Low-rank singular value thresholding for recovering missing air quality data

With the increasing awareness of the harmful impacts of urban air pollution, air quality monitoring stations have been deployed in many metropolitan areas. These stations provide air quality data to the public. However, due to sampling device failures and data processing errors, missing data in air quality measurements is common. Data integrity becomes a critical challenge when such data are employed for public services. In this paper, we investigate the mathematical property of air quality measurements, and attempt to recover the missing data. First, we empirically study the low rank property of these measurements. Second, we formulate the low rank matrix completion (LRMC) optimization problem to reconstruct the missing air quality data. The problem is transformed using duality theory, and singular value thresholding (SVT) is employed to develop sub-optimal solutions. Third, to evaluate the performance of our methodology, we conduct a series of case studies including different types of missing data patterns. The simulation results demonstrate that the proposed SVT methodology can effectively recover missing air quality data, and outperform the existing Interpolation. Finally, we investigate the parameter sensitivity of SVT. Our study can serve as a guideline for missing data recovery in the real world.