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Fast optimization of non-negative matrix tri-factorization

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  • Andrej Čopar
  • Blaž Zupan
  • Marinka Zitnik

Abstract

Non-negative matrix tri-factorization (NMTF) is a popular technique for learning low-dimensional feature representation of relational data. Currently, NMTF learns a representation of a dataset through an optimization procedure that typically uses multiplicative update rules. This procedure has had limited success, and its failure cases have not been well understood. We here perform an empirical study involving six large datasets comparing multiplicative update rules with three alternative optimization methods, including alternating least squares, projected gradients, and coordinate descent. We find that methods based on projected gradients and coordinate descent converge up to twenty-four times faster than multiplicative update rules. Furthermore, alternating least squares method can quickly train NMTF models on sparse datasets but often fails on dense datasets. Coordinate descent-based NMTF converges up to sixteen times faster compared to well-established methods.

Suggested Citation

  • Andrej Čopar & Blaž Zupan & Marinka Zitnik, 2019. "Fast optimization of non-negative matrix tri-factorization," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-15, June.
  • Handle: RePEc:plo:pone00:0217994
    DOI: 10.1371/journal.pone.0217994
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    References listed on IDEAS

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    5. M. Merritt & Y. Zhang, 2005. "Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 191-202, July.
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    Cited by:

    1. Rok Hribar & Timotej Hrga & Gregor Papa & Gašper Petelin & Janez Povh & Nataša Pržulj & Vida Vukašinović, 2022. "Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem," Journal of Global Optimization, Springer, vol. 82(2), pages 283-312, February.

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