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Nonnegative matrix factorization with manifold regularization and maximum discriminant information

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Abstract

Nonnegative matrix factorization (NMF) has been successfully used in different applications including computer vision, pattern recognition and text mining. NMF aims to decompose a data matrix into the product of two matrices (respectively denoted as the basis vectors and the encoding vectors), whose entries are constrained to be nonnegative. Unlike the ordinary NMF, we propose a novel NMF, denoted as MMNMF, which considers both geometrical information and discriminative information hidden in the data. The geometrical information is discovered by minimizing the distance among the encoding vectors, while the discriminative information is uncovered by maximizing the distance among base vectors. Clustering experiments are performed on the real-world data sets of faces, images, and documents to demonstrate the effectiveness of the proposed algorithm.

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Notes

  1. http://www1.cs.columbia.edu/CAVE/software/softlib/coil-20.php.

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Acknowledgments

This work was supported in part by General Research Fund of the Hong Kong Research Grants Council under Grant PolyU 5134/12E; the National Natural Science Foundation of China under Grants 61170122, 61272210 and 61202311; the Natural Science Foundation of Zhejiang Province under Grants LY13F020011, LY14F010010 and LY14F020009; the Humanities and Social Science Foundation of Ministry of Education of China under Grant 13YJAZH084; the Natural Science Foundation of Jiangsu Province under Grants BK2011003 and BK2011417; the Natural Science Foundation of Huzhou City under Grant 2013YZ05; Huzhou University science research project under Grants KX24063 and KX24058.

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Authors and Affiliations

  1. School of Information Engineering, Huzhou University, Huzhou, Zhejiang, China

    Wenjun Hu & Yunliang Jiang

  2. School of Digital Media, Jiangnan University, Wuxi, Jiangsu, China

    Wenjun Hu & Shitong Wang

  3. School of Nursing, Centre for Smart Health, Hong Kong Polytechnic University, Hong Kong, China

    Wenjun Hu & Kup-Sze Choi

  4. School of Information Science and Engineering, Ningbo Institute of Technology, Zhejiang University, Ningbo, Zhejiang, China

    Jianwen Tao

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  1. Wenjun Hu
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  2. Kup-Sze Choi
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  3. Jianwen Tao
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  4. Yunliang Jiang
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  5. Shitong Wang
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Correspondence to Wenjun Hu.

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Hu, W., Choi, KS., Tao, J. et al. Nonnegative matrix factorization with manifold regularization and maximum discriminant information. Int. J. Mach. Learn. & Cyber. 6, 837–846 (2015). https://doi.org/10.1007/s13042-015-0396-8

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  • DOI: https://doi.org/10.1007/s13042-015-0396-8

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