Convolutional Low-Rank Tensor Representation for Structural Missing Traffic Data Imputation

Recently, low-rank tensor completion (LRTC) methods by exploiting the global low-rankness of the target tensor have shown great potential for traffic data imputation. However, in real-world transportation networks, traffic data usually suffer from more complicated structural missing patterns than random-missing patterns, e.g., tube-missing patterns due to disruptions in wireless connections or slice-missing mechanism caused by sensor maintenance. As the naturally low-rank structure of traffic data in several missing scenarios, the existing LRTC methods indeed refrain from desirable performance for imputing traffic data. To tackle the complicated missing scenarios, we propose a convolutional low-rank tensor representation (CLRTR). Especially, CLRTR represents each unfolding matrix of the tensor as a sum of convolutions between two-dimensional (2D) filters and the corresponding low-rank coefficients, which allows us to simultaneously reveal the local patterns and the low-rankness of traffic data. Based on the CLRTR, we introduce the corresponding low-rank metric CLRTR-rank. Based on the suggested low-rank metric, we propose a traffic data imputation model that is well-suited to the complicated missing data scenarios. To implement the resultant imputation model, we design the alternating direction method of multipliers (ADMM) based algorithm with a theoretical convergence guarantee. Extensive numerical experiments on several real-world traffic datasets for both traffic data imputation and downstream traffic data prediction highlight the superiority of our model over the existing state-of-the-art matrix/tensor models for extensive missing scenarios.