摘要： 针对传统时空序列建模过程中估计空间权重矩阵时难度较高的问题，提出一种基于奇异值分解（SVD）的时空序列分解模型ST-SVD。对原始时空序列矩阵进行平稳性检测并中心化为零均值平稳时空序列，在假设时间和空间没有交互作用的前提下，利用SVD技术将时空序列分解为空间模式、时间模式以及模式强度的乘积，通过ARIMA模型对平稳的时间模式进行建模并得到其预测结果，在此基础上，将时间模式的预测结果与分解得到的空间模式相结合，利用SVD技术对真实的时空序列进行重建，得到各个空间点的最终预测结果。实验结果表明，与ARIMA、Lasso-VAR、LSTM和STARMA模型相比，ST-SVD模型的训练时间成本降低50%以上，预测精度提升10%以上，其在实际工程应用中能够有效完成时空序列预测任务。

关键词: 时空序列预测, 奇异值分解, STARMA模型, VAR模型, 长短时记忆网络, 基站流量

Abstract: To address the difficulty of estimating the spatial weight matrix in the traditional spatial-temporal sequence modeling process,this paper proposes a spatial-temporal sequence decomposition model,ST-SVD,based on singular value decomposition.The original spatial-temporal sequence matrix receives the stationary test and is centralized into a zero-mean stationary spatial-temporal sequence.Then,assuming that there is no interaction between time and space,the spatial-temporal sequence is decomposed into the product of the spatial pattern,the temporal pattern,and the pattern intensity.Then the ARIMA model is used to model the stable time pattern and get the prediction result of the time pattern.On this basis,the prediction result of the time pattern is combined with the spatial pattern obtained from the decomposition.The real spatial-temporal sequence is reconstructed by using the singular value decomposition technique to obtain the final prediction results of each spatial point.The experimental results show that compared with the ARIMA,Lasso-VAR,LSTM and STARMA models,ST-SVD reduces the model training time cost by more than 50%,while improving the prediction accuracy by over 10%.It can efficiently complete the prediction of spatial-temporal sequence in actual engineering applications.

Key words: spatio-temporal sequence prediction, Singular Value Decomposition(SVD), STARMA model, VAR model, Long and Short Term Memory(LSTM) network, base station traffic

中图分类号: 

• TP301.6