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Orthogonal nonnegative matrix tri-factorization based on Tweedie distributions

Author

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  • Hiroyasu Abe

    (Kyoto University)

  • Hiroshi Yadohisa

    (Doshisha University)

Abstract

Orthogonal nonnegative matrix tri-factorization (ONMTF) is a biclustering method using a given nonnegative data matrix and has been applied to document-term clustering, collaborative filtering, and so on. In previously proposed ONMTF methods, it is assumed that the error distribution is normal. However, the assumption of normal distribution is not always appropriate for nonnegative data. In this paper, we propose three new ONMTF methods, which respectively employ the following error distributions: normal, Poisson, and compound Poisson. To develop the new methods, we adopt a k-means based algorithm but not a multiplicative updating algorithm, which was the main method used for obtaining estimators in previous methods. A simulation study and an application involving document-term matrices demonstrate that our method can outperform previous methods, in terms of the goodness of clustering and in the estimation of the factor matrix.

Suggested Citation

  • Hiroyasu Abe & Hiroshi Yadohisa, 2019. "Orthogonal nonnegative matrix tri-factorization based on Tweedie distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 825-853, December.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:4:d:10.1007_s11634-018-0348-8
    DOI: 10.1007/s11634-018-0348-8
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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.
    3. POMPILI, Filippo & GILLIS, Nicolas & ABSIL, Pierre-Antoine & GLINEUR, François, 2014. "Two algorithms for orthogonal nonnegative matrix factorization with application to clusterin," LIDAM Reprints CORE 2581, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 143-157, May.
    5. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
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    Cited by:

    1. Andri Mirzal, 2021. "A convergent algorithm for bi-orthogonal nonnegative matrix tri-factorization," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 1069-1102, December.

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