Sparse subspace clustering via Low-Rank structure propagation. (November 2019) - Sui, Yao; Wang, Guanghui; Zhang, Li
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.