# A Novel Process Recommendation Method That Integrates Disjoint Paths and Sequential Patterns
## 3 Proposed Method
### Process Node Recommendation  
To recommend the best next node for the current node 'A' of the reference model, first, all edge-disjoint paths of the reference model are extracted. Then, the edge-disjoint path \(L\) whose last node is 'A' is searched to find the longest common substring between \(L\) and the CPSP \(S\) of each sequence rule. The similarity of \(L\) and \(S\) is calculated using the following formula:  
\[LCS\_Sim(L,S)=\frac{|LCS(L,S)|\times 2}{(|L|+|S|)} \tag{4}\]  
where \(LCS\_Sim\) denotes the similarity and \(LCS\)(\(L\),\(S\)) denotes the longest common subsequence owned by \(L\) and \(S\)[26; 36]. To measure the importance of nodes in different positions in edge-disjoint paths, we proposed the concept of node recommendation degree. As an example, given an edge-disjoint path \(<\)A,B\(>\), there exist two sequential rules \(<\)A,C,1.5,1.5,2\(>\) and \(<\)B,D,1.5,1.5,2\(>\) with a similarity of 0.5. However, we considered that \(<\)B,D\(>\) has a greater impact on the recommended node than \(<\)A,C\(>\). Thus, the node recommendation degree was introduced. For the two nodes in \(<\)A,B\(>\), the node recommendation degree of node 'A' was 0.9, and the node recommendation degree of node 'B' was 1. Therefore, the position importance of node 'B' was considered higher than that of node 'A'. **Definition 3**. : _Node Recommendation Degree: Let \(L\) =\(<l_{1}l_{2}\),... \(l_{n}\)\(>\) be the edge-disjoint path of the reference model and \(S\) be the CPSP, then the node recommendation of \(l_{i}(1\leq i\leq n)\) is shown in Equation (5):_  
\[REC\_Node(l_{i},S)\] \[=\left\{ \begin{array}{ll}0,&l_{i}\in S\\ 1,&l_{i}\in S\cap S_{index}=-1\\ 1.1-\Big{(}\frac{len(L)-L_{index}}{10}\Big{)},&l_{i}\in S\cap S_{index}\
eq-1 \end{array} \right. \tag{5}\]  
where \(REC\_Node\) is the node recommendation degree, \(S_{index}\) is the index of \(l_{i}\) in \(S\), \(L_{index}\) is the index of \(l_{i}\) in \(L\), and \(len\) is the sequence length. The process-matching degree is then calculated using the following formula:  
\[P\_m(L,S)=\lambda LCS\_Sim(L,S)+\varphi REC(L,S) \tag{6}\]where \(P\_m\) is the process-matching degree; \(REC\) is the maximum value of node recommendation degrees for all nodes in the edge-disjoint path; and \(\lambda+\varphi=1\), where \(\lambda=0.5\) and \(\varphi=0.5\) were selected in this study. As shown in Table 1, when mining the CPSP of edge-disjoint paths of length \(n\), a great deal of knowledge of process nodes is discovered, and CPSPs of length \(i\) (\(2\leq i\leq n\)) will all be mined as process segments to be matched. Therefore, we set the following recommended node of node 'A' to the last node in the CPSP with the highest process-matching degree, thus avoiding interference with duplicate nodes in the CPSP. Finally, the recommended node was added to the execution sequence of the reference model. When recommending \(k\) candidates for the next node for node 'A', the CPSPs in the sequential rule were first sorted according to the process-matching degree. When there were CPSPs with the same process-matching degree, the lift, confidence, and support degrees were introduced to measure the sequential rules with greater recommendation values. The lift degree, confidence degree, and support degree serve as the basis for determining the behavioral association relationship between the prefix and the last node in a CPSP. Among them, the support degree of a CPSP indicates the frequency of simultaneous occurrence of the prefix and the last node in this sequence pattern. The confidence degree indicates the probability of the last node's simultaneous occurrence when this prefix occurs, which is more reliable than the support degree. However, since the support degree of the last node is not calculated, it may misestimate the sequential rule's importance. The lift degree best reflects the correlation between the prefix and the last node in that sequence pattern, and a higher lift indicates a higher positive correlation [37; 38].