Process Mining: The α Algorithm. prof.dr.ir. Wil van der Aalst

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1 Proess Mining: The α Algorithm prof.dr.ir. Wil vn der Alst

2 Design-time nlysis vs run-time nlysis vlidtion world usiness proesses people servies omponents orgniztions models nlyzes supports/ ontrols speifies onfigures implements nlyzes (softwre) system reords events, e.g., messges, trnstions, et. e.g., systems like WeSphere, Orle, TIBCO/ Stffwre, SAP, FLOWer, et. verifition disovery performne nlysis (proess) model onformne extension event logs design-time nlysis e.g. proess models represented in BPMN, BPEL, EPCs, Petri nets, UML AD, et. or other types of models suh s soil networks, orgniztionl networks, deision trees, et. run-time nlysis e.g., dedited formts suh s IBM s Common Event Infrstruture (CEI) nd MXML or proprietry formts stored in flt files or dtse tles. PAGE 1

3 Relevnt mteril 1. Jörg Desel, Wolfgng Reisig: Ple/Trnsition Petri Nets. Petri Nets 1996: DOI: / _ Tdo Murt, Petri Nets: Properties, Anlysis nd Applitions, Proeedings of the IEEE. 77(4): , April, Wil vn der Alst: Proess Mining: Disovery, Conformne nd Enhnement of Business Proesses, Springer Verlg 2011 (hpters 1 & 5) ) Chpter 1: DOI: / _1 ) Chpter 5: DOI: / _5 ) Events logs: Tody's fous is on 3. PAGE 2

4 PAGE 3

5 Proess Disovery

6 Proess disovery world usiness proesses people mhines omponents orgniztions models nlyzes supports/ ontrols speifies onfigures implements nlyzes softwre system reords events, e.g., messges, trnstions, et. (proess) model disovery onformne enhnement event logs PAGE 5

7 Proess disovery = Ply-In Ply-In event log proess model Ply-Out proess model event log Reply event log proess model extended model showing times, frequenies, et. dignostis preditions reommendtions PAGE 6

8 Exmple p1 e p3 d strt end p2 p4 Event log ontins ll possile tres of model nd vie vers. PAGE 7

9 Another exmple p1 p3 f e d strt p5 end p2 p4 Generliztion: event log ontins only suset of ll possile tres of model. PAGE 8

10 Nottion is less relevnt (e.g. BPMN) strt p1 e p3 d end p2 p4 d strt e end PAGE 9

11 Another BPMN exmple p1 p3 strt f p5 e d end p2 p4 d strt end f e PAGE 10

12 Chllenge In generl, there is trde-off etween the following four qulity riteri: 1.Fitness: the disovered model should llow for the ehvior seen in the event log. 2.Preision (void underfitting): the disovered model should not llow for ehvior ompletely unrelted to wht ws seen in the event log. 3.Generliztion (void overfitting): the disovered model should generlize the exmple ehvior seen in the event log. 4.Simpliity: the disovered model should e s simple s possile. PAGE 11

13 α Algorithm

14 Proess Disovery: exmple of lgorithm α PAGE 13

15 >,,,# reltions Diret suession: x>y iff for some se x is diretly followed y y. Cuslity: x y iff x>y nd not y>x. Prllel: x y iff x>y nd y>x Choie: x#y iff not x>y nd not y>x. > > >e > >d > >d e>d e d d e d d d ed #e e# #e #d PAGE 14

16 Bsi Ide Used y α Algorithm (1) () sequene pttern: PAGE 15

17 Bsi Ide Used y α Algorithm (2) () XOR-join pttern:,, nd # () XOR-split pttern:,, nd # () XOR-split pttern:,, nd # PAGE 16

18 Bsi Ide Used y α Algorithm (3) (e) AND-join pttern:,, nd (d) AND-split pttern:,, nd (d) AND-split pttern:,, nd PAGE 17

19 Exmple Revisited > > >e > >d > >d e>d e d d e d #e e# #e #d p1 e p3 d strt end p2 p4 Result produed y α lgorithm PAGE 18

