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Numerical method for the generalized nonnegative tensor factorization problem

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Abstract

In this paper, we consider the generalized nonnegative tensor factorization (GNTF) problem, which arises in multiple-tissue gene expression and multi-target tracking. Based on the Karhsh-Kuhn-Tucker conditions, the necessary condition of the local solution for the GNTF problem is given. The proximal alternating nonnegative least squares method is designed to solve it, and its convergence theorem is also derived. Numerical examples show that the new method is feasible and effective.

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Authors and Affiliations

  1. College of Mathematics and Computational Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Xue-Feng Duan, Juan Li & Shan-Qi Duan

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Qing-Wen Wang

Authors
  1. Xue-Feng Duan
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  2. Juan Li
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  3. Shan-Qi Duan
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  4. Qing-Wen Wang
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Correspondence to Xue-Feng Duan.

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The work was supported by the National Natural Science Foundation of China (No. 11561015; 11761024; 11961012), and the Natural Science Foundation of Guangxi Province (No. 2016GXNSFFA380009; 2017GXNSFBA198082; 2016GXNSFAA380074).

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Duan, XF., Li, J., Duan, SQ. et al. Numerical method for the generalized nonnegative tensor factorization problem. Numer Algor 87, 499–510 (2021). https://doi.org/10.1007/s11075-020-00975-w

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