Subspace clustering using a symmetric low-rank representation

Jie Chen, Hua Mao, Yongsheng Sang, Zhang Yi

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)
33 Downloads (Pure)


In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can simultaneously recover the dimension and members of each subspace. LRRSC extends the original low-rank representation algorithm by integrating a symmetric constraint into the low-rankness property of high-dimensional data representation. The symmetric low-rank representation, which preserves the subspace structures of high-dimensional data, guarantees weight consistency for each pair of data points so that highly correlated data points of subspaces are represented together. Moreover, it can be efficiently calculated by solving a convex optimization problem. We provide a proof for minimizing the nuclear-norm regularized least square problem with a symmetric constraint. The affinity matrix for spectral clustering can be obtained by further exploiting the angular information of the principal directions of the symmetric low-rank representation. This is a critical step towards evaluating the memberships between data points. Besides, we also develop eLRRSC algorithm to improve the scalability of the original LRRSC by considering its closed form solution. Experimental results on benchmark databases demonstrate the effectiveness and robustness of LRRSC and its variant compared with several state-of-the-art subspace clustering algorithms.
Original languageEnglish
Pages (from-to)46-57
Number of pages12
JournalKnowledge-Based Systems
Early online date1 Mar 2017
Publication statusPublished - 1 Jul 2017


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