Dynamic-Static Fusion for Spatial-Temporal Anomaly Detection and Interpretation in Multivariate Time Series

Multivariate time series (MTS) anomaly detection is crucial for ensuring security and avoiding economic losses in various domains. Existing research based on the unified model’s information representation method have not adequately considered the differences between temporal and spatial features, leading to interference in information representation and reduced model performance and interpretability. They also failed to consider the joint effect of static and dynamic patterns on time series modeling, which hinders an accurate reflection of the evolution process of sequences. In this paper, we propose a Hierarchical Cross Temporal and Spatial Graph (HCroSTG) model, a fully unsupervised anomaly detection approach for MTS. We first extract features of MTS in a more fine-grained manner from four perspectives: the dynamic and static characteristics in both temporal and spatial dimensions and integrate them into an effective spatial-temporal conditional constraints through graph convolution operations. During this process, we design a Dual Temporal Graph Attention Module and a Graph Neural Ordinary Differential Equations Module to capture non-stationary temporal features and fully continuous spatial dynamics to alleviate the impact of concept drift. Based on the above conditional constraints, we map each time series to different Gaussian distributions using an autoregressive flow. This allows our model to accommodate the diverse distribution patterns and statistical characteristics, thereby enabling density estimation for enhancing anomaly detection and traceability. Extensive experiments show that HCroSTG outperforms the SOTA methods by up to 2.5 AUCROC% averagely, which a maximum improvement of 5.6 on the best-performing dataset.