Spatial-Temporal Transformer with Error-Restricted Variance Estimation for Time Series Anomaly Detection

Due to the intricate dynamics of multivariate time series in cyber-physical system, unsupervised anomaly detection has always been a research hotspot. Common methods are mainly based on reducing reconstruction error or maximizing estimated probability for normal data, however, both of them may be sensitive to particular fluctuations in data. Meanwhile, these methods tend to model temporal dependency or spatial correlation individually, which is insufficient to detect diverse anomalies. In this paper, we propose an error-restricted framework with variance estimation, namely Spatial-Temporal Anomaly Transformer (S-TAR), which can provide a corresponding confidence for each reconstruction. First, it presents Error-Restricted Probability (ERP) loss by restricting the reconstruction error and its estimated probability skillfully, further improving the capability to distinguish outliers from normal data. Second, we adopt Spatial-Temporal Transformer with distinct attention modules to detect diverse anomalies. Extensive experiments on five real-world datasets are conducted, the results show that our method is superior to existing state-of-the-art approaches.