Spatiotemporal traffic data imputation (STDI), estimating the missing data from partially observed traffic data, is an inevitable and challenging task in data-driven intelligent transportation systems (ITS). Due to traffic data's multidimensional and spatiotemporal properties, we treat the missing data imputation as a tensor completion problem. Many studies have been on STDI based on tensor decomposition in the past decade. However, how to use spatiotemporal correlations and core tensor sparsity to improve the imputation performance still needs to be solved. This paper reshapes a 3rd/4th order Hankel tensor and proposes an innovative manifold regularized Tucker decomposition (ManiRTD) model for STDI. Expressly, we represent the sensory traffic state data as the 3rd/4th tensors by introducing Multiway Delay Embedding Transforms. Then, ManiRTD improves the sparsity of the Tucker core using a sparse regularization term and employs manifold regularization and temporal constraint terms of factor matrices to characterize the spatiotemporal correlations. Finally, we address the ManiRTD model through a block coordinate descent framework under alternating proximal gradient updating rules with convergence-guaranteed. Numerical experiments are conducted on real-world spatiotemporal traffic datasets (STDs). Our results demonstrate that the proposed model outperforms the other factorization approaches and reconstructs the STD more precisely under various missing scenarios.

翻译：时空交通数据填补（STDI）旨在根据部分观测的交通数据估计缺失值，是数据驱动智能交通系统（ITS）中一项不可避免且极具挑战性的任务。鉴于交通数据的多维时空特性，本文将缺失数据填补问题视为张量补全问题。过去十年中，基于张量分解的STDI方法已得到广泛研究，然而如何利用时空相关性与核心张量稀疏性来提升填补性能仍是亟待解决的问题。本文通过重构三/四阶Hankel张量，创新性地提出了一种流形正则化Tucker分解（ManiRTD）模型用于STDI。具体而言，我们引入多路延迟嵌入变换，将传感交通状态数据表示为三/四阶张量；进而通过稀疏正则项增强Tucker核心的稀疏性，并利用因子矩阵的流形正则化与时间约束项刻画时空相关性。最后，我们采用基于交替近端梯度更新规则的块坐标下降框架求解ManiRTD模型，该框架具有收敛性保证。在真实时空交通数据集（STD）上的数值实验表明，所提模型在不同缺失场景下的填补精度均优于其他分解方法，能够更精确地重构STD数据。