Robust Subspace Segmentation Via Low-Rank Representation

Recently the low-rank representation (LRR) has been successfully used in exploring the multiple subspace structures of data. It assumes that the observed data is drawn from several low-rank subspaces and sometimes contaminated by outliers and occlusions. However, the noise (low-rank representation residual) is assumed to be sparse, which is generally characterized by minimizing the l₁-norm of the residual. This actually assumes that the residual follows the Laplacian distribution. The Laplacian assumption, however, may not be accurate enough to describe various noises in real scenarios. In this paper, we propose a new framework, termed robust low-rank representation, by considering the low-rank representation as a low-rank constrained estimation for the errors in the observed data. This framework aims to find the maximum likelihood estimation solution of the low-rank representation residuals. We present an efficient iteratively reweighted inexact augmented Lagrange multiplier algorithm to solve the new problem. Extensive experimental results show that our framework is more robust to various noises (illumination, occlusion, etc) than LRR, and also outperforms other state-of-the-art methods.