Robust Semi-Supervised Subspace Clustering via Non-Negative Low-Rank Representation

Xiaozhao Fang, Yong Xu, Xuelong Li, Zhihui Lai, Wai Keung Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

95 Citations (Scopus)


Low-rank representation (LRR) has been successfully applied in exploring the subspace structures of data. However, in previous LRR-based semi-supervised subspace clustering methods, the label information is not used to guide the affinity matrix construction so that the affinity matrix cannot deliver strong discriminant information. Moreover, these methods cannot guarantee an overall optimum since the affinity matrix construction and subspace clustering are often independent steps. In this paper, we propose a robust semi-supervised subspace clustering method based on non-negative LRR (NNLRR) to address these problems. By combining the LRR framework and the Gaussian fields and harmonic functions method in a single optimization problem, the supervision information is explicitly incorporated to guide the affinity matrix construction and the affinity matrix construction and subspace clustering are accomplished in one step to guarantee the overall optimum. The affinity matrix is obtained by seeking a non-negative low-rank matrix that represents each sample as a linear combination of others. We also explicitly impose the sparse constraint on the affinity matrix such that the affinity matrix obtained by NNLRR is non-negative low-rank and sparse. We introduce an efficient linearized alternating direction method with adaptive penalty to solve the corresponding optimization problem. Extensive experimental results demonstrate that NNLRR is effective in semi-supervised subspace clustering and robust to different types of noise than other state-of-the-art methods.
Original languageEnglish
Article number7175026
Pages (from-to)1828-1838
Number of pages11
JournalIEEE Transactions on Cybernetics
Issue number8
Publication statusPublished - 1 Aug 2016


  • Affinity matrix
  • low-rank representation (LRR)
  • subspace clustering
  • supervision information

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


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