# Distributed Action-Rule Discovery Based on Attribute Correlation and Vertical Data Partitioning
## 4 Materials and Methods
### Experimental Setup
#### 4.3.5 Evaluation Metrics  
To facilitate the method comparison, we assessed various metrics including the run time (in seconds), the number of generated rules, precision, and the lightness. The run timerefers to the duration it takes for a method or process to complete its execution. In the context of our study, the run time is measured in seconds and indicates how long it takes for each method to run. This metric provides insights into the efficiency and computational speed of the method being evaluated. The computational efficiency of our method is paramount, especially when dealing with large datasets. By evaluating the run time, we ensure that our approach not only produces accurate results but also does so in a time-efficient manner, making it feasible for real-world applications. The precision is previously defined in Equation (12) in Section 4.1.1. Precision provides information on the quality of the generated rules by reflecting both their support and confidence. A higher precision ensures that the rules are not only widely applicable but also reliable, making them invaluable for decision-making processes. The number of generated rules represents the count of distinct rules produced by each method. In the context of this work, this metric reflects the richness and complexity of the rule set derived from each dataset. The quantity of generated rules can offer valuable information about the comprehensiveness and granularity of the rule-based system being analyzed. A greater number of rules offers a richer set of insights and actionable items. This directly corresponds with the lightness metric, further described below, wherein a higher value signifies more options for actionable insights. \begin{table}
\begin{tabular}{c p{284.5 pt}} \hline \hline
**Abbreviation** & **Attribute Name and Description** \\ \hline DC & BenchmarkAllDealerCommunication: Evaluates communication effectiveness within the dealer network. \\ \hline RC & BenchmarkAllLikelihoodtobeRepeatCustomer: Measures the likelihood of customer repeat business. \\ \hline OS & BenchmarkAllOverallSatisfaction: Assesses overall customer satisfaction levels. \\ \hline ECP & BenchmarkPartsEaseofCompletingPartsOrder: Gauges the ease of completing parts orders. \\ \hline PA & BenchmarkPartsPartsAvailability: Examines component availability for order fulfillment. \\ \hline TPO & BenchmarkPartsTimeitTooktoPlaceOrder: Measures the time taken for order processing. \\ \hline EDOC & BenchmarkPartsExplanationofDeliveryOptionsCosts: Explores the elucidation of delivery options and related costs. \\ \hline OA & BenchmarkPartsOrderAccuracy: Scrutinizes the accuracy of order processing. \\ \hline NBO & BenchmarkPartsPromptNotificationofBackOrders: Examines the timeliness of back-order notifications. \\ \hline KP & BenchmarkPartsKnowledgeofPersonnel: Assesses personnel knowledge about parts and their applications. \\ \hline RB & BenchmarkReferralBehavior: Explores referral behaviors. \\ \hline HOP & BenchmarkPartsHowOrdersArePlaced: Examines the methods of placing orders. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of Attribute Abbreviations with Corresponding Names and Descriptions. The lightness is a ratio that serves as a measure of how evenly the coverage is distributed across the set of rules. By representing the average number of action rules that apply to each object, lightness helps distinguish between random and correlation-based partitioning. In business and healthcare, where actionable insights are vital, a lightness  
Figure 3: Dendrograms for Flexible Attribute Groupings used for Vertical Correlation Partitioning Method. value between five and ten is considered ideal. The lightness for a generated set of action rules is defined in Equation (14) below:  
\[\text{Lightness}=\frac{\sum\text{Coverage of each action rule}}{\text{Coverage of entire set of action rules}} \tag{14}\]  
The Coverage for each individual action rule is defined as the number of tuples or items that the action rule encompasses in the dataset.