Robust Nonnegative Matrix Factorization Based on Cosine Similarity Induced Metric

  • Wen-Sheng Chen
  • Haitao Chen
  • Binbin PanEmail author
  • Bo Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11936)


Nonnegative matrix factorization (NMF) is a low-rank decomposition based image representation method under the nonnegativity constraint. However, a lot of NMF based approaches utilize Frobenius-norm or KL-divergence as the metrics to model the loss functions. These metrics are not dilation-invariant and thus sensitive to the scale-change illuminations. To solve this problem, this paper proposes a novel robust NMF method (CSNMF) using cosine similarity induced metric, which is both rotation-invariant and dilation-invariant. The invariant properties are beneficial to improving the performance of our method. Based on cosine similarity induced metric and auxiliary function technique, the update rules of CSNMF are derived and theoretically shown to be convergent. Finally, we empirically evaluate the performance and convergence of the proposed CSNMF algorithm. Compared with the state-of-the-art NMF-based algorithms on face recognition, experimental results demonstrate that the proposed CSNMF method has superior performance and is more robust to the variation of illumination.


Nonnegative matrix factorization Face recognition Cosine similarity induced metric 



This paper was partially supported by the Interdisciplinary Innovation Team of Shenzhen University and NNSF of China (Grants 61272252) and NSF of Guangdong Province (2018A030313364). We would like to thank the US Army Research Laboratory and Yale University for providing the facial image databases.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Wen-Sheng Chen
    • 1
    • 2
  • Haitao Chen
    • 1
  • Binbin Pan
    • 1
    • 2
    Email author
  • Bo Chen
    • 1
    • 2
  1. 1.College of Mathematics and StatisticsShenzhen UniversityShenzhenChina
  2. 2.Guangdong Key Laboratory of Media SecurityShenzhen UniversityShenzhenPeople’s Republic of China

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