基于张量加权与截断核范数的交通数据修复方法

Traffic Data Restoration Method Based on Tensor Weighting and Truncated Nuclear Norm

数据缺失问题严重影响了智能交通系统中通过数据监控交通态势、预测交通流量、部署交通规划等一系列活动。为此,运用基于张量奇异值分解的低秩张量补全框架提出了加权与截断核范数相结合的交通流数据重构模型WLRTC-TTNN(Low Rank Tensor Completion of Weighted and Truncated Nuclear Norm),该模型可以有效地对缺失的时空交通数据进行修复。WLRTC-TTNN方法主要有两方面的优点:一是加入权重因子解决了原始模型对数据输入方向的依赖问题,实现了模型方向的灵活性;二是运用张量的截断核范数来代替张量的核范数作为张量秩最小化的凸代理,保留了时空交通数据内部主要的特征信息,且根据广义奇异值阈值理论,对较小奇异值进行惩罚处理,进一步优化了模型,最终使用交替乘子法实现了WLRTC-TTNN算法。在两个公开的时空交通数据集上选取不同的缺失场景与缺失率进行实验,结果表明:WLRTC-TTNN的补全性能优于其他基线模型,整体的补全精度提高了3%~37%,在数据极端缺失的情况下,其补全效果更加稳定。

The problem of missing data seriously affects a series of activities in intelligent transportation systems,such as monitoring traffic dynamics,predicting traffic flow,and deploying traffic planning through data.Therefore,a traffic flow data reconstruction model WLRTC-TTNN(low rank tensor completion of weighted and truncated nuclear norm)combined with weighted and truncated nuclear norm is proposed by using the low-rank tensor completion framework based on tensor singular value decomposition,which can effectively repair the missing spatio-temporal traffic data.The truncated nuclear norm of the tensor is used as a convex proxy for tensor rank minimization instead of tensor rank minimization,which preserves the main feature information inside the spatio-temporal traffic data,and further optimizes the model by penalizing smaller singular values according to the gene-ralized singular value threshold theory,and finally the WLRTC-TTNN algorithm is implemented using the alternating multiplier method.Experiments are conducted on two publicly available spatio-temporal traffic datasets selected with different missing scenarios and missing rates,and the results show that the complementary performance of WLRTC-TTNNN is better than that of other baseline models,and the overall complementary accuracy improves by 3%~37%,and the complementary effect is more stable in extreme missing scenarios.