# An Interpretable Method for Anomaly Detection in Multivariate Time Series Predictions
## 4 Experiments
### Algorithm Performance Comparisons  
(1) Baseline methods  
In this section, in order to verify the effectiveness of the proposed method, we compared the constructed scheme with several baseline methods. The baseline methods include Baseline 1: DeepAID [16] is a general unsupervised deep neural network interpretation method. The author provides interpretation methods for tabular data, univariate time-series data, and graph-type data based on different data types. In addition, they proposed a model-based extended still to improve safety systems and facilitate interaction between humans and deep learning models. This method only considers the independent effects of important features when selecting them. Baseline 2: A method based on attention mechanism, replacing the method of calculating the correlation matrix in this article with an attention mechanism to extract correlations between different dimensions. Baseline 3: A scheme that uses gradient multiplication input method to select important features. This method assumes that each feature is independent and only considers the independent effects of the features without considering their interrelationships. Baseline 4: A method based on Pearson correlation coefficient, replacing the method of calculating the correlation matrix in this article with the Pearson correlation coefficient method to extract linear correlations between different dimensions. SHAP [20]: SHAP is a model interpretation method based on Shapley values in game theory, aimed at fairly allocating the contribution of each feature to model predictions. It provides a consistent and interpretable measure of feature importance by calculating the marginal contributions of all possible feature combinations. SHAP is suitable for \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **SWAT** & **WADI** \\ \hline learning rate & 0.1 & 0.1 \\ Optimization frequency & 100 & 50 \\ \(th\) & 0.7 & 0.7 \\ \(\varepsilon\) & 0.005 & 0.005 \\ \(\lambda\) & 0.001 & 0.001 \\ \(K\) & 3 & 3 \\ \(\max\_lag\) & 25 & 25 \\ \(w\) & 0.9 & 0.6 \\ \(k_{0}\) & 2 & 2 \\ \(k_{1}\) & 7 & 7 \\ \(k_{2}\) & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimal parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attack Index** & **Features Affected by Attacks** & **Trend of Changes** \\ \hline Attack 1, sample 1892 & P-203 & Value increased \\ Attack 1, sample 1892 & FIT-201 & Value increased \\ Attack 1, sample 1892 & LIT-101 & Value decreased \\ Attack 1, sample 1892 & MV-101 & Value increased \\ \hline Attack 30, sample 280322 & MV-101 & Value decreased \\ Attack 30, sample 280322 & P-101 & Value increased \\ Attack 30, sample 280322 & MV-201 & Value increased \\ Attack 30, sample 280322 & P-102 & Value increased \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Trends of component changes after being attacked. various machine learning models and can generate global and local interpretations to help understand the decision-making mechanism of the model. LIME [21]: LIME is a local model-independent interpretable method that can faithfully interpret the prediction results of any classifier or regressor through local interpretable model approximation and generate easily understandable explanations for individual predictions. (2) Comparisons  
In order to compare the performance of different algorithms, we set experimental conditions such as data processing, models to be explained, and batch interpretation of data to be the same. From the experimental results in Figure 3(a), it can be seen that, when the value of \(k_{2}\) gradually decreases to 40%, 30%, 20%, and 10% of the total dimension, the method proposed in this paper has significant advantages in SAR metrics. Specifically, Figure 3(a) shows that the SAR value of baseline 1 is significantly lower than other methods, mainly due to its focus on only multiplying the gradient by the positive larger value of the input while ignoring the important influence of negative features.