Sparse subspace clustering via Low-Rank structure propagation

Yao Sui, Guanghui Wang, Li Zhang

Abstract: Highlights • A novel data sample representation is proposed, where a low-rank structure is propagated in the sparse representation. Based on the representation, a self-expression is constructed for subspace clustering. Experimental results on synthesis datasets and several real datasets demonstrate that the proposed subspace clustering algorithm performs comparably against state-of-the-art methods. • A theoretical proof is provided to show the proposed approach can reveal the true membership of the data samples being clustered. • Discussions from both geometric and physical perspectives on the proposed approach are made as an explanation and an algorithm analysis. Abstract The paper formulates the subspace clustering as a problem of structured representation learning. It is proved that the sparsity of the data representation is significantly promoted by propagating a low-rank structure, leading to a more robust description of the clustering structure. Based on a theoretical proof to support this observation, a novel subspace clustering algorithm is proposed with the structured representation. Two cascade self-expressions are leveraged to implement the propagation. One leads to a low-rank representation of the data samples by exploiting the global structure; whereas the other generates a sparse representation of the former low-rank representation to capture the neighborhood structure. The proposed representation strategy is further investigated from both a geometric and a physical perspective. Extensive evaluations on both synthetic and real datasets demonstrate that the proposed approach outperforms most state-of-the-art methods.