Robust subspace clustering via tighter rank approximation

Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict its capability in dealing with many practical problems. In this paper, an arctangent function is used as a tighter approximation to the rank function. We use it on the challenging subspace clustering problem. For this nonconvex minimization problem, we develop an effective optimization procedure based on a type of augmented Lagrange multipliers (ALM) method. Extensive experiments on face clustering and motion segmentation show that the proposed method is effective for rank approximation.