LogDet Rank Minimization with Application to Subspace Clustering

Zhao Kang, Chong Peng, Jie Cheng, Qiang Cheng

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose using a log-determinant (LogDet) function as a smooth and closer, though nonconvex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the LogDet-based nonconvex objective function on potentially large-scale data. By making use of the angular information of principal directions of the resultant low-rank representation, an affinity graph matrix is constructed for spectral clustering. Experimental results on motion segmentation and face clustering data demonstrate that the proposed method often outperforms state-of-the-art subspace clustering algorithms.

Original languageEnglish
Article number824289
JournalComputational Intelligence and Neuroscience
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Zhao Kang et al.

ASJC Scopus subject areas

  • General Computer Science
  • General Neuroscience
  • General Mathematics


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