## 3 Results and Discussion
where TP, TN, FP, and FN denote the number of true positive, true negative, false positive, and false negative cases, respectively. Recall that positive and negative refer to COVID-19-positive (infected) and COVID-19-negative (uninfected) cases. The Xception CNN performed slightly better than the VGG16 architecture. The respective confusion matrices are displayed in Tables 4 and 6. Comparing Tables 4 and 6, it is observed that the Xception-based CNN did not produce any false negative case and, consequently, every positive case was classified as such. The VGG16-based CNN yielded three false negative cases. False negative cases indicate people who are classified as uninfected when they are actually infected; keeping this number as low as possible is thus crucial to avoid misleading treatments. In this sense, considering the tests conducted in this work, Xception looks more promising. This is reflected in the sensitivity statistic, which jumped from 95.4% for VGG16 to 100% for Xception. Regarding the classification of the actual negative cases, the proportion of tests correctly classified was very similar in both cases. Table 7 yields the following statistics for the Xception CNN (disregarding cases that were not \"COVID-19\", \"Pneumonia\", or \"Normal\"):  
* Sensitivity (Recall) \(=\frac{65}{65}=100\%\);
* Specificity \(=\frac{123}{126}=97.6\%\);
* \(F_{\text{1}}=\frac{2\cdot\text{TP}}{\text{2-TP+FP+FN}}=97.7\%\). The progress attained during the training process is depicted in Figure 7.  
Regarding the architectures of the Xception and VGG16 networks, it is worth mentioning that they differ in terms of the number of parameters each CNN has. The Xception-based CNN consisted of a total of 25,580,266 parameters, 4,718,786 of which were trainable. By contrast, the VGG16-based CNN had 15,894,530 parameters, only 1,179,842 of which were trainable. Roughly speaking, this provides an indication that the Xception architecture implemented herein had a better capacity to learn to classify the images than the VGG16 version. [PERSON] et al. (2018) developed a deep-learning-based system called COVID-XNet, which preprocesses chest X-ray images and then classifies them as normal or infected with \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Pred. Positive** & **Pred. Negative** \\ \hline
**True Positive** & 65 & 0 \\
**True Negative** & 10 & 127 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Confusion matrix for the entire testing set: CNN Xception. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Pred. Positive** & **Pred. Negative** \\ \hline
**True Positive** & 65 & 0 \\
**True Negative** & 10 & 123 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion matrix for the testing set without the cases labeled as “Others”: CNN Xception. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Pred. Positive** & **Pred. Negative** \\ \hline
**True Positive** & 62 & 3 \\
**True Negative** & 3 & 123 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Confusion matrix for the testing set without the cases labeled as “Others”: CNN VGG16. COVID-19. To train their systems, they used a total of 6926 images, with 5541 images for training and 1385 images for validation. The COVID-XNet system achieved a 92.53% sensitivity and 96.33% specificity. These values are lower than those obtained by our model, given that our model was trained using a much smaller training set. [PERSON] et al. [14] extracted HOG and CNN features from X-ray images and then fused them to train a VGGNet classifier for COVID-19 detection. They used a total of 5090 images, with 4072 images for training and 1018 images for testing. The proposed model achieved a sensitivity of 93.65% and a specificity of 95.7%. Again, these values are lower than those obtained by our model, given that our model was trained using a much smaller training set. Additionally, it is worth mentioning that fusing more features will generally result in better performance, as shown in our previous work [67].