Double low-rank representation with projection distance penalty for clustering

This paper presents a novel, simple yet robust self-representation method, i.e., Double Low-Rank Representation with Projection Distance penalty (DLRRPD) for clustering. With the learned optimal projected representations, DLRRPD is capable of obtaining an effective similarity graph to capture the multi-subspace structure. Besides the global low-rank constraint, the local geometrical structure is additionally exploited via a projection distance penalty in our DLRRPD, thus facilitating a more favorable graph. Moreover, to improve the robustness of DLRRPD to noises, we introduce a Laplacian rank constraint, which can further encourage the learned graph to be more discriminative for clustering tasks. Meanwhile, Frobenius norm (instead of the popularly used nuclear norm) is employed to enforce the graph to be more block-diagonal with lower complexity. Extensive experiments have been conducted on synthetic, real, and noisy data to show that the proposed method outperforms currently available alternatives by a margin of 1.0%similar to 10.1%.