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Process Mining: Process Mining: An iterative algorithm An iterative algorithm using the using the
Theory of RegionsTheory of Regions
Kristian Bisgaard LassenKristian Bisgaard Lassen
Boudewijn van DongenBoudewijn van Dongen
Wil van der AalstWil van der Aalst
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Overview
1. Introduction to Theory of Regions
2. Introduction to Process Mining
3. Applying Theory of Regions to Process Mining
4. Conclusion
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Theory of Regions (for Transition Systems)
A Region in a Transition System is a set of states, such that for all
transitions in the system holds that:
1) If that transition enters the region, then all equally labeled transitions
enter the region,
2) If that transition exists the region, then all equally labeled transitions
exit the region,
3) If that transition does not cross the region, then no equally labeled
transition crosses the region.
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Theory of Regions (for Transition Systems)
When all regions are found, a Petri net is built, where these regions
correspond to places in the net.
The resulting Petri net is such that its statespace is bisimilar to the
transition system that served as input.
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Process Mining: an overview
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Log Files
Information systems typically log all kinds of events. We use a XML
format for storing event logs. The basic assumption is that the log
contains information about specific tasks executed for specific process
instances (cases, event-lists, audit trails). Any knowledge of the
underlying process is not assumed.
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Process Mining VS. Theory of Regions
Process Mining
-Event logs
-Completeness unknown
-Abstract representation required
Theory of Regions
-State-based models / (regular)
languages
-Complete information provided
-Exact and compact representation
required
Big chunks of data, unable to fit in memory.
Entire model needs to be present in memory.
Completeness of information is very unlikely.
Completeness of information is guaranteed by the input model.
Main conceptual difference
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Some existing Process Mining approaches
Translation
Abstraction
TranslationAlpha-algorithm
Aggregation
TranslationTranslation
EPCs
Event logs
Ordering relations
Aggregationgraphs
Instancegraphs
Petri nets
Partial orderGeneration
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The goal: Applying Theory of Regions in the context of PM
Translation
Abstraction
TranslationAlpha-algorithm
Theory of Regions
Aggregation
TranslationTranslation
EPCs
Event logs
Ordering relations
Aggregationgraphs
Instancegraphs
Petri nets
Partial orderGeneration
Assume an event log isA Transition System, such that each trace starts in a global state
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Example Log
A
B
C
D
(W,-1)
(case1 ,0)
(case1 ,1)
(case1 ,2)
(case1 ,3)
A
C
B
D
(W,-1)
(case2 ,0)
(case2 ,1)
(case2 ,2)
(case2 ,3)
A
B
C
D
(W,-1)
(case3 ,0)
(case3 ,1)
(case3 ,2)
(case3 ,3)
A
C
B
D
(W,-1)
(case4 ,0)
(case4 ,1)
(case4 ,2)
(case4 ,3)
A
E
D
(W,-1)
(case5 ,0)
(case5 ,1)
(case5 ,2)
Log:
A,B,C,D
A,C,B,D
A,B,C,D
A,C,B,D
A,E,D
Transition systems
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Merging the initial state
A
B
C
D
(case1 ,0)
(case1 ,1)
(case1 ,2)
(case1 ,3)
A
C
B
D
(case2 ,0)
(case2 ,1)
(case2 ,2)
(case2 ,3)
A
B
C
D
(case3 ,0)
(case3 ,1)
(case3 ,2)
(case3 ,3)
A
C
B
D
(case4 ,0)
(case4 ,1)
(case4 ,2)
(case4 ,3)
A
E
D
(case5 ,0)
(case5 ,1)
(case5 ,2)
(W,-1)
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Identifying regions
A
B
C
D
(case1 ,0)
(case1 ,1)
(case1 ,2)
(case1 ,3)
A
C
B
D
(case2 ,0)
(case2 ,1)
(case2 ,2)
(case2 ,3)
A
B
C
D
(case3 ,0)
(case3 ,1)
(case3 ,2)
(case3 ,3)
A
C
B
D
(case4 ,0)
(case4 ,1)
(case4 ,2)
(case4 ,3)
A
E
D
(case5 ,0)
(case5 ,1)
(case5 ,2)
(W,-1) A
B C
D
E
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Making the algorithm iterative (i.e. linear in the log)
Trace 1 Trace 2 Trace n...
TS 1 TS 2 TS n...
Regions 1 Regions 2 Regions n...
Regions 1,2
Regions 1,2,…,n
Petri net
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Future work, other approaches
Several other approaches are possible:
1) Constructing a transition system for the whole log in a smart way:
Rubin et al. propose 36 ways of doing so, but they require the
entire transition system to be build in memory. Their approach
however can handle “incomplete” information.
2) Considering the event log as a regular language and use language-
based regions as proposed by Darondeau et al. and Lorenz et al.
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Conclusions
Using our approach, the Theory of Regions can be applied in the context
of process mining, in such a way that the approach is linear in the
number of cases in the log.
Downsides remain the completeness assumption and the resulting model,
since this is not an abstraction of the log, which is often required in
process mining.
