Abstract
Some of the data collected from practical applications are usually heavily corrupted. In sub-space clustering, the common method is to use the specific regularization strategy to cor-rect 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 & POUND;1,2 and & POUND;2,1 (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 & POUND;1,2 norm on the representation matrix, and improve the robustness to outliers by enforcing the & POUND;2,1 con-straint on the error matrix. The joint & POUND;1,2 and & POUND;2,1 minimization leads to a good representa-tion matrix which enhances the clustering performance. Related & POUND;1,2 and & POUND;2,1 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.