Process Mining - Chapter 5 - Process Discovery
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Chapter 5 of the document covers the concept of process discovery, detailing techniques and challenges in deriving process models from event logs. It discusses the importance of balancing between quality criteria such as fitness, precision, generalization, and simplicity when creating these models. Additionally, algorithms, such as the α algorithm, are presented along with examples demonstrating their application in process discovery.
Process Mining - Chapter 5 - Process Discovery
- 1. Chapter 5 Process Discovery: An Introduction prof.dr.ir. Wil van der Aalst www.processmining.org
- 2. Overview Chapter 1 Introduction Part I: Preliminaries Chapter 2 Chapter 3 Process Modeling and Data Mining Analysis Part II: From Event Logs to Process Models Chapter 4 Chapter 5 Chapter 6 Getting the Data Process Discovery: An Advanced Process Introduction Discovery Techniques Part III: Beyond Process Discovery Chapter 7 Chapter 8 Chapter 9 Conformance Mining Additional Operational Support Checking Perspectives Part IV: Putting Process Mining to Work Chapter 10 Chapter 11 Chapter 12 Tool Support Analyzing “Lasagna Analyzing “Spaghetti Processes” Processes” Part V: Reflection Chapter 13 Chapter 14 Cartography and Epilogue Navigation PAGE 1
- 3. Process discovery supports/ “world” business controls processes software people machines system components organizations records events, e.g., messages, specifies transactions, models configures etc. analyzes implements analyzes discovery (process) event conformance model logs enhancement PAGE 2
- 4. Process discovery = Play-In Play-In event log process model Play-Out process model event log Replay • extended model showing times, frequencies, etc. • diagnostics • predictions • recommendations event log process model PAGE 3
- 5. Example b a p1 e p3 d start end p2 c p4 Event log contains all possible traces of model and vice versa. PAGE 4
- 6. Another example p1 b p3 a f e d start p5 end p2 c p4 Generalization: event log contains only subset of all possible traces of model. PAGE 5
- 7. Notation is less relevant (e.g. BPMN) b a p1 e p3 d start end b p2 c p4 c a d start end e PAGE 6
- 8. Another BPMN example p1 b p3 a f e d start p5 end b p2 c p4 c a d start end f e PAGE 7
- 9. Challenge • In general, there is a trade-off between the following four quality criteria: 1.Fitness: the discovered model should allow for the behavior seen in the event log. 2.Precision (avoid underfitting): the discovered model should not allow for behavior completely unrelated to what was seen in the event log. 3.Generalization (avoid overfitting): the discovered model should generalize the example behavior seen in the event log. 4.Simplicity: the discovered model should be as simple as possible. PAGE 8
- 10. Process Discovery: example of algorithm α PAGE 9
- 11. >,→,||,# relations • Direct succession: x>y iff for some case x is directly followed by y. abcd • Causality: x→y iff x>y and acbd not y>x. aed • Parallel: x||y iff x>y and a>b y>x a>c a→b b#e a>e • Choice: x#y iff not x>y and a→c e#b b>c b||c c#e not y>x. a→e b>d c||b c>b b→d a#d … c>d c→d e>d e→d PAGE 10
- 12. Basic Idea Used by α Algorithm (1) a b (a) sequence pattern: a→b PAGE 11
- 13. Basic Idea Used by α Algorithm (2) a b c b a (c) XOR-join pattern: b a→c, b→c, and a#b a c c (b) XOR-split pattern: (b) XOR-split pattern:a→c, and b#c a→b, a→b, a→c, and b#c PAGE 12
