Spatiotemporal traffic data completion with truncated minimax-concave penalty

The rapid development of sensor technology has prompted a large amount of data, including spatiotemporal traffic data, which can be used to predict traffic conditions and better traffic management. However, the data-missing problem is common in reality due to detectors malfunctioning or communication failure. Therefore, quickly and accurately missing data completion is critical for data-driven intelligent transportation applications. To this end, numerous low-rank tensor completion (LRTC) based imputation model has been attempted in previous work, whose core is how to describe the rank of the tensor and efficiently tackle the related minimization problem. In this work, we propose a novel nonconvex truncated minimax-concave penalty (TMCP) for tensors to approximate the rank of the tensor and derive an efficient iterative algorithm by combining with the alternating direction method of multipliers (ADMM) framework. Moreover, we demonstrate that the proposed LRTC-TMCP method has global convergence properties. Simultaneously, based on four different real-world spatiotemporal traffic data, we conducted simulated numerical experiments on various missing scenarios. In general, our method shows remarkable performance compared to some state-of-the-art completion methods. For example, on the Portland dataset, the performance of the proposed LRTC-TMCP achieves up to an average 6.21% improvement in root mean square error (RMSE) compared to the most competitive completion method while only spending 26.2% of its total CPU running time. In addition, theoretical and numerical experiments exemplify that the LRTC-TMCP method has strong robustness and efficient convergence performance.