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Bidirectional Nonnegative Deep Model and Its Optimization in Learning

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  • Xianhua Zeng
  • Zhengyi He
  • Hong Yu
  • Shengwei Qu

Abstract

Nonnegative matrix factorization (NMF) has been successfully applied in signal processing as a simple two-layer nonnegative neural network. Projective NMF (PNMF) with fewer parameters was proposed, which projects a high-dimensional nonnegative data onto a lower-dimensional nonnegative subspace. Although PNMF overcomes the problem of out-of-sample of NMF, it does not consider the nonlinear characteristic of data and is only a kind of narrow signal decomposition method. In this paper, we combine the PNMF with deep learning and nonlinear fitting to propose a bidirectional nonnegative deep learning (BNDL) model and its optimization learning algorithm, which can obtain nonlinear multilayer deep nonnegative feature representation. Experiments show that the proposed model can not only solve the problem of out-of-sample of NMF but also learn hierarchical nonnegative feature representations with better clustering performance than classical NMF, PNMF, and Deep Semi-NMF algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjopti:5975120
    DOI: 10.1155/2016/5975120
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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. 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.
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    Cited by:

    1. Peng Liu & Xiaoli Wang, 2017. "Maximum Lateness Scheduling on Two-Person Cooperative Games with Variable Processing Times and Common Due Date," Journal of Optimization, Hindawi, vol. 2017, pages 1-7, April.

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