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arXiv · 1705.06730

Algorithms for $\ell_p$ Low Rank Approximation

Flavio Chierichetti·Sreenivas Gollapudi·Ravi Kumar·Silvio Lattanzi·Rina Panigrahy·David P. Woodruff
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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 version of low-rank approximation that work for every value of $p \geq 1$, including $p = \infty$. 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.

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Flavio Chierichetti, Sreenivas Gollapudi, Ravi Kumar, Silvio Lattanzi, Rina Panigrahy, David P. Woodruff. 2017-05-18. Algorithms for $\ell_p$ Low Rank Approximation. https://arxiv.org/abs/1705.06730

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