# An Interpretable Method for Anomaly Detection in Multivariate Time Series Predictions
## 4 Experiments
### Algorithm Performance Comparisons
In fact, regardless of the sign of the product of gradients and eigenvalues, as long as their absolute values are large, it indicates that the feature plays an important role in model decision-making. Figure 3(b) further indicates that the performance of baseline 1 and baseline 3 is poor as these two methods only consider the independent characteristics of features during feature selection and fail to effectively capture the correlation between features, resulting in the omission of some key features. In contrast, the method proposed in this article achieves a more comprehensive feature selection by comprehensively considering the importance and correlation of features, thus successfully identifying attack features. From the experimental results in Figure 4(a), it can be seen that, when the value of \(k_{1}\) gradually decreases to 60%-20% of the total dimension, our method overlaps with the baseline 2 and baseline 4 curves and is significantly better than the other two methods in terms of label reversal rate indicators. This result indicates that, in the optimization process of abnormal data, methods that simultaneously consider the interaction between features can more effectively convert abnormal data into normal data, while methods that rely solely on feature independence perform poorly. From Figure 4(b), it can be observed that, when the value of \(k_{1}\) decreases to 20% of the total dimension, both our method and the Pearson correlation coefficient method achieve optimal \(LFR\) performance. In other  
Figure 4: Comparison of \(SAR\)s obtained by different algorithms. dimensions, the \(LFR\) index based on the Pearson correlation coefficient method is better. This result indicates that, in the scenario of being attacked, the interrelationships between important features exhibit stronger linear characteristics. As shown in Figure 6, this method exhibits certain advantages in \(ESR\) indicators on the SWAT dataset and is slightly lower than the Pearson correlation coefficient method on the WADI dataset. This result indicates that the method proposed in this paper has good stability in explaining the trend prediction of attack points, especially demonstrating better explanatory power on the SWAT dataset. The performance differences on different datasets may stem from the distribution characteristics of the data, but, overall, this method has certain advantages in specific scenarios while maintaining stability across datasets. From Tables 3 and 4, it can be seen that the method proposed in this paper exhibits certain advantages in key evaluation indicators: in Table 3, it simultaneously achieves the optimal values of \(LFR\) and \(ESR\), while, in Table 4, it performs the best on \(LFR\). However, LIME only focuses on local areas and may not reflect global behavior or capture the global trend of important features. Although SHAP has global explanatory power, its trend prediction relies on difficult-to-obtain basic data. Therefore, neither of these methods can  
Figure 5: Comparison of \(LFR\)s obtained by different algorithms. Figure 6: Comparison of \(ESR\)s obtained by different algorithms. calculate \(ESR\) and \(LFR\) indicators. Specifically, the \(SAR\) performance of SHAP on the WADI dataset is relatively low, possibly due to limited computer memory and a small number of background data samples, which can lead to lower \(SAR\) performance of SHAP on the WADI dataset. Therefore, in situations where memory is limited, our method also has certain advantages.