NeNMF

NeNMF: An optimal gradient method for non-negative matrix factorization. Nonnegative matrix factorization (NMF) is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low-rank nonnegative matrix factors. It has been widely applied to signal processing, computer vision, and data mining. Traditional NMF solvers include the multiplicative update rule (MUR), the projected gradient method (PG), the projected nonnegative least squares (PNLS), and the active set method (AS). However, they suffer from one or some of the following three problems: slow convergence rate, numerical instability and nonconvergence. In this paper, we present a new efficient NeNMF solver to simultaneously overcome the aforementioned problems. It applies Nesterov’s optimal gradient method to alternatively optimize one factor with another fixed. In particular, at each iteration round, the matrix factor is updated by using the PG method performed on a smartly chosen search point, where the step size is determined by the Lipschitz constant. Since NeNMF does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor, it is superior to MUR and PG in terms of efficiency as well as approximation accuracy. Compared to PNLS and AS that suffer from numerical instability problem in the worst case, NeNMF overcomes this deficiency. In addition, NeNMF can be used to solve -norm, -norm and manifold regularized NMF with the optimal convergence rate. Numerical experiments on both synthetic and real-world datasets show the efficiency of NeNMF for NMF and its variants comparing to representative NMF solvers. Extensive experiments on document clustering suggest the effectiveness of NeNMF.


References in zbMATH (referenced in 17 articles )

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  1. Chen, Wen-Sheng; Liu, Jingmin; Pan, Binbin; Li, Yugao: Block kernel nonnegative matrix factorization for face recognition (2019)
  2. Kang, Kai; Maroulas, Vasileios; Schizas, Ioannis; Bao, Feng: Improved distributed particle filters for tracking in a wireless sensor network (2018)
  3. Takahashi, Norikazu; Katayama, Jiro; Seki, Masato; Takeuchi, Jun’ichi: A unified global convergence analysis of multiplicative update rules for nonnegative matrix factorization (2018)
  4. Chow, Yat Tin; Wu, Tianyu; Yin, Wotao: Cyclic coordinate-update algorithms for fixed-point problems: analysis and applications (2017)
  5. Chow, Yat Tin; Ito, Kazufumi; Zou, Jun: Analysis on a nonnegative matrix factorization and its applications (2016)
  6. Huang, Yakui; Liu, Hongwei; Zhou, Sha: An efficient monotone projected Barzilai-Borwein method for nonnegative matrix factorization (2015)
  7. Huang, Yakui; Liu, Hongwei; Zhou, Shuisheng: Quadratic regularization projected Barzilai-Borwein method for nonnegative matrix factorization (2015)
  8. Tomé, Ana M.; Schachtner, R.; Vigneron, V.; Puntonet, C. G.; Lang, E. W.: A logistic non-negative matrix factorization approach to binary data sets (2015) ioport
  9. Huang, Jie; Huang, Ting-Zhu; Zhao, Xi-Le; Xu, Zong-Ben; Lv, Xiao-Guang: Two soft-thresholding based iterative algorithms for image deblurring (2014) ioport
  10. Licciardi, Giorgio; Avezzano, Ruggero Giuseppe; Del Frate, Fabio; Schiavon, Giovanni; Chanussot, Jocelyn: A novel approach to polarimetric SAR data processing based on nonlinear PCA (2014) ioport
  11. Wang, Jun; Chung, Fu-Lai; Wang, Shitong; Deng, Zhaohong: Double indices-induced FCM clustering and its integration with fuzzy subspace clustering (2014)
  12. Hong, Wien: Adaptive image data hiding in edges using patched reference table and pair-wise embedding technique (2013) ioport
  13. Wang, Junhui; Fang, Yixin: Analysis of presence-only data via semi-supervised learning approaches (2013)
  14. Yu, Jun; Tao, Dacheng; Rui, Yong; Cheng, Jun: Pairwise constraints based multiview features fusion for scene classification (2013)
  15. Guan, Naiyang; Tao, Dacheng; Luo, Zhigang; Yuan, Bo: NeNMF: an optimal gradient method for nonnegative matrix factorization (2012)
  16. Li, Jun; Tao, Dacheng; Li, Xuelong: A probabilistic model for image representation via multiple patterns (2012)
  17. Zheng, Shuai; Huang, Kaiqi; Tan, Tieniu; Tao, Dacheng: A cascade fusion scheme for gait and cumulative foot pressure image recognition (2012) ioport