Traffic Data Imputation Based on Graph Regularization and Schatten-p Norm Minimization

To make full use of the low-rank characteristics and local neighbor relationship of the traffic data, and accurately recover the missing data in traffic data acquisition system, firstly, the traffic data matrix is pre-interpolated by the low-rank matrix completion model based on kernel norm to obtain the initial estimate of the missing data. Based on this, a graph model that characterizes the local neighbor structure of the data is constructed. Then, a missing value imputation model combining graph regularization and Schatten-p norm minimization is proposed. Furthermore, an optimization algorithm based on alternating direction multiplier framework is proposed to solve the optimization of missing value imputation, so as to obtain the final imputation result. Finally, the real expressway traffic volume and speed data are used to compare the imputation errors of several methods, and the parameter sensitivity of the proposed method is analyzed. The experimental results show that compared with local least squares, probabilistic principal component analysis and low-rank matrix completion, the proposed method reduces the error of traffic data imputation by 3.02%−28.49% when the missing rate is 10%−50% in missing completely at random mode, missing at random mode and mixed missing mode.