Pross Disovry prof.r.ir. Wil vn r Alst www.prossmining.org
Positioning Pross Mining prformn-orint qustions, prolms n solutions pross mol nlysis (simultion, vrifition, t.) pross mining t-orint nlysis (t mining, mhin lrning, usinss intllign) omplin-orint qustions, prolms n solutions 1
www.olifntnpjs.nl PAGE 2
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Ovrviw worl usinss prosss popl mhins omponnts orgniztions mols nlyzs supports/ ontrols spifis onfigurs implmnts nlyzs softwr systm rors vnts,.g., mssgs, trnstions, t. (pross) mol isovry onformn nhnmnt vnt logs PAGE 4
Hunrs of plug-ins vill ovring th whol pross mining sptrum opn-sour (L-GPL) Downlo from: www.prossmining.org PAGE 5
Commril Altrntivs Diso (Fluxion) Prptiv Pross Mining (for Futur Rflt n BPM on) ARIS Pross Prformn Mngr QPR ProssAnlyzr Intrstg Pross Disovry (Fujitsu) Disovry Anlyst (StroLOGIC) XMAnlyzr (XMPro) 6
Pross Disovry PAGE 7
Pross Disovry (smll sltion) utomt-s lrning huristi mining istriut gnti mining lngug-s rgions gnti mining stohsti tsk grphs stt-s rgions LTL mining nurl ntworks fuzzy mining mining lok struturs hin Mrkov mols α lgorithm α# lgorithm onforml pross grph multi-phs mining prtil-orr s mining α++ lgorithm ILP mining PAGE 8
Typil Rprsnttionl Bis (Ll) Ptri Nts, WFnts, t. Susts of BPMN igrms, UML Ativity Digrms, Evnt-Drivn Pross Chins (EPCs), YAWL, Stthrts? t. Trnsition Systms (Hin) Mrkov Mols PAGE 9 [strt] rgistr rqust strt strt strt rgistr rqust [1,2] rgistr rqust xmin thoroughly xmin sully hk tikt rgistr rqust XOR [2,3] [1,4] OR AND hk tikt 1 rinitit rqust xmin sully xmin thoroughly [5] 2 1 2 3 i [3,4] xmin thoroughly xmin sully hk tikt py ompnstion xmin thoroughly rjt rqust xmin sully hk tikt xmin thoroughly xmin sully hk tikt [n] 3 4 rinitit rqust OR AND strt rgistr rqust i f i rinitit rqust 4 i XOR 1 2 5 OR-split 5 6 xmin thoroughly xmin sully py ompnstion py ompnstion rjt rqust py ompnstion hk tikt OR-join rjt rqust i nw informtion 3 g h rjt rqust n py ompnstion rjt rqust n n n n
Altrntiv Rprsnttionl Bis 1. C-nts (XOR/AND/ORsplit/join grphs; mor likly to soun u to lrtiv smntis). 2. Dlr mols (onstrint s, groun in LTL; nything is possil unlss forin) 3. Pross Trs (similr to susts of vrious pross lgrs; soun y strutur) rgistr rqust toy's fous xmin thoroughly xmin sully hk tikt f rinitit rqust i rgistr rqust g py ompnstion h rjt rqust z n py ompnstion g h rjt rqust i PAGE 10
Ptri nt/rgion-s Viw PAGE 11
Ptri nt viw: Just isovr th pls Aing pl limits hvior: ovrfitting ing too mny pls unrfitting ing too fw pls 1 1 2... 2 p (A,B)... m n A={ 1, 2, m } B={ 1, 2, n } PAGE 12
Th Ptri nt low n rply ny tr ovr {,,,,} 1. 1. 1. 2. 2. 2. 3. 3. 3. 4. 4. 4. 5. 5. 5. 6. 6. 7. 6. 7. 8. 8. PAGE 13
Pl limits hvior 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. PAGE 14
Exmpl: Pross Disovry Using Stt-Bs Rgions 01011001101101001 01111110110100011 01100111101110000 01101101001001100 vnt log [ ] [] [,] [,] [,,] [,] [,,] [,,,] p1 p3 strt n p2 p4 PAGE 15
Exmpl of Stt-Bs Rgion [,] [,] [,,] [ ] [] [,] [,,] [,,,] ntr:, lv: o-not-ross:, p1 p3 strt n p2 p4 PAGE 16
