Spatial imputation for air pollutants data sets via low rank matrix completion algorithm

Abstract

Incomplete observation of hourly air-pollutants concentration data is a common issue existing in urban air quality monitoring networks. This research proposes a spatial interpolation method to impute missing values presented in air pollutants data sets based on low rank matrix completion (LRMC). It considers air pollutants data of high correlation and consistency in its spatial distribution. We evaluate the performance of the proposed method when imputing various air pollutants concentration time series (NO_x,O₃,SO₂,PM_2.5,PM₁₀) in terms of root mean square error (RMSE), index of agreement (D²), and goodness of fit (R²). It systematically compared with existing established imputation techniques, including nearest neighboring, mean substitution, regression-based method, spline interpolation, spectral method, and regularized expectation maximization algorithm (EM). As a spatial imputation method, LRMC outperforms these methods used in this research under the condition of larger missing ratio (such as 30% removal) on the central air pollutants monitoring station. For all monitoring stations, comprehensive experimental results show that LRMC always generates robust results to replace missing data with reasonable substitutions, and it is not sensitive to the length of missing gaps. The promising imputation performance in terms of the indicator R² obtained by the proposed LRMC demonstrates that it can effectively impute missing values of air pollutants time series based on their inherent patterns.

Keywords: Air pollutants; Low rank matrix completion; Missing data; Spatial imputation.