Graph constraint-based robust latent space low-rank and sparse subspace clustering

Recently, low-rank and sparse representation-based methods have achieved great success in subspace clustering, which aims to cluster data lying in a union of subspaces. However, most methods fail if the data samples are corrupted by noise and outliers. To solve this problem, we propose a novel robust method that uses the F-norm for dealing with universal noise and the $$l_1$$ l 1 norm or the $$l_{2,1}$$ l 2 , 1 norm for capturing outliers. The proposed method can find a low-dimensional latent space and a low-rank and sparse representation simultaneously. To preserve the local manifold structure of the data, we have adopted a graph constraint in our model to obtain a discriminative latent space. Extensive experiments on several face benchmark datasets show that our proposed method performs better than state-of-the-art subspace clustering methods.