# Process Discovery for Event Logs with Multi-Occurrence Event Types
## 4 Test Experiments
### Tests on Schema Induction  
In the next subsection, we present the comparison test results on the proposed schema induction method. In the tests, we also involved the industry standard PM4 PY methods, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Schema Complexity** & **GraphSAGE** & **Hin2 Vec** & **Proposed** \\ \hline homogeneous & & & \\ dataset & & & \\ (1, 0) & 0.60/0.52 & 0.58/0.51 & 0.98/0.91 \\ (1, 0) & 0.59/0.46 & 0.54/0.50 & 0.98/0.87 \\ (2, 0) & 0.57/0.58 & 0.56/0.51 & 0.93/0.89 \\ (1, 1) & 0.69/0.68 & 0.65/0.52 & 0.98/0.97 \\ (0, 1) & 0.60/0.59 & 0.65/0.51 & 0.99/0.98 \\ (0, 2) & 0.71/0.55 & 0.58/0.49 & 0.98/0.88 \\ (2, 1) & 0.53/0.54 & 0.61/0.52 & 0.96/0.86 \\ (1, 2) & 0.54/0.53 & 0.62/0.52 & 0.97/0.88 \\ (0, 3) & 0.78/0.61 & 0.61/0.51 & 0.97/0.87 \\ heterogeneous & & & \\ dataset & & & \\ ALL\_1 & 0.80/0.75 & 0.56/0.51 & 0.99/0.98 \\ ALL\_2 & 0.56/0.53 & 0.56/0.52 & 0.99/0.98 \\ ALL\_3 & 0.56/0.54 & 0.55/0.53 & 1.00/0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy of the different embedding methods in equivalence link prediction. such as the alpha miner, the heuristic miner, and the inductive miner methods. The implementation of all these methods is available at Github repository [[https://github.com/process-intelligence-solutions/pm4](https://github.com/process-intelligence-solutions/pm4) py]([https://github.com/process-intelligence-solutions/pm4](https://github.com/process-intelligence-solutions/pm4) py) (accessed on 28 November 2024). In the tests, we applied the simple invocation of these methods, as presented in Listing 2. **Listing 2. ** Testing the PM4 PY methods. \begin{tabular}{l} \hline _(event_log_datatf) = conv_to_df(traces_1)_ \\ _pnet, initial_marking, final_marking = alpha_miner.apply(event_log)_ \\ _pm4 py.view_petri_net(pnet, initial_marking, final_marking, format = 'png')_ \\ _tree = pm4 py.discover_process_tree_inductive(event_log)_ \\ _pnet, initial_marking, final_marking = pm4 py.convert_to_petri_net(tree)_ \\ _pm4 py.view_petri_net(pnet, initial_marking, final_marking, format = 'png')_ \\ _heu_net = pm4 py.discover_heuristics_net(event_log, dependency_threshold = 0.0)_ \\ _pm4 py.view_heuristics_net(heu_net)_ \\ \hline \end{tabular}   
In addition to the PM4 PY methods, the efficiency comparison tests also cover the GNN-based process mining method proposed in [61]. Unlike the PM4 PY methods, this method applies machine learning engines for enhanced efficiency in schema induction. Regarding the test datasets, we involved both synthetic and real-world benchmark datasets. For the generation of synthetic datasets, we have developed a log data generation framework, where we can build trace datasets of different complexity levels. The complexity level is measured by the nesting level of the control structures and by the size of the schema graph. The input for the schema induction task is a list of traces, which all belong to the same hidden schema. For the generation of the input trace list, first, a target schema was constructed, which was used for the generation of the traces. The events in the traces were identified by the event type. As the schema may contain the same event type at different nodes, the trace may also contain the repetition of the event types. In the resulting graph of our proposed method, the nodes are symbolized with \(t\_j\) where \(t\) is the event type and \(i\) denotes the index of the corresponding quasi-cluster. The event type is input data, while the cluster indexes are generated during the induction process. The quality of schema generation is evaluated with the process mining measures proposed in [66]. In the efficiency comparison tests, we applied the following measures. * Simplicity (ms): This metric is calculated as the average of the number of both incoming and outgoing arcs calculated per node. A higher S value means larger complexity and it may show over-generalization.