# Distributed Action-Rule Discovery Based on Attribute Correlation and Vertical Data Partitioning
## 5 Results
### Comparative Insights  
Table 2 presents the results of two different vertical partitioning methods for action rule discovery along with the default (no vertical partitioning applied). These methods are applied to multiple datasets (A, B, and C). The methods evaluated are \"No Partition\", representing the default approach with no vertical partitioning method, \"Random\", which involves random vertical partitioning of flexible attributes, and \"Correlation\", the proposed method utilizing correlation-based vertical partitioning through hierarchical clustering. The Random and Correlation methods iterate through different numbers of groupings of flexible attributes. The \"Level\" column illustrates this. For each dataset, method, and level, the table then shows the execution time (in seconds), the number of generated rules, the precision, and the lightness metrics. Note that the \"Random\" method results are averaged across ten different iterations. Methods for both \"No Partition\" and \"Correlation\" methods are only run once, as results are consistent each time. It can be observed that the \"Correlation\" method achieves varying performance across different datasets, outperforming both the \"No Partition\" and \"Random\" methods in some cases. These results highlight the importance of considering correlation-based vertical partitioning for improved performance in certain scenarios. Our analysis of the 'Random' method and the correlation-based partitioning method on datasets A, B, and C revealed interesting insights into their respective performances. The 'Random' method, with its random vertical partitioning of flexible attributes, demonstrated faster individual runs compared to the correlation-based method. However, achieving reliable and meaningful results required a relatively high number of extracted action rules, high confidence, and high lightness. In all three of these measures, the correlation-based method outperformed the random partitioning method. The random-based method required extensive iterations (in our examples we used 10 iterations to get the averages). In contrast, the correlation-based partitioning method consistently produced results in each run without the need for extensive iterations. Although the correlation-based method generally exhibited slightly longer execution times than the 'Random' method, the time spent on obtaining averages was significantly reduced. The correlation-based partitioning method's ability to generate consistent results enabled us to achieve reliable performance metrics in a single run, leading to a more efficient overall analysis. Table 3 shows the results of the action rule generation method described in Section 4.1.2. The RSES-based action rule generation method produced significantly more rules compared to the approach utilizing [PERSON]'s package. For instance, in Dataset A, the RSES-based method extracted 1933 rules compared to only 10 rules by [PERSON]'s package. However, this increase in rule generation came at the cost of increased execution time, as seen in the longer runtime for the RSES-based method for Datasets A and C. Extracting action rules using the RSES-based method was faster for Dataset B. Notably, for Dataset A when employing the vertical partitioning method, the execution time was 193.552 seconds at level 2. However, with the correlation vertical partitioning, we observed faster runtimes. Our findings here underscore the importance of considering not only execution time but also the quality, and consistency of results when evaluating vertical partitioning methods for action rule discovery tasks. The correlation-based partitioning's capacity to yield