Automatic instance selection via locality constrained sparse representation for missing value estimation

Missing values in real application can significantly disturb the result of knowledge discovery, and it is thus vital to estimate this unknown data accurately. This paper focuses on applying sparse representation to improve the quality of estimation of the absent values. Firstly, a novel sparse representation scheme called locality constrained sparse representation (LCSR) is presented, introducing locality l₁-norm and l₂-norm regularization. Taking the advantage of sparsity, smoothness and locality structure, LCSR is capable of automatically selecting instance and avoiding overfitting. Then LCSR-based missing value estimation (LCSR-MVE) is proposed to estimate the unobserved values through the linear combination of automatically selected atoms from dictionary due to the sparsity in reconstruction coefficient vector, while three dictionary constructions are also developed respectively. The proposed LCSR-MVE is evaluated on 6 datasets from UCI and gene expression databases, compared with other instance-based missing value estimation methods. Results show that the proposed LCSR-MVE outperforms other state-of-arts methods in terms of normalized root mean squared error (NRMSE), and is not much sensitive to the dictionary size and regularization parameters.