  In this paper, a novel unsupervised low-rank representation model, i.e.,
Auto-weighted Low-Rank Representation (ALRR), is proposed to construct a more
favorable similarity graph (SG) for clustering. In particular, ALRR enhances
the discriminability of SG by capturing the multi-subspace structure and
extracting the salient features simultaneously. Specifically, an auto-weighted
penalty is introduced to learn a similarity graph by highlighting the effective
features, and meanwhile, overshadowing the disturbed features. Consequently,
ALRR obtains a similarity graph that can preserve the intrinsic geometrical
structures within the data by enforcing a smaller similarity on two dissimilar
samples. Moreover, we employ a block-diagonal regularizer to guarantee the
learned graph contains $k$ diagonal blocks. This can facilitate a more
discriminative representation learning for clustering tasks. Extensive
experimental results on synthetic and real databases demonstrate the
superiority of ALRR over other state-of-the-art methods with a margin of
1.8\%$\sim$10.8\%.
