# Process Discovery for Event Logs with Multi-Occurrence Event Types
## 5 Discussion  
We have tested our proposed method in two phases. In the first phase, we investigated the \(\Lambda\) equivalence miner, which predicts which nodes from the different traces belong to the same node in the source schema graph. In the tests, we also analyzed two benchmark methods for the labeled graphs: Hin2 Vec and GraphSAGE. As the test results show, our proposal could achieve significantly better accuracy in all test cases. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Measure** & **Experiment** & **Heuristic Method** & **GNN Method** & **Proposed Method** \\ \hline \multirow{8}{*}{Number of activity nodes} & T1 & 8 & 8 & 8 \\ \cline{2-4}  & T2 & 9 & 9 & 10 \\ \cline{2-4}  & T3 & 6 & 6 & 7 \\ \cline{2-4}  & T4 & 5 & 5 & 5 \\ \cline{2-4}  & T5 & 6 & 6 & 8 \\ \cline{2-4}  & T6 & 7 & 7 & 10 \\ \cline{2-4}  & T7 & 8 & 8 & 10 \\ \cline{2-4}  & T8 & 18 & 18 & 25 \\ \cline{2-4}  & Average & **8.4** & **8.4** & **10.4** \\ \hline \multirow{8}{*}{Simplicity (ms)} & T1 & 1 & 1 & 1 \\ \cline{2-4}  & T2 & 1.3 & 1.3 & 1.2 \\ \cline{2-4}  & T3 & 1.3 & 1.2 & 1.1 \\ \cline{2-4}  & T4 & 1 & 1 & 1.2 \\ \cline{2-4}  & T5 & 1.3 & 1.3 & 1.1 \\ \cline{2-4}  & T6 & 2.4 & 2.7 & 2.3 \\ \cline{2-4}  & T7 & 2.3 & 2.2 & 2.0 \\ \cline{2-4}  & T8 & 1.6 & 1.4 & 1.3 \\ \cline{2-4}  & Average & **1.5** & **1.5** & **1.4** \\ \hline \multirow{8}{*}{Precision (m\({}_{\text{p}}\))} & T1 (2) & 1 & 1 & 1 \\ \cline{2-4}  & T2 (8) & 0.05 & 0.05 & 1 \\ \cline{2-4}  & T3 (3) & 0.08 & 0.09 & 1 \\ \cline{2-4}  & T4 (11) & 0.18 & 0.18 & 1 \\ \cline{2-4}  & T5 (11) & 0.08 & 0.11 & 1 \\ \cline{2-4}  & T6 (14) & 0.08 & 0.12 & 0.5 \\ \cline{2-4}  & T7 (10) & 0.04 & 0.03 & 0.03 \\ \cline{2-4}  & T8 (13) & 0.03 & 0.06 & 0.09 \\ \cline{2-4}  & Average & **0.19** & **0.21** & **0.70** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Efficiency measures of the investigated methods. Figure 29: Result schema by the proposed method for T8. Having a precise equivalence classifier, we can construct the schema graph using a straightforward method: We discover the maximal quasi-cliques in the equivalence graph and the cliques are converted into the nodes of the result schema. The performed comparison tests show that the proposed method provides similar or better results for all the investigated cases. The main benefit of the proposed method is that it can also be used for cases when the schemas and the traces may contain multi-occurrence event types. The standard process discovery methods cannot separate the different occurrences of the same type, which results in incorrect and inaccurate outcomes. The results of the performed efficiency tests demonstrate that the proposed method can manage such complex cases which are not covered by the standard process discovery methods, and it provides more compact and more precise schema graphs. As Table 4 shows, the proposed method can distinguish the different occurrence contexts of the same evet type. The main consequences of this feature are that the resulted schema is less over generalized, the precision related to the training set is better, and the simplicity level is improved. Regarding more complex schemas, we can summarize the gained experiences in the following points:  
* The quality of the output significantly depends on the accuracy of the equivalence mining. * The increase in training datasets improves the accuracy of the prediction. For example, considering Example T5, using only 100,000 items in the training set, the engine generated some incorrect edges, as shown in Figure 30. With a double-sized training set, the neural networks system was able to perform a perfect prediction. * The precise detection of the nested loops requires additional investigations, as with increased nesting depth, the uncertainty level also increases. The tests also revealed areas where further research is needed in the next phase. During the tests, we experienced the following limitations of the proposed method:  
* The quality of the training set is an important factor in the equivalence prediction.