Hello experts on inductive mining,
here's a conundrum about fitness preservation in the Inductive Miner framework based on directly-follows graphs (IM-D), as presented by Sander Leemans in his Ph. D. thesis.
In section 6.1.1 of his thesis, dealing with the basic log-based IM, Leemans presents tHe following log L69:
<b, c, d, e>
<d, b, e>
<b, d, e, c>
To L69 he applies a parallel cut, and splits the log so that the non-atomic part of the cut is represented by log L71:
<c, d, e>
<d, e, c>
That log has a directly-follows graph (DFG71) in which activity d, although it does not occur at the end of a trace, is classified as an end node after the split, on account of having an outgoing connection to activity b in the parent graph.
Leemans states that no cut can be found for DFG71, and using IM he applies a fall-through, namely activityConcurrent. That fall-through takes out d and places it concurrently to the other activities. Moreover, when applying a parallel cut to the remaining part of the log containing c and e, empty traces are introduced into the log (to fill up traces to equal length, I guess).
With IM-D, which does not use the log at all, but only the DFG, we can do neither of these things.
- the information for the introduction of empty traces is just not present in the DFG. So even if we could adapt the activityConcurrent fall-through, we'd finally end up with a simple parallelism over c, d, e. That would not preserve fitness.
- as Leemans discusses later, the activityConcurrent fall-through is too expensive to adapt to IM-D. The next more specific fall-through that is part of IM-D is strictTauLoop. This fall-through will remove every edge from an end activity to a start activity. In our case, as every activity is both an end and a start activity, it will remove ALL edges between c, d and e, leaving us with three isolated activities, which in turn will be translated to a process tree with an XOR over these activities. This is not fitness preserving either.
I must be getting something wrong, because I trust Leemans' claim that fall-throughs preserve fitness. His thesis has been reviewed many times. But still I do not see how to apply the rules of the IM-D framework in a fitness preserving way to this example. As fitness preservation is said to be one of the main features of inductive mining, I feel bad about this. Can someone please enlighten me?