Circuits, Systems, and Signal Processing

, Volume 38, Issue 7, pp 3211–3226 | Cite as

Nonnegative Matrix Factorization with Fixed L2-Norm Constraint

  • Zuyuan Yang
  • Yifei Hu
  • Naiyao LiangEmail author
  • Jun Lv


Nonnegative matrix factorization (NMF) is a very attractive scheme in learning data representation, and constrained NMF further improves its ability. In this paper, we focus on the L2-norm constraint due to its wide applications in face recognition, hyperspectral unmixing, and so on. A new algorithm of NMF with fixed L2-norm constraint is proposed by using the Lagrange multiplier scheme. In our method, we derive the involved Lagrange multiplier and learning rate which are hard to tune. As a result, our method can preserve the constraint exactly during the iteration. Simulations in both computer-generated data and real-world data show the performance of our algorithm.


Nonnegative matrix factorization Multiplicative updates L2-norm Constrained NMF 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Guangdong Key Laboratory of IoT Information Technology, School of AutomationGuangdong University of TechnologyGuangzhouChina

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