## 4 Results and Discussion
### Compilation and Comparison of Results
Figure 3a-g shows that our proposed BGM-GAN technique achieved detection accuracy higher than the GAN-based model of [36] for all epochs. The proposed technique also outperformed the accuracy of other deep learning models like CNN and DBN. This is attributed to the ability of the proposed Bi-Gradual Minimax loss function in estimating the distance between the probability distributions of real and artificial instances in the pre-encryption data of ransomware attacks where the data that represent ransomware's early behavior is insufficient. This supports our assumption that the existing works failed to consider the effect of data insufficiency on the generator and discriminator, which makes them unable to produce artificially realistic metamorphic ransomware samples. The comparison results shown in Figure 3a-g also show that the accuracy increases by increasing the number of features up to a certain limit. When the limit is reached, the accuracy either drops or show no significant improvement. The limit to which the number of selected features contributes to improving the accuracy varies based on the number of epochs in each run. For example, when the model is trained using 30 epochs, the maximum accuracy was achieved when the number of the selected features was 45, while for 60 epochs the maximum accuracy was achieved using 30 features. The reason that the accuracy drops when number is the overfitting caused by increased number of features and number of epochs during model training. When the number of features increases, the data dimensionality increases as well. Such data dimensionality negatively affects the accuracy of the detection model. The issue is aggravated when dealing with data that have insufficient ransomware behavior during the early phases. Likewise, when the number of epochs during the model's training increases, the likelihood that overfitting occurs also increases which makes the loss function unable to accurately measure the distance between real and artificial patterns. This explains the deterioration of the accuracy after a certain number of features and epochs. Likewise, Figure 4a,b show that on average, our proposed BGM-GAN outperformed the existing techniques in terms of recall and false positive rate, respectively. The comparison was carried out by measuring both the recalls and the false positive rate over several number of epochs using several feature set sizes (as has been done in Figure 3). The average was taken with respect to the feature set size. The improvement shown by BGM-GAN is attributed to the ability of the BGM method to capture the early patterns even when less data are available. This conforms with the results shown in Figure 3. Additionally, Table 2 shows the training time that the BGM-GAN takes per number of epochs. We observed that the training time was between 2 to 4 milliseconds (ms) per step and around 2 s per epoch. Therefore, the greater number of epochs the training uses, the more time it takes to develop the model. Figure 3: _Cont._  
Figure 3: **(a)** Comparison of accuracy between our proposed BGM-GAN and the related models, standard GAN, CNN, and DBN, when trained for 30 epochs across a varying number of features. **(b)** Comparison of accuracy between our proposed BGM-GAN and related models, standard GAN, CNN, and DBN, when trained for 60 epochs across a varying number of features. **(c)** Comparison of accuracy between our proposed BGM-GAN and related models, standard GAN, CNN, and DBN, when trained for 90 epochs across a varying number of features. **(d)** Comparison of accuracy between our proposed BGM-GAN and related models, standard GAN, CNN, and DBN, when trained for 120 epochs across a varying number of features. **(e)** Comparison of accuracy between our proposed BGM-GAN and related models, standard GAN, CNN, and DBN, when trained for 150 epochs across a varying number of features. **(f)** Comparison of accuracy between our proposed BGM-GAN and related models, standard GAN, CNN, and DBN, when trained for 180 epochs across a varying number of features.