FreCT: Frequency-augmented Convolutional Transformer for Robust Time Series Anomaly Detection

TL;DR

FreCT tackles robust anomaly detection in multivariate time series by embedding frequency-domain information into a patch-based Transformer with a CNN module, trained via stop-gradient KL-based contrastive losses. It generates two time-domain contrastive views through patch operations and enforces cross-domain consistency with FFT-derived frequency representations, enabling detection of anomalies beyond time-domain autocorrelations. FreCT achieves state-of-the-art results on four public datasets against 11 baselines, with ablations confirming the contributions of normalization, convolution, and frequency augmentation. The approach offers a scalable, unsupervised alternative to reconstruction-based methods, with potential impact on real-world monitoring systems requiring robust anomaly detection.

Abstract

Time series anomaly detection is critical for system monitoring and risk identification, across various domains, such as finance and healthcare. However, for most reconstruction-based approaches, detecting anomalies remains a challenge due to the complexity of sequential patterns in time series data. On the one hand, reconstruction-based techniques are susceptible to computational deviation stemming from anomalies, which can lead to impure representations of normal sequence patterns. On the other hand, they often focus on the time-domain dependencies of time series, while ignoring the alignment of frequency information beyond the time domain. To address these challenges, we propose a novel Frequency-augmented Convolutional Transformer (FreCT). FreCT utilizes patch operations to generate contrastive views and employs an improved Transformer architecture integrated with a convolution module to capture long-term dependencies while preserving local topology information. The introduced frequency analysis based on Fourier transformation could enhance the model's ability to capture crucial characteristics beyond the time domain. To protect the training quality from anomalies and improve the robustness, FreCT deploys stop-gradient Kullback-Leibler (KL) divergence and absolute error to optimize consistency information in both time and frequency domains. Extensive experiments on four public datasets demonstrate that FreCT outperforms existing methods in identifying anomalies.

Figures (7)

• Figure 1: The overall framework of FreCT. First, FreCT leverages the preprocessing module to normalize the time series and generate patches. Then, FreCT captures intra-patch and inter-patch dependencies through the Transformer integrated with the convolution module. Then, FreCT utilizes KL-based contrastive learning to capture the consistency in the time domain and implements the Fast Fourier Transform to capture consistency in the frequency domain. Last, FreCT detects time series anomalies based on the consistencies in the time and frequency domain.
• Figure 2: The sequence-level preprocessing, including sequence-level normalization module and patch-based channels generation.
• Figure 3: The rationality validation experiments of the loss function.
• Figure 4: The sensitivity experimental results of patch size.
• Figure 5: The sensitivity experimental results of window size.