A Novel Method for Air Quality Data Imputation by Nuclear Norm Minimization

Abstract EN

Missing data is a frequently encountered problem in environment research community.

To facilitate the analysis and management of air quality data, for example, PM2.5 concentration in this study, a commonly adopted strategy for handling missing values in the samples is to generate a complete data set using imputation methods.

Many imputation methods based on temporal or spatial correlation have been developed for this purpose in the existing literatures.

The difference of various methods lies in characterizing the dependence relationship of data samples with different mathematical models, which is crucial for missing data imputation.

In this paper, we propose two novel and principled imputation methods based on the nuclear norm of a matrix since it measures such dependence in a global fashion.

The first method, termed as global nuclear norm minimization (GNNM), tries to impute missing values through directly minimizing the nuclear norm of the whole sample matrix, thus at the same time maximizing the linear dependence of samples.

The second method, called local nuclear norm minimization (LNNM), concentrates more on each sample and its most similar samples which are estimated from the imputation results of the first method.

In such a way, the nuclear norm minimization can be performed on those highly correlated samples instead of the whole sample matrix as in GNNM, thus reducing the adverse impact of irrelevant samples.

The two methods are evaluated on a data set of PM2.5 concentration measured every 1 h by 22 monitoring stations.

The missing values are simulated with different percentages.

The imputed values are compared with the ground truth values to evaluate the imputation performance of different methods.

The experimental results verify the effectiveness of our methods, especially LNNM, for missing air quality data imputation.