用高维超复数空间分解时间序列,自动捕捉低频特征。
Numerion: A Multi-Hypercomplex Model for Time Series Forecasting
- 将线性层和激活函数推广至任意2的幂次超复数空间
- 多尺度RHR-MLP架构实现时间序列自然分解与独立建模
- 动态融合机制提升预测性能,适合高频复杂序列建模
现有时间序列预测方法依赖复杂模型结构与先验知识,但受限于计算开销和假设鲁棒性。本文发现,在复数域及高阶超复数空间中,时间序列的特征频率会自然降低。基于此,提出Numerion模型,通过多超复数空间映射实现时间序列的自然分解。具体地,理论上推广了线性层与激活函数至任意2的幂次维度的超复数空间,并设计新型实-超复数-实域多层感知机(RHR-MLP)。Numerion采用多个RHR-MLP将序列映射至不同维度的超复数空间,分别建模并利用动态融合机制自适应整合各空间的潜在模式。实验在多个公开数据集上验证其有效性,达到当前最优性能。可视化与定量分析表明,高维超复数空间更擅长捕捉低频特征,且多尺度结构可自然实现序列分解。
原文摘要 · Abstract (English)
Many methods aim to enhance time series forecasting by decomposing the series through intricate model structures and prior knowledge, yet they are inevitably limited by computational complexity and the robustness of the assumptions. Our research uncovers that in the complex domain and higher-order hypercomplex spaces, the characteristic frequencies of time series naturally decrease. Leveraging this insight, we propose Numerion, a time series forecasting model based on multiple hypercomplex spaces. Specifically, grounded in theoretical support, we generalize linear layers and activation functions to hypercomplex spaces of arbitrary power-of-two dimensions and introduce a novel Real-Hypercomplex-Real Domain Multi-Layer Perceptron (RHR-MLP) architecture. Numerion utilizes multiple RHR-MLPs to map time series into hypercomplex spaces of varying dimensions, naturally decomposing and independently modeling the series, and adaptively fuses the latent patterns exhibited in different spaces through a dynamic fusion mechanism. Experiments validate the model`s performance, achieving state-of-the-art results on multiple public datasets. Visualizations and quantitative analyses comprehensively demonstrate the ability of multi-dimensional RHR-MLPs to naturally decompose time series and reveal the tendency of higher dimensional hypercomplex spaces to capture lower frequency features.
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