20 Footprint of L 1 p1 e p3 d strt end p2 p4 PAGE 19

21 Footprint of L 2 p1 p3 f e d strt p5 end p2 p4 PAGE 20

22 Simple ptterns () sequene pttern: () XOR-split pttern:,, nd # () XOR-join pttern:,, nd # (d) AND-split pttern:,, nd (e) AND-join pttern:,, nd PAGE 21

23 Algorithm Let L e n event log over T. α(l) is defined s follows. 1. T L = { t T σ L t σ}, 2. T I = { t T σ L t = first(σ) }, 3. T O = { t T σ L t = lst(σ) }, 4. X L = { (A,B) A T L A ø B T L B ø A B L 1,2 A 1 # L 2 1,2 B 1 # L 2 }, 5. Y L = { (A,B) X L (A,B ) XL A A B B (A,B) = (A,B ) }, 6. P L = { p (A,B) (A,B) Y L } {i L,o L }, 7. F L = { (,p (A,B) ) (A,B) Y L A } { (p (A,B),) (A,B) Y L B } { (i L,t) t T I } { (t,o L ) t T O }, nd 8. α(l) = (P L,T L,F L ). PAGE 22

24 Key ide: find ples p (A,B)... m n A={ 1, 2, m } B={ 1, 2, n } 4. X L = { (A,B) A T L A ø B T L B ø A B L 1,2 A 1 # L 2 1,2 B 1 # L 2 }, 5. Y L = { (A,B) X L (A,B ) XL A A B B (A,B) = (A,B ) }, PAGE 23

25 Ples s footprints p (A,B)... m n A={ 1, 2, m } B={ 1, 2, n } PAGE 24

26 p1 e p3 d strt end p2 p4 PAGE 25

27 Another event log L 3 PAGE 26

28 Model for L 3 f p ({},{}) p ({},{e}) e g i L p ({,f},{}) d p ({e},{f,g}) o L p ({},{d}) p ({d},{e}) PAGE 27

29 Another event log L 4 d i L p ({,},{}) p ({},{d,e}) e o L PAGE 28

30 Event log L 5 PAGE 29

31 PAGE 30

32 Disovered model d p ({},{d}) i L p ({,d},{}) p ({},{,f}) f o L e p ({},{e}) p ({e},{f}) PAGE 31

33 Limittions of the α Algorithm

34 Limittion of α lgorithm (impliit ples) d e f p 1 p 2 g Green ples re impliit! PAGE 33

35 Limittion of α lgorithm (loops of length 1) PAGE 34

36 Limittion of α lgorithm (loops of length 2) d d PAGE 35

37 Limittion of α lgorithm (non-lol dependenies) p 1 d p 2 e Green ples re not disovered! PAGE 36

38 Diffiult onstruts for α lgorithm PAGE 37

39 Tking the trnstionl life-yle into ount ssign ssign ssigned strt suspend ssigned strt running suspended strt running omplete resume running omplete omplete PAGE 38

40 Redisovering proess models originl proess model simulte event log disover disovered proess model N N N=N? The redisovery prolem: Is the disovered model N equivlent to the originl model N? PAGE 39

41 Chllenge: finding the right representtionl is strt p end There is no WF-net with unique visile lels tht exhiits this ehvior. PAGE 40

42 Another exmple τ strt p1 p1 end () strt p1 () p1 end There is no WFnet with unique visile lels tht exhiits this ehvior. strt p1 p1 end () PAGE 41

43 Chllenge: noise nd inompleteness To disover suitle proess model it is ssumed tht the event log ontins representtive smple of ehvior. Two relted phenomen: Noise: the event log ontins rre nd infrequent ehvior not representtive for the typil ehvior of the proess. Inompleteness: the event log ontins too few events to e le to disover some of the underlying ontrol-flow strutures. PAGE 42

44 More on inompleteness See lso hpter 3 (ross-vlidtion, preision, rell, et.) PAGE 43

45 Chllenge: Blning Between Underfitting nd Overfitting PAGE 44

46 Chllenge: four ompeting qulity riteri le to reply event log fitness Om s rzor simpliity proess disovery generliztion not overfitting the log preision not underfitting the log PAGE 45