- 14. Basic Idea Used by α Algorithm (3) a b c b a (e) AND-join pattern: b a→c, b→c, and a||b a c c (d) AND-split pattern: (d) AND-split pattern: a→b, a→c, and b||c a→b, a→c, and b||c PAGE 13
- 15. Example Revisited a>b a→b b||c b#e a>c a→c c||b e#b a>e a→e c#e b>c a#d b→d b>d … c>b c→ d c>d e→d b e>d a p1 e p3 d start end p2 c p4 Result produced by α algorithm PAGE 14
- 16. Footprint of L1 b a p1 e p3 d start end p2 c p4 PAGE 15
- 17. Footprint of L2 p1 b p3 a f e d start p5 end p2 c p4 PAGE 16
- 18. Simple patterns a b (a) sequence pattern: a→b b a a c c b (b) XOR-split pattern: (c) XOR-join pattern: a→b, a→c, and b#c a→c, b→c, and a#b b a a c c b (d) AND-split pattern: (e) AND-join pattern: PAGE 17 a→b, a→c, and b||c a→c, b→c, and a||b
- 19. Algorithm Let L be an event log over T. α(L) is defined as follows. 1. TL = { t ∈ T | ∃σ ∈ L t ∈ σ}, 2. TI = { t ∈ T | ∃σ ∈ L t = first(σ) }, 3. TO = { t ∈ T | ∃σ ∈ L t = last(σ) }, 4. XL = { (A,B) | A ⊆ TL ∧ A ≠ ø ∧ B ⊆ TL ∧ B ≠ ø ∧ ∀a ∈ A∀b ∈ B a →L b ∧ ∀a1,a2 ∈ A a1#L a2 ∧ ∀b1,b2 ∈ B b1#L b2 }, 5. YL = { (A,B) ∈ XL | ∀(A′,B′) ∈ XL A ⊆ A′ ∧B ⊆ B′⇒ (A,B) = (A′,B′) }, 6. PL = { p(A,B) | (A,B) ∈ YL } ∪{iL,oL}, 7. FL = { (a,p(A,B)) | (A,B) ∈ YL ∧ a ∈ A } ∪ { (p(A,B),b) | (A,B) ∈ YL ∧ b ∈ B } ∪{ (iL,t) | t ∈ TI} ∪{ (t,oL) | t ∈ TO}, and 8. α(L) = (PL,TL,FL). PAGE 18
- 20. Key idea: find places a1 b1 a2 b2 ... p(A,B) ... am bn A={a1,a2, … am} B={b1,b2, … bn} 4. XL = { (A,B) | A ⊆ TL ∧ A ≠ ø ∧ B ⊆ TL ∧ B ≠ ø ∧ ∀a ∈ A∀b ∈ B a →L b ∧ ∀a1,a2 ∈ A a1#L a2 ∧ ∀b1,b2 ∈ B b1#L b2 }, 5. YL = { (A,B) ∈ XL | ∀(A′,B′) ∈ XL A ⊆ A′ ∧B ⊆ B′⇒ (A,B) = (A′,B′) }, PAGE 19
- 21. Places as footprints a1 b1 a2 b2 ... p(A,B) ... am bn A={a1,a2, … am} B={b1,b2, … bn} PAGE 20
- 22. b a p1 e p3 d start end p2 c p4 PAGE 21
- 23. Another event log L3 PAGE 22
- 24. Model for L3 f c a b p({b},{c}) p({c},{e}) e g iL p({a,f},{b}) d p({e},{f,g}) oL p({b},{d}) p({d},{e}) PAGE 23
- 25. Another event log L4 a d c iL p({a,b},{c}) p({c},{d,e}) oL b e PAGE 24
- 26. Event log L5 PAGE 25
- 27. PAGE 26
- 28. Discovered model d c p({c},{d}) b p({a,d},{b}) p({b},{c,f}) iL a f oL e p({a},{e}) p({e},{f}) PAGE 27
- 29. Limitation of α algorithm (implicit places) c a d p1 g e p2 b f Green places are implicit! PAGE 28
- 30. Limitation of α algorithm (loops of length 1) b a c b a c PAGE 29
- 31. Limitation of α algorithm (loops of length 2) c a b d b a d c PAGE 30
- 32. Limitation of α algorithm (non-local dependencies) a p1 d c b p2 e Green places are not discovered! PAGE 31
- 33. Difficult constructs for α algorithm a c b PAGE 32
- 34. Taking the transactional life-cycle into account a c assign assign b start assigned assigned suspend running start start suspended resume complete running running complete complete PAGE 33
- 35. Rediscovering process models simulate discover discovered original process event process model log model N N’ N=N’ ? The rediscovery problem: Is the discovered model N’ equivalent to the original model N? PAGE 34
- 36. Equivalence: trace equivalence, bisimilarity, and branching bisimilarity s1 s5 s8 birth curse birth birth curse curse s6 curse curse ? s9 s10 s2 curse heaven hell heaven hell heaven hell hell heaven curse heaven s3 s4 s7 s11 TS1 TS2 TS3 Three trace equivalent transition systems: TS1 and TS2 are not bisimilar, but TS2 and TS3 are bisimilar PAGE 35
