Matrix approximation is a common tool in machine learning for building accurate
prediction models for recommendation systems, text mining, and computer vision. A
prevalent assumption in constructing matrix approximations is that the partially
observed matrix is of low-rank. We propose a new matrix approximation model where
we assume instead that the matrix is only locally of low-rank, leading to a
representation of the observed matrix as a weighted sum of low-rank matrices. We
analyze the accuracy of the proposed local low-rank modeling. Our experiments show
improvements of prediction accuracy in recommendation tasks.