TEDA: Time-Frequency Entropy-Aware Distribution Modeling for Time Series Anomaly Detection

Time series anomaly detection plays an important role in many real-world systems. Existing advanced unsupervised methods mainly rely on prediction or reconstruction errors to identify abnormal patterns. However, such a paradigm only focuses on sample-wise errors and fails to capture whether a sample conforms to the distribution of whole data. As a result, simple anomalies but with low-probability may be well reconstructed, while complex but normal patterns may be failed. In this paper, we propose TEDA, a time-frequency distribution-aware framework for unsupervised time series anomaly detection. TEDA learns distributional centroids and introduces optimal transport into the reconstruction-based paradigm to model normal patterns in the latent distributional space. Specifically, a patch-based branch captures local temporal distributions, while a frequency-domain branch models long-term periodicity, trends, and global distributions. To improve the stability and discriminative ability of optimal transport, TEDA uses entropy regularization to preserve smooth transport plans during training, and removes it to perform sharp assignment during inference. The final anomaly score combines reconstruction errors and distribution-aware optimal transport costs. Extensive experiments on six real-world datasets show that TEDA achieves better performance compared with classical and recent state-of-the-art methods. The results demonstrate the effectiveness of enhancing time series anomaly detection with the distribution of whole data.