CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2011 vol.33 Issue No.08 - August

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Issue No.08 - August (2011 vol.33)

pp: 1548-1560

Deng Cai , Zhejiang University, Hangzhou

Xiaofei He , Zhejiang University, Hangzhou

Jiawei Han , University of Illinois at Urbana-Champaign, Urbana

Thomas S. Huang , University of Illinois at Urbana-Champaign, Urbana

ABSTRACT

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.

INDEX TERMS

Nonnegative matrix factorization, graph Laplacian, manifold regularization, clustering.

CITATION

Deng Cai, Xiaofei He, Jiawei Han, Thomas S. Huang, "Graph Regularized Nonnegative Matrix Factorization for Data Representation",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.33, no. 8, pp. 1548-1560, August 2011, doi:10.1109/TPAMI.2010.231REFERENCES