Efficient subspace clustering and feature extraction via l2, 1- norm and l1, 2-norm minimization

The nuclear norm -based Latent Low -Rank Representation (LatLRR) has gained much attention due to its success in subspace clustering and feature extraction. However, it suffers from high computational costs due to the calculation of singular value decomposition for large matrices. To this end, we develop an efficient subspace clustering and feature extraction method (ESCFE) which substitutes the nuclear norm with the l(2, 1) -norm and l(1, 2) -norm respectively. Theoretically proof shows both the l(2, 1 )-norm and l(1, 2)- norm can serve as the convex surrogates of the nuclear norm while can derive closed -form solutions. Furthermore, the l(2, 1) -norm (or l(1, 2)- norm) regularization promotes column (or row) structure sparsity due to the discriminative nature inherited from the l (1) -norm. Thus the proposed ESCFE is robust to outliers in data and can extract features with joint sparsity. Extensive experiments on multiple benchmark datasets demonstrate the superiority of our method in both efficiency and effectiveness.