# Local Low-Rank Matrix Approximation

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Joonseok Lee,
Seungyeon Kim,
Guy Lebanon,
Yoram Singer
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Proceedings of the 30th International Conference on Machine Learning, PMLR 28(2):82-90, 2013.

#### Abstract

Matrix approximation is a common tool in 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 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 over classical approaches for recommendation tasks.

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