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
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
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
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
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
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
