Latent space robust subspace segmentation based on low-rank and locality constraints

Low-rank representation (LRR) and its extensions have proven to be effective methods to handle different kinds of subspace segmentation applications. In this paper, we propose a new subspace segmentation algorithm, termed latent space robust subspace segmentation based on low-rank and locality constraints (LSRS2). Different from LRR, LSRS2 learns a low-dimensional space and a coefficient matrix for a data set simultaneously. In the obtained latent space, the coefficient matrix can faithfully reveal both the global and local structures for the data set. Furthermore, we build the connections between LSRS2 and robust coding methods, and show LSRS2 can be regarded as a kind of robust LRR method. Therefore, it can be guaranteed in theory that LSRS2 shows good performance. In addition, an efficient optimization method for solving LSRS2 is presented and its convergence is also proven. Extensive experiments show that the proposed algorithm outperforms the related subspace segmentation methods.