Subspace clustering with first-order log-determinant rank approximation

Yunhong Hu, Qiang Cheng, Baoli Wang, Liang Fang

Research output: Contribution to journalArticlepeer-review


It is natural to assume a data matrix to be of low-rank in many machine learning and computer vision problems, e.g., matrix completion and subspace clustering. To ensure low-rank, the nuclear norm minimization is widely used as a rank approximation and minimization technique. The nuclear norm treats all the singular values through adding them together with equal weights. With this liner addition, large singulars will con-tribute too much and make the approximation very inaccurate. To reduce this undesirable effect, we make use of a first-order log-determinant approximation which assigns small weights to large singular values and is close to vanishing for small ones. A low-rank representation is obtained using this function and the affinity is then constructed based on angular in-formation. Experimentally we achieve promising results on face clustering and motion segmentation using this affinity.

Original languageEnglish
Pages (from-to)140-147
Number of pages8
JournalIPPTA: Quarterly Journal of Indian Pulp and Paper Technical Association
Issue number1
StatePublished - Mar 1 2018

Bibliographical note

Publisher Copyright:
© 2018 Indian Pulp and Paper Technical Association. All rights reserved.


  • Face Clustering
  • Motion Segmentation
  • Spectral Clustering
  • Subspace Clustering

ASJC Scopus subject areas

  • General Chemistry
  • General Chemical Engineering
  • Media Technology
  • Materials Chemistry


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