otr tn numrtin ll possil intrlvins. To mol pross wit 10 prlll tivitis, low-lvl mol will n to numrt ll 2 10 = 1024 stts n = 5120 trnsitions. Hir lvl mols (lik Ptri nts n BPMN) only n to pit 10 tivitis n 2 10 = 20 lol stts (stts for n ftr tivity). Inility to rprsnt silnt tions. In som nottions, it is impossil to mol silnt tions lik t skippin of n tivity. Altou su vnts r not xpliitly ror in t vnt lo, ty n to rflt in t mol (s illustrt y Fi. 4). Inility to rprsnt uplit tions. In mny nottions tr nnot two tivitis vin t sm ll. If t sm tivity pprs in iffrnt prts of t pross, ut ts iffrnt instns of t sm tivity nnot istinuis in t vnt lo, tn most loritms will ssum sinl tivity tus rtin usl pnnis (.., non-xistin loops) tt o not xist in t tul pross. Inility to mol OR-splits/joins. Hir lvl nottions su s YAWL, BPMN, EPCs, usl nts, t. llow for t molin of OR-splits n OR-joins. If t rprsnttionl is of isovry loritm os not llow for OR-splits n OR-joins, tn t isovr mol my mor omplx or t loritm is unl to fin suitl mol. Inility to rprsnt non-fr-oi vior. Most loritms o not llow for non-fr-oi onstruts, i.., onstruts wr onurrny n oi mt. Nonfr-oi onstruts n us to rprsnt non-lol pnnis s is illustrt y t WF-nt in Fi. 5(). Mny nottions o not llow for su onstruts. Inility to rprsnt irry. Most pross isovry loritms work on flt mols. A notl xption is t Fuzzy Minr [8] tt xtrts irril mols. Ativitis tt v lowr frquny ut tt r losly rlt to otr low frqunt tivitis r roup into suprosss. T rprsnttionl is trmins wtr, in prinipl, irril mols n isovr or not. C. Improvin t Rprsnttionl Bis T rprsnttionl is lps limitin t sr sp of possil nit mols. Tis n mk isovry lo-

6 ritms mor ffiint. Morovr, it n lso us to iv prfrn to prtiulr typs of mols. It sms tt xistin ppros n nfit from sltin mor suitl rprsnttionl is. Most pross isovry loritms llow for mols tt v ll kins of ovious prolms,.., loks, livloks, inility to trmint, impropr trmintion, n tivitis. T sounnss proprty [9] fin for WF-nts n otr nottions is omin-inpnnt rquirmnt. It is sirl to v rprsnttionl is tt limits t sr sp to only soun mols (i.., fr of loks n otr nomlis). Unfortuntly, tis is not t s for most of t xistin ppros. For instn, t α-loritm my yil mols tt v loks or livloks. Gnti pross minin loritms tn ontinuously xplor nits [1]. Trfor, on woul lik to v rprsnttionl is nforin sounnss. Unfortuntly, urrntly, tis n typilly only iv y svrly limitin t xprssivnss of t molin lnu or y usin mor tim-onsumin nlysis tniqus. Consir, for xmpl, t so-ll lokstrutur pross mols. A mol is lok-strutur if it stisfis numr of synttil rquirmnts su tt sounnss is urnt y ts rquirmnts. S [10] [12] for pointrs to vrious finitions. Most of ts finitions rquir on-to-on orrsponn twn splits n joins,.., onurrnt pts rt y n AND-split n to synroniz y t orrsponin AND-join. Sin mny rl-lif prosss r not lok strutur, on soul rful to not limit t xprssivnss too mu. Not tt tniqus tt turn unstrutur mols into lok-strutur pross mols tn to introu mny uplit or silnt tivitis. Trfor, su trnsformtions o not llvit t or prolms. Sounnss is iffiult to inorport us it is rlt to vior rtr tn strutur. Struturl rquirmnts n inorport mor sily. As n xmpl, w rfr to rion-s pross minin tniqus [13] [16]. Stt-s rions n us to onstrut Ptri nt from trnsition systm [14]. T trnsition systm n xtrt from n vnt lo usin iffrnt strtion mnisms (s [13] for n ovrviw). Lnu-s rions n us to onstrut