## 3 Results and Discussion  
As described above, a total of five different datasets were available, four associated with different pH conditions (3, 5, 7.4 and 9) and one with the IP. Each distinctive dataset was individually processed; consequently, five different classification models have been developed. In order to perform the external validation of the models, prior to their creation, each dataset was divided into a training and a test set. It is trivial that, given the different distribution of the samples in the two classes as the pH varies, the training and the test sets of the different models do not correspond. In order to ensure the representativeness of the populations of the two sub-sets, the molecules were split into calibration and validation sets by the Duplex algorithm [21]. A summary diagram of the distribution of the samples into the two classes at the different pH levels is shown in Table 2.  
As mentioned above, five different PLS-DA models were calculated, one per each auto-scaled dataset. In particular, the training data were used to build the corresponding classification models, the optimal complexity of which (in terms of number of latent variables (LVs)) was defined as the one leading to the lowest classification error (%CECV) in a five-fold cross-validation procedure. For each dataset, once the classification model was built on the training set with the selected optimal complexity, it was then applied to the test set to be validated. The overall accuracy and the correct classification rate (CCR%) for each category are reported in Table 3.  
As can be observed, from the prediction point of view, there is a general improvement with the increase in the pH. This is probably due to a higher stability of the system, and a greater balance of compounds between the classes. In agreement with this observation, it can be noticed that the less accurate model, i.e., the one that led to the lowest CCR, is built on the data collected at pH 3; however, this provided a completely acceptable result, successfully predicting the permeability category of 83% of all the test samples, completely in agreement with the individual classification models discussed by [PERSON] et al., whose predictive accuracies ranged between 81% and 88%. However, the highest accuracy was provided by the model built on the IP dataset, which achieved an overall correct classification rate of -93% on the external test set. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & \multirow{2}{*}{pH} & \multicolumn{3}{c}{**Training Set**} & \multicolumn{3}{c}{**Test Set**} \\ \cline{3-8}  & & **Class** & **Class** & **Class** & **Class** & **Class** \\  & & **High-Permeable** & **Low-Permeable** & **Total** & **High-Permeable** & **Low-Permeable** & **Total** \\ \hline Dataset 1 & 3 & 35 & 118 & 153 & 23 & 52 & 75 \\ Dataset 2 & 5 & 54 & 99 & 153 & 27 & 48 & 75 \\ Dataset 3 & 7.4 & 82 & 71 & 153 & 51 & 24 & 75 \\ Dataset 4 & 9 & 87 & 65 & 152 & 40 & 36 & 76 \\ Dataset 5 & IP & 106 & 47 & 153 & 57 & 18 & 75 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Distribution of the samples into the two classes at the different pH levels for the training and the test set.