{"paper":{"title":"Fast Subspace Approximation via Greedy Least-Squares","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.CG","authors_text":"Felix Krahmer, Mark Iwen","submitted_at":"2013-12-05T02:30:19Z","abstract_excerpt":"In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\\subset \\mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n \\log M)$-dimensional subspace that is guaranteed to always contain a near-best fit $n$-dimensional hyperplane $\\mathcal{H}$ for $P$ with respect to the cumulative projection error $(\\sum_{{\\bf x} \\in P} \\| {\\bf x} - \\Pi_\\mathcal{H} {\\bf x} \\|^p_2)^{1/p}$, for any chosen $p > 2$. The deterministic algorithm runs in $\\tilde{O} (MN^2)$-time, and can be randomized "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1413","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"}