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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 Matrixfactorization (NMF) method. The objective of this research work is to extendthis method to the case of missing and/or corrupted data due to outliers. To doso, data are denoised, missing values are imputed, and outliers are detectedwhile performing a low-rank non-negative matrix factorization of the recoveredmatrix. To achieve this goal, a mixture of Bregman proximal methods and of theAugmented Lagrangian scheme are used, in a similar way to the so-calledAlternating Direction of Multipliers method. An application to the analysis ofgene expression data of patients with bladder cancer is finally proposed.

A Bregman Proximal ADMM for NMF with Outliers: Estimating features with  missing values and outliers: a Bregman-proximal point algorithm for robust  Non-negative Matrix Factorization with application to gene expression  analysis