Constrained nonnegative matrix factorization for image representation

Haifeng Liu, Zhaohui Wu, Xuelong Li, Deng Cai, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review


Nonnegative matrix factorization (NMF) is a popular technique for finding parts-based, linear representations of nonnegative data. It has been successfully applied in a wide range of applications such as pattern recognition, information retrieval, and computer vision. However, NMF is essentially an unsupervised method and cannot make use of label information. In this paper, we propose a novel semi-supervised matrix decomposition method, called Constrained Nonnegative Matrix Factorization (CNMF), which incorporates the label information as additional constraints. Specifically, we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition. We explore the proposed CNMF method with two cost function formulations and provide the corresponding update solutions for the optimization problems. Empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state-of-the-art approaches through a set of evaluations based on real-world applications.

Original languageEnglish (US)
Article number6072214
Pages (from-to)1299-1311
Number of pages13
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number7
StatePublished - 2012


  • Nonnegative matrix factorization
  • clustering
  • dimension reduction
  • semi-supervised learning

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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