IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1155-d1080999.html
   My bibliography  Save this article

Low-Rank Matrix Completion via QR-Based Retraction on Manifolds

Author

Listed:
  • Ke Wang

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Zhuo Chen

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Shihui Ying

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Xinjian Xu

    (Qianweichang College, Shanghai University, Shanghai 200444, China)

Abstract

Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate gradient descent, and demonstrate their superiority over the promising baseline with the ratio of at least 24 % .

Suggested Citation

  • Ke Wang & Zhuo Chen & Shihui Ying & Xinjian Xu, 2023. "Low-Rank Matrix Completion via QR-Based Retraction on Manifolds," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1155-:d:1080999
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1155/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1155/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiaojing Zhu, 2017. "A Riemannian conjugate gradient method for optimization on the Stiefel manifold," Computational Optimization and Applications, Springer, vol. 67(1), pages 73-110, May.
    2. Bamdev Mishra & Gilles Meyer & Silvère Bonnabel & Rodolphe Sepulchre, 2014. "Fixed-rank matrix factorizations and Riemannian low-rank optimization," Computational Statistics, Springer, vol. 29(3), pages 591-621, June.
    3. Hiroyuki Sato & Kensuke Aihara, 2019. "Cholesky QR-based retraction on the generalized Stiefel manifold," Computational Optimization and Applications, Springer, vol. 72(2), pages 293-308, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nickolay Trendafilov & Martin Kleinsteuber & Hui Zou, 2014. "Sparse matrices in data analysis," Computational Statistics, Springer, vol. 29(3), pages 403-405, June.
    2. Marie Billaud-Friess & Antonio Falcó & Anthony Nouy, 2021. "Principal Bundle Structure of Matrix Manifolds," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
    3. Lei Wang & Xin Liu & Yin Zhang, 2023. "A communication-efficient and privacy-aware distributed algorithm for sparse PCA," Computational Optimization and Applications, Springer, vol. 85(3), pages 1033-1072, July.
    4. Yuya Yamakawa & Hiroyuki Sato, 2022. "Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method," Computational Optimization and Applications, Springer, vol. 81(2), pages 397-421, March.
    5. Hiroyuki Sakai & Hideaki Iiduka, 2021. "Sufficient Descent Riemannian Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 130-150, July.
    6. Harry Oviedo, 2023. "Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold," Mathematics, MDPI, vol. 11(11), pages 1-17, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1155-:d:1080999. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.