In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality and spatiotemporal correlations, but they are vital to traffic data recovery, especially for high-level missing scenarios. To address this problem, we propose a novel spatiotemporal regularized Tucker decomposition method. First, the traffic matrix is converted into a third-order tensor. Then, based on Tucker decomposition, the tensor is approximated by multiplying non-negative factor matrices with a sparse core tensor. Notably, we do not need to set the tensor rank or determine it through matrix nuclear-norm minimization or tensor rank minimization. The low rankness is characterized by the $l_1$-norm of the core tensor, while the manifold regularization and temporal constraint are employed to capture spatiotemporal correlations and further improve imputation performance. We use an alternating proximal gradient method with guaranteed convergence to address the proposed model. Numerical experiments show that our proposal outperforms matrix-based and tensor-based baselines on real-world spatiotemporal traffic datasets in various missing scenarios.

翻译：在智能交通系统中，交通数据补全——即从部分观测数据中估计缺失值——是一项不可避免且具有挑战性的任务。现有研究尚未充分考虑交通数据的多维性和时空相关性，而这些特性对于数据恢复至关重要，尤其是在高缺失率场景下。为解决这一问题，我们提出了一种新颖的时空正则化Tucker分解方法。首先，将交通矩阵转换为三阶张量；然后，基于Tucker分解，通过非负因子矩阵与稀疏核心张量的乘积逼近该张量。值得注意的是，我们无需预设张量秩或通过矩阵核范数最小化及张量秩最小化确定秩。低秩性通过核心张量的$l_1$范数表征，同时利用流形正则化与时间约束捕获时空相关性，进一步提升补全性能。我们采用具有收敛保证的交替近端梯度方法求解所提模型。数值实验表明，在真实时空交通数据集的各种缺失场景下，我们的方法优于基于矩阵和基于张量的基线方法。