Fuzzy State-Driven Cross-Time Spatial Dependence Learning for Multivariate Time-Series Anomaly Detection

Cross-time spatial dependence (i.e., the interaction between different variables at different time points) is indispensable for detecting anomalies in multivariate time series, as certain anomalies may have time delays in their propagation from one variable to another. However, accurately capturing cross-time spatial dependence remains a challenge. Specifically, real-world time series usually exhibits complex and incomprehensible evolutions that may be compounded by multiple temporal states (i.e., temporal patterns, such as rising, fluctuating, and peak). These temporal states mix and overlap with each other and exhibit dynamic and heterogeneous evolution laws in different time series, making the cross-time spatial dependence extremely intricate and mutable. Therefore, a cross-time spatial graph network with fuzzy embedding is proposed to disentangle latent and mixing temporal states and exploit it to meticulously learn cross-time spatial dependence. First, considering that temporal states are diversiform and their mixing modes are unknown, we introduce a fuzzy state set to uniformly characterize potential temporal states and adaptively generate corresponding membership degrees to depict how these states mix. Further, we propose a cross-time spatial graph, quantifying similarities among fuzzy states and sensing their dynamic evolutions, to flexibly learn mutable cross-time spatial dependence. Finally, we design state diversity and temporal proximity constraints to ensure the differences among fuzzy states and the evolution continuity of fuzzy states. Experiments on real-world datasets show that the proposed model outperforms the state-of-the-art models.