arXiv Analytics

Sign in

arXiv:1705.06730 [cs.DS]AbstractReferencesReviewsResources

Algorithms for $\ell_p$ Low Rank Approximation

Flavio Chierichetti, Sreenivas Gollapudi, Ravi Kumar, Silvio Lattanzi, Rina Panigrahy, David P. Woodruff

Published 2017-05-18Version 1

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.

Related articles: Most relevant | Search more
arXiv:1402.1107 [cs.DS] (Published 2014-02-05)
Approximation Algorithms for Covering and Packing Problems on Paths
arXiv:1104.4597 [cs.DS] (Published 2011-04-24)
The Entropy Rounding Method in Approximation Algorithms
arXiv:1701.07299 [cs.DS] (Published 2017-01-25)
Improved approximation algorithms and disjunctive relaxations for some knapsack problems