FreFilterTST: a dynamic channel graph sparsification approach to multivariate time series anomaly detection with frequency-domain restoration.

The scope of time series anomaly detection is increasingly shifting from univariate to multivariate contexts, as a growing number of real-world problems can no longer be adequately addressed by analyzing individual variables in isolation. Consequently, multivariate time series anomaly detection is not only in high demand but also presents significant challenges. However, existing methods struggle with a dual challenge: capturing subtle, fine-grained frequency features, and effectively modeling complex inter-channel dependencies. Current channel-handling strategies are often either too restrictive, like Channel-Independent (CI) methods that ignore valuable correlations, or susceptible to noise, like Channel-Dependent (CD) methods that indiscriminately integrate all relationships. To address these challenges, we propose the Frequency Filtering Time Series Transformer (FreFilterTST), a novel framework that uniquely combines frequency-domain inpainting with adaptive Frequency-Amplitude filtering. Specifically, FreFilterTST first reconstructs the input sequence from spectral patches to establish a rich representation of normative patterns. Subsequently, a Transformer-based Mixture-of-Experts (MoE) architecture acts as an adaptive filter, dynamically identifying and preserving the most critical Frequency-Amplitude dependencies while pruning irrelevant or noisy ones. This can allow our model to overcome the inherent trade-offs of conventional CI and CD approaches. Our Extensive experiments on six benchmark public datasets demonstrate that FreFilterTST achieves an excellent performance.