A Tensor Train Decomposition Model Based Traffic Big Data Completion Method

With the development of the data storage technology and the growth of ways to collect data,traditional traffic data has evolved into traffic big data.At the same time,making full use of traffic big data becomes the foundation of modern traffic researches.However,breakdown of equipments and worse weather often lead to low observation in traffic data.How to complete the unobserved absent traffic data quickly and accurately hence becomes a research focus.Tensor completion is one of the most effective methods to impute missing traffic data,but existing tensor completion methods can't guarantee the robustness and high speed when dealing with ultra high dimensional data.A research on completion of missing high-dimensional traffic data has been carried out in this paper.Through building the multi-dimensional tensor model of traffic data based on its the time-spatial correlation and making use of the advantages of the tensor train decomposition model in analyzing high dimensional data,a missing traffic data completion method based on tensor train decomposition is proposed.,This paper proposes corresponding optimization schemes for the purpose of accelerating the algorithm and constraining the tensor train rank adaptively respectively,and conducts the experiments in incomplete traffic data with different missing rates.The experimental results show that the proposed method has advantages in completing the high dimensional traffic big data compared with other completion methods.The main researches are as follows:(1)This paper builds the tensor model of traffic flow data through analyzing its time-spatial-correlated features and validates the low rank characteristic of model in the moment mode,day mode,week mode,year mode and section mode,which provides a priori condition for data completion.(2)This paper proposes a tensor train decomposition based completion method.Specifically,based on the foundation of existing tensor train decomposition theories,this paper researches on the optimization solution methods for tensor train models with adding L2 regularization and trace norm regularization constraint on the core tensors,which can optimize each core tensor separately and reduce their interactive influences.For the problem of slower convergence speed,it uses the conjugate gradient method to optimize the objective function.For the inconvenience of setting tensor rank in advance,it adopts trace norm constraint to adjust tensor rank adaptively,and optimize the objective function with augmented Lagrange method.(3)This paper proposes a completion method for incomplete multi-dimensional traffic data based on tensor train decomposition.Combining the completion method with the multi-dimensional properties of traffic data to solve the problem that traditional methods are unstable in completing the multi-dimensional traffic data.Focusing on different missing rate,experiments are implemented base on the database of the Caltrans Performance Measurement System(Pe Ms)in the United States.The results show that the proposed method can effectively complete the missing data of high-dimensional traffic big data with high speed and maintain its stability under high missing rates,which controls the value of MAPE under 15%.Even when missing rate is up to 90%,the traffic data can also be accurately completed in a reliable way.