Unsupervised Feature Selection Based on Reconstruction Error Minimization

In this paper, we propose a novel unsupervised feature selection method, which is to minimize the data reconstruction error between each sample and a linear combination of its neighbors. Different from the conventional reconstruction-based feature selection method, we impose a nonnegative orthogonal constraint on the reconstruction weight matrix, so that an ideal neighbor assignment is adaptively captured. To enhance the robustness of the residual term and select the most valuable features, {\ell -{2,1}}-norm is applied to both reconstruction error term and feature selection matrix. At last, we derive an iterative algorithm to effectively solve the proposed objective function, and perform extensive experiments on four benchmark datasets to validate the effectiveness of the proposed method.