Nonnegative Matrix Factorization (NMF) is a widely used technique in manyapplications such as face recognition, motion segmentation, etc. Itapproximates the nonnegative data in an original high dimensional space with alinear representation in a low dimensional space by using the product of twononnegative matrices. In many applications data are often partially corruptedwith large additive noise. When the positions of noise are known, some existingvariants of NMF can be applied by treating these corrupted entries as missingvalues. However, the positions are often unknown in many real worldapplications, which prevents the usage of traditional NMF or other existingvariants of NMF. This paper proposes a Robust Nonnegative Matrix Factorization(RobustNMF) algorithm that explicitly models the partial corruption as largeadditive noise without requiring the information of positions of noise. Inpractice, large additive noise can be used to model outliers. In particular,the proposed method jointly approximates the clean data matrix with the productof two nonnegative matrices and estimates the positions and values ofoutliers/noise. An efficient iterative optimization algorithm with a solidtheoretical justification has been proposed to learn the desired matrixfactorization. Experimental results demonstrate the advantages of the proposedalgorithm.
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