Spectral clustering steered low-rank representation for subspace segmentation

• A spectral clustering steered low-rank representation algorithm is proposed.
• An optimization approach for solving SCSLRR problem is presented.
• The convergence of the optimization approach is proved.
• The relationships between SCSLRR and some related methods are discussed.

Low-rank representation (LRR) and its variations have achieved great successes in subspace segmentation tasks. However, the segmentation processes of the existing LRR-related methods are all divided into two separated steps: affinity graphs construction and segmentation results obtainment. In the second step, normalize cut (Ncut) algorithm is used to get the final results based on the constructed graphs. This implies that the affinity graphs obtained by LRR-related algorithms may not be most suitable for Ncut, and the best results are not guaranteed to be achieved. In this paper, we propose a spectral clustering steered LRR representation algorithm (SCSLRR) which combines the objection functions of Ncut, K-means and LRR together. By solving a joint optimization problem, SCSLRR is able to find low-rank affinity matrices which are most beneficial for Ncut to get best segmentation results. The extensive experiments of subspace segmentation on several benchmark datasets show that SCSLRR dominates the related methods.