Particle swarm optimization and covariance matrix based data imputation

We propose a data imputation method based on Particle Swarm Optimization (PSO) and covariance matrix of the data. PSO is used to minimize the following error functions in a nested form (i) Mean squared error between the covariance matrix of the set of complete records and the covariance matrix of the set of total records including imputed ones. (ii) Absolute difference between the determinants of the two covariance matrices. The algorithm is designed to stop only when these two errors become very small across two consecutive iterations. The proposed method was tested on several regression, classification and banking datasets using 10 fold cross validation. The quality of the imputation is tested by using Mean Absolute Percentage Error (MAPE) value. We compared the results of the proposed method with that of a hybrid data imputation method based on K-means and Multi-layer Perceptron (MLP). We observed that while the the proposed preserves the covariance structure of the data, it achieved better imputation in most of the datasets as evidenced by the Wilcoxon signed rank test to test the statistical significance of the results.