张量加权Schatten范数交通数据补全估计

Estimation on Tensor Weighted Schatten Norm for Missing Traffic Data Completion

智慧交通蓬勃发展,但受限于技术因素和外部环境因素,导致收集的数据存在缺失而不能直接使用,降低了数据的直接利用率和有效性。为了合理有效地填补缺失的数据,鉴于交通数据集具有低秩特性,在低秩张量补全框架下,将数据构建成"位点×时间×天"模式的张量结构。在此结构上,提出使用加权的Schatten范数进行数值逼近,同时利用交替方向乘子法和贝叶斯优化算法对参数进行更新和寻优。将构建的补全模型和对比补全模型放在广州城市交通数据集上进行数值试验,并选取平均百分比误差和均方根误差2个评价指标。结果表明:提出的张量加权Schatten范数最小化(Tensor Weighted Schatten Norm Minimization,TWSNM)模型具有竞争性和鲁棒性。在随机缺失场景中,从低缺失率10%到高缺失率90%,TWSNM模型得到的平均百分比误差和均方根误差均小于其他补全模型。在非随机缺失场景中,低缺失率情形下,TWSNM模型的表现与其他模型相比具有竞争性。在70%和80%缺失率情况下,低秩框架下的其他模型表现出了不稳定性,误差率上升,而TWSNM模型在不同缺失率下的表现都非常稳定,即TWSNM模型兼有鲁棒性。可见,TWSNM模型能够有效完成数据补全任务,提高对交通数据的利用率,可为交通决策者提供分析与决策的依据。

The intelligent transport is booming.However,it is bound by the technical factors and the external factors,and the collected data cannot be used directly for the reason of missing,which reduces the utilization rate and effectiveness of the data.In order to fill in the missing data reasonably and effectively,considering the low-rank characteristics of the traffic data sets,it is architected to a tensor structure of"location×time of days×days"mode under the low-rank tensor completion framework.Based on this framework,it is forward to use the weighted Schatten norm for numerical approximation.At the same time,the parameters are updated and optimized by using both alternating multiplier method and Bayesian optimization algorithm.The built completion model and the comparison completion model are put on the Guangzhou urban traffic data set for numerical experiments,and the mean percentage error and the root mean square error are selected as evaluation indicators.The result shows that(1)the proposed tensor weighted Schatten norm minimization(TWSNM)model is competitive and robust;(2)the mean absolute percentage error and root mean square error derived from TWSNM model are both more smaller than those derived from other completion models from the low missing rate of 10%to the high missing rate of 90%in the scene of random missing;(3)in the scene of both nonrandom missing and low missing rate,TWSNM model is more competitive than other models,since other models which under the low rank framework show instability and increased error rates at 70%and 80%miss rates,while the performance of TWSNM model is very stable at different missing rates,that is TWSNM model has robustness.It is visible that the TWSNM model can effectively complete data completion tasks and improve the utilization of traffic data,so transit decision-makers could have the basis to analyze and decide.