## 5 Evaluation
### Assessment on Quality of Synthetic anomaly
The SWaT dataset exhibited much more subtle variations in the values of each variable compared to HAI. This issue appears to have caused a decrease in the data reconstruction performance of the decoder in AVRAE. Figure 3: Visual comparison of the original source data for AVRAE and the synthetic anomaly on HAI. Figure 5 visualizes the original source data and the synthetic time-series anomalies given to AVRAE in a lower dimension using principal component analysis (PCA) [50] and t-distributed stochastic neighbor embedding (SNE) [51]. Although PCA is not ideally suited for visualizing high-dimensional data, it can be used to examine the data's variance. On the other hand, t-SNE excels at projecting high-dimensional data into a low-dimensional space to reveal local similarities within the data. In the figure, the two subplots on the left represent the HAI dataset, while the two subplots on the right depict the SWaT dataset. In each subplot, blue dots represent the original source data, and red dots represent anomalies. Each dot corresponds to a \(100\times d\) vector, meaning the input to AVRAE's encoder. Additionally, the anomalies used in this figure were generated by the collective anomaly generation method, which produced the greatest variations compared to the original source data. In the HAI dataset, it was confirmed that the original data and the synthetic anomalies had similar distributions in both the PCA and t-SNE plots. This indicates that the synthetic anomalies share structural similarities and variance characteristics with the original data. However, it is evident that the distributions of the two datasets did not completely overlap. This suggests that new variance was introduced during the generation of synthetic anomalies through mutation. This observation is even more pronounced in the SWaT dataset. The PCA plot shows that most of the data in the SWaT dataset has nearly similar variance characteristics. However, some synthetic anomalies appeared somewhat distinguishable from the original  
Figure 4: Visual comparison of the original source data for AVRAE and the synthetic anomaly on SWaT. Figure 5: Visual comparison between the original source data and the synthetic anomaly using PCA and t-SNE. data. Additionally, in the t-SNE plot, the synthetic anomalies exhibited a distribution similar to the original data but were relatively more clustered. These two observations could imply that the anomaly generation method proposed in this study might be less effective for the SWaT dataset compared to the HAI dataset. We interpret this as the differences in the values of the features in the SWaT dataset being very subtle compared to the HAI dataset, which resulted in the mutation-induced changes in hidden states ultimately producing anomalies that differ from the original data. Figure 6 shows the kernel density estimation (KDE) between the original source data and the synthetic anomaly used as input for AVRAE. In the figure, the first row displays the results for the HAI data, while the second row presents the results for the SWaT dataset. Additionally, the blue area represents the distribution of the original data, and the red area indicates the distribution of the synthetic anomaly. The synthetic anomaly used in Figure 6 was generated through collective anomaly generation, similar to Figure 5. As seen in the figure, the distributions of the original data and the anomaly are almost identical. Table 2 shows the Jensen-Shannon divergence (JSD) for each variable measured using KDE. The upper part of the table presents the results for the HAI dataset, and the lower part shows the results for the SWaT dataset. Furthermore, six variables with the largest JSD values were selected from each dataset. As shown in the table, even the variable with the largest JSD value had a value close to 0.