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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.