Semi-supervised learning with nuclear norm regularization

Fanhua Shang, L. C. Jiao, Yuanyuan Liu, Hanghang Tong

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Integrating new knowledge sources into various learning tasks to improve their performance has recently become an interesting topic. In this paper we propose a novel semi-supervised learning (SSL) approach, called semi-supervised learning with nuclear norm regularization (SSL-NNR), which can simultaneously handle both sparse labeled data and additional pairwise constraints together with unlabeled data. Specifically, we first construct a unified SSL framework to combine the manifold assumption and the pairwise constraints assumption for classification tasks. Then we provide a modified fixed point continuous algorithm to learn a low-rank kernel matrix that takes advantage of Laplacian spectral regularization. Finally, we develop a two-stage optimization strategy, and present a semi-supervised classification algorithm with enhanced spectral kernel (ESK). Moreover, we also present a theoretical analysis of the proposed ESK algorithm, and derive an easy approach to extend it to out-of-sample data. Experimental results on a variety of synthetic and real-world data sets demonstrate the effectiveness of the proposed ESK algorithm.

Original languageEnglish (US)
Pages (from-to)2323-2336
Number of pages14
JournalPattern Recognition
Issue number8
StatePublished - Aug 2013
Externally publishedYes


  • Graph Laplacian
  • Low-rank kernel learning
  • Nuclear norm regularization
  • Pairwise constraints
  • Semi-supervised learning (SSL)

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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