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# Algorithms for $\ell_p$ Low-Rank Approximation

*Proceedings of the 34th International Conference on Machine Learning*, PMLR 70:806-814, 2017.

#### Abstract

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise $\ell_p$-approximation error, for any $p \geq 1$; the case $p = 2$ is the classical SVD problem. We obtain the first provably good approximation algorithms for this robust version of low-rank approximation that work for every value of $p$. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approximation quality, the running time, and the rank of the approximating matrix.