The document discusses process discovery and introduces the α algorithm. It begins by defining key terms like process discovery, fitness, precision, generalization, and simplicity. It then walks through examples of event logs and the corresponding process models that could be discovered from them. The α algorithm is introduced and explained as a basic process discovery technique. Limitations of the α algorithm are also discussed, such as its inability to handle implicit places, loops, and non-local dependencies. The challenges of process discovery are summarized, including noise, incompleteness, and balancing between underfitting and overfitting models.

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