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A non-negative matrix factorization model based on the zero-inflated Tweedie distribution

Author

Listed:
  • Hiroyasu Abe

    (Doshisha University)

  • Hiroshi Yadohisa

    (Doshisha University)

Abstract

Non-negative matrix factorization (NMF) is a technique of multivariate analysis used to approximate a given matrix containing non-negative data using two non-negative factor matrices that has been applied to a number of fields. However, when a matrix containing non-negative data has many zeroes, NMF encounters an approximation difficulty. This zero-inflated situation occurs often when a data matrix is given as count data, and becomes more challenging with matrices of increasing size. To solve this problem, we propose a new NMF model for zero-inflated non-negative matrices. Our model is based on the zero-inflated Tweedie distribution. The Tweedie distribution is a generalization of the normal, the Poisson, and the gamma distributions, and differs from each of the other distributions in the degree of robustness of its estimated parameters. In this paper, we show through numerical examples that the proposed model is superior to the basic NMF model in terms of approximation of zero-inflated data. Furthermore, we show the differences between the estimated basis vectors found using the basic and the proposed NMF models for $$\beta $$ β divergence by applying it to real purchasing data.

Suggested Citation

  • Hiroyasu Abe & Hiroshi Yadohisa, 2017. "A non-negative matrix factorization model based on the zero-inflated Tweedie distribution," Computational Statistics, Springer, vol. 32(2), pages 475-499, June.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0689-8
    DOI: 10.1007/s00180-016-0689-8
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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. Berry, Michael W. & Browne, Murray & Langville, Amy N. & Pauca, V. Paul & Plemmons, Robert J., 2007. "Algorithms and applications for approximate nonnegative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 155-173, September.
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