- 37. Branching bisimilarity defined for YAWL start s1 s6 start check check check check s2 τ τ s7 c1 c2 s3 s4 c3 ? reject accept reject accept reject accept reject accept end s8 end s5 TS1 TS2 TS1 and TS2 are not branching bisimilar (although trace equivalent). PAGE 36
- 38. Challenge: finding the right representational bias a a start p end There is no WF-net with unique visible labels that exhibits this behavior. PAGE 37
- 39. Another example τ a b c start p1 p1 end (a) a a b c There is no WF- start p1 p1 end net with unique (b) visible labels that exhibits this behavior. a b c start p1 p1 end PAGE 38 (c)
- 40. Challenge: noise and incompleteness • To discover a suitable process model it is assumed that the event log contains a representative sample of behavior. • Two related phenomena: − Noise: the event log contains rare and infrequent behavior not representative for the typical behavior of the process. − Incompleteness: the event log contains too few events to be able to discover some of the underlying control-flow structures. PAGE 39
- 41. More on incompleteness See also chapter 3 (cross-validation, precision, recall, etc.) PAGE 40
- 42. Challenge: Balancing Between Underfitting and Overfitting PAGE 41
- 43. Challenge: four competing quality criteria “able to replay event log” “Occam’s razor” fitness simplicity process discovery generalization precision “not overfitting the log” “not underfitting the log” PAGE 42
- 44. Flower model b c a d start end e h f g PAGE 43
- 45. What is the best model? A D C ACD 99 B E ACE 0 BCE 85 A D BCD 0 C B E PAGE 44
- 46. What is the best model? A D C ACD 99 B E ACE 88 BCE 85 A D BCD 78 C B E PAGE 45
- 47. What is the best model? A D C ACD 99 B E ACE 2 BCE 85 A D BCD 3 C B E PAGE 46
- 48. Example: one log four models b examine thoroughly g pay c compensation a examine e start register casually decide end # trace request h 455 acdeh d reject check ticket request 191 abdeg f reinitiate request 177 adceh N1 : fitness = +, precision = +, generalization = +, simplicity = + 144 abdeh 111 acdeg a c d e h 82 adceg start register examine check decide reject end request casually ticket request 56 adbeh N2 : fitness = -, precision = +, generalization = -, simplicity = + 47 acdefdbeh “able to replay event log” “Occam’s razor” 38 adbeg examine check thoroughly b d ticket g 33 acdefbdeh fitness simplicity pay compensation a 14 acdefbdeg start register examine c end 11 acdefdbeg request casually e f reinitiate h process decide request reject request 9 adcefcdeh discovery N3 : fitness = +, precision = -, generalization = +, simplicity = + 8 adcefdbeh 5 adcefbdeg a d c e g 3 acdefbdefdbeg generalization precision register request check ticket examine casually decide pay compensation 2 adcefdbeg a c d e g 2 adcefbdefbdeg “not overfitting the log” “not underfitting the log” register examine check decide pay request casually ticket compensation 1 adcefdbefbdeh a d c e h 1 adbefbdefdbeg register check examine decide reject request ticket casually request 1 adcefdbefcdefdbeg a c d e h 1391 start end register examine check decide reject request casually ticket request … (all 21 variants seen in the log) a b d e g register examine check decide pay request thoroughly ticket compensation a d b e h register check examine decide reject request ticket thoroughly request a b d e h register examine check decide reject request thoroughly ticket request PAGE 47 N4 : fitness = +, precision = +, generalization = -, simplicity = -
