# Explainable Internet Traffic Classification
## 4 Experimental Results
### Comparison among the Different Classification Models
Given such fuzzy sets, the following are a few examples of classification rules:  
R1: **IF**\(f\_S_{\mu}\) is VL **THEN** Y is Skype  
R2: **IF**\(f\_N\) is L **THEN** Y is Amule  
R3: **IF**\(f\_S_{M}\) is H **AND**\(r\_T_{M}\) is **M THEN** Y is Mail  
R4: **IF**\(f\_N\) is H **AND**\(f\_V\) is VH **AND**\(r\_V\) is **H **AND**\(r\_S_{m}\) is L **AND**\(f\_S_{M}\) is F ML **AND**\(r\_S_{M}\) is H **AND**\(r\_S_{\mu}\) is H **AND**\(f\_S_{\sigma}\) is VH **AND**\(r\_S_{\sigma}\) is VH **AND**\(f\_T_{M}\) is H **THEN** Y is Mail \begin{table}
\begin{tabular}{c l c c c c} \hline \hline \multirow{2}{*}{**Data-Set**} & \multicolumn{3}{c}{**C4.5**} & \multicolumn{3}{c}{**PAES-RCS**} \\  & **Feature** & **Tree Dimension** & **Leaves** & **TRL** & **Rules** \\ \hline \multirow{3}{*}{UniBS} & Statistical & 449 & 228 & 95.8 & 17.86 \\  & Composite (\(H=3\)) & 194 & 118 & 98.13 & 35.3 \\  & Composite (\(H=5\)) & 889 & 435 & 41.86 & 21.4 \\  & Composite (\(H=10\)) & 712 & 383 & 40.53 & 15.6 \\ \hline \multirow{3}{*}{UPC} & Statistical & 3321 & 147 & 59.06 & 15.93 \\  & Composite (\(H=3\)) & 247 & 134 & 22.2 & 14.86 \\ \cline{1-1}  & Composite (\(H=5\)) & 364 & 176 & 36.46 & 17.53 \\ \cline{1-1}  & Composite (\(H=10\)) & 447 & 223 & 50.87 & 16.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Performance comparison: Complexity (for the PAES-RCS algorithm the _First solution_ has been considered). \begin{table}
\begin{tabular}{c l c c c c c c} \hline \hline \multirow{2}{*}{**Data-Set**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Test**} \\  & **Feature** & **SVM** & **C4.5** & **PAES-RCS** & **SVM** & **C4.5** & **PAES-RCS** \\ \hline \multirow{3}{*}{UniBS} & Statistical & 0.864 & 0.972 & 0.893 & 0.759 & 0.969 & 0.875 \\  & Composite (\(H=3\)) & 0.741 & 0.842 & 0.752 & 0.662 & 0.828 & 0.704 \\  & Composite (\(H=5\)) & 0.85 & 0.871 & 0.804 & 0.717 & 0.86 & 0.72 \\  & Composite (\(H=10\)) & 0.964 & 0.974 & 0.839 & 0.874 & 0.961 & 0.802 \\ \hline \multirow{3}{*}{UPC} & Statistical & 0.854 & 0.99 & 0.883 & 0.71 & 0.981 & 0.861 \\  & Composite (\(H=3\)) & 0.635 & 0.887 & 0.721 & 0.538 & 0.867 & 0.662 \\ \cline{1-1}  & Composite (\(H=5\)) & 0.884 & 0.983 & 0.892 & 0.776 & 0.964 & 0.816 \\ \cline{1-1}  & Composite (\(H=10\)) & 0.977 & 0.973 & 0.904 & 0.896 & 0.966 & 0.886 \\ \hline \hline \end{tabular}
\end{table} 
Table 19: Performance comparison: Accuracy (for the PAES-RCS algorithm the _First solution_ has been considered). It is clear, that such rules, being linguistic rules, can be easily read and understood by an operator. For the sake of completeness, we highlight that both UniBS and UPC are data sets that exhibit some level of imbalance. Therefore, we have applied a set of re-balancing techniques, but the obtained results did not show appreciable improvements. This is probably due to the fact that the level of unbalancing is not very high. Indeed, as can be seen from the tables and the confusion matrices discussed above, we have verified that poor results on specific classes are not due to the imbalance level but rather to the adopted feature extraction procedure and/or to classification model selected. Due to space reasons and to their scarce relevance, we have not reported all the results achieved adopting a re-balancing step of the training set.