ICML 2017poster67 citations
Algorithms for $\ell_p$ Low-Rank Approximation
Flavio Chierichetti, Sreenivas Gollapudi, Ravi Kumar, Silvio Lattanzi, Rina Panigrahy, David P. Woodruff
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.
BibTeX
@InProceedings{pmlr-v70-chierichetti17a,
title = {Algorithms for $\ell_p$ Low-Rank Approximation},
author = {Flavio Chierichetti and Sreenivas Gollapudi and Ravi Kumar and Silvio Lattanzi and Rina Panigrahy and David P. Woodruff},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {806--814},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/chierichetti17a/chierichetti17a.pdf},
url = {https://proceedings.mlr.press/v70/chierichetti17a.html},
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.}
}