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Several approximation algorithms for sparse best rank-1 approximation to higher-order tensors

Author

Listed:
  • Xianpeng Mao

    (Guangxi University)

  • Yuning Yang

    (Guangxi University)

Abstract

Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor decomposition and related problems arising from statistics and machine learning. By exploiting the multilinearity as well as the sparsity structure of the problem, four polynomial-time approximation algorithms are proposed, which are easily implemented, of low computational complexity, and can serve as initial procedures for iterative algorithms. In addition, theoretically guaranteed approximation lower bounds are derived for all the algorithms. We provide numerical experiments on synthetic and real data to illustrate the efficiency and effectiveness of the proposed algorithms; in particular, serving as initialization procedures, the approximation algorithms can help in improving the solution quality of iterative algorithms while reducing the computational time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01140-4
    DOI: 10.1007/s10898-022-01140-4
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    References listed on IDEAS

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    Cited by:

    1. Mao, Xianpeng & Yang, Yuning, 2022. "Best sparse rank-1 approximation to higher-order tensors via a truncated exponential induced regularizer," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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