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<p>With the increasing demand for large-scale and practical anomaly detection in fields such as the Internet of Things, financial risk control, and industrial monitoring, accurately detecting anomalies in multivariate time series data has become a critical yet computationally intensive task. Existing methods mainly rely on the fast Fourier transform (FFT) and other techniques to extract periodic and frequency features. However, FFT only provides global spectral information, which makes it difficult to capture local time-frequency variations in non-smooth signals. At the same time, converting time series data into a 2D structure leads to information inconsistency due to fixed window segmentation and period estimation errors, making it challenging to adequately capture and model high-frequency details in the mapping process. To address these challenges, we propose the Wavelet-Enhanced Temporal Encoding Network (WETEN), which mainly consists of the Temporal-Frequency Adaptive Encoding (TFAE) module and the Null-Range Detail Compensation (NRDC) module, designed to improve local time-frequency analysis capability and compensate for the loss of high-frequency information, respectively. Specifically, TFAE extracts time-frequency features using the wavelet transform and adaptively adjusts window length via dominant period detection, ensuring that periodic patterns at different scales can be consistently represented in 2D space. This effectively overcomes the limitations of traditional FFT with fixed window segmentation in capturing local non-smooth signals. NRDC further applies null space modeling to represent local high-frequency residual information based on extracted time-frequency features and integrates it into the final 2D representation using a cycle-aligned reconstruction strategy, thus enhancing detail expressiveness. The proposed framework integrates time-frequency analysis with deep representation learning over high-dimensional time series, forming a computationally intensive processing pipeline that is well suited for deployment in GPU-accelerated and high-performance computing (HPC) environments. Experiments on four real-world benchmarks demonstrate that WETEN not only achieves state-of-the-art performance, but also highlights the value of explicit null space modeling for capturing localized frequency residual anomalies, which is largely overlooked in existing architectures.</p>

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WETEN: a wavelet-enhanced encoding framework with null-range compensation for time series anomaly detection

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Xiao Li,
  • Hong Li,
  • Yixing Xie

摘要

With the increasing demand for large-scale and practical anomaly detection in fields such as the Internet of Things, financial risk control, and industrial monitoring, accurately detecting anomalies in multivariate time series data has become a critical yet computationally intensive task. Existing methods mainly rely on the fast Fourier transform (FFT) and other techniques to extract periodic and frequency features. However, FFT only provides global spectral information, which makes it difficult to capture local time-frequency variations in non-smooth signals. At the same time, converting time series data into a 2D structure leads to information inconsistency due to fixed window segmentation and period estimation errors, making it challenging to adequately capture and model high-frequency details in the mapping process. To address these challenges, we propose the Wavelet-Enhanced Temporal Encoding Network (WETEN), which mainly consists of the Temporal-Frequency Adaptive Encoding (TFAE) module and the Null-Range Detail Compensation (NRDC) module, designed to improve local time-frequency analysis capability and compensate for the loss of high-frequency information, respectively. Specifically, TFAE extracts time-frequency features using the wavelet transform and adaptively adjusts window length via dominant period detection, ensuring that periodic patterns at different scales can be consistently represented in 2D space. This effectively overcomes the limitations of traditional FFT with fixed window segmentation in capturing local non-smooth signals. NRDC further applies null space modeling to represent local high-frequency residual information based on extracted time-frequency features and integrates it into the final 2D representation using a cycle-aligned reconstruction strategy, thus enhancing detail expressiveness. The proposed framework integrates time-frequency analysis with deep representation learning over high-dimensional time series, forming a computationally intensive processing pipeline that is well suited for deployment in GPU-accelerated and high-performance computing (HPC) environments. Experiments on four real-world benchmarks demonstrate that WETEN not only achieves state-of-the-art performance, but also highlights the value of explicit null space modeling for capturing localized frequency residual anomalies, which is largely overlooked in existing architectures.