Exmpl: Pross Disovry Using Lngug-Bs Rgions f 1 A pl is fsil if it n without isling ny of th trs in th vnt log. 1 1 2 p R 2 X Y PAGE 17
Exmpl of Lngug-Bs Rgions 1. 2. 3. : 0 + 0-0 0 : 0 + 1-1 0 4. 5. 6. : 0 + 2-2 0 : 0 + 3-3 0 7. : 0 + 0-0 0 X Y : 0 + 1-1 0 : 0 + 1-2 < 0 PAGE 18
Crting Trnsition Systm PAGE 19
Lrning Trnsition Systm urrnt stt tr: f g h h h i pst futur pst n futur pst, futur, pst+futur squn, multist, st strtion limit horizon to strt furthr filtring.g. s on trnstion typ, nms, t. lls s on tivity nm or othr fturs PAGE 20
Pst Without Astrtion (Full Squn) Somtims ll th "prfix utomton",,,,,,,,,,,,,,, PAGE 21
Futur Without Astrtion,,,,,,,,,,,,,,, PAGE 22
Pst with Multist Astrtion [,] [,] [,,] [ ] [] [,] [,,] [,,,] PAGE 23
Only Lst Evnt Mttrs For Stt PAGE 24
Using ProM PAGE 25
Inspt Evnt Log PAGE 26
Inspt Trs PAGE 27
Run Plugin PAGE 28
Slt (sroll or y nm) PAGE 29
Strt Plugin "Min Trnsition Systm" PAGE 30
Strt Winow pst futur ttriuts PAGE 31
Astrtion list, multist, or st ll, or only lst k vnts PAGE 32
Whih vnts to filtr? PAGE 33
Whih lls n to visil? PAGE 34
Any rpir tions? x rmov slf loops improv imon strutur mrg stts with intil inflow PAGE 35
Chk onfigurtion PAGE 36
Rsulting trnsition systm,,,,,,,,,,,,,,, PAGE 37
Convrt trnsition systm to Ptri nt PAGE 38
Rsulting Ptri nt B A p1 E p3 D strt n p2 C p4 PAGE 39
Summry 01011001101101001 01111110110100011 01100111101110000 01101101001001100 vnt log [ ] [] [,] [,] [,,] [,] [,,] [,,,] p1 p3 strt n p2 p4 PAGE 40
Stt-Bs Rgions PAGE 41
Wht is (stt-s) rgion? f = ntr = ntr = xit = xit = o not ross f = o not ross f R f p R PAGE 42
Strting point: A Trnsition Systm s1 s2 W ssum tht thr is only on initil stt (othrwis prprossing n). s3 s6 s4 s7 s9 s5 s8 It is onvnint to lso hv just on finl stt tht n lwys rh (not stritly nssry) s10 All stts n to rhl! PAGE 43
Dfinition A rgion r is st of stts, suh tht for ll trnsitions (s 0,, s 0 ), (s 1,, s 1 ) in th trnsition systm hols tht: 1) s 0 r n s 0 r implis tht s 1 r n s 1 r 2) s 0 r n s 0 r implis tht s 1 r n s 1 r In wors: A rgion is st of stts, suh tht, if trnsition xits th rgion, thn ll qully ll trnsitions xit th rgion, n if trnsition ntrs th rgion, thn ll qully ll trnsitions ntr th rgion. All vnts not ntring or xiting th rgion o not ross th rgion. PAGE 44
Exmpl of rgion s1 ntrs xits s3 s2 s4 s5 os not ross os not ross os not ross s6 s7 s8 s9 s10 PAGE 45
Exmpl of rgion s1 os not ross ntrs s3 s2 s4 s5 os not ross os not ross xits s6 s7 s8 s9 s10 PAGE 46
Exmpl of rgion s1 xits os not ross s3 s2 s4 s5 os not ross os not ross os not ross s6 s7 s8 s9 s10 Pls orrsponing to rgions ontining th initil stt r initilly mrk. PAGE 47
Exmpl of rgion s1 ntrs os not ross s3 s2 s4 s5 os not ross xits os not ross s6 s7 s8 s9 s10 PAGE 48
Not rgion s1 ntrs s3 s6 s2 s4 s7 s9 s5 s8 os not ross n xits os not ross n xits os not ross n xits os not ross s10 PAGE 49
Not rgion s1 os not ross s3 s6 s2 s4 s7 s9 s5 s8 os not ross n xits os not ross n xits os not ross n xits os not ross s10 PAGE 50
Multipl rgions PAGE 51 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 Et.
