# A Novel Process Recommendation Method That Integrates Disjoint Paths and Sequential Patterns
## 4 Experimental Results and Analysis
### Validity Test  
The EPE and CPSPan proposed in this study directly impact the effectiveness of the process recommendation. Therefore, to verify the effectiveness of the proposed algorithms, this experiment compared the VPE and Prefixspan with the methods proposed in this study to examine the enhanced effect of the proposed algorithms in the process recommendation. The experiment consisted of three stages: preprocessing, sequential pattern mining, and node recommendation. In the VPE experiment, the VPE was applied in the preprocessing stage to obtain the vertex-disjoint path of the process model, and CPSPan was utilized in the sequential pattern mining stage. In the Prefixspan method experiments, the EPE was employed in the preprocessing stage, and Prefixspan was utilized in the sequential pattern mining stage. This study used the EPE in the preprocessing stage and CPSPan was employed in the sequential pattern mining stage. For the node recommendation stage, all three methods utilized Algorithm 3 in Section 4.3. The effectiveness of the two proposed algorithms was verified by comparing the VPE and Prefixspan methods with the method proposed in this study. In the experiment, a five-fold cross-validation strategy was employed. The real dataset was randomly divided into five subsets of similar size, namely, _G1_, _G2_, _G3_, _G4_, and _G5_. Four subsets were selected in turn as training sets for disjoint path extraction and sequential pattern mining, and the remaining subset was used as a cross-validation test set. Finally, the five experimental results were used to evaluate the recommendation effect. For each process model in the test set, the recommendation started from the second node because there was no recommendation basis for the starting node. The correct recommendation node was determined as the next node of the process model in the original model. If the recommendation result included the correct recommendation node, it was considered a recommended hit. The recommended hit rate was calculated using the following equation:  
\[HitRate=\frac{hit\_times}{rec\_times} \tag{7}\]  
where _hit_times_ denotes the number of hits and _rec_times_ denotes the number of recommendations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Experimental Process Model** & **Process Nodes** & **Shortest/Longest Model Nodes** & **Sequential Rules** & **Complex Structures** \\ \hline Real dataset & 337 & 276 & 2/8 & 4268 & \(\surd\) \\ Simulation dataset & 75 & 222 & 8/18 & 10,833 & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Process dataset. _HitRate_ verified the recommended effectiveness of the experiment. Suppose the recommended _HitRate_ increased, and the application of the algorithm was confirmed to be effective. The effectiveness of the algorithm was examined by calculating the _HitRate_ for different numbers of recommendations (i.e., top k). The comparison results in Figure 8 show that the _HitRate_ for all three methods increased as the number of recommended results (\(k\)) increased. When \(k\) was greater than 3, the _HitRate_ of the proposed method exceeded 95%. Specifically, for \(k=1\), the _HitRate_ of the VPE method was 45%, while it was 68% for the proposed method; for \(k=5\), the _HitRate_ of the VPE method was 88%, while the proposed method reached 100%, demonstrating the effectiveness of the proposed EPE. These results demonstrate that the EPE outperformed the VPE regarding process recommendation, as the former could extract a larger set of disjoint paths, which could better capture the behavioral semantics of a process. In contrast, the vertex-disjoint paths extracted by VPE were a subset of the edge-disjoint paths, and there were an infinite number of vertex-disjoint paths under the 'Loop' structures. In the Prefixspan method experiments, the _HitRate_ was 33% for \(k=1\), which was 35% lower than for the proposed method; for \(k=5\), it was 37% lower than the _HitRate_ of the proposed method, confirming the effectiveness of CPSpan in the proposed method.