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：时空交通数据补全（STDI）旨在从部分观测的交通数据中估计缺失数据，这是数据驱动智能交通系统（ITS）中一项不可避免且具有挑战性的任务。由于交通数据具有多维和时空特性，我们将缺失数据补全视为张量补全问题。过去十年中，已有许多基于张量分解的STDI研究。然而，如何利用时空相关性和核心张量稀疏性来提升补全性能仍有待解决。本文重构了3阶/4阶Hankel张量，并提出了一种创新的流形正则化Tucker分解（ManiRTD）模型用于STDI。具体而言，我们通过引入多路延迟嵌入变换，将感知的交通状态数据表示为3阶/4阶张量。然后，ManiRTD利用稀疏正则化项提高Tucker核心的稀疏性，并采用流形正则化和因子矩阵的时间约束项来表征时空相关性。最后，我们在交替近端梯度更新规则下，通过块坐标下降框架求解ManiRTD模型，并保证收敛性。在真实时空交通数据集（STDs）上进行了数值实验。结果表明，所提模型优于其他分解方法，并在各种缺失场景下更精确地重构了STD。