- 49. # trace 455 acdeh Model N1 191 abdeg 177 adceh 144 abdeh 111 acdeg 82 adceg 56 adbeh b 47 acdefdbeh examine thoroughly 38 adbeg g 33 acdefbdeh pay c compensation 14 acdefbdeg a examine e 11 acdefdbeg start register casually decide end request 9 adcefcdeh h d reject 8 adcefdbeh check ticket request 5 adcefbdeg f reinitiate 3 acdefbdefdbeg request N1 : fitness = +, precision = +, generalization = +, simplicity = + 2 adcefdbeg 2 adcefbdefbdeg 1 adcefdbefbdeh 1 adbefbdefdbeg 1 adcefdbefcdefdbeg PAGE 48 1391
- 50. # trace 455 acdeh Model N2 191 abdeg 177 adceh 144 abdeh 111 acdeg 82 adceg 56 adbeh 47 acdefdbeh 38 adbeg a c d e h 33 acdefbdeh start register examine check decide reject end 14 acdefbdeg request casually ticket request N2 : fitness = -, precision = +, generalization = -, simplicity = + 11 acdefdbeg 9 adcefcdeh 8 adcefdbeh 5 adcefbdeg 3 acdefbdefdbeg 2 adcefdbeg 2 adcefbdefbdeg 1 adcefdbefbdeh 1 adbefbdefdbeg 1 adcefdbefcdefdbeg PAGE 49 1391
- 51. # trace 455 acdeh Model N3 191 abdeg 177 adceh 144 abdeh 111 acdeg 82 adceg 56 adbeh 47 acdefdbeh examine check thoroughly b d ticket g 38 adbeg pay 33 acdefbdeh compensation a 14 acdefbdeg start register examine end 11 acdefdbeg request casually c e f reinitiate reject h 9 adcefcdeh decide request request 8 adcefdbeh N3 : fitness = +, precision = -, generalization = +, simplicity = + 5 adcefbdeg 3 acdefbdefdbeg 2 adcefdbeg 2 adcefbdefbdeg 1 adcefdbefbdeh 1 adbefbdefdbeg 1 adcefdbefcdefdbeg PAGE 50 1391
- 52. # trace 455 acdeh Model N4 191 abdeg 177 adceh 144 abdeh a d c e g 111 acdeg register check examine decide pay request ticket casually compensation 82 adceg a c d e g 56 adbeh register examine check decide pay request casually ticket compensation 47 acdefdbeh a d c e h 38 adbeg register check examine decide reject request ticket casually request 33 acdefbdeh a c d e h 14 acdefbdeg start end register examine check decide reject request casually ticket request 11 acdefdbeg … (all 21 variants seen in the log) 9 adcefcdeh 8 adcefdbeh 5 adcefbdeg a b d e g register examine check decide pay 3 acdefbdefdbeg request thoroughly ticket compensation 2 adcefdbeg a d b e h register check examine decide reject 2 adcefbdefbdeg request ticket thoroughly request 1 adcefdbefbdeh a b d e h register examine check decide reject 1 adbefbdefdbeg request thoroughly ticket request 1 adcefdbefcdefdbeg N4 : fitness = +, precision = +, generalization = -, simplicity = - PAGE 51 1391
- 53. Why is process mining such a difficult problem? • There are no negative examples (i.e., a log shows what has happened but does not show what could not happen). • Due to concurrency, loops, and choices the search space has a complex structure and the log typically contains only a fraction of all possible behaviors. • There is no clear relation between the size of a model and its behavior (i.e., a smaller model may generate more or less behavior although classical analysis and evaluation methods typically assume some monotonicity property). PAGE 52
- 54. Creating a 2-D slice of a 3-D reality Creating a 2-D slice of a 3-D reality: the process is viewed from a specific angle, the process is scoped using a frame, and the resolution determines the granularity of the resulting model PAGE 53