Subspace clustering using log-determinant rank approximation

Chong Peng, Zhao Kang, Huiqing Li, Qiang Cheng

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

60 Scopus citations


A number of machine learning and computer vision problems, such as matrix completion and subspace clustering, require a matrix to be of low-rank. To meet this requirement, most existing methods use the nuclear norm as a convex proxy of the rank function and minimize it. However, the nuclear norm simply adds all nonzero singular values together instead of treating them equally as the rank function does, which may not be a good rank approximation when some singular values are very large. To reduce this undesirable weighting effect, we use a log-determinant function as a non-convex rank approximation which reduces the contributions of large singular values while keeping those of small singular values close to zero. We apply the method of augmented Lagrangian multipliers to optimize this non-convex rank approximation-based objective function and obtain closed-form solutions for all subproblems of minimizing different variables alternatively. The log-determinant low-rank optimization method is used to solve subspace clustering problem, for which we construct an affinity matrix based on the angular information of the low-rank representation to enhance its separability property. Extensive experimental results on face clustering and motion segmentation data demonstrate the effectiveness of the proposed method.

Original languageEnglish
Title of host publicationKDD 2015 - Proceedings of the 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining
Number of pages10
ISBN (Electronic)9781450336642
StatePublished - Aug 10 2015
Event21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2015 - Sydney, Australia
Duration: Aug 10 2015Aug 13 2015

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining


Conference21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2015

Bibliographical note

Publisher Copyright:
© 2015 ACM.


  • Low-rank representation
  • Nuclear norm
  • Rank approximation
  • Subspace clustering

ASJC Scopus subject areas

  • Software
  • Information Systems


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