IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v114y2019i528p1708-1725.html
   My bibliography  Save this article

Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data

Author

Listed:
  • Anru Zhang
  • Rungang Han

Abstract

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named sparse tensor alternating thresholding for singular value decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates. Supplementary materials for this article are available online.

Suggested Citation

  • Anru Zhang & Rungang Han, 2019. "Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1708-1725, October.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:528:p:1708-1725
    DOI: 10.1080/01621459.2018.1527227
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2018.1527227
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2018.1527227?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rungang Han & Yuetian Luo & Miaoyan Wang & Anru R. Zhang, 2022. "Exact clustering in tensor block model: Statistical optimality and computational limit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1666-1698, November.
    2. Xianpeng Mao & Yuning Yang, 2022. "Several approximation algorithms for sparse best rank-1 approximation to higher-order tensors," Journal of Global Optimization, Springer, vol. 84(1), pages 229-253, September.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlasa:v:114:y:2019:i:528:p:1708-1725. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.