  To extract the relevant features in a given dataset is a difficult task,
recently resolved in the non-negative data case with the Non-negative Matrix
factorization (NMF) method. The objective of this research work is to extend
this method to the case of missing and/or corrupted data due to outliers. To do
so, data are denoised, missing values are imputed, and outliers are detected
while performing a low-rank non-negative matrix factorization of the recovered
matrix. To achieve this goal, a mixture of Bregman proximal methods and of the
Augmented Lagrangian scheme are used, in a similar way to the so-called
Alternating Direction of Multipliers method. An application to the analysis of
gene expression data of patients with bladder cancer is finally proposed.