Sltivly hosn rgions PAGE 52 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 p1 p2 p3 p4 p5 p6 p7 p8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8
Rgions Rgion Proprtis Lt S th st of ll stts of trnsition systm. Trivil Rgions: Both S n r ll th trivil rgions, Complmnts: If r is rgion, thn S\ r is rgion, Pr-/Post-rgions: If vnt xits (ntrs) rgion r, thn r is pr- (post-)rgion of, Miniml rgions: If r 0 n r 1 r rgions, n r 0 is sust of r 1, thn r 1 \ r 0 is rgion. Th lttr implis th xistn of (non-trivil) miniml rgions. PAGE 53
Trivil rgions PAGE 54 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8,,,, o not ross
Complmnt: If r is rgion, thn S\ r is rgion s1 s1 s2 s2 s3 s4 s5 s3 s4 s5 s6 s7 s9 s10 s8 "xits" n "ntrs" r swpp s6 s7 s9 s10 s8 PAGE 55
If r 0 n r 1 r rgions, n r 0 is sust of r 1, thn r 1 \ r 0 is rgion. s1 s1 s1 s2 s2 s2 s3 s4 s5 s3 s4 s5 s3 s4 s5 s6 s7 s8 s6 s7 s8 s6 s7 s8 s9 s9 s9 s10 s10 s10 PAGE 56
Not miniml yt PAGE 57 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8 s1 s10 s2 s4 s3 s5 s6 s9 s7 s8
Pr n post rgions - If vnt ntrs rgion r, thn r is post-rgion of. - r is post-rgion of - r is post-rgion of f g h h r - If vnt xits rgion r, thn r is pr-rgion of. - r is pr-rgion of - r is pr-rgion of pr() is th st of ll (miniml) pr-rgions or. pr() is th st of ll (miniml) pr-rgions or. Both r sts of sts!
