{"paper":{"title":"Algorithms for $\\ell_p$ Low Rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Flavio Chierichetti, Ravi Kumar, Rina Panigrahy, Silvio Lattanzi, Sreenivas Gollapudi","submitted_at":"2017-05-18T19:01:33Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06730","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}