47 Flower model d strt end e f g h PAGE 46

48 Wht is the est model? A D C ACD ACE BCE BCD B A E D C B E PAGE 47

49 Wht is the est model? A D C ACD ACE BCE BCD B A E D C B E PAGE 48

50 Wht is the est model? A D C ACD ACE BCE BCD B A E D C B E PAGE 49

51 Exmple: one log four models strt register exmine thoroughly exmine sully d hek tiket e deide f reinitite g py ompenstion h rejet N 1 : fitness = +, preision = +, generliztion = +, simpliity = + end # tre 455 deh 191 deg 177 deh 144 deh le to reply event log fitness proess disovery Om s rzor simpliity strt strt register register exmine sully exmine sully exmine thoroughly deide e d hek tiket d f hek tiket e deide reinitite py ompenstion rejet rejet N 2 : fitness = -, preision = +, generliztion = -, simpliity = + N 3 : fitness = +, preision = -, generliztion = +, simpliity = + g h h end end 111 deg 82 deg 56 deh 47 defdeh 38 deg 33 defdeh 14 defdeg 11 defdeg 9 defdeh 8 defdeh generliztion not overfitting the log preision not underfitting the log strt register register register register d hek tiket exmine sully d hek tiket exmine sully (ll exmine sully d hek tiket exmine sully d hek tiket e deide e deide e deide e deide 21 vrints seen in the log) g py ompenstion g py ompenstion h rejet h rejet end 5 defdeg 3 defdefdeg 2 defdeg 2 defdefdeg 1 defdefdeh 1 defdefdeg 1 defdefdefdeg 1391 d register exmine thoroughly hek tiket e deide g py ompenstion register d hek tiket exmine thoroughly e deide h rejet register exmine thoroughly d hek tiket deide rejet N 4 : fitness = +, preision = +, generliztion = -, simpliity = - e h PAGE 50

52 strt Model N 1 register exmine thoroughly exmine sully d hek tiket deide reinitite py ompenstion rejet N 1 : fitness = +, preision = +, generliztion = +, simpliity = + f e g h end # tre 455 deh 191 deg 177 deh 144 deh 111 deg 82 deg 56 deh 47 defdeh 38 deg 33 defdeh 14 defdeg 11 defdeg 9 defdeh 8 defdeh 5 defdeg 3 defdefdeg 2 defdeg 2 defdefdeg 1 defdefdeh 1 defdefdeg 1 defdefdefdeg 1391 PAGE 51

53 strt Model N 2 register exmine sully d hek tiket deide rejet N 2 : fitness = -, preision = +, generliztion = -, simpliity = + e h end # tre 455 deh 191 deg 177 deh 144 deh 111 deg 82 deg 56 deh 47 defdeh 38 deg 33 defdeh 14 defdeg 11 defdeg 9 defdeh 8 defdeh 5 defdeg 3 defdefdeg 2 defdeg 2 defdefdeg 1 defdefdeh 1 defdefdeg 1 defdefdefdeg 1391 PAGE 52

54 strt Model N 3 register exmine sully exmine thoroughly deide e d hek tiket reinitite py ompenstion rejet N 3 : fitness = +, preision = -, generliztion = +, simpliity = + f g h end # tre 455 deh 191 deg 177 deh 144 deh 111 deg 82 deg 56 deh 47 defdeh 38 deg 33 defdeh 14 defdeg 11 defdeg 9 defdeh 8 defdeh 5 defdeg 3 defdefdeg 2 defdeg 2 defdefdeg 1 defdefdeh 1 defdefdeg 1 defdefdefdeg 1391 PAGE 53

