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Probabilistic Non-Negative Matrix Factorization with Binary Components

Author

Listed:
  • Xindi Ma

    (College of Computer Science, Chongqing University, Chongqing 400044, China)

  • Jie Gao

    (College of Computer Science, Chongqing University, Chongqing 400044, China)

  • Xiaoyu Liu

    (National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 400044, China)

  • Taiping Zhang

    (College of Computer Science, Chongqing University, Chongqing 400044, China)

  • Yuanyan Tang

    (Zhuhai UM Science & Technology Research Institute, Zhuhai 519000, China)

Abstract

Non-negative matrix factorization is used to find a basic matrix and a weight matrix to approximate the non-negative matrix. It has proven to be a powerful low-rank decomposition technique for non-negative multivariate data. However, its performance largely depends on the assumption of a fixed number of features. This work proposes a new probabilistic non-negative matrix factorization which factorizes a non-negative matrix into a low-rank factor matrix with 0 , 1 constraints and a non-negative weight matrix. In order to automatically learn the potential binary features and feature number, a deterministic Indian buffet process variational inference is introduced to obtain the binary factor matrix. Further, the weight matrix is set to satisfy the exponential prior. To obtain the real posterior distribution of the two factor matrices, a variational Bayesian exponential Gaussian inference model is established. The comparative experiments on the synthetic and real-world datasets show the efficacy of the proposed method.

Suggested Citation

  • Xindi Ma & Jie Gao & Xiaoyu Liu & Taiping Zhang & Yuanyan Tang, 2021. "Probabilistic Non-Negative Matrix Factorization with Binary Components," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1189-:d:561284
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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.
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