Nonconvex Low-Tubal-Rank Tensor Completion With Temporal Regularization for Spatiotemporal Traffic Data Recovery

Spatiotemporal traffic data collected by sensor networks is paramount for intelligent transportation systems, but it often suffers from significant missing values, making accurate recovery a critical challenge. This paper introduces a nonconvex low-tubal-rank tensor completion model with temporal regularization (NLTC-TR) to fill in missing data based on the underlying physical properties of spatiotemporal traffic data, including similarity and periodicity. Our model can capture both the global correlations across different modes of traffic data and the local temporal variations. Specifically, we first present a unified nonconvex model to capture tubal rank along different dimensions while considering the specificity in each mode. The nonconvexity achieved by synergizing logarithm and Schatten-p norm serves as a tight rank approximation. In doing so, the low-rank property of traffic data can be better modeled in the transformed domains. Furthermore, by introducing a temporal regularization, we can make better use of the local variation between adjacent moments. To solve this problem, we propose an efficient iterative algorithm based on the alternating direction method of multipliers (ADMM), where each step can be solved in closed form. Numerical experiments on two real-world traffic datasets with varying missing patterns show that our method outperforms existing algorithms, demonstrating its effectiveness in accurately recovering missing traffic data.