A Bregman-proximal point algorithm for robust non-negative matrix factorization with possible missing values and outliers - application to gene expression analysis

Stéphane Chrétien, Christophe Guyeux, Bastien Conesa, Régis Delage-Mouroux, Michèle Jouvenot, Philippe Huetz, Françoise Descôtes

Non-Negative Matrix factorization has become an essential tool for feature extraction in a wide spectrum of applications. In the present work, our objective is to extend the applicability of the method to the case of missing and/or corrupted data due to outliers. An essential property for missing data imputation and detection of outliers is that the uncorrupted data matrix is low rank, i.e. has only a small number of degrees of freedom. We devise a new version of the Bregman proximal idea which preserves nonnegativity and mix it with the Augmented Lagrangian approach for simultaneous reconstruction of the features of interest and detection of the outliers using a sparsity promoting ℓ 1 penality. An application to the analysis of gene expression data of patients with bladder cancer is finally proposed.