## 3 Methodology
### Results  
To understand the behaviour of metrics on the datasets, we plotted the performance of each metric in both regimes. The performance graph depicts the changes in quality ratings against one control element (either activity or path rate). We have analysed each metric individually and contrasted them against each other as groups. Every metric has two performance graphs showcasing either regime individually for all seven datasets. Within the performance graphs, each sample (S) is represented using abbreviations S1-S7. _\"Fitness is the amount of behaviour present in the event log that can be reproduced by the model\"_. Figures 6 and 7 show the fitness in R1 and R2, respectively. At a glance, there seems to be more than one behaviour of fitness in R1. However, by observing individually, the fitness for all datasets increases gradually or stays steady. Fitness in \(S1\), \(S2\) and \(S3\) differ in steps of varying sizes. These steps indicate the addition of an event into the process model. Adding new events increases the number of paths within the model. This allows for an increased number of replayable traces. Therefore, the overall fitness of the model increases with the addition of new events. Figures 14 and 15 show an example of S1 in R1 @ PR 80. The number of paths is seen to be increasing as the number of activities increases from 9 to 12. At path rates less than 100, we can observe that the fitness does not reach 100% in any dataset. This is because there is always a certain number of paths hidden due to their low frequency of occurrence; they are only viewable at 100% control rates. Hence, the fitness does not reach 100%, as all traces cannot be replayed by the process model. In S4, S5, S6 and S7, the fitness remains constant for certain periods of activity rates as no new paths are being added to the model; therefore, there is no increase in the number of repayable traces. In R2, we see similar behaviour as in R1, except the increasing nature of fitness is faster and more gradual. The number of paths seems to have more influence in replaying the traces when activities remain constant. Figure 6: Fitness ratings of datasets 1 to 7 in R1. _A measure of the amount of behaviour only possible in the model and not in the event log is called Precision_. Figures 8 and 9 show the behaviour of precision in R1 and R2, respectively. Figure 8: Precision ratings of datasets 1 to 7 in R1. Figure 7: Fitness ratings of datasets 1 to 7 in R2. In general, the precision for all the datasets is decreasing in R1. In Figure 8, activity rate gradually impacts the precision of the model. As the path rate increases, the precision reduces. All the samples follow consistent behaviour of gradual decrease in precision with varying step sizes. The precision reaches the lowest value when both path rate and activity rate are at 100%. This is because, despite showing all available traces and events, there are still many possible combinations that were not shown in the log but are theoretically possible in the model. The slow change in precision is seen in path rates of smaller magnitude; for path rates with higher magnitude, the precision reduces faster since the number of possible combinations increases exponentially. Similar to R1, the precision in R2, shown in Figure 9, reduces as it approaches 100% of activity rate and path rate. The rate of precision reduction in R2 is lesser than in R1, as the number of activities does not have a major impact on creating paths for new combinations. _Generalisation is a measure of the level of abstraction that takes place in a process model._ A model with uniform usage across all parts has good generalisation, while a model with infrequent usage across some parts has bad generalisation. Figures 10 and 11 show the behaviour of generalisation in R1 and R2. Figure 9: Precision ratings of datasets 1 to 7 in R2. The behaviour of generalisation across all datasets is similar in R1.