# Boosting the Learning for Ranking Patterns
## 6 Experiments
### Passive Learning Results
We observed that RankingSVM.0 outperformed AHPRank.0 in terms of ranking accuracy for all user feedback emulators, although AHPRank.0 remained competitive with acceptable accuracy. The same trend was observed in terms of recall at the 10% and 1% top of the ranking (R@10% and R@1%). We noted that AHPRank.0 achieved a high correlation with the user ranking functions on most datasets. However, on Connect, we observed a weak correlation with Chi-Emu, while a high correlation was observed with Rand-Emu and Lex-Emu. This can be attributed to the fact that Rand-Emu and Lex-Emu are linear functions expressed with the given seven interestingness measures, which explains their high accuracy, while Chi-Emu is a complex function that requires more extensive statistics to learn. Notably, the high accuracy of RankingSVM.0 came at the expense of longer running times. For instance, it took more than 15 min for RankingSVM.0 to learn from a training set of 100K rules, and exceeding 100K rules, RankingSVM.0 required more than one hour, while AHPRank.0 was able to handle 7.5 M rules in less than 4 min. In what follows, the observations and the conclusions drawn from Chi-Emu remain true for Rand-Emu and Lex-Emu. For the sake of simplicity, we only report the results on the complex function Chi-Emu. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{Rand-Emu} \\ \hline  & \multicolumn{6}{c}{RankingSVM.0} & \multicolumn{6}{c}{AHPRank.0} \\ \hline  & \(\rho\) & R@10\% & R@1\% & t(s) & \(\rho\) & R@10\% & R@1\% & t(s) \\ \hline Hepatitis & 0.94 & 0.74 & 0.77 & 851 & 0.93 & 0.79 & 0.71 & 9 \\ Connect & - & - & - & TO & 0.95 & 0.72 & 0.63 & 26 \\ Mushroom & - & - & - & TO & 0.89 & 0.69 & 0.66 & 32 \\ T40 & - & - & - & TO & 0.99 & 0.93 & 0.58 & 63 \\ Retail & - & - & - & TO & 0.93 & 0.95 & 0.96 & 66 \\ \hline _mean_ & - & - & - & - & 0.94 & 0.82 & 0.71 & 39 \\ \hline \multicolumn{6}{c}{Lex-Emu} \\ \hline  & \multicolumn{6}{c}{RankingSVM.0} & \multicolumn{6}{c}{AHPRank.0} \\ \hline  & \(\rho\) & R@10\% & R@1\% & t(s) & \(\rho\) & R@10\% & R@1\% & t(s) \\ \hline Hepatitis & 0.99 & 0.99 & 0.99 & 902 & 0.92 & 0.86 & 0.81 & 13 \\ Connect & - & - & - & TO & 0.60 & 0.46 & 0.50 & 21 \\ Mushroom & - & - & - & TO & 0.86 & 0.56 & 0.65 & 32 \\ T40 & - & - & - & TO & 0.99 & 0.93 & 0.46 & 71 \\ Retail & - & - & - & TO & 0.78 & 0.68 & 0.65 & 68 \\ \hline _mean_ & - & - & - & - & 0.83 & 0.70 & 0.61 & 41 \\ \hline \multicolumn{6}{c}{Chi-Emu} \\ \hline  & \multicolumn{6}{c}{RankingSVM.0} & \multicolumn{6}{c}{AHPRank.0} \\ \hline  & \(\rho\) & R@10\% & R@1\% & t(s) & \(\rho\) & R@10\% & R@1\% & t(s) \\ \hline Hepatitis & 0.99 & 0.97 & 0.92 & 979 & 0.94 & 0.90 & 0.77 & 10 \\ Connect & - & - & - & TO & 0.15 & 0.28 & 0.67 & 17 \\ Mushroom & - & - & - & TO & 0.98 & 0.91 & 0.93 & 28 \\ T40 & - & - & - & TO & 0.99 & 0.99 & 0.96 & 84 \\ Retail & - & - & - & TO & 0.91 & 0.96 & 0.95 & 50 \\ \hline _mean_ & - & - & - & - & 0.79 & 0.81 & 0.86 & 38 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Five-fold cross-validation results (passive learning). **(C) Impact of varying the size of the training data on learning. ** It is crucial to emphasize that our proposed AHPRank approach aims to achieve a fast learning process while providing high accuracy in ranking patterns. To further support our observation on the scalability of AHPRank.0 compared to RankingSVM.0, we present in Figures 2 and 3 a performance comparison by varying the size of the training data when learning the Chi-Emu function, as similar results were obtained for Rand-Emu and Lex-Emu functions. For each dataset, we randomly select \(nb\) rules, and we compare the two approaches for \(nb\in~{}10\), \(100\), \(1\)K, \(10\)K, \(100\)K. The results are averaged over ten runs. Regarding the Spearman correlation \(\rho\), Figure 2 shows that the two approaches have a discrepancy of only 5% when the training data does not exceed 1K. However, the gap becomes significantly more substantial (exceeding 10%) and in favor of AHPRank.0 when the training data contains 10K and 100K rules.