{"paper":{"title":"Optimal Principal Component Analysis in Distributed and Streaming Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christos Boutsidis, David P. Woodruff, Peilin Zhong","submitted_at":"2015-04-25T14:22:21Z","abstract_excerpt":"We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \\in R^{m \\times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \\epsilon < 1$, we want to output an $m \\times k$ orthonormal matrix $U$ for which $$ || A - U U^T A ||_F^2 \\le \\left(1 + \\epsilon \\right) \\cdot || A - A_k||_F^2, $$ where $A_k \\in R^{m \\times n}$ is the best rank-$k$ approximation to $A$.\n  This paper provides improved algorithms for distributed PCA and streaming PCA."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06729","kind":"arxiv","version":4},"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"}