# An Interpretable Method for Anomaly Detection in Multivariate Time Series Predictions
## 5 Summary  
In this paper, we propose a gradient-based interpretable method for anomaly detection. When selecting important features, we not only consider the independent effects of different dimensions of data but also extract the mutual influence of different dimensions in the same sliding window, thereby further reducing the number of important features. We identify the main features that cause anomalies by accumulating gradients and input changes. The experiments have been conducted on public datasets, which can effectively explain the changing trend of attack points affected by attacks without affecting the performance of the original anomaly detection system.  
Nevertheless, there is still room for improvement in our work. Since the model we explained is based on prediction, additional algorithms need to be introduced to preliminarily determine the trend of the time series if the original interpretable model lacks predictive function.  
Conceptualization, S.T. and Y.D.; methodology, H.W.; software, S.T.; validation, S.T.; formal analysis, Y.D.; investigation, H.W.; resources, H.W.; data curation, S.T.; writing--original draft preparation, S.T.; writing--review and editing, S.T.; visualization, S.T.; supervision, Y.D.; project administration, Y.D.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
This article is supported in part by the National Key R&D Program of China under project 2023 YFB3107301 and the Guangxi Key Laboratory of Digital Infrastructure under project GXDIOP2023006.  
**Institutional Review Board Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(LFR\) (\%) & \(SAR\) (\%) & \(ESR\) (\%) \\ \hline Baseline 1 & 56.84 & 81.16 & 57.48 \\ Baseline 2 & **60.82** & **84.18** & 56.94 \\ Baseline 3 & 47.58 & 78.15 & **58.23** \\ Baseline 4 & **60.82** & **84.18** & 56.97 \\ LIME & - & 53.71 & - \\ SHARP & - & 13.02 & - \\ Our method & **60.82** & 79.01 & 57.16 \\ \hline \hline \end{tabular} Note: “-” indicates that the baseline method provides nothing about this indicator.  
\end{table}
Table 4: Performance comparison between our method and baseline methods on WADI dataset.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(LFR\) (\%) & \(SAR\) (\%) & \(ESR\) (\%) \\ \hline Baseline 1 & 76.45 & 63.99 & 38.75 \\ Baseline 2 & 95.78 & 97.04 & 56.28 \\ Baseline 3 & 76.34 & **97.36** & 45.93 \\ Baseline 4 & 95.78 & 96.94 & 61.67 \\ LIME & - & 66.42 & - \\ SHARP & - & 90.39 & - \\ Our method & **96.73** & 95.78 & **65.05** \\ \hline \hline \end{tabular} Note: “-” indicates that the baseline method provides nothing about this indicator.  
\end{table}
Table 3: Performance comparison between our method and baseline methods on SWAT dataset.  
Data Availability Statement: The datasets generated and/or analyzed during the current study are available in the (SWAT and WADI) repository, [[https://itrust.sutd.edu.sg/itrust-labs_datasets/dataset_info/](https://itrust.sutd.edu.sg/itrust-labs_datasets/dataset_info/)]([https://itrust.sutd.edu.sg/itrust-labs_datasets/dataset_info/](https://itrust.sutd.edu.sg/itrust-labs_datasets/dataset_info/)) (accessed on 21 February 2025).  
During the preparation of this manuscript/study, the authors used the SWAT and WADI datasets for the purposes of the experiments. The authors have reviewed and edited the output and take full responsibility for the content of this publication.  
The authors declare no conflicts of interest.