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Non-monotone projection gradient method for non-negative matrix factorization

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Abstract

Since Non-negative Matrix Factorization (NMF) was first proposed over a decade ago, it has attracted much attention, particularly when applied to numerous data analysis problems. Most of the existing algorithms for NMF are based on multiplicative iterative and alternating least squares algorithms. However, algorithms based on the optimization method are few, especially in the case where two variables are derived at the same time. In this paper, we propose a non-monotone projection gradient method for NMF and establish the convergence results of our algorithm. Experimental results show that our algorithm converges to better solutions than popular multiplicative update-based algorithms.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, Xi’an, China

    Xiangli Li, Hongwei Liu & Xiuyun Zheng

Authors
  1. Xiangli Li
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  2. Hongwei Liu
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  3. Xiuyun Zheng
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Corresponding author

Correspondence to Xiangli Li.

Additional information

This project was supported by the National Natural Science Foundation of China (Grant No. F010406).

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Li, X., Liu, H. & Zheng, X. Non-monotone projection gradient method for non-negative matrix factorization. Comput Optim Appl 51, 1163–1171 (2012). https://doi.org/10.1007/s10589-010-9387-6

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  • DOI: https://doi.org/10.1007/s10589-010-9387-6

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