Process Mining

Suppose we have a log of our process, but do not have the model of this process

  • the process mining is a way to find a process from the logs
  • the model can be a Workflow Net, YAWL or BPMN model.


Definitions

A process mining algorithm is a function that

  • maps an event log $L$ to some workflow model
  • ideally the model should be sound

play-in = process discovery

  • event logs $\to$ workflow model
  • process-discovery.png


the ability to rediscover

  • is a property of a process mining algorithm to discover a model of some process
  • from logs that have been generated from this model
  • i.e. in case of Petri Nets, if $N$ is the original model and $N'$ is the discovered model, then $N \equiv N'$


Some Notes

Usually, first a Petri Net model is discovered

  • and then this model is converted to YAWL or BPMN
  • because Petri Nets are simpler


Measures

There are four conflicting criteria

  • Fitness
    • the discovered network should allow the behavior seen in the logs
  • Precision
    • the discovered network should not allow the behavior not seen in the logs
    • too precise $\to$ bad generalization
  • Generalization
    • the discovered model should generalize the behavior seen in the logs
  • Simplicity
    • it should be as simple as possible
    • too simple $\to$ low fitness

pm-criteria.png

  • The main challenge of Process Mining is that all these criteria are conflicting:
  • It's really hard to simultaneously satisfy all of them
  • this makes Process Mining to be a Multi-Objective Optimization problem


Fitness

Can we replay the log?

  • we try to replay each sequences from the logs
  • so for each we see if this sequences is allowed
  • if each sequence can be replayed - 100% fitness
  • special notion for fitness is also defined for the Genetic Process Miner


Precision

Do we underfit the log?

  • play out the model, capture logs
  • see what's generated and compare to the original logs
  • is it far? (need to have some distance measure)

if produced logs $\subseteq$ original logs

  • then we have 100% precision


Generalization

Do we overfit the log?

  • very hard to measure


Simplicity

The simpler the model - the better

  • may add some penalty for each added place
  • (the more places we add, the more complex the model becomes)


Examples

The Flower Model

pm-flower.png

  • this model in at the one end of spectrum
  • very simple
  • good fitness: every possible trace can be reproduced
  • generalization: allows a lot of behavior
  • but precision is very low: it allows a lot of behavior not seen in the logs


The Enumerating Model

pm-enum.png

  • another end of the spectrum
  • behavior only seen in the logs: not more, not less
  • good fitness and good precision
  • no generalization at all
  • no simplicity


Conclusions

So Process Mining is difficult

  • it's a Multi-Objective Optimization problem
  • there are no negative examples
  • the search space is too complex
  • logs typically show only a fraction of possible behavior


Algorithms

These algorithms let you find a Petri Net from logs


Sources

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