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

• Main Authors: Xiaobo Chen, Yingfeng Cai, Qingchao Liu, Lei Chen
• Format: Article
• Language: English
• Published: IEEE 2018-01-01
• Series: IEEE Access
• Subjects: Traffic sensor data; missing values; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">lp</italic>-norm regularization; sparse self-representation
• Online Access: https://ieeexplore.ieee.org/document/8353230/

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 l₁-norm or l₂-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 &lt;; p &lt;; 1 as regularization. In such a way, it is able to produce more sparsity than l₁-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.