Subspace clustering using a symmetric low-rank representation

Chen, Jie, Mao, Hua, Sang, Yongsheng and Yi, Zhang (2017) Subspace clustering using a symmetric low-rank representation. Knowledge-Based Systems, 127. pp. 46-57. ISSN 0950-7051

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Chen et al - Symmetric low-rank preserving projections for subspace learning AAM.pdf - Accepted Version

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Official URL: http://dx.doi.org/10.1016/j.knosys.2017.02.031

Abstract

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.

Item Type: Article
Uncontrolled Keywords: Low-rank representation, Subspace clustering, Affinity matrix learning, Spectral clustering
Subjects: G400 Computer Science
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Paul Burns
Date Deposited: 13 Jun 2019 12:37
Last Modified: 11 Oct 2019 09:18
URI: http://nrl.northumbria.ac.uk/id/eprint/39676

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