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Discriminant Projective Non-Negative Matrix Factorization

Author

Listed:
  • Naiyang Guan
  • Xiang Zhang
  • Zhigang Luo
  • Dacheng Tao
  • Xuejun Yang

Abstract

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers WT X as their coefficients, i.e., X≈WWT X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher's criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.

Suggested Citation

  • Naiyang Guan & Xiang Zhang & Zhigang Luo & Dacheng Tao & Xuejun Yang, 2013. "Discriminant Projective Non-Negative Matrix Factorization," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-12, December.
    • Handle: RePEc:plo:pone00:0083291
    DOI: 10.1371/journal.pone.0083291
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    References listed on IDEAS

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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Leo Taslaman & Björn Nilsson, 2012. "A Framework for Regularized Non-Negative Matrix Factorization, with Application to the Analysis of Gene Expression Data," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
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    1. Xiang Zhang & Naiyang Guan & Dacheng Tao & Xiaogang Qiu & Zhigang Luo, 2015. "Online Multi-Modal Robust Non-Negative Dictionary Learning for Visual Tracking," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-17, May.
    2. Xianhua Zeng & Zhengyi He & Hong Yu & Shengwei Qu, 2016. "Bidirectional Nonnegative Deep Model and Its Optimization in Learning," Journal of Optimization, Hindawi, vol. 2016, pages 1-8, November.

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