Two Rank Approximations for Low-Rank Based Subspace Clustering

Rank approximation and minimization problem is widely applied in machine learning and computer vision. As the minimum convex envelope of the rank function, the nuclear norm is often used for rank approximation and has achieved satisfactory results in different tasks. However, the nuclear norm may not be an appropriate rank approximation especially when there are large singular values. In this paper, we propose two different functions to more accurately approximate the rank function. Then based on the low-rank representation model, we use these approximations for robust subspace clustering with desirable low rank and robustness to noise. Experimental results show the effectiveness of our proposed methods.