## 5 Evaluation
### Assessment on Quality of Synthetic anomaly  
This section assesses the quality of the synthetic ICS time-series anomaly both visually and statistically. Visually inspecting the quality of generated time-series anomaly data is crucial because it allows evaluation of whether an anomaly detection model accurately captures real anomaly situations and whether the data patterns are realistic. This helps in intuitively understanding the detection model's performance and identifying potential areas for improvement. Figure 3 shows the ICS time-series anomalies generated by the proposed method. In the figure, the blue line represents the real data used as the source for AVRAE to generate anomalous data, and the red line represents the generated anomaly. Each subplot depicts the changes in the values of a variable over time in the dataset (the y-axis represents the variable's value, and the x-axis represents the time sequence). The first row of Figure 3 represents point anomaly generation, the second row represents context anomaly generation, the third row represents collective anomaly generation with a constant value, the fourth row represents collective anomaly generation with a random value, and the fifth \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multicolumn{3}{c}{**Encoder**} & \multicolumn{3}{c}{**Decoder**} \\ \cline{2-7}  & **Type** & **Input Size** & **Output Size** & **Type** & **Input Size** & **Output Size** \\ \hline
**Layer 1** & LSTM & \(100\times d\) & \(100\times p\) & LSTM & \(100\times p\) & \(100\times p\) \\
**Layer 2** & LSTM & \(100\times p\) & \(100\times p\) & LSTM & \(100\times p\) & \(100\times p\) \\
**Layer 3** & & & & Cross-Attention & \(100\times p\), & \(100\times p\) \\
**Layer 4** & & & & & \(100\times p\), & \\  & & & & & \(100\times p\) & \(100\times p\) \\
**Layer 5** & & & & Dense & \(100\times p\) & \(100\times d\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The architecture of AVRAE. row represents collective anomaly generation with swap. The sections where the mutation operation is applied are marked with green circles. The results of this experiment were extremely interesting. In the case of point anomaly generation, the anomalous values significantly differed from the surrounding context. Additionally, the direction of the outliers varied depending on the variables, which indicates that AVRAE learned the multivariate relationships of the HAI dataset. The context anomaly generation creates anomalies by swapping the hidden states at two arbitrary timesteps in the embedding space. As a result, the range of anomaly values occurring early did not exceed the surrounding context. In fact, the anomaly values matched the values at the swapped location (i.e., the normal values of the later time). Conversely, the values at the later time remained unchanged, and the exact cause of this phenomenon has not been determined yet, although it is suspected to be due to the influence of the attention layer. The collective anomaly generations with constant value and random value both exhibited similar effects. Anomalous data ignoring the pattern of the data were placed in a randomly selected interval. Lastly, the collective anomaly generation with swap selects two intervals of the same length at random and swaps their hidden states in the embedding space. Except for the anomaly occurring within the interval, the effect is similar to the context anomaly generation. In this method as well, the anomaly pattern occurring early matched the pattern at the swapped location, while the pattern at the later time remained unchanged. This phenomenon is also suspected to be due to the influence of the attention layer. Figure 4 shows the results of ICS time-series anomaly generation using the SWaT dataset. Overall, results similar to the experiments using HAI were observed. However, for SWaT, the quality of the generated time-series was lower compared to HAI. This issue was analyzed as a limitation of AVRAE rather than a problem with the anomaly generation method.