A Novel Nonconvex Low-rank Tensor Completion Approach for Traffic Sensor Data Recovery from Incomplete Measurements

Complete traffic sensor data is considered to be one of the critical ingredients for intelligent transportation systems (ITS). However, the traffic measurements prevalently suffer from the inevitable and ubiquitous missing values. Current missing data completion algorithms are difficult to leverage the global low-rank property and the fine-grained spatial-temporal structure simultaneously. To circumvent this problem, this work presents a novel collaborative nonconvex low-rank spatial-temporal data tensor completion model that can take full advantage of the inherent spatial-temporal characteristics of traffic measurement data. First, the tensor Schatten p-norm, as an effective nonconvex surrogate of rank function, is used to exploit the global multi-dimensional correlation of traffic data. Then, we present an elastic net self-representation method and utilize an autoregression model in order to simultaneously capture the self-similarity and the temporal continuity of traffic data acquired in the same sensor network. By integrating the above elements in a unified nonconvex learning model, our method can explore the inherent structure of traffic data from the viewpoints of both global multi-dimensional correlation and fine-grained spatial and temporal dependency. Then, in the view of the general framework of the alternating directions method of multipliers (ADMM), an efficient iterative algorithm is designed to solve our model. Besides, to optimize the parameter combination of the model, a Bayesian optimization-based parameter selection algorithm is developed, which avoids manual parameter adjustment. Extensive experiments and analyses on two real-world traffic datasets are carried out. The results demonstrate the advantages of our model under diverse missing patterns and missing ratios.