Nonconvex <inline-formula> <tex-math notation="LaTeX">$l_p$ </tex-math> </inline-formula>-Norm Regularized Sparse Self-Representation for Traffic Sensor Data Recovery

Abstract

Recovering missing values from incomplete traffic sensor data is an important task for intelligent transportation system because most algorithms require data with complete entries as input. Self-representation-based matrix completion attempts to optimally represent each sample by linearly combining other samples when conducting missing values recovery. Typically, it implements sparse or dense combination through imposing either $l_{1}$ -norm or $l_{2}$ -norm regularization over the representation coefficients, which is not always optimal in practice. To permit more flexibility, we propose in this paper a novel approach termed as $l_{p}$ -norm regularized sparse self-representation (SSR- $l_{p}$ ) by incorporating nonconvex $l_{p}$ -norm with $0 as regularization. In such a way, it is able to produce more sparsity than $l_{1}$ -norm and in turn facilitates the accurate recovery of missing data. We further develop an efficient iterative algorithm for solving SSR- $l_{p}$ . The performance of this method is evaluated on a real-world road network traffic flow data set. The experimental results verify the advantage of our method over other competing algorithms in recovering missing values.