Subspace clustering via joint ℓ1,2 and ℓ2,1

Some of the data collected from practical applications are usually heavily corrupted. In subspace clustering, the common method is to use the specific regularization strategy to correct these corrupted data by virtue of the prior knowledge, which could result in a suboptimal clustering solution. To alleviate the problem, we develop a novel formulation named subspace clustering via joint ℓ1,2 and ℓ2,1 (L12-21) norms (SCJL12-21). Specifically, we identify and exclude the heavily corrupted data points (unimportant data points) from participating in the linear representation of other points by imposing the ℓ1,2 norm on the representation matrix, and improve the robustness to outliers by enforcing the ℓ2,1 constraint on the error matrix. The joint ℓ1,2 and ℓ2,1 minimization leads to a good representation matrix which enhances the clustering performance. Related ℓ1,2 and ℓ2,1 norm constrained optimization problem is solved by utilizing the augmented Lagrange multiplier method. The effectiveness of the proposed method is demonstrated through experiments on the constructed datasets as well as the two practical problems of motion segmentation and face clustering.