Graph regularized nonnegative matrix factorization for data representation

Deng Cai, Xiaofei He, Jiawei Han, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review


Matrix factorization techniques have been frequently applied in information retrieval, computer vision, and pattern recognition. Among them, Nonnegative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain. On the other hand, from the geometric perspective, the data is usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space. One then hopes to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called Graph Regularized Nonnegative Matrix Factorization (GNMF), for this purpose. In GNMF, an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization, which respects the graph structure. Our empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.

Original languageEnglish (US)
Article number5674058
Pages (from-to)1548-1560
Number of pages13
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number8
StatePublished - 2011


  • Nonnegative matrix factorization
  • clustering
  • graph Laplacian
  • manifold regularization

ASJC Scopus subject areas

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


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