{
"id": "1705.06730",
"version": "v1",
"published": "2017-05-18T19:01:33.000Z",
"updated": "2017-05-18T19:01:33.000Z",
"title": "Algorithms for $\\ell_p$ Low Rank Approximation",
"authors": [
"Flavio Chierichetti",
"Sreenivas Gollapudi",
"Ravi Kumar",
"Silvio Lattanzi",
"Rina Panigrahy",
"David P. Woodruff"
],
"comment": "To appear in ICML",
"categories": [
"cs.DS"
],
"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.",
"revisions": [
{
"version": "v1",
"updated": "2017-05-18T19:01:33.000Z"
}
],
"analyses": {
"keywords": [
"low rank approximation",
"approximation error",
"classical svd problem",
"approximation quality",
"approximation algorithms"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}