# Numerical Association Rule Mining from a Defined Schema Using the VMO Algorithm
## 5 Results and Discussion
### QM_VMO Performance Evaluation  
We compared QM_VMO with the genetic version of QUANTUMINER and three evolutionary algorithms from the literature: GAR [43], GENER [50], and MODENAR [51]. The experimentation was carried out in the R project environment with the RKEEL version 1.3.1 library, which includes the last three algorithms mentioned. The tests were performed with nine databases, as described in Table 6. The algorithms' parameters were configured according to the specifications from the literature, and QM_VMO used the values found by our analysis. In Table 7, we show the initial configurations for the cited algorithms. The minimum support and confidence values in the case of the first two algorithms in the list were established at ten percent and sixty percent, respectively; for the others, they were adjusted according to need. In general, the comparison between algorithms with totally similar properties was not very achievable when referencing those existing in the literature. The configuration \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(P\) & \(it\) = 200 & \(it\) = 300 &... & \(it\) = 1000 & R \\ \hline
8 & 1 & 2 &... & 4 & 31.4 \\
12 & 3 & 3 &... & 3 & 28.0 \\
24 & 2 & 1 &... & 5 & 25.8 \\
50 & 4 & 4 &... & 2 & 26.2 \\
100 & 5 & 5 &... & 1 & 30.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ranking of the sizes of populations with iterations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(P\) & 5 K & 10 K & 20 K & 50 K & 100 K & R \\ \hline
8 & 4 & 2 & 3 & 4 & 4 & 17.9 \\
12 & 5 & 5 & 4 & 5 & 5 & 24.5 \\
24 & 1 & 1 & 1 & 1 & 3 & 7.9 \\
50 & 2 & 4 & 5 & 2 & 1 & 15.6 \\
100 & 3 & 3 & 2 & 3 & 2 & 13.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ranking of the sizes of populations with rows of datasets. structure and requirements of our QM_VMO algorithm could be said to be very similar to those of QUANTMINER, and both required a rule scheme to start the process. This specification allowed the user to obtain the desired rules more quickly. However, it could only explore rules generated by combining the attributes defined in the schema. The additional techniques that are cited do not define a rule template. They explore the entire set of a dataset's attributes, thus allowing greater diversity to be achieved, but with the risk of converging on less understandable rules. Figure 3 shows the average values of the support measure achieved for each dataset. Figure 4 presents the measure of confidence. With respect to the first two algorithms, the advantage obtained by our technique is more notable than that of QUANTMINER. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Dataset** & **Attributes** & **Rows** \\ \hline Abalone19 & 9 & 4174 \\ Basketball & 5 & 96 \\ Bupa & 6 & 345 \\ Dee & 7 & 365 \\ Glass & 10 & 214 \\ iris & 5 & 150 \\ Vehicle & 9 & 846 \\ Vowel0 & 13 & 988 \\ Wine & 13 & 178 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Datasets’ properties. Figure 3: Support measures for each dataset. High coverage values for rule support are very significant when frequent patterns are found for qualitative variables. On the contrary, for quantitative attributes, they constitute a disadvantage in the quality of the rule. In fact, the average width of the interval is a criterion that was considered in the objective function that we used for our technique. Another criterion of interest is the number of rules. However, the configuration of the parameters can condition the number of visible rules when the amount generated is too extensive. In general, the most representative rules are shown in order of the metric of interest. Table 8 shows average values obtained in each of the metrics. Rules of all dimensions are considered to calculate the average number. However, there is a greater concentration on rules of 2, 3 and 4 attributes for all algorithms. Comparing QARMVMO and QUANTMINER is more precise due to their similarity in both configuration parameters and method.