## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**pH**} & \multirow{2}{*}{**LVs**} & \multirow{2}{*}{**Accuracy**} & \multicolumn{3}{c}{**CCR (\%)**} \\ \cline{3-5}  & & & & **Class High** & **Class Low** \\ \hline \multirow{3}{*}{3} & Calibration & & 100.00 & 100.00 & 100.00 \\  & CV & & 92.16 & 77.14 & 96.61 \\  & Prediction & & 82.67 & 65.22 & 90.38 \\ \hline \multirow{3}{*}{5} & Calibration & & 100.00 & 100.00 & 100.00 \\  & CV & 10 & 89.54 & 85.19 & 91.92 \\  & Prediction & & 89.33 & 81.48 & 93.75 \\ \hline \multirow{3}{*}{7.4} & Calibration & & 100.00 & 100.00 & 100.00 \\  & CV & 7 & 91.50 & 93.90 & 88.73 \\  & Prediction & & 89.33 & 84.31 & 100.00 \\ \hline \multirow{3}{*}{9} & Calibration & & 100.00 & 100.00 & 100.00 \\  & CV & 7 & 90.13 & 93.10 & 86.15 \\  & Prediction & & 88.16 & 77.50 & 100.00 \\ \hline \multirow{3}{*}{IP} & Calibration & & 100.00 & 100.00 & 100.00 \\  & CV & 11 & 96.08 & 96.23 & 95.74 \\ \cline{1-1}  & Prediction & & 93.33 & 91.23 & 100.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PLS-DA: number of latent variables (LVs), overall accuracy and correct classification rate (CCR%) for the individual categories on the training set (in calibration, and cross-validation (CV)) and the test set (prediction). A graphical representation of the results can be seen in Figure 2, where calibration (empty symbols) and validation molecules (filled symbols) have been projected onto the space spanned by the first two latent variables (LVs). From the plot, it is possible to notice a clear grouping tendency among observations belonging to the two classes. In particular, the greatest part of the compounds presenting low permeability (red diamonds) falls at the positive values of both LV1 and LV2; however, high-permeating molecules (blue triangles) spread along LV1, but mainly present negative scores for LV2. This representation does not completely reflect the accuracy of the achieved results (a total accuracy of 93.33%), which corresponds to the misclassification of only five test samples (over 75), all belonging to class _high-permeable_. Nevertheless, this is due to the fact that the displayed scores plot provides a substandard representation of the results, because it takes into account only the variability modelled by two (over eleven) components. Eventually, in order to investigate which molecular descriptors contribute the most to the prediction of the permeability characteristics of the investigated molecules, and, at the same time, to verify whether retaining only the most relevant predictors could improve the classification models, a variable selection strategy based on the covariance selection (CovSel) algorithm [22] was adopted. In particular, for each dataset, models including an increasing number of descriptors (selected by CovSel, up to a maximum of 50) were built and cross-validated (using five cancelation groups). Eventually, the number of variables (nVar) leading to the lowest classification error in cross-validation was selected, and the optimal one and the corresponding descriptors were used to build the final PLS-DA classification model, which was then validated on the test molecules. In all cases, the selected descriptors can be considered as the ones being more relevant in determining the discrimination between high- and low-permeable substances, providing the basis for a molecular interpretation of the permeation process. The number of selected molecular descriptors and the classification results of the PLS-DA models built on the reduced sets of variables (both in cross-validation on the training data and in prediction on the external test sets) are summarized in Table 4.  
Figure 2: PLS-DA: model on the IP-based categorization. Projection of the training and test molecules onto the first two latent variables. In general, variable selection of the variables has led to an improvement from the point of view of prediction.