Attention reweighted sparse subspace clustering

Subspace clustering has attracted much attention in many applications of computer vision and pattern recognition. Spectral clustering based methods, such as sparse subspace clustering (SSC) and low-rank representation (LRR), have become popular due to their theoretical guarantees and impressive performance. However, many state-of-the-art subspace clustering methods specify the mean square error (MSE) criterion as the loss function, which is sensitive to outliers and complex noises in reality. These methods have poor performance when the data are corrupted by complex noise. In this paper, we propose a robust sparse subspace clustering method, termed Attention Reweighted SSC (ARSSC), by paying less attention to the corrupted entries (adaptively assigning small weights to the corrupted entries in each data point). To reduce the extra bias in estimation introduced by ℓ1 regularization, we also utilize non-convex penalties to overcome the overpenalized problem. In addition, we provide theoretical guarantees for ARSSC and theoretically show that our method gives a subspace-preserving affinity matrix under appropriate conditions. To solve the ARSSC optimization problem, we devise an optimization algorithm using an Alternating Direction Method of Multipliers (ADMM) method. Experiments on real-world databases validate the effectiveness of the proposed method.