Asymptotic Consistent Graph Structure Learning for Multivariate Time-Series Anomaly Detection

Capturing complex intervariable relationships is crucial for anomaly detection for multivariate time-series (MTS) data. In recent years, graph neural networks (GNNs) have been introduced to explicitly model complex intervariable relationships from global static or local dynamic views, improving the performance of anomaly detection tasks significantly. However, these approaches usually ignore exploring distinct interaction patterns within short context windows or fail to capture unbiased intervariable relationships over longer time windows. To address this limitation, we propose a novel asymptotic consistent graph structure learning (ACGSL) framework for MTS anomaly detection. Specifically, a sequence aggregation module (SeAM) together with a denoising filter is developed to learn the unbiased representation for each temporal variable more effectively. Furthermore, a feature-accumulation graph construct module (FA-GCM) enhanced by asymptotic consistent graph optimization (ACGO) loss is proposed to construct stable interaction graphs over adaptive time windows. We conduct experiments on five benchmarks and achieve remarkable performance enhancement in anomaly detection, even acquiring a maximum gain of 3.64% over the second-best baseline. Furthermore, ACGSL can explicitly give stable intervariable interacted graphs over arbitrary local normal or anomalous states. Extensive experiments and ablation studies demonstrate the effectiveness and robustness of our proposed ACGSL in anomaly detection.