基于张量奇异值理论的交通数据重构方法

由于探测器和通信设备的故障，交通数据的缺失是不可避免的，这种缺失给智能交通系统（ITS）带来了不利的影响。针对此问题，运用张量平均秩的概念，对张量核范数进行最小化，从而构建了新的低秩张量补全模型，并且在此基础上，基于张量奇异值分解（T-SVD）和阈值分解（TSVT）理论，分别使用坐标梯度下降法（CGD）和交替乘子法（ADMM）对模型进行求解，提出两个张量补全算法LRTC-CGD和LRTC-TSVT。在公开的真实时空交通数据集上进行实验。结果表明，LRTC-CGD和LRTC-TSVT算法在不同的缺失场景和缺失率条件下，补全精度要优于现行的其他补全算法，并且在数据极端缺失情况下（70%~80%），补全的效果更加稳定。

Data reconstruction method based on tensor singular value theory

Due to the failure of detectors and communication equipment, the lack of traffic data is inevitable, and this kind of lack has an adverse impact on intelligent transportation systems(ITS). To solve this problem, this paper used the concept of tensor average rank to minimize the tensor kernel norm, thereby constructed a new low-rank tensor completion model. And on this basis, based on tensor singular value decomposition(T-SVD) and threshold decomposition(TSVT) theories, it respectively used coordinate gradient descent(CGD) and alternating multiplier method(ADMM) to solve the model, and proposed two tensor completion algorithms LRTC-CGD and LRTC-TSVT. Experiments on the real spatio-temporal traffic data set show that the LRTC-CGD and LRTC-TSVT algorithms have better completion accuracy than other existing completion algorithms under different missing scenarios and missing rates. And in the case of extreme data missing(70%~80%), the effect of completion is more stable.