Ptri nt from prfix-los lnu. Syntsis ppros usin lnu-s rions n ppli irtly to vnt los [15], [16]. In [14] it is sown ow itionl rquirmnts n impos on t Ptri nt onstrut s on t trnsition systm. For xmpl, on n mk sur tt t rsultin mol is fr-oi or witout slf-loops. T tniqu sri in [14] uss ll-splittin n in [13] it is sown ow tis n us in t ontxt of pross minin. As sown in [16], similr rquirmnts n impos on t rsultin mols wn usin lnu-s rions. T rprsnttionl is n moifi to nfor rtin struturl proprtis, su s mrk rps, stt mins, pur nts, lmntry nts, n fr-oi nts. Morovr, propr trmintion n otr sirl proprtis n no in t ILP formultion of t prolm [16]. IV. CONCLUSION In tis ppr, w mpsiz t importn of sltin t rit rprsnttionl is wn isovrin pross mols from vnt los. T rprsnttionl is soul s on ssntil proprtis of pross mol (.., sounnss [9]), n not rivn y t sir rpil prsnttion. Improvin t rprsnttionl is will improv ot t qulity of t rsults n t ffiiny of t loritms. ACKNOWLEDGMENT T utor woul lik to tnk t mmrs of t IEEE Tsk For on Pross Minin (www.win.tu.nl/itfpm/) n ll tt ontriut to t vlopmnt of ProM (www. prossminin.or). REFERENCES [1] W. vn r Alst, Pross Minin: Disovry, Conformn n Ennmnt of Businss Prosss. Sprinr-Vrl, Brlin, [2] M. Hilrt n P. Lopz, T Worl s Tnoloil Cpity to Stor, Communit, n Comput Informtion, Sin, [3] W. vn r Alst, A. Wijtrs, n L. Mrustr, Workflow Minin: Disovrin Pross Mols from Evnt Los, IEEE Trnstions on Knowl n Dt Eninrin, vol. 16, no. 9, pp , [4] A. Rozint n W. vn r Alst, Conformn Ckin of Prosss Bs on Monitorin Rl Bvior, Informtion Systms, vol. 33, no. 1, pp , [5] J. Dsl n J. Esprz, Fr Coi Ptri Nts, Cmri Trts in Tortil Computr Sin. Cmri Univrsity Prss, Cmri, UK, 1995, vol. 40. [6] W. vn r Alst, A. tr Hofst, B. Kipuszwski, n A. Brros, Workflow Pttrns, Distriut n Prlll Dtss, vol. 14, no. 1, pp. 5 51, [7] Workflow Pttrns Hom P, ttp://www.workflowpttrns.om. [8] C. Güntr n W. vn r Alst, Fuzzy Minin: Aptiv Pross Simplifition Bs on Multi-prsptiv Mtris, in Intrntionl Confrn on Businss Pross Mnmnt (BPM 2007), Ltur Nots in Computr Sin, G. Alonso, P. Dm, n M. Rosmnn, Es., vol Sprinr-Vrl, Brlin, 2007, pp [9] W. vn r Alst, K. vn H, A. tr Hofst, N. Siorov, H. Vrk, M. Voorov, n M. Wynn, Sounnss of Workflow Nts: Clssifition, Diility, n Anlysis, Forml Aspts of Computin, 2011, x.oi.or/ /s [10] M. Dums, W. vn r Alst, n A. tr Hofst, Pross-Awr Informtion Systms: Briin Popl n Softwr trou Pross Tnoloy. Wily & Sons, [11] A. tr Hofst, W. vn r Alst, M. Ams, n N. Russll, Morn Businss Pross Automtion: YAWL n its Support Environmnt. Sprinr-Vrl, Brlin, [12] M. Wsk, Businss Pross Mnmnt: Conpts, Lnus, Aritturs. Sprinr-Vrl, Brlin, [13] W. vn r Alst, V. Ruin, H. Vrk, B. vn Donn, E. Kinlr, n C. Güntr, Pross Minin: A Two-Stp Appro to Bln Btwn Unrfittin n Ovrfittin, Softwr n Systms Molin, vol. 9, no. 1, pp , [14] J. Cortll, M. Kisinvsky, L. Lvno, n A. Ykovlv, Drivin Ptri Nts from Finit Trnsition Systms, IEEE Trnstions on Computrs, vol. 47, no. 8, pp , Au [15] R. Brntum, J. Dsl, R. Lornz, n S. Musr, Pross Minin Bs on Rions of Lnus, in Intrntionl Confrn on Businss Pross Mnmnt (BPM 2007), Ltur Nots in Computr Sin, G. Alonso, P. Dm, n M. Rosmnn, Es., vol Sprinr-Vrl, Brlin, 2007, pp [16] J. vn r Wrf, B. vn Donn, C. Hurkns, n A. Srrnik, Pross Disovry usin Intr Linr Prormmin, Funmnt Informti, vol. 94, pp , 2010.

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