Three New Subspace Clustering Models And Their Applications In Face Recognition

Subspace clustering is one of the important methods for high-dimensional data clustering,which has been successfully applied in machine learning,pattern recognition,image processing and other fields.Subspace clustering aims to segment a set of high-dimensional data drawn from a union of subspaces into clusters with each cluster corresponding to a low-dimensional subspace.Low-rank representation model and sparse representation model are commonly used in subspace clustering,but these existing models do not make full use of the structure information of the data set.To fully capture the local and global information of the data and achieve better clustering effect,by combining elastic net regularized low-rank repre-sentation and non-negative low-rank and sparse representation,this paper firstly proposes a subspace clustering model based on low-rank and sparse representation,which uses the combination of nuclear norm,Frobenius nor-m and l1-norm of the coefficient matrix as the regular terms.Because the l2,1-norm has both sparsity and grouping effect,replacing the l2,1-norm of the coefficient matrix with Frobenius norm and l1-norm,a subspace clus-tering model based on joint sparse and low-rank representation is further investigated.Two models are solved by linearized alternating direction method with adaptive penalty,and the affinity matrix is built by the ob-tained coefficient matrix.The spectral clustering method is employed to cluster.Numerical results on the artificial data set and Extended Yale B face database demonstrate the two models bring more obvious clustering effect and higher accuracy than existing models.Note that the above subspace clustering model based on joint sparse and low-rank representation may lead to dense representation,a subspace clustering model based on class-wise sparse and low-rank representation is then proposed,which is solved by linearized alternating direction method with parallel splitting and adaptive penalty.In addition,we adopt an adaptive rule for the estimation of the regularization parameters instead of manually adjusting them in existing models.Numerical results show that the subspace clustering model based on class-wise sparse and low-rank rep-resentation has better clustering performance than the former two models.