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Nonnegative Matrix Factorization with Group and Basis Restrictions

Author

Listed:
  • Phillip Shreeves

    (University of British Columbia - Okanagan
    Simon Fraser University)

  • Jeffrey L. Andrews

    (University of British Columbia - Okanagan)

  • Xinchen Deng

    (University of British Columbia - Okanagan)

  • Ramie Ali-Adeeb

    (University of British Columbia - Okanagan)

  • Andrew Jirasek

    (University of British Columbia - Okanagan)

Abstract

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, X, into two lower rank nonnegative matrices multiplied together. These two matrices can be described as the latent factors, represented in the rows of H, and the scores of the observations on these factors that are found in the rows of W. This paper provides an extension of this method which allows one to specify prior knowledge of the data, including both group information and possible underlying factors. This is done by further decomposing the matrix, H, into matrices A and S multiplied together. These matrices represent an ’auxiliary’ matrix and a semi-constrained factor matrix, respectively. This method and its updating criterion are proposed, followed by its application on both simulated and real-world examples displaying different uses of the algorithm.

Suggested Citation

  • Phillip Shreeves & Jeffrey L. Andrews & Xinchen Deng & Ramie Ali-Adeeb & Andrew Jirasek, 2023. "Nonnegative Matrix Factorization with Group and Basis Restrictions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(3), pages 608-632, December.
    • Handle: RePEc:spr:stabio:v:15:y:2023:i:3:d:10.1007_s12561-023-09398-2
    DOI: 10.1007/s12561-023-09398-2
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    References listed on IDEAS

    as
    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. Karthik Devarajan, 2008. "Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology," PLOS Computational Biology, Public Library of Science, vol. 4(7), pages 1-12, July.
    3. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
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