Alpha Algorithm: A Process Discovery Algorithm

Transcription

1 Proess Mining: Dt Siene in Ation Alph Algorithm: A Proess Disovery Algorithm prof.dr.ir. Wil vn der Alst

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

3 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

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5 Simplifying event logs when fousing on ontrol-flow order numer tivity timestmp user produt quntity 9901 register order Sr Jones iphone5s register order @09.18 Sr Jones iphone5s register order @09.27 Sr Jones iphone4s hek stok @09.49 Pete Sott iphone5s ship order @10.11 Sue Fox iphone5s hek stok @10.34 Pete Sott iphone4s hndle pyment @10.41 Crol Hope iphone5s hek stok @10.57 Pete Sott iphone5s nel order @11.08 Crol Hope iphone5s 2 [ register_order, hek_stok,ship_order,hndle_pyment, register_order, hek_stok,nel_order, register_order, hek_stok, ]

6 Simple event log An event log is multiset of tres (sme tre my pper multiple times). A tre is sequene of tivity nmes (we strt from ll other ttriutes, ut events re ordered).

7 Gol of Alph lgorithm Event log ontins ll possile tres of model nd vie vers. p1 e p3 d strt end p2 p4

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

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

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

11 Chllenge for proess disovery: Four ompeting fores lift fitness (ility to explin oserved ehvior) thrust generliztion (voiding overfitting) drg preision (voiding underfitting) simpliity ("Om's rzor") grvity Will e disussed lter

12 >,,,# 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 #e e# #e #d d d ed

13 Bsi Ide Used y Alph Algorithm (1) () sequene pttern:

14 Bsi Ide Used y Alph Algorithm (2) d () XOR-split pttern:,, nd # () XOR-split pttern:,, nd # () XOR-join pttern: d, d, nd #

15 Bsi Ide Used y Alph Algorithm (3) d (d) AND-split pttern:,, nd (d) AND-split pttern:,, nd (e) AND-join pttern: d, d, nd

16 Exmple Revisited > > >e > >d > >d e>d e d d e d #e e# #e #d p1 e p3 Result produed y the Alph lgorithm d strt end p2 p4

17 Footprint of L 1 One of the following:, #,

18 Disovered model hs the sme footprint p1 e p3 d strt end p2 p4 Log nd model gree on footprint

19 Footprint of L 2 p1 p3 f e d strt p5 end p2 p4 Log nd model gree on footprint

20 Summry: Simple proess ptterns n e disovered from event logs d () sequene pttern: () XOR-split pttern:,, nd # () XOR-join pttern: d, d, nd # d (d) AND-split pttern:,, nd (e) AND-join pttern: d, d, nd

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22 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 ).

23 The α lgorithm Let L e n event log over T. Then, α(l) is defined s follows: 1. T L = { t T σ L t σ}, Eh tivity in L orresponds to trnsition in α(l). 2. T I = { t T σ L t = first(σ) } Fix the set of strt tivities tht is, the first elements of eh tre: t 1,, t n,, t 1,, t m 3. T O = { t T σ L t = lst(σ) } Fix the set of end tivities tht is, elements tht pper lst in tre : t 1,, t n,, t 1,, t m PAGE 22

24 Next steps im t finding ples p (A,B)... m n Step 4: Clulte pirs (A, B) Step 5: Delete non-mximl pirs (A, B) Step 6: Determine ples p (A, B) from pirs (A, B) PAGE 23 A={ 1, 2, m } B={ 1, 2, n }

25 The α lgorithm (ont.) 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 }, A 1 2 # 3 PAGE # B Find pirs (A, B) of sets of tivities suh tht every element A nd every element B re uslly relted (i.e., L ), ll elements in A re independent ( 1 # L 2 ), nd ll elements in B re independent ( 1 # L 2 ).

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

27 The α lgorithm (ont.) 5. Y L = { (A,B) X L (A,B ) XL A A B B (A,B) = (A,B ) } A Delete from set X L ll pirs (A, B) tht re not mximl! 1 2 # # B A' A 1 2 # # # 1 # B' B

28 The α lgorithm (ont.) 6. P L = { p (A,B) (A,B) Y L } {i L,o L }, 1 1 Determine the ple set: Eh element (A, B) of Y L is ple. To ensure the workflow struture, dd soure ple i L nd trget ple o L p (A,B)... i L m n o L PAGE 27 A={ 1, 2, m } B={ 1, 2, n }

29 The α lgorithm (ont.) 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 } Determine the flow reltion: Connet eh ple p (A,B) with eh element of its set A of soure trnsitions nd with eh element of its set B of trget trnsitions. In ddition, drw n r from the soure ple i L to eh strt trnsition t T I nd n r from eh end trnsition t T O to the sink ple o L. 8. α(l) = (P L, T L, F L ) PAGE 28

30 strt p1 p1 e e p3 p3 d d end strt p2 p2 p4 p4 end

31 ProM's output for event log L 1

32 Question: Give footprint mtrix for event log L 3 PAGE 31

33 Answer: Footprint mtrix for event log L 3

34 Question: Apply the 8 steps of the Alph lgorithm.

35 Model for L 3 disovered y the Alph lgorithm f p ({},{}) p ({},{e}) e g i L p ({,f},{}) d p ({e},{f,g}) o L p ({},{d}) p ({d},{e}) PAGE 34

36 ProM's output for event log L 3

37 Another event log L 4 d i L p ({,},{}) p ({},{d,e}) e o L PAGE 36

38 Event log L 5 PAGE 37

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40 Disovered model d p ({},{d}) i L p ({,d},{}) p ({},{,f}) f o L e p ({},{e}) p ({e},{f})

41 Summry The Alph lgorithm provides si proess disovery pproh. It hs mny limittions. These will e disussed lter. However, it niely illustrtes the key ingredients of proess disovery. Hene, it is importnt to understnd the lgorithm nd prtie using onrete exmples.

42 Prt I: Preliminries Prt III: Beyond Proess Disovery Chpter 1 Introdution Chpter 2 Proess Modeling nd Anlysis Chpter 3 Dt Mining Chpter 7 Conformne Cheking Chpter 8 Mining Additionl Perspetives Chpter 9 Opertionl Support Prt II: From Event Logs to Proess Models Chpter 4 Getting the Dt Chpter 5 Proess Disovery: An Introdution Chpter 6 Advned Proess Disovery Tehniques Prt IV: Putting Proess Mining to Work Chpter 10 Tool Support Chpter 11 Anlyzing Lsgn Proesses Chpter 12 Anlyzing Spghetti Proesses Prt V: Refletion Chpter 13 Crtogrphy nd Nvigtion Chpter 14 Epilogue