# Boosting the Learning for Ranking Patterns
## 6 Experiments
### Passive Learning Results  
In this section, we address the first two research questions (**RQ1** and **RQ2**). To that end, we perform a five-fold cross-validation on each dataset, where we randomly select 20% of the rules as training data and use the remaining 80% for testing. This type of cross-validation allows us to evaluate the effectiveness of the approaches in learning from relatively small training sets. We report the results averaged over the five folds. **(A) Analyzing the different user feedback emulators. ** Table 4 presents the results of the correlation analysis between the user-specific ranking functions (Rand-Emu, Lex-Emu, and Chi-Emu) and the seven interestingness measures, as well as the virtual best measure (VBM), which returns the best rank correlation \(\rho\) provided by one of the seven measures. The analysis was performed on all datasets, and the results are reported in terms of Spearman's rank correlation coefficient \(\rho\). The results show that the correlation between a given measure and a user-specific ranking function can vary significantly depending on the dataset. For instance, the Lambda measure is highly correlated with Chi-Emu on the T40 dataset (\(\rho=98\%\)), but it is weakly correlated on the Connect dataset (\(\rho=29\%\)). Similarly, the correlation between Rand-Emu or Lex-Emu and the measures also varies significantly across the datasets. However, the VBM approach, which selects the best measure for each dataset, achieves a high level of accuracy (with a mean of 91%). These results suggest that a weighted aggregation of the selected measures could lead to a good trade-off between accuracy and robustness. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multicolumn{8}{c}{**Measures**} \\ \cline{2-9}  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** & **(6)** & **(7)** & VBM \\ \hline \multicolumn{9}{c}{Rand-Emu} \\ \hline Hepatitis & 0.78 & 0.92 & 0.29 & **0.97** & 0.79 & 0.85 & 0.45 & **0.97** \\ Connect & 0.68 & 0.62 & **0.95** & 0.70 & 0.60 & 0.45 & 0.57 & **0.95** \\ Mushroom & 0.84 & **0.97** & 0.28 & 0.83 & 0.55 & 0.73 & 0.36 & **0.97** \\ T40 & 0.71 & **0.99** & 0 & 0.76 & **0.99** & **0.99** & 0 & **0.99** \\ Retail & 0 & **0.98** & 0.43 & 0.71 & 0.84 & **0.98** & 0.51 & **0.98** \\ \hline \multicolumn{9}{c}{Lex-Emu} \\ \hline Hepatitis & 0.79 & 0.64 & 0 & 0.68 & **0.92** & 0.63 & 0 & **0.92** \\ Connect & 0.21 & 0.47 & **0.76** & 0.26 & 0 & 0.23 & 0.50 & **0.76** \\ Mushroom & 0.21 & **0.82** & 0.38 & 0.77 & 0.78 & 0.37 & 0 & **0.82** \\ T40 & 0.76 & 0.98 & 0 & 0.77 & **0.99** & 0.97 & 0 & **0.99** \\ Retail & 0.10 & 0.78 & 0.54 & 0.49 & **0.84** & 0.80 & 0.58 & **0.84** \\ \hline \multicolumn{9}{c}{Chi-Emu} \\ \hline Hepatitis & 0.20 & 0.92 & 0.36 & **0.96** & 0.73 & 0.85 & 0.43 & **0.96** \\ Connect & 0.09 & 0.15 & 0 & 0.02 & **0.29** & 0.01 & 0 & **0.29** \\ Mushroom & 0.51 & 0.64 & 0 & 0.46 & 0.28 & **0.88** & 0 & **0.88** \\ T40 & 0.71 & 0.98 & 0.17 & 0.64 & 0.98 & **0.99** & 0.29 & **0.99** \\ Retail & 0 & **0.94** & 0.53 & 0.60 & 0.83 & 0.57 & 0.61 & **0.94** \\ \hline \hline \end{tabular} (1): Tukey, (2): Cosine, (3): Laplace, (4): Leverage, (5): Lambda, (6): InteractFactor, (7): Certainty.  
\end{table} 
Table 4: Correlation results with user ranking for using the emulators. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{\(|\mathcal{T}|\)} & \multirow{2}{*}{\(|\mathcal{I}|\)} & **Density** & \multirow{2}{*}{**Type of Data**} & \multirow{2}{*}{**\#Rules**} \\ \cline{1-1} \cline{6-6} \cline{6-  
**(B) Comparing AHPRank.0 with RankingSVM.0. ** Table 5 presents the results of the k-folds cross-validation for RankingSVM.0 and AHPRank.0, where we report the averaged rank correlation \(\rho\), recall values (R@10% and R@1%), and CPU time in seconds averaged over the folds. Since RankingSVM.0 can handle a training set of up to 100 K rules within an hour, we compared it with our approach with the Hepatitis dataset only.