## 5 Results and Discussions
### Experiment Analysis  
From Tables 2-5, the results from our experiments show that the VAEGA model surpasses the other benchmark models, particularly in terms of accuracy on all five datasets. Our VAEGA model utilizes a variational method that offers better flexibility for underlying \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Outlier Data** & **Outlier Degree** & **Data Serial Number** \\ \hline
1 & [4, 5, 10] & 9.10 & 86 \\
2 & [1, 2, 7] & 4.33 & 112 \\
3 & [0, 1, 15] & 4.02 & 302 \\
4 & [1, 3, 22] & 3.56 & 29 \\
5 & [0, 1, 5] & 3.41 & 54 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: An example: abnormal subspace ’V4,V5,V10’ in the ground truth of the abnormal subspaces for the dataset. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Methods** & **Cardio** & **Credit Card** & **Satellite** & **MUSK** & **Arrhythmia** \\ \hline PCA & 0.861 & 0.831 & 0.723 & 0.819 & 0.753 \\ OC-SVM & 0.898 & 0.812 & 0.439 & 0.799 & 0.795 \\ ABOD & 0.647 & 0.689 & 0.657 & 0.703 & 0.718 \\ HBOS & 0.703 & 0.770 & 0.490 & 0.763 & 0.762 \\ GAN & 0.500 & 0.791 & 0.226 & 0.795 & 0.700 \\ MOGAAL & 0.578 & 0.677 & 0.627 & 0.731 & 0.688 \\ DSEBM & 0.909 & 0.782 & 0.732 & 0.782 & 0.742 \\ AE & 0.661 & 0.872 & 0.589 & 0.861 & 0.741 \\ VAE & 0.820 & 0.901 & 0.817 & 0.916 & 0.831 \\ VAEGA & 0.805 & 0.927 & 0.827 & 0.940 & 0.813 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: F1 scores of 10 models for outlier detection on 5 datasets. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Methods** & **Cardio** & **Credit Card** & **Satellite** & **MUSK** & **Arrhythmia** \\ \hline PCA & 0.890 & 0.830 & 0.768 & 0.829 & 0.751 \\ OC-SVM & 0.957 & 0.827 & 0.773 & 0.800 & 0.852 \\ ABOD & 0.983 & 0.895 & 0.893 & 0.797 & 0.805 \\ HBOS & 0.625 & 0.675 & 0.853 & 0.816 & 0.830 \\ GAN & 0.903 & 0.895 & 0.747 & 0.799 & 0.753 \\ MOGAAL & 0.455 & 0.543 & 0.493 & 0.674 & 0.682 \\ DSEBM & 0.869 & 0.781 & 0.758 & 0.782 & 0.747 \\ AE & 0.830 & 0.878 & 0.840 & 0.867 & 0.739 \\ VAE & 0.801 & 0.905 & 0.897 & 0.917 & 0.780 \\ VAEGA & 0.938 & 0.936 & 0.853 & 0.924 & 0.773 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Recall of 10 models for outlier detection on 5 datasets. generative models. It employs latent variables with a small amount of noise to generate data more reasonably in order to make the VAEGA model more effective. We found that on datasets with low outlier rates (such as the credit card fraud dataset), the model maintains good performance. By contrast, PCA's performance in detecting linear outliers is generally lower than other benchmark models, indicating that it is difficult to determine the intrinsic relationship between data points. The \"curse of dimensionality\" limits the outlier detection capability of OC-SVM. It performs well on the Cardio, CreditCard, and Satellite datasets but produces inferior results on the high-dimensional Arrhythmia dataset. Distance-based ABOD and HBOS perform slightly better, but they also suffer from dimensionality problems. Another reason for unstable performance is that such methods usually pre-end the training data with prior knowledge. The performance of these algorithms may be adversely affected by high-dimensional data or by data that have a distribution that is inconsistent with their prior knowledge. In contrast, the remaining five neural network-based methods do not demand strict distribution assumptions; therefore, they can perform better with high-dimensional datasets or datasets whose distributions are very different. OC-SVM, on the other hand, has limited performance because of the curse of dimensionality. The AE model with low-dimensional information and dimensionality reduction reconstruction error and the energy-based DSEBM-e model perform well on multiple data sets. From the results, the methods based on dimensionality reduction perform much better. In VAEGA, the VAE layer utilizes the variational approach, which offers higher flexibility in the potential generation model, thereby improving outlier detection.