Unsupervised feature selection by non-convex regularized self-representation

•An ℓ2,1-2 self-representation unsupervised feature selection is proposed.•ℓ2,1-2 is proved to guarantee the sparsity of selection matrix in theory.•An iterative CCCP algorithm is designed to tackle the nonconvexity of ℓ2,1-2.•The global convergence of our CCCP is theoretically analyzed.•Extensive experimental results verify the effectiveness of the proposed method.