55 Model N 4 strt register register register register d hek tiket exmine sully d hek tiket exmine sully (ll exmine sully d hek tiket exmine sully d hek tiket d register register register exmine thoroughly d hek tiket exmine thoroughly d hek tiket deide deide deide e deide rejet h rejet N 4 : fitness = +, preision = +, generliztion = -, simpliity = - e e e 21 vrints seen in the log) hek tiket exmine thoroughly e deide e deide e deide g py ompenstion g py ompenstion h g py ompenstion h rejet h rejet end # tre 455 deh 191 deg 177 deh 144 deh 111 deg 82 deg 56 deh 47 defdeh 38 deg 33 defdeh 14 defdeg 11 defdeg 9 defdeh 8 defdeh 5 defdeg 3 defdefdeg 2 defdeg 2 defdefdeg 1 defdefdeh 1 defdefdeg 1 defdefdefdeg 1391 PAGE 54

56 Why is proess mining suh diffiult prolem? There re no negtive exmples (i.e., log shows wht hs hppened ut does not show wht ould not hppen). Due to onurreny, loops, nd hoies the serh spe hs omplex struture nd the log typilly ontins only frtion of ll possile ehviors. There is no ler reltion etween the size of model nd its ehvior (i.e., smller model my generte more or less ehvior lthough lssil nlysis nd evlution methods typilly ssume some monotoniity property). PAGE 55

57 Anlyzing Lsgn nd Spghetti Proesses

58 How n proess mining help? Detet ottleneks Detet devitions Performne mesurement Suggest improvements Deision support (e.g., reommendtion nd predition) Provide mirror Highlight importnt prolems Avoid ICT filures Avoid mngement y PowerPoint From politis to nlytis PAGE 57

59 Exmple of Lsgn proess: WMO proess of Duth muniiplity Eh line orresponds to one of the 528 s tht were hndled in the period from until In totl there re 5498 events represented s dots. The men time needed to hndled se is pproximtely 25 dys. PAGE 58

60 WMO proess (Wet Mtshppelijke Ondersteuning) WMO refers to the soil support t tht me into fore in The Netherlnds on Jnury 1st, The im of this t is to ssist people with disilities nd impirments. Under the t, lol uthorities re required to give support to those who need it, e.g., household help, providing wheelhirs nd sootmoiles, nd dpttions to homes. There re different proesses for the different kinds of help. We fous on the proess for hndling s for household help. In period of out one yer, 528 s for household WMO support were reeived. These 528 s generted 5498 events. PAGE 59

61 C-net disovered using heuristi miner (1/3) PAGE 60

62 C-net disovered using heuristi miner (2/3) PAGE 61

63 C-net disovered using heuristi miner (3/3) PAGE 62

64 Conformne hek WMO proess (1/3) PAGE 63

65 Conformne hek WMO proess (2/3) PAGE 64

66 Conformne hek WMO proess (3/3) The fitness of the disovered proess is Of the 528 ses, 496 ses fit perfetly wheres for 32 ses there re missing or remining tokens. PAGE 65

67 Bottlenek nlysis WMO proess (1/3) PAGE 66

68 Bottlenek nlysis WMO proess (2/3) PAGE 67

69 Bottlenek nlysis WMO proess (3/3) flow time of pprox. 25 dys with stndrd devition of pprox. 28 PAGE 68

70 Exmple of Spghetti proess Spghetti proess desriing the dignosis nd tretment of 2765 ptients in Duth hospitl. The proess model ws onstruted sed on n event log ontining 114,592 events. There re 619 different tivities (tking event types into ount) exeuted y 266 different individuls (dotors, nurses, et.). PAGE 69

71 Frgment 18 tivities of the 619 tivities (2.9%) PAGE 70

72 Another exmple (event log of Duth housing geny) The event log ontins 208 ses tht generted 5987 events. There re 74 different tivities. PAGE 71

73 PAGE 72

74 How n proess mining help? Detet ottleneks Detet devitions Performne mesurement Suggest improvements Deision support (e.g., reommendtion nd predition) Provide mirror Highlight importnt prolems Avoid ICT filures Avoid mngement y PowerPoint From politis to nlytis PAGE 73

75 After this leture you should e le to: Provide n overview of proess mining nd ProM's funtionlity. Disover Petri net sed on onrete event log using the α lgorithm. Tell out the limittions of the α lgorithm. Construt event logs (or trgeted Petri nets) for whih the α lgorithm produes n inorret result. Explin the delite lne etween overfitting nd underfitting. PAGE 74

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