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.