Robust subspace segmentation via nonconvex low rank representation

• A nonconvex formulation to determine the low rank representation from contaminated data is proposed.
• We provide a proximal iteratively reweighed algorithm for solving the nonconvex model.
• The proposed nonconvex model can recover the underlying low rank structure of subspaces in spite of noisy corruptions.

Recently, low rank representation (LRR) has been successfully applied to explore subspace segmentation of data. In this paper, we propose a nonconvex formulation to determine the LRR from contaminated data. Unlike in traditional methods, which directly utilize the nuclear norm to approximate the rank function and penalize noise using the ℓ2,1-norm, our method introduces the Ky Fan p-k-norm and the ℓ2,q-norm, to better approximate the rank minimization problem and enhance the robustness against noise. An efficient algorithm is derived for solving the novel objective function, and this is followed by a rigorous theoretical proof of the convergence. Extensive experiments on face datasets clearly demonstrate that the proposed methods are more robust to illumination variations, corruptions, and occlusions.