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

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  • 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
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    Cited by:

    1. 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.
    2. 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.

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