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An alternating direction and projection algorithm for structure-enforced matrix factorization

Author

Listed:
  • Lijun Xu

    (Dalian University of Technology)

  • Bo Yu

    (Dalian University of Technology)

  • Yin Zhang

    (Rice University)

Abstract

Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.

Suggested Citation

  • Lijun Xu & Bo Yu & Yin Zhang, 2017. "An alternating direction and projection algorithm for structure-enforced matrix factorization," Computational Optimization and Applications, Springer, vol. 68(2), pages 333-362, November.
  • Handle: RePEc:spr:coopap:v:68:y:2017:i:2:d:10.1007_s10589-017-9913-x
    DOI: 10.1007/s10589-017-9913-x
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    References listed on IDEAS

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    1. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    2. 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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    Cited by:

    1. Temadher A. Almaadeed & Saeid Ansary Karbasy & Maziar Salahi & Abdelouahed Hamdi, 2022. "On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 246-264, July.
    2. Sebastián Arpón & Tito Homem-de-Mello & Bernardo K. Pagnoncelli, 2020. "An ADMM algorithm for two-stage stochastic programming problems," Annals of Operations Research, Springer, vol. 286(1), pages 559-582, March.

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