Multimedia Tools and Applications

, Volume 72, Issue 2, pp 1441–1463 | Cite as

Semi-supervised non-negative matrix factorization for image clustering with graph Laplacian

  • Yangcheng He
  • Hongtao Lu
  • Saining Xie


Non-negative matrix factorization (NMF) plays an important role in multivariate data analysis, and has been widely applied in information retrieval, computer vision, and pattern recognition. NMF is an effective method to capture the underlying structure of the data in the parts-based low dimensional representation space. However, NMF is actually an unsupervised method without making use of supervisory information of data. In recent years, semi-supervised learning has received a lot of attentions, because partial label information can significantly improve learning quality of the algorithms. In this paper, we propose a novel semi-supervised non-negative matrix factorization (SEMINMF) algorithm, which not only utilizes the local structure of the data characterized by the graph Laplacian, but also incorporates the label information as the fitting constraints to learn. Hence, it can learn from labeled and unlabeled data. By this means our SEMINMF can obtain a more discriminative powerful representation space. Experimental results show the effectiveness of our proposed novel method in comparison to the state-of-the-art algorithms on several real world applications.


Non-negative matrix factorization Clustering Semi-supervised learning Image clustering 



This work was supported in part by the National Basic Research Program of China (973 program) under Grant 2009CB320901, NSFC (no. 61272247), the National High Technology Research and Development Program of China (863 program) under Grant 2008AA02Z310, the National Natural Science Foundation of China under Grant 60873133, and the Innovation Ability Special Fund of Shanghai Jiao Tong University under Grant Z030026.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.MOE-Microsoft Laboratory for Intelligent Computing and Intelligent Systems, Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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