Robust Non-negative Matrix Factorization

Non-negative matrix factorization (NMF) approximates a non-negative matrix A by a product of two non-negative low-rank factor matrices W and H. Classical NMF

methods minimize either the Euclidean distance or the Kullback-Leibler divergence between X and W^TH to model the Gaussian noise or the Poisson noise. Practically, these methods do not perform well when the noise distribution is heavy tailed as in real appplications. Robust Non-negative matrix factorization estimates the low-rank part and the sparse part of a non-negative matrix and thus performs effectively when data are contaminated by outliers.

• Manhattan Non-negative Matrix Factorization (MahNMF) (1 paper)
• Near-separable Non-negative Matrix Factorization (NS-NMF) (2 papers)
• Robust Asymmetric Non-negative Matrix Factorization (RANMF) (1 paper)
• MPI-Based Framework Alternating-Updating Nonnegative Matrix Factorization (MIP-FAUN) (1 paper)
• Nonnegative Matrix Factorization (NMF) (1 paper)

Author: Thierry BOUWMANS, Associate Professor, Lab. MIA, Univ. Rochelle, France.

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As this website gives many information that come from my research, please cite my following survey papers:

T. Bouwmans . A. Sobral, S. Javed, S. Jung, E. Zahzah, "Background/Foreground Separation via Decomposition in Low-rank and Additive Matrices: A Review for a Comparative Evaluation with a Large-Scale Dataset", to be submitted.

T. Bouwmans, E. Zahzah, “Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance”, Special Issue on Background Models Challenge, Computer Vision and Image Understanding, CVIU 2014, Volume 122, pages 22–34, May 2014. [pdf]

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