LaGraph: Laplacian-Guided Graph Learning for Time Series Anomaly Detection

Time series anomaly detection is crucial in fields such as industrial monitoring, financial risk management, and network security. Graph Neural Networks (GNNs) have demon strated strong capabilities in capturing multivariate dependencies. However, existing methods often fail to adequately account for the temporal proximity between adjacent time points and are susceptible to the influence of weak or noisy connections during graph-based representation learning. To address these challenges, we propose LaGraph, a novel framework that integrates GNNs with a mask-optimized attention mechanism. Specifically, LaGraph decomposes input sequences into stable and trend components using an Expert Decomposition Block. The trend component is processed via a Multi-layer Convolution Block, while the stable component is modeled with a Proximity enhanced Graph Convolutional Network that incorporates a Laplacian kernel to capture local temporal dependencies. Additionally, a Mask-optimized Multi-head Attention Block, based on the Straight-Through Estimator (STE), mitigates the negative effects of less informative edges, enhancing both representation quality and reconstruction performance. Extensive experiments on five real-world benchmark datasets demonstrate that La Graph consistently outperforms state-of-the-art methods, veri fying its effectiveness and superiority for time series anomaly detection. To promote reproducibility and support future research, we have publicly released the full implementation at https://github.com/hit-zsc/LaGraph.