# Prediction of COVID-19 from Chest CT Images Using an Ensemble of Deep Learning Models
## 5 Experimental Results and Discussion  
Training DL models with limited data without overfitting is indeed a challenging task. The proposed TL-based approach resolves the problem with significant improvement in the performance by involving the models VGG-16, ResNet50, and Xception. Afterward, these models are used to create a stacking ensemble classifier for improvement of the overall recognition accuracy. The stacking ensemble classifier used in the present experiment can be thought of as a complex model combining all the mentioned base learners. It has a single input layer that duplicates and distributes the input data into three base learners. These input images are propagated through each base learner separately, and finally, a prediction vector is generated from each base learner predicting the class labels of the input data. These prediction vectors generated from all these three base learners are concatenated and used as a feature for the meta learner. The meta-learner then tries to classify the input data into appropriate classes in an efficient way. In the stacking ensemble model, only the meta-learner is trained on the training data while the base learners are frozen. In the current experiment, the base models are trained for 100 epochs each with batch size 32, and the meta-learner has been trained for 100 epochs on training data. All possible combinations of the base learners have been experimented with to estimate the usage and performance  
Figure 3: The general architecture of a two-level ensemble model. of the ensembled architecture. In the present experiment, the training and test sets are split into an 8:2 ratio. To evaluate how effective the proposed model is, we have measured its performance in terms of five metrics that include classification accuracy, precision, recall, \(F_{1}\)-score, and area under the curve (AUC). The receiver operating curve (ROC) is a plot of true positive rate (i.e., TPR or sensitivity) versus false-positive rate (FPR). Equations (1)-(5) have been used to measure the value of \(FPR\), accuracy (\(a_{c}\)), precision (\(P_{r}\)), recall (\(R_{c}\)), and \(F_{1}\)-score (\(F_{s}\)). \[FPR=\frac{FP}{TN+FP} \tag{1}\]  
\[a_{c}=\frac{TP+TN}{TP+TN+FP+FN} \tag{2}\]  
\[P_{r}=\frac{TP}{TP+FP} \tag{3}\]  
\[R_{c}=\frac{TP}{TP+FN} \tag{4}\]  
\[F_{s}=2\times\frac{P_{r}\times R_{c}}{P_{r}+R_{c}} \tag{5}\]  
where true positive (\(TP\)) represents COVID-19 (+ve) patients that are correctly recognized as COVID-19 (+ve). False positive (\(FP\)) represents COVID-19 (-ve) patients that are incorrectly recognized as COVID-19 (+ve). True negative (\(TN\)) represents COVID-19 (-ve) patients that are correctly recognized as COVID-19 (-ve). Finally, false negative (\(FN\)) represents COVID-19 (+ve) patients that are incorrectly recognized as COVID-19 (-ve). Table 1 reflects a summary of accuracy, precision, recall, \(F_{1}\)-score, and AUC measurements achieved from the mentioned three models for the prediction of COVID-19 on the SARS-CoV-2 CT scan dataset. Figure 4 reflects the ROC curve obtained for the above mentioned three models. From Table 1, we can observe that the VGG-16 model outperforms the other pre-trained models taken into consideration. VGG-16 (with around 138M parameters) has a kernel of size 3 \(\times\) 3 for all the convolution layers and the size of the kernel in the Maxpool layer is 2 \(\times\) 2 with a stride of 2. The number of trainable parameters has been reduced by 44.9%. A reduced number of trainable variables means faster learning and is more robust against over-fitting. This might be the reason why it performs better. ResNet50 has around 23 million trainable parameters. It consists of convolution layers with filters of size 3 \(\times\) 3 (just like VGGNet). Two pooling layers are used throughout the network. Hence, there is a large number of trainable variables, unlike VGG-16. In the Xception model, there is no intermediate rectified linear unit (ReLU) non-linearity.