## 5 Results and Discussions
### Sensitivity Analysis  
The hidden layer of the VAEGA model is critical for training the model. It relies on the outlier detection module to compress the original high-dimensional data into the latent space. We retrain the VAEGA model by adjusting the dimension dim of the hidden layer z to half and twice. It can be seen from Figure 9(a) that reducing the dimensionality of the hidden layers to half of the experimental setting results in a decrease in outlier detection accuracy. The performance of outlier detection results on other datasets does not substantially improve with doubling the hidden layer dimension z, except for the Arrhythmia dataset of dimension 275. This is due to the data being prone to overfitting as a result of the high dimensionality of the hidden layer. The model's performance will decrease if it is too low since the hidden layer will not learn enough from the input data. In addition, we progressively adjust the number of hidden layers from two to six in the VAEGA model. Figure 9(b) illustrates how the outlier detection performance is poor when there are just two hidden layers in the VAEGA model but improves as more layers are added. This is because the network layers do not suffice to fully learn the information contained in the training data. Generally, the number of layers and the size of the latent space do not have a significant effect on the results as long as the neural network is large enough. Thus, a reasonable setting of the neural network size of the model can lead to a robust network structure. In the VAEGA model, VAEGA's \(\epsilon\) threshold is determined by the proportion of outliers in the dataset. Observing Figure 9(c), it is seen that the higher the threshold \(\epsilon\) is set, the higher the detection accuracy of the model, and the relative recall rate will be greatly reduced. Based on Figure 9(c), it can be observed that the higher the threshold is set, the higher the model's detection accuracy, and the lower the relative recall rate. \begin{table}
\begin{tabular}{c c} \hline \hline
**Scope of Data** & **Accuracy** \\ \hline Complete sample dataset & 0.859 \\ Random sample sub dataset & 0.823 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: An analysis of the calculated SOD results before and after random sampling was used. Nevertheless, after exceeding the 99% threshold, the accuracy will fluctuate. When the threshold is set to 99%, the limit of outlier detection is higher, and only outliers with obvious anomalous characteristics (high anomaly scores) will be detected. Although this will lead to fewer errors in the model, it will leave most outliers unidentified. Increasing the threshold setting in the model to 85% will result in a higher rate of false positives. Therefore, setting the thresholds to 90% and 95% anomaly percentages is reasonable for the VAEGA model. However, because of the low outlier rate in the selected data set, the threshold is set at 95% in order to maintain the indicators in a more balanced position and minimize the impact of human factors on the model's performance. Additionally, we verify the influence of the training data size on the VAEGA model performance on the Creditcard dataset, which consists of 200,000 records. As can be seen in Figure 10d, the higher the number of training samples, the higher the learning ability and accuracy of the outlier detection model. In this sense, a sufficient amount of training data are needed to ensure that the learning task performs robustly and achieves better results. A crucial hyperparameter in the VAEGA model is _lambda_, which is obtained from training the VAE, and the value of _gamma_ is fixed at 0.01. From Figure 10e, it can be seen that the anomaly detection model performs best when lambda = 0.01, and its accuracy decreases below this value. To test the model's sensitivity when the data are polluted, we retrain the model using training data containing varying levels of noise.