# Distributed Action-Rule Discovery Based on Attribute Correlation and Vertical Data Partitioning
## 5 Results
### Individual Action Rules
#### 5.2.1 Illustrating Vertical Correlation Method Combinations  
In this section, we focused on utilizing the Vertical Correlation Method to generate action rules to illustrate instances of action rules being generated within one dendrogram level and making their combinations. This iteration employed a confidence threshold of 50% and a support threshold of two for rule generation. Our analysis centered on Dataset C and exploreed results obtained from examining \"Level 5\" of the dendrogram. Refer to Figure 3 for the Dataset C dendrogram and how flexible attributes were clustered. Within this level, distinct clusters emerged, with attributes such as OA, DC, TPO, and ECP forming one cluster, and OS and RC forming another. By showcasing these specific configurations, we aim to offer insights into the patterns and relationships revealed by the vertical correlation approach. **Example 1**. : _In one of the instances of generated action rules, we examined one rule at level 5. This rule, shown in Equation (16) reads as follows: if the division attribute equals \"parts\" and simultaneously experiences changes in the TPO attribute from \"high\" to \"very high\", changes in ECP from \"high\" to \"very high\", and changes in RC from \"high\" to \"very high\", the resulting implication is a shift in PromoterStatus from \"Passive\" to \"Promoter\". In other words, we want to increase the company's ratings for the time it took to place the parts order, the ease of completing the parts order, and the customer's rating to be a likely repeat customer. If all of these change from high to very high, we can infer a change in the promoter status from passive to a promoter. This rule had a support of 15 and a confidence of 0.755._  
\[(Division,\text{parts})\wedge(TPO,\text{high}\rightarrow\text{very high})\wedge(ECP,\text{high}\rightarrow\text{very high}) \tag{16}\] \[\wedge(RC,\text{high}\rightarrow\text{very high})\] \[\Rightarrow(PromoterStatus,\text{Passive}\rightarrow\text{Promoter})\]  
This rule represented a synthesis of two distinct rules from each of the clusters at this level. As we can see in our earlier Figure 3, one cluster for Dataset C at level 5 consists of the flexible attributes OA, DC, TPO, and ECP while the other consists of OS, and RC. The first rule, shown in Equation (17) entails: \"_if division = parts, TPO changes from high to very high, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **Method** & **Level** &
\begin{tabular}{c} **Time** \\ **(Seconds)** \\ \end{tabular} & **Rules** & **Precision** & **Lightness** \\ \hline A & No Partition & 1 & 2726.625 & 1933.0 & 0.908 & 164.268 \\  & Correlation & 2 & 193.552 & 130.0 & 0.945 & 12.895 \\ \hline B & No Partition & 1 & 58.101 & 36.0 & 0.843 & 12.958 \\  & Correlation & 2 & 20.484 & 22.0 & 0.855 & 5.099 \\ \hline C & No Partition & 1 & 2019.907 & 4042.0 & 0.855 & 786.190 \\  & Correlation & 2 & 1158.997 & 602.0 & 0.893 & 70.293 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of Preliminary Performance Metrics for Secondary RSES-Based Action Rule Generation Method. ECP changes from high to very high, the implication is a transition in promoter status from passive to promoter\". This first rule had a support of 22 and a confidence of 0.499. The second rule, shown in Equation (18), contributing to this combination is: _\"if division = parts and RC changes from high to very high, we infer a change in promoter status from passive to promoter\"._ This rule had a support of 39 and a confidence of 0.7211. \[ \begin{split}(Division,\text{parts})\wedge(TPO,\text{high}& \rightarrow\text{very high})\wedge(ECP,\text{high}\rightarrow\text{ very high})\\ \Rightarrow(PromoterStatus,\text{Passive}& \rightarrow\text{Promoter})\end{split}  \tag{17}\]  
\[ \begin{split}(Division,\text{parts})\wedge(RC,\text{high} \rightarrow\text{very high})\\ \Rightarrow(PromoterStatus,\text{Passive}& \rightarrow\text{Promoter})\end{split}  \tag{18}\]  
**Example 2**. : _In this second example, also from level 5, our rule is shown in Equation (19).