FECAM: Frequency Enhanced Channel Attention Mechanism for Time Series Forecasting (2212.01209v1)

Abstract: Time series forecasting is a long-standing challenge due to the real-world information is in various scenario (e.g., energy, weather, traffic, economics, earthquake warning). However some mainstream forecasting model forecasting result is derailed dramatically from ground truth. We believe it's the reason that model's lacking ability of capturing frequency information which richly contains in real world datasets. At present, the mainstream frequency information extraction methods are Fourier transform(FT) based. However, use of FT is problematic due to Gibbs phenomenon. If the values on both sides of sequences differ significantly, oscillatory approximations are observed around both sides and high frequency noise will be introduced. Therefore We propose a novel frequency enhanced channel attention that adaptively modelling frequency interdependencies between channels based on Discrete Cosine Transform which would intrinsically avoid high frequency noise caused by problematic periodity during Fourier Transform, which is defined as Gibbs Phenomenon. We show that this network generalize extremely effectively across six real-world datasets and achieve state-of-the-art performance, we further demonstrate that frequency enhanced channel attention mechanism module can be flexibly applied to different networks. This module can improve the prediction ability of existing mainstream networks, which reduces 35.99% MSE on LSTM, 10.01% on Reformer, 8.71% on Informer, 8.29% on Autoformer, 8.06% on Transformer, etc., at a slight computational cost ,with just a few line of code. Our codes and data are available at https://github.com/Zero-coder/FECAM.

• The paper presents FECAM, a novel DCT-based channel attention mechanism that enhances time series forecasting by incorporating frequency analysis.
• It achieves up to 35.99% MSE reduction on benchmarks like LSTM, demonstrating significant improvements in prediction accuracy.
• The method overcomes limitations of Fourier-based techniques by mitigating the Gibbs phenomenon with minimal parameter overhead.

FECAM: Enhancing Time Series Forecasting with Frequency-Aware Attention

The paper "FECAM: Frequency Enhanced Channel Attention Mechanism for Time Series Forecasting" introduces a novel approach designed to augment the performance of time series forecasting models by leveraging frequency domain analysis. This technique is particularly relevant for improving prediction accuracy in diverse real-world applications such as energy load forecasting, traffic management, and financial analytics.

The proposed Frequency Enhanced Channel Attention Mechanism (FECAM) addresses a well-recognized limitation in many existing time series models: the insufficient capture of frequency information within real datasets. Traditional models, particularly those based on Transformer's self-attention mechanisms, often fall short when it comes to disentangling the frequency components inherent in time series data. The authors specifically identify the deficiencies of Fourier Transform-based methods, which are prone to the Gibbs phenomenon—introducing high-frequency noise due to periodicity issues.

The core contribution of this work is the introduction of a channel attention mechanism enhanced by Discrete Cosine Transform (DCT). This approach naturally circumvents the Gibbs phenomenon by using DCT to model frequency interdependencies among data channels inherently, without the need for inverse operations that are characteristic of Fourier-based methodologies. A noteworthy aspect of FECAM is its versatility; the authors demonstrate that it can be easily integrated with several state-of-the-art forecasting models, such as LSTM, Reformer, Informer, Autoformer, and vanilla Transformer, leading to substantial improvements in forecast accuracy.

Quantitative results substantiate the efficacy of this method across six benchmark datasets—namely Exchange, ILI, ETTm2, Electricity, Traffic, and Weather—showing significant reductions in Mean Squared Error (MSE) compared to baseline models. For instance, when applied to LSTM, FECAM reduces the MSE by 35.99%, which exemplifies its potential to enhance existing forecasting networks significantly. Furthermore, this advancement entails minimal parameter overhead, underscoring FECAM’s efficiency.

Theoretically, the paper underscores the advantage of DCT over traditional Fourier methods by presenting a formal proof of its ability to mitigate boundary discontinuities and the associated Gibbs phenomenon. Additionally, through experimental analysis, the energy compaction advantage of DCT is highlighted, demonstrating superior performance in preserving signal fidelity with fewer frequency components.

The implications of this work are manifold. Practically, the improved recognition of frequency components can directly lead to more reliable short-term and long-term predictions in time series data, which is critical for sectors relying on precise forecasting. Theoretically, this approach enriches the existing array of tools available for time series analysis by integrating frequency domain attention mechanisms into the neural architecture.

Looking forward, this paper opens several avenues for future research. One potential direction is exploring the applicability of FECAM in more complex neural architectures beyond those studied, perhaps extending into temporal convolutional networks or hybrid architectures. Additionally, applying this mechanism to multivariate time series forecasting in domains such as IoT sensor networks or healthcare data could yield further insights. Given the demonstrated effectiveness of frequency domain modeling, there’s also scope to investigate adaptive frequency-aware designs tailored for other data modalities.

In summary, the FECAM mechanism presents an advanced method for enhancing temporal forecasting models by successfully integrating frequency domain analysis through DCT-based attention. By providing a robust framework that mitigates the deficiencies inherent in FT-based methods, this research enhances the toolkit available to data scientists and researchers in the time series domain, paving the way for more accurate and scalable solutions.