  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 in prediction accuracy in
recommendation tasks.
