Nonnegative Matrix Factoriaztion on Manifold (Graph)
Introduction
Matrix factorization techniques have been frequently applied in
information retrieval, computer vision and pattern
recognition. Among them, Nonnegative Matrix
Factorization (NMF) have received considerable attentions due to its
psychological and physiological interpretation of naturally
occurring data whose representation may be partsbased in human
brain. On the other hand, from geometric perspective the data is
usually sampled from a low dimensional manifold embedded in high
dimensional ambient space. One hopes then 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 {\em 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 the encouraging results of the proposed
algorithm in comparisons to the stateoftheart algorithms on on real world problems.
Codes
GNMF: Graphregularized NMF (Fnorm formulation). GNMF_Multi is required.
 Examples here
 Deng Cai, Xiaofei He, Xiaoyun Wu and Jiawei Han, "Nonnegative Matrix Factorization on Manifold", ICDM 2008.
Bibtex source
 Deng Cai, Xiaofei He, Jiawei Han, Thomas Huang, "Graph Regularized Nonnegative Matrix Factorization for Data Representation", IEEE TPAMI 2011. (pdf)
Bibtex source
GNMF_KL: Graphregularized NMF (Divergence formulation) GNMF_KL_Multi is required.
 (The efficiency of the code has been significantly improved. If you are using GNMF_KL, please update the code. 2012/1/17)
 Examples here
 Deng Cai, Xiaofei He, Xuanhui Wang, Hujun Bao and Jiawei Han, "Locality Preserving Nonnegative Matrix Factorization", IJCAI 2009.
Bibtex source
 Deng Cai, Xiaofei He, Jiawei Han, Thomas Huang, "Graph Regularized Nonnegative Matrix Factorization for Data Representation", IEEE TPAMI 2011. (pdf)
Bibtex source
LCCF: Locally Consistant Concept Factorization. LCCF_Multi is required.
 Examples here
 Deng Cai, Xiaofei He, Jiawei Han, "Locally Consistent Concept Factorization for Document Clustering", IEEE TKDE 2011. (pdf)
Bibtex source
Data sets
If you find these algoirthms useful, we appreciate it very much if you can cite our following works:
Papers
 Deng Cai, Xiaofei He, Jiawei Han, Thomas Huang, "Graph Regularized Nonnegative Matrix Factorization for Data Representation",
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 33, No. 8, pp. 15481560, 2011.
Bibtex source

PDF
 Deng Cai, Xiaofei He, Xuanhui Wang, Hujun Bao and Jiawei Han, "Locality Preserving Nonnegative Matrix Factorization",
Proc. 2009 Int. Joint Conference on Artificial Intelligence (IJCAI'09), Pasadena, CA, July 2009.
Bibtex source
 Deng Cai, Xiaofei He, Xiaoyun Wu and Jiawei Han, "Nonnegative Matrix Factorization on Manifold",
Proc. 2008 Int. Conf. on Data Mining (ICDM'08), Pisa, Italy, Dec. 2008.
Bibtex source
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