Bsi lgorithm to onstrut Ptri nt For h vnt in th trnsition systm, trnsition is gnrt in th Ptri nt. Comput th miniml non-trivil rgions. For h miniml non-trivil in th trnsition systm, pl is gnrt in th Ptri nt. A orrsponing rs (post-rgions r output pls n pr-rgions r input pls). A tokn is to h pl tht orrspons to rgion ontining th initil stt. Th rsulting Ptri nt is ll th miniml sturt nt. PAGE 59
Lo Ptri nt with 10 prlll tivitis PAGE 60
Construt rhility grph PAGE 61
Rhility grph (1+2 10 +1 =1026 stts) PAGE 62
Apply stt-s rgions to fol stt sp PAGE 63
Disovr Ptri nt Ptri nt is risovr! O xmpl, normlly th trnsition systm is onstrut from n vnt log. PAGE 64
40.825 stts, 221.618 trnsitions 26 trnsitions, 28 pls, 1 tokn
It is not tht simpl (ut ll prolms n rpir) PAGE 67
Consir n vnt log ontining just <,> trs prfix utomton s1 s2 s3 Only trivil rgions: n {s1,s2,s3} Ptri nt Also llows for: PAGE 68
Consir n vnt log ontining trs <,>, <,,>, <,,,>,<,,,,>, trnsition systm l to gnrt log s1 s2 s3 Rgions: {s1} ( xits, n o not ross) {s2} ( ntrs, os not ross, xits) {s3} ( n os not ross, ntrs) Ptri nt Also llows for: {s1} {s2} {s3} PAGE 69
Consir n vnt log ontining trs <,>, <> trnsition systm l to gnrt log s1 s1 s2 s3 s2 s3 s4 s4 Rgions: {s1,s2} ( os not ross, xits) {s3,s4} ( os not ross, ntrs) {s1,s3} ( xits n os not ross) {s2,s4} ( ntrs n os not ross) s2 s1 s4 s3 PAGE 70
Ptri nt s2 s1 s3 {s1,s3} {s1,s2} s4 s1 s2 s3 {s2,s4} {s3,s4} s4 Also llows for tr <,>! PAGE 71
All unrfitting, ut fsil s1 s2 s3 s1 s2 s3 {s1} {s2} {s3} s1 {s1,s3} {s1,s2} s2 s3 s4 {s2,s4} {s3,s4} PAGE 72
Using ProM (uss ll splitting to solv prolm) s1 s2 s3 two "" trnsitions PAGE 73
Using ProM (rsss slf-loop prolm) s1 s2 s3 PAGE 74
Using ProM (uss ll splitting to solv prolm) s1 s2 s3 s4 two "" trnsitions PAGE 75
At th othr n of th sptrum PAGE 76
A ompltly iffrnt xmpl of pross isovry thniqu: Gnti Mining rquirs lot of omputing powr, ut n istriut sily, n l with nois, infrqunt hvior, uplit tsks, invisil tsks, llows for inrmntl improvmnt n omintions with othr pprohs (huristis post-optimiztion, t.). PAGE 77
Gnti pross mining: Ovrviw rt initil popultion vnt log muttion trmintion omput fitnss tournmnt nxt gnrtion litism hilrn rossovr slt st iniviul prnts iniviuls PAGE 78
Exmpl: rossovr PAGE 79 strt rgistr rqust xmin thoroughly xmin sully hk tikt i py ompnstion rjt rqust rinitit rqust g h f n strt rgistr rqust xmin thoroughly xmin sully hk tikt i py ompnstion rjt rqust rinitit rqust g h f n strt rgistr rqust xmin thoroughly xmin sully hk tikt i rinitit rqust f strt rgistr rqust xmin thoroughly xmin sully hk tikt i py ompnstion rjt rqust rinitit rqust g h f n py ompnstion rjt rqust g h n
Exmpl: muttion rmov pl xmin thoroughly g xmin thoroughly g strt rgistr rqust xmin sully hk tikt i f rinitit rqust py ompnstion h rjt rqust n strt rgistr rqust r xmin sully hk tikt i f rinitit rqust py ompnstion h rjt rqust n PAGE 80
Link twn pross isovry n onformn hking rt initil popultion vnt log muttion trmintion omput fitnss tournmnt nxt gnrtion litism hilrn rossovr slt st iniviul prnts iniviuls PAGE 81
