# A Novel Process Recommendation Method That Integrates Disjoint Paths and Sequential Patterns
## 3 Proposed Method
### CPSP Mining Method
The occurrence of each item was counted and the frequent 1-sequence <A><C><D><B> was obtained by selecting the items that met the minimum support threshold. The CPSP was then recursively mined. First, we traversed the database and obtained the continuous path suffix projection database SD\(\mid{}_{A}=\) [<C,D,B><D,C,B>] for the prefix <A>. For each suffix in SD\(\mid{}_{A}\), such as <C,D,B>, only the first item <C> was mined to ensure the continuity of the sequential pattern. The frequent 2-sequence <A,C> was obtained and used as a new prefix. Then, the suffix projection database SD\(\mid{}_{A,C}=\) [<D,B>], was built and further mined to obtain the frequent 3-sequence <A,C,D>. <A,C,D> was used as a new prefix, and the suffix projection database became SD\(\mid{}_{A,C,D}=\) [<B>]. <A,C,D,B> was mined from it. As the suffix projection database was empty, mining for the frequent 1-sequence <A> was finished and all its CPSPs were obtained: <A><A,C><A,C,D><A,C,D,B> <A,D><A,D,C><A,D,B>. Using the same approach, CPSPs were mined with other frequent 1-sequences <C>, <D>, and <B> as prefixes. The set of CPSPs was then reduced by deleting the frequent 1-sequences that were not meaningful for the recommendation. Table 1 compares the mining results of three sequential pattern mining algorithms for <A,C,D,B> and <A,D,C,B>. The results show that Prefixspan was too redundant in its mining results due to its lack of contiguous sequence constraint, resulting in discontiguous sequential patterns that did not follow the execution sequence of path sequences in the process library model and had a low reference. CCSpan [29] is a closed contiguous mining algorithm that generates only superset sequences with different degrees of support, excluding many sequence patterns with the same degree of support but the same recommendation value. In contrast, the proposed CPSPan can mine each sequential pattern of consecutive positions in the knowledge discovery process of edge-disjoint path sequences without disrupting the execution order of the process model, providing a greater range of options and more dependable guidance for process recommendation. This advantage becomes more apparent when mining long edge-disjoint path sequences. \begin{table}
\begin{tabular}{l} \hline
**Algorithm** \\ \hline PrefixSpan & A:2,AC:2,AD:2,AB:2,ACD:1,ACB:2,ADC:1,ADB:2,ACDB:1,ADCB:1,B:2,C:2,CD:1,CB:2,CDB:1,D:2,DB:2,DC:1,DCB:1 \\ CCSpan & ACDB:1,ADCB:1,CB:1,CDB:1,DB:1,DCB:1 \\ CPSPan & AC:1,AD:1,ACD:1,ADC:1,ACDB:1,ADCB:1,CDB:1,CDB:1,DC:1,DCB:1 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of sequential pattern mining results. After mining the CPSP, the support, confidence, and lift of the CPSP were calculated according to the following formulas:  
\[Sup(S)=Sup(\alpha\rightarrow\beta)=num(\alpha\cup\beta) \tag{1}\]  
\[Conf(S)=Conf(\alpha\rightarrow\beta)=P\bigg{(}\frac{\beta}{\alpha}\bigg{)}=\frac{ num(\alpha\cup\beta)}{num(\alpha)} \tag{2}\]  
\[Lift(S)=Lift(\alpha\rightarrow\beta)=\frac{P(\beta/\alpha)}{P(\beta)}=\frac{P( \alpha,\beta)}{P(\alpha)\times P(\beta)}=\frac{num(\alpha\cup\beta)\times num( D)}{num(\alpha)\times num(\beta)} \tag{3}\]  
In process recommendation, the recommended node is always the last node of a CPSP. Therefore, when calculating the support, confidence, and lift of the CPSP \(S\) =\(<s_{1}s_{2},\ldots\)\(s_{n}\)\(>\), the contiguous path suffix \(\beta\) is always the last node \(s_{n}\) and the prefix \(\alpha\) is always \(<\)\(s_{1}s_{2},\ldots\)\(s_{n}\)\(>\). **Definition 2**. : _Sequential rule: We define sequence rules as quadruples \(T\) = (\(S\), Lift(\(S\)), Conf(\(S\)), Sup(\(S\))), where \(S\) is a CPSP, and Lift(\(S\)), Conf(\(S\)), and Sup(\(S\)) are its lift, confidence, and support, respectively._  
Save all sequential rules in the sequential rule library for the subsequent process node recommendation.