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Matrix factorization methods are widely used for extracting latent factors for low rank matrix completion and rating prediction problems arising in recommender systems of on-line retailers. Most of the exist- ing models are based on L2 delity (quadratic functions of factorization error). In this work, a coordinate descent (CD) method is developed for matrix factorization under L1 delity so that the related minimization is done one variable at a time and the factorization error is sparsely distributed. In low rank random matrix completion and rating predic- tion of MovieLens 100k datasets, the CDL1 method shows remarkable stability and accuracy under gross corruption of training (observation) data while the L2 delity based methods rapidly deteriorate. A closed form analytical solution is found for the one-dimensional L1-delity sub- problem, and is used as a building block of CDL1 algorithm whose con- vergence is analyzed. A connection with robust principal component analysis is drawn.

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