title: A Bregman-proximal point algorithm for robust non-negative matrix factorization with possible missing values and outliers - application to gene expression analysis.
abstract: BACKGROUND
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  An application to the analysis of gene expression data of patients with bladder cancer is finally proposed.
authors: National Physical Laboratory, Hampton Road, Teddington, Middlesex, UK. stephane.chretien@npl.co.uk.
authors: Stéphane
authors: S
authors: Chrétien
authors: FEMTO-ST Institute, UMR 6174 CNRS, DISC Computer Science Department, Université de Bourgogne Franche-Comté, 16, route de Gray, Besançon, 25000, France.
authors: Christophe
authors: C
authors: Guyeux
authors: ISIFC, Université de Bourgogne Franche-Comté, 23, rue Alain Savary, Besançon, 25000, France.
authors: Bastien
authors: B
authors: Conesa
authors: EA 3922/IFR133, UFR Sciences et Techniques, Université de Bourgogne Franche-Comté, 16, route de Gray, Besançon, 25000, France.
authors: Régis
authors: R
authors: Delage-Mouroux
authors: EA 3922/IFR133, UFR Sciences et Techniques, Université de Bourgogne Franche-Comté, 16, route de Gray, Besançon, 25000, France.
authors: Michèle
authors: M
authors: Jouvenot
authors: ABC&T, 33, rue Charles Nodier, Besançon, 25000, France.
authors: Philippe
authors: P
authors: Huetz
authors: Service de Biochimie et Biologie Moléculaire Sud, Pavillon 3D, Centre Hospitalier Lyon Sud, Pierre Bénite, Lyon, Cedex 69495, France.
authors: Françoise
authors: F
authors: Descôtes
mesh_terms: D000465:Algorithms; D030541:Databases, Genetic; D020869:Gene Expression Profiling; D015972:Gene Expression Regulation, Neoplastic; D006801:Humans; D008957:Models, Genetic; D016011:Normal Distribution; D025341:Principal Component Analysis; D001749:Urinary Bladder Neoplasms / Q000235:genetics
keywords: Feature extraction; Gene expression analysis; Non-negative matrix factorization; Outliers and missing data