Robust Subspace Clustering via Tighter Rank Approximation
This work addresses subspace clustering challenges for applications like computer vision, but it is incremental as it builds on existing nuclear norm methods.
The authors tackled the NP-hard matrix rank minimization problem by proposing a tighter rank approximation using an arctangent function, applied to subspace clustering, and demonstrated effectiveness through experiments on face clustering and motion segmentation.
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.