提高时间序列预测在频率领域使用一个多分辨率双分支混合器与噪声不敏感的ArcTanLoss
Yahao Zhang1,2,3, Xiaofeng Zhou4,5, Yichi Zhang1,2
1Key Laboratory of Networked Control Systems, Chinese Academy of Sciences, Shenyang, 110016, China.
Scientific reports
|April 12, 2025
概括
这项研究介绍了FreMixer,一种新的频域预测模型. 它通过使用多分辨率分析和对噪声不敏感的损失函数来提高长期时间序列预测的准确性.
科学领域:
- 数据科学数据科学数据科学
- 机器学习 机器学习
- 信号处理 信号处理
背景情况:
- 准确的长期时间序列预测在各个学科中至关重要.
- 离散里埃转换 (DFT) 用于频域分析,捕获周期性模式.
- 现有的DFT方法存在局限性:固定的分辨率,忽视局部细节和噪声敏感性.
研究的目的:
- 提出一个新的轻量级架构,FreMixer,用于完全在频率领域运行的时间序列预测.
- 解决固定分辨率DFT的局限性,并改善全球和本地时间模式的捕获.
- 引入对噪声不敏感的损失函数,以提高模型稳定性和减少过度装配.
主要方法:
- 开发了FreMixer,一种频率域架构.
- 在频域中实施多分辨率细分,以克服DFT的稀疏分辨率.
- 使用双分支网络在每个频率分辨率上提取全球和本地特征.
- 引入了ArcTanLoss,一种对噪声不敏感的损失函数,以减轻异常影响.
主要成果:
- FreMixer 在时间序列预测准确度方面表现出显著的改进.
- 多分辨率方法有效地捕捉了不同频率分辨率的互补特征.
- 双分支架构成功地提取了全面的全球和本地时间模式.
- ArcTanLoss降低了模型对噪声和异常值的敏感性,从而导致更稳定的预测.
- 在七个数据集上的实验验验证了该模型的有效性.
结论:
- FreMixer为长期时间序列预测提供了一种有效和轻量级的方法.
- 在频率域中运行多分辨率分析和强大的损失函数可以提高预测准确度.
- 提出的方法克服了传统的基于DFT的预测技术的关键局限性.
相关概念视频
01:26Linear Approximation in Frequency Domain
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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01:21Linear Approximation in Time Domain
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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01:11Sampling Continuous Time Signal
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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01:10Reconstruction of Signal using Interpolation
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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
150
01:20Discrete-Time Fourier Series
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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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01:26Discrete-time Fourier transform
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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
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