## 3 Results and Discussion  
Both CNNs were trained and tested on the same sets. As previously described, the training process was run multiple times. Each time, the total training set (834 images) was randomly split into 200 images for validation and 634 images for training. After every training process, the performance of the obtained CNN was evaluated using the testing set. The obtained results were very similar for all the experiments, providing an indication of the robustness of the training process. Tables 2 and 3 display the obtained performance for each of the conducted experiments for each CNN architecture. The following paragraphs elaborate on the results of Experiment 1 for both CNNs. Figure 5 illustrates the progress regarding the prediction capability of the VGG16 CNN as the training advanced. It can be seen that, after 15 epochs of training, the loss function attained a steady value of \(\mathcal{J}\sim 0.1\). Likewise, the accuracy computed over the testing set was around 94%. Examining the distributions of the VGG16 CNN predictions over the original labels reveals the following for one of the aforementioned ten experiments. There were originally 65 cases labeled as \"COVID-19\", of which 62 (95.4%) were predicted as such and 3 were wrongly identified as false negatives. On the other hand, out of the 63 cases labeled as \"Pneumonia\", only 1 (1.6%) was wrongly predicted as COVID-19, whereas the other 62 were properly classified as no COVID-19. With respect to the 63 test cases labeled as \"Normal\", 2 (3.2%) were wrongly identified as COVID-19, while 61 were properly determined as no COVID-19. For this analysis, we grouped all the other 11 cases as \"Others\", which should be properly predicted as no COVID-19. The idea of incorporating the latter images grouped as \"Others\", as well as pneumonia images, into the testing set was to explore the performance of the classifier with images of lungs affected by diseases other than COVID-19. However, the number of pulmonary images in the group \"Others\" was considerably smaller than the number of images of lungs infected with COVID-19 or pneumonia; hence, they were grouped together. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sensitivity** & **Specificity** & \(\mathbf{F_{I}}\) \\ \hline
**Experiment 1** & 95.4\% & 97.6\% & 95.4\% \\
**Experiment 2** & 96.9\% & 97.6\% & 96.1\% \\
**Experiment 3** & 94.2\% & 100\% & 97.0\% \\
**Experiment 4** & 96.7\% & 99.2\% & 97.7\% \\
**Experiment 5** & 97.0\% & 100\% & 98.5\% \\
**Experiment 6** & 96.9\% & 98.4\% & 96.9\% \\
**Experiment 7** & 96.9\% & 97.6\% & 96.1\% \\
**Experiment 8** & 96.9\% & 98.4\% & 96.9\% \\
**Experiment 9** & 92.9\% & 100\% & 96.3\% \\
**Experiment 10** & 96.9\% & 97.6\% & 96.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance obtained across the 10 experiments for the VGG16-based CNN. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sensitivity** & **Specificity** & \(\mathbf{F_{I}}\) \\ \hline
**Experiment 1** & 100\% & 97.6\% & 97.7\% \\
**Experiment 2** & 95.6\% & 100\% & 97.7\% \\
**Experiment 3** & 97.0\% & 99.2\% & 97.7\% \\
**Experiment 4** & 97.0\% & 100\% & 98.5\% \\
**Experiment 5** & 95.6\% & 100\% & 97.7\% \\
**Experiment 6** & 95.4\% & 97.6\% & 95.4\% \\
**Experiment 7** & 97.0\% & 99.2\% & 97.7\% \\
**Experiment 8** & 96.6\% & 93.9\% & 91.9\% \\
**Experiment 9** & 97.0\% & 100\% & 98.5\% \\
**Experiment 10** & 96.9\% & 98.4\% & 96.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance obtained across the 10 experiments for the Xception-based CNN. Based on the aforementioned numbers and considering only the groups \"COVID-19\", \"Pneumonia\", or \"Normal\" for the detection of COVID-19, the following statistics were obtained:  
* Sensitivity (Recall) \(\triangleq\frac{\text{TP}}{\text{TP+FN}}=\frac{62}{65}=95.4\%\);
* Specificity \(\triangleq\frac{\text{TN}}{\text{TN+FP}}=\frac{123}{126}=97.6\%\);
* \(F_{\text{1}}\triangleq\frac{2\cdot\text{TP}}{\text{2-TP+FP+FN}}=95.4\%\).