Traffic Data Recovery and Outlier Detection Based on Non-negative Matrix Factorization and Truncated-Quadratic Loss Function

Intelligent Transportation System (ITS) plays a critical role in managing traffic flow and ensuring safe transportation. However, the presence of missing and corrupted traffic data may undermine the accuracy and reliability of the system. The problem of recovering traffic data can often be transformed into a low-rank matrix factorization problem by exploiting the intrinsic low-rank characteristics of the traffic matrix. While many existing methods demonstrate excellent recovery performance under the assumption of noiseless or Gaussian noise, they often exhibit suboptimal performance in the presence of outliers. In this paper, we propose a novel method for recovering traffic data using non-negative matrix factorization with a truncated-quadratic loss function. Although the objective function in our model is non-convex and non-smooth, we convert it to a convex formulation using half-quadratic theory. Then, a solver based on block coordinate descent is developed. Our experiments on real-world traffic datasets demonstrate superior performance compared to state-of-the-art methods.