Robust Subspace Clustering via Smoothed Rank Approximation
This work addresses subspace clustering for applications like face clustering and motion segmentation, offering incremental improvements over existing methods.
The paper tackled the problem of matrix rank minimization for subspace clustering by proposing a Logarithm-Determinant rank approximation to improve accuracy over nuclear norm methods, achieving promising results on face clustering and motion segmentation tasks compared to state-of-the-art algorithms.
Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world applications, nuclear norm approximation to the rank function can only produce a result far from the optimum. To seek a solution of higher accuracy than the nuclear norm, in this paper, we propose a rank approximation based on Logarithm-Determinant. We consider using this rank approximation for subspace clustering application. Our framework can model different kinds of errors and noise. Effective optimization strategy is developed with theoretical guarantee to converge to a stationary point. The proposed method gives promising results on face clustering and motion segmentation tasks compared to the state-of-the-art subspace clustering algorithms.