基于频域图卷积网络的时空序列预测

doi:10.6040/j.issn.1672-3961.0.2025.134

摘要/Abstract

摘要： 为解决多尺度时空序列预测中非线性多尺度时空耦合依赖关系建模困难、传统方法因分离处理时空特征而难以捕捉跨尺度交互、现有深度学习方法受吉布斯噪声干扰与局部-全局特征融合不足等问题,提出一种频域图卷积网络(frequency domain graph convolution network, FDGCN),通过3阶段协同框架实现多尺度时空统一建模。构建超变量图,将多尺度时间维度与空间拓扑联合编码为图节点,利用自适应邻接矩阵显式建模跨尺度依赖;设计离散余弦变换-离散傅里叶变换(discrete cosine transform-discrete Fourier transform, DCT-DFT)协同降噪机制,通过DCT的偶对称扩展抑制DFT的吉布斯现象,结合尺度感知频域滤波器分离低频趋势与高频噪声;引入指数平滑注意力机制,动态融合多尺度特征,平衡局部波动与长期趋势。基于多领域试验验证,FDGCN能够实现多尺度时空统一建模,有效捕捉复杂时空依赖,降低高频噪声,提升训练效率,在交通、电力等多领域数据集上均取得优异的预测性能,兼具预测精度高、计算效率优和跨领域泛化能力强等综合优势,为时空预测提供高效解决方案。

关键词: 时空序列预测, 多尺度时间相关性建模, 门控注意力机制, 深度学习, 数据挖掘

Abstract: To address the difficulties in modeling nonlinear multi-scale spatio-temporal coupling dependencies in multi-scale spatio-temporal series prediction, the challenges faced by traditional methods in capturing cross-scale interactions due to separate processing of spatio-temporal features, and the issues with existing deep learning methods such as interference from Gibbs noise and insufficient fusion of local-global features, a frequency domain graph convolution network(FDGCN)was proposed, and multi-scale spatio-temporal unified modeling was achieved through a three-stage collaborative framework. A hypervariable graph was constructed to jointly encode multi-scale temporal dimensions and spatial topology as graph nodes, and an adaptive adjacency matrix was used to explicitly model cross-scale dependencies. A discrete cosine transform-discrete Fourier transform(DCT-DFT)collaborative noise reduction mechanism was designed, which suppressed the Gibbs phenomenon in DFT through even-symmetric extension in DCT, combined with a scale-aware frequency domain filter to separate low-frequency trends and high-frequency noise. An exponential smoothing attention mechanism was introduced to dynamically fuse multi-scale features, balancing local fluctuations and long-term trends. Based on validation across multiple domains, FDGCN could achieve spatio-temporal unified modeling at multiple scales, effectively capturing complex spatio-temporal dependencies, reducing high-frequency noise, and improving training efficiency. FDGCN achieved excellent prediction performance on datasets in multiple fields such as transportation and power, which demonstrated comprehensive advantages including high prediction accuracy, superior computational efficiency, and strong cross-domain generalization ability, providing an efficient solution for spatio-temporal prediction.

Key words: spatio-temporal series prediction, multi-scale temporal correlation modeling, gated attention mechanism, deep learning, data mining

中图分类号:

TP181

王倩,张瑞敏,李明津,孟宪静,耿蕾蕾. 基于频域图卷积网络的时空序列预测[J]. 山东大学学报 (工学版), 2026, 56(3): 84-92.

WANG Qian, ZHANG Ruimin, LI Mingjin, MENG Xianjing, GENG Leilei. Spatio-temporal series prediction based on frequency domain graph convolution network[J]. Journal of Shandong University(Engineering Science), 2026, 56(3): 84-92.

