MGCL: Multiorder Graph Neural Network With Cross-Learning for Multivariate Time-Series Anomaly Detection

Multivariate time series anomaly detection is critical for industrial systems. However, for inter-variable dimensional modeling, existing work mainly focuses on low-order dependencies between variable pairs, overlooking high-order interactions among multiple variables. Additionally, for temporal dimension modeling, time series are influenced by various system factors, posing challenges in simultaneously capturing long-term and short-term dependencies. To address these challenges, we propose a Multi-Order Graph Neural Network with Cross-Learning (MGCL). First, we design a multi-scale temporal module that captures long-term seasonal dependencies and short-term trend dependencies by employing a temporal global attention network and a gated temporal convolution network, respectively. Second, we construct an adaptive hypergraph generator to explicitly represent the dynamic high-order interactions among multiple variables. Finally, we develop a multi-order graph cross-learning module, which integrates a dynamic memory graph convolution network, a tri-directional diffusion hypergraph convolution network, and a cross-learner to comprehensively capture multi-order inter-variable dependencies. Extensive experiments on eight real-world datasets demonstrate that MGCL outperforms state-of-the-art baselines.