Auto-weighted low-rank representation for clustering

摘要

Low-rank representation (LRR) is an effective method to learn the subspace structure embedded in the data. However, most LRR methods make use of different features equally, causing the useless features may degrade the performance of the model. In order to solve this problem, 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 distance 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, a block-diagonal regularizer is employed to guarantee that the learned graph contains c 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.