## 7 Imbalanced Learning Models Result Analysis
### Oversampling-Based Imbalanced Learning Models Results Analysis  
To analyze the classification performance of the PCA- and oSVM-based AMiDS using oversampling methods, we first considered the degree of separability (AUC) and the probability curve (ROC). Then, we examined the other metrics, including the training time and inference time. According to Figure 7, oversampling the unbalanced PiB dataset using the KMS, ROS, and SMT methods improved the performance of the PCA-based AMiDS compared to its performance when using the LRS and SVMSMT methods. When applying the KMS, ROS, and SMT methods, the PCA-based AMiDS could distinguish between the normal and anomalous examples with a probability of 75%. Furthermore, the difference in the AUC values between the training and testing data was substantially small, thus suggesting that the model was able to learn a generalizable pattern from the training data. On the other hand, in contrast to the three methods mentioned above, the model exhibited a poor performance when applying the SVMSMT and LRS methods. The model had probabilities of 32% and 53%, respectively, thus indicating a model with a low degree of separability in the case of SVMSMT or no capacity to distinguish between examples in the case of LRS. An observation to note is that when applying imbalanced learning using the LRS method, the model exhibited a high AUC for the training data (0.86) but a relatively low AUC for the testing data (0.53). The big gap between the two values suggests that the PCA-based AMiDS model either exhibited overfitting where the model fitted the training data but not the testing data, failing to learn a generalizable pattern from the training data that could be applied when using the testing data, or the distributions of the training and testing data differed. On the other hand, the model performance when using the SVMSMT method suggests underfitting, since both the training and testing data AUC values are less than 0.5. Based on Figure 8, the oSVM-based AMiDS distinguished between the normal and anomalous examples with 63% and 60% probabilities when using the ROS and SMT methods, respectively. Although it performed slightly better when using the SVMSMT method with a 70% chance of distinguishing between the different examples, the model had a low AUC value (0.50) for the training data compared to the AUC value (0.70) for the testing data. When the testing data's AUC value was larger than the training data's AUC values, random variation or sampling variability was often the underlying reason. Generally, a trained model with a 50% chance of separating normal from anomalous examples randomly classifies the examples; hence, there is no capacity to distinguish between the two types of examples. Applying the LRS method, on the other hand, improved the trained model's degree of separability. The trained model could distinguish between examples with an 80% probability; however, it showed a poor performance when tested. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **A** & **P** & **R** & **F** & **AUC** & **Training** & **Inference** & **No. of** \\  & & & & & & **Time (s)** & **Time (s)** & **Examples** \\ \hline ER-AE\({}_{p}\) &... & 0.94 & 1.0 & 0.97 &... &... &... & 375 \\ ER-VAEO\({}_{p}\) &... & 0.94 & 1.0 & 0.97 &... &... &... & 378 \\ ER-AE\({}_{O}\) &... & 0.94 & 1.0 & 0.97 &... &... &... & 375 \\ ER-VAEO\({}_{O}\) &... & 0.90 & 0.53 & 0.66 &... &... &... & 378 \\ \hline \hline \end{tabular}
\end{table} 
Table 33: Scored PCA- and oSVM-based AMiDS evaluation results for the generative-based methods based on the anomalous case. The tested model was able to distinguish between the examples with a 40% probability. In the LRS method case, the big gap between the AUC values suggests model overfitting or the inability to learn a generalizable pattern from the training data.