## 5 Results and Discussions
### Experiment Analysis
Compared to the unimproved pure VAE, the VAEGA model achieves an average performance improvement of around 3%. We observe that on datasets with low outlier rates (such as credit card fraud) the model performs well. Furthermore, unlike other benchmark models, our proposed method can identify outlier features and evaluate the causes of data anomalies. Based on the analysis of the experimental results from multiple datasets, the adversarial network-based methods--GAN and MOGAAL--showed to be less effective in detecting outliers compared to reconstruction-based methods, such as DSEBM, AE, VAE and VAEGA. The analysis showed that GANs lack reasoning about the training data in the hidden space, so they learn an incomplete data distribution, which leads to mode collapse. In addition, the GAN mislabels normal data as abnormal data, resulting in false positives in outlier detection results. The MOGAAL method, on the other hand, tries to elude the mode collapse by stopping the optimization of the generator before convergence to better learn the distribution of normal data and extends the network structure to multiple generators with different objectives from the initial single generator. Consequently, MOGAAL's detection results outperform the ordinary GANs; however, the caveat is that it is difficult to know for certain what the model has learned, which leads to uncertain experimental results. Thus, there is still a performance gap compared with the reconstruction-based neural network models AE, VAE, and DSEBM. This is because reconstruction-based methods combine latent space information and reconstruction error to detect outliers. Unsupervised outlier detection will, however, generate some misjudgment points if the threshold is set too high. Our improved VAEGA model establishes a genetic algorithm to search the abnormal subspace for the outlier set containing the misjudged points and classify the outliers in accordance with the abnormal subspace. Misjudged points are considered outliers that cannot form clusters in the classification results. In order to improve the model's performance, the VAEGA model feeds the detected misjudgment points to the VAE layer for parameter adjustment. The reason for the slight improvement is that we cannot eliminate all misjudgment points through a unified standard when classifying outliers based on abnormal subspaces. Filtering out too few false positives or removing some of the features of false positives will have little effect on the weight adjustment of upper-layer feedback, which will result in an insufficient improvement in model performance. As a result, when training the model, we should use a large amount of data to ensure that important outliers are not isolated cases before formulating more effective criteria to filter false positives. Our proposed VAEGA model can output abnormal subspace features for analyzing data anomalies, whereas other benchmark models lack the ability to locate outliers. In GA, the search for abnormal subspaces uses a heuristic search instead of traversing all the possible subspaces, which can save time and memory. As shown in Table 7, 85.95% accuracy can be achieved when comparing the abnormal subspaces obtained using the genetic algorithm with the standard set. The results demonstrate that our proposed method can obtain abnormal subspace features much more quickly since the search cost is greatly reduced. In addition, the fitness function of the GA for calculating the subspace fitness in the VAEGA experiment makes use of the redefined SOD measurement. A subspace with the highest SOD value is returned as the abnormal subspace for each detected outlier. This increases the comparability of the outlier measure in comparison to simply calculating the outlier degree. Furthermore, with the progress of evolution, we can see in the three datasets an increase in the number of individuals with high fitness, which indicates that our approach features good convergence.