参考文献

[1] 李伊林, 段海龙, 林振荣. 数据平衡与模型融合的用户购买行为预测[J]. 计算机应用与软件, 2022, 39(9): 50-55. LI Yilin, DUAN Hailong, LIN Zhenrong. Prediction of user purchase behavior based on data balance and model fusion[J]. Computer Applications and Software, 2022, 39(9): 50-55.
[2] XU F L, LIN Y Y, HUANG J X, et al. Big data driven mobile traffic understanding and forecasting: a time series approach[J]. IEEE Transactions on Services Computing, 2016, 9(5): 796-805.
[3] ARIFIN A S, HABIBIE M I. The prediction of mobile data traffic based on the ARIMA model and disruptive formula in industry 4.0: a case study in Jakarta, Indonesia[J]. TELKOMNIKA(Telecommunication Computing Electronics and Control), 2020, 18(2): 907-918.
[4] LI Y G, YU R, SHAHABI C, et al. Diffusion convolutional recurrent neural network: data-driven traffic forecasting[EB/OL].(2018-02-22)[2025-07-15]. https://arxiv.org/abs/1707.01926
[5] SALINAS D, FLUNKERT V, GASTHAUS J, et al. DeepAR: probabilistic forecasting with autoregressive recurrent networks[J]. International Journal of Fore-casting, 2020, 36(3): 1181-1191.
[6] WANG Y B, WU H X, ZHANG J J, et al. PredRNN: a recurrent neural network for spatiotemporal predictive learning[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023, 45(2): 2208-2225.
[7] BAI S J, KOLTER J Z, KOLTUN V. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling[EB/OL].(2018-04-19)[2025-07-15]. https://arxiv.org/abs/1803.01271
[8] ZHOU H Y, ZHANG S H, PENG J Q, et al. Informer: beyond efficient transformer for long sequence time-series forecasting[C] //Proceedings of the Thirty-Fifth AAAI Conference on Artificial Intelligence. Palo Alto, USA: AAAI, 2021: 11106-11115.
[9] ZHOU T, MA Z Q, WANG X, et al. FiLM: frequency improved Legendre memory model for long-term time series forecasting[EB/OL].(2022-09-16)[2025-07-15]. https://arxiv.org/abs/2205.08897
[10] YU B, YIN H T, ZHU Z X. Spatio-temporal graph convolutional networks: a deep learning framework for traffic forecasting[EB/OL].(2018-07-12)[2025-07-15]. https://arxiv.org/abs/1709.04875
[11] CHEN Y, SEGOVIA-DOMINGUEZ I, COSKUNUZER B, et al. TAMP-S2GCNets: coupling time-aware multipersistence knowledge representation with spatio-supra graph convolutional networks for time-series forecasting[EB/OL].(2023-02-14)[2025-07-15]. https://openreview.net/pdf id=wv6g8fWLX2q
[12] CAO D F, WANG Y J, DUAN J Y, et al. Spectral temporal graph neural network for multivariate time-series forecasting[EB/OL].(2021-03-13)[2025-07-15]. https://arxiv.org/abs/2103.07719
[13] WU Z H, PAN S R, LONG G D, et al. Connecting the dots: multivariate time series forecasting with graph neural networks[C] //Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. [S.l.] : ACM, 2020: 753-763.
[14] BAI L, YAO L N, LI C, et al. Adaptive graph convolutional recurrent network for traffic forecasting[EB/OL].(2020-10-22)[2025-07-15]. https://arxiv.org/abs/2007.02842
[15] GREFF K, SRIVASTAVA R K, KOUTNÍK J, et al. LSTM: a search space odyssey[J]. IEEE Transactions on Neural Networks and Learning Systems, 2016, 28(10): 2222-2232.
[16] YI K, ZHANG Q, CAO L B, et al. A survey on deep learning based time series analysis with frequency transformation[C] //Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining. Toronto, Canada: ACM, 2025: 6206-6215.
[17] WANG X Y, DAI R, LIU K K, et al. Effective probabilistic time series forecasting with Fourier adaptive noise-separated diffusion[EB/OL].(2025-05-16)[2025-07-15]. https://arxiv.org/abs/2505.11306
[18] LEE-THORP J, AINSLIE J, ECKSTEIN I, et al. FNet: mixing tokens with Fourier Transforms[EB/OL].(2022-05-26)[2025-07-15]. https://arxiv.org/abs/2105.03824
[19] ZHANG L H, AGGARWAL C, QI G J. Stock price prediction via discovering multi-frequency trading patterns[C] //Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Halifax, Canada: ACM, 2017: 2141-2149.
[20] WANG J Y, WANG Z, LI J F, et al. Multilevel wavelet decomposition network for interpretable time series analysis[C] //Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. London, UK: ACM, 2018: 2437-2446.
[21] ZHOU T, MA Z Q, WEN Q S, et al. FEDformer: frequency enhanced decomposed transformer for long-term series forecasting[EB/OL].(2022-06-16)[2025-07-15]. https://arxiv.org/abs/2201.12740
[22] XIA H W, WEI X, GAO Y, et al. Traffic prediction based on ensemble machine learning strategies with bagging and LightGBM[C] //2019 IEEE International Conference on Communications Workshops(ICC Workshops). Shanghai, China: IEEE, 2019: 8757058.
[23] WU H X, XU J H, WANG J M, et al. Autoformer: decomposition Transformers with auto-correlation for long-term series forecasting[EB/OL].(2022-01-07)[2025-07-15]. https://arxiv.org/abs/2106.13008
[24] NIE Y Q, NGUYEN N H, SINTHONG P, et al. A time series is worth 64 words: long-term forecasting with Transformers[EB/OL].(2023-03-05)[2025-07-15]. https://arxiv.org/abs/2211.14730
[25] YI K, ZHANG Q, FAN W, et al. Frequency-domain MLPs are more effective learners in time series forecasting[C] //Proceedings of the 37th International Conference on Neural Information Processing Systems. New Orleans, USA: ACM, 2023: 76656-76679.
[26] LIU Y, HU T G, ZHANG H R, et al. iTransformer: inverted Transformers are effective for time series forecasting[EB/OL].(2024-03-14)[2025-07-15]. https://arxiv.org/abs/2310.06625
[27] ZENG A L, CHEN M X, ZHANG L, et al. Are Transformers effective for time series forecasting[C] //Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence. Washington, DC, USA: AAAI, 2023: 11121-11128.

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