How goo is my mol? PAGE 82
Four Compting Qulity Critri l to rply vnt log fitnss Om s rzor simpliity pross isovry gnrliztion not ovrfitting th log prision not unrfitting th log PAGE 83
Exmpl: on log four mols strt rgistr rqust xmin thoroughly xmin sully hk tikt i f rinitit rqust g py ompnstion h rjt rqust N 1 : fitnss = +, prision = +, gnrliztion = +, simpliity = + n # tr 455 h 191 g 177 h 144 h l to rply vnt log fitnss pross isovry Om s rzor simpliity strt strt rgistr rqust rgistr rqust xmin sully xmin sully xmin thoroughly i hk tikt f hk tikt i rinitit rqust py ompnstion rjt rqust rjt rqust N 2 : fitnss = -, prision = +, gnrliztion = -, simpliity = + N 3 : fitnss = +, prision = -, gnrliztion = +, simpliity = + g h h n n 111 g 82 g 56 h 47 fh 38 g 33 fh 14 fg 11 fg 9 fh 8 fh gnrliztion not ovrfitting th log prision not unrfitting th log strt rgistr rqust rgistr rqust rgistr rqust rgistr rqust hk tikt xmin sully hk tikt xmin sully (ll xmin sully hk tikt xmin sully hk tikt i i i i 21 vrints sn in th log) g py ompnstion g py ompnstion h rjt rqust h rjt rqust n 5 fg 3 ffg 2 fg 2 ffg 1 ffh 1 ffg 1 fffg 1391 rgistr rqust xmin thoroughly hk tikt i g py ompnstion rgistr rqust hk tikt xmin thoroughly i h rjt rqust rgistr rqust xmin thoroughly hk tikt i rjt rqust N 4 : fitnss = +, prision = +, gnrliztion = -, simpliity = - h PAGE 84
strt Mol N 1 rgistr rqust xmin thoroughly xmin sully hk tikt i rinitit rqust py ompnstion rjt rqust N 1 : fitnss = +, prision = +, gnrliztion = +, simpliity = + f g h n # tr 455 h 191 g 177 h 144 h 111 g 82 g 56 h 47 fh 38 g 33 fh 14 fg 11 fg 9 fh 8 fh 5 fg 3 ffg 2 fg 2 ffg 1 ffh 1 ffg 1 fffg 1391 PAGE 85
strt Mol N 2 rgistr rqust xmin sully hk tikt i rjt rqust N 2 : fitnss = -, prision = +, gnrliztion = -, simpliity = + h n # tr 455 h 191 g 177 h 144 h 111 g 82 g 56 h 47 fh 38 g 33 fh 14 fg 11 fg 9 fh 8 fh 5 fg 3 ffg 2 fg 2 ffg 1 ffh 1 ffg 1 fffg 1391 PAGE 86
strt Mol N 3 rgistr rqust xmin sully xmin thoroughly i hk tikt rinitit rqust py ompnstion rjt rqust N 3 : fitnss = +, prision = -, gnrliztion = +, simpliity = + f g h n # tr 455 h 191 g 177 h 144 h 111 g 82 g 56 h 47 fh 38 g 33 fh 14 fg 11 fg 9 fh 8 fh 5 fg 3 ffg 2 fg 2 ffg 1 ffh 1 ffg 1 fffg 1391 PAGE 87
Mol N 4 strt rgistr rqust rgistr rqust rgistr rqust rgistr rqust hk tikt xmin sully hk tikt xmin sully (ll xmin sully hk tikt xmin sully hk tikt rgistr rqust rgistr rqust rgistr rqust xmin thoroughly hk tikt xmin thoroughly hk tikt i i i i rjt rqust h rjt rqust N 4 : fitnss = +, prision = +, gnrliztion = -, simpliity = - 21 vrints sn in th log) hk tikt xmin thoroughly i i i g py ompnstion g py ompnstion h g py ompnstion h rjt rqust h rjt rqust n # tr 455 h 191 g 177 h 144 h 111 g 82 g 56 h 47 fh 38 g 33 fh 14 fg 11 fg 9 fh 8 fh 5 fg 3 ffg 2 fg 2 ffg 1 ffh 1 ffg 1 fffg 1391 PAGE 88
Conlusion Still mny hllnging n highly rlvnt opn prolms in pross isovry! prformn-orint qustions, prolms n solutions pross mol nlysis (simultion, vrifition, t.) pross mining t-orint nlysis (t mining, mhin lrning, usinss intllign) omplin-orint qustions, prolms n solutions PAGE 89