{"paper":{"title":"Sublinear Time Low-Rank Approximation of Positive Semidefinite Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.NA"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, David P. Woodruff","submitted_at":"2017-04-11T15:44:49Z","abstract_excerpt":"We show how to compute a relative-error low-rank approximation to any positive semidefinite (PSD) matrix in sublinear time, i.e., for any $n \\times n$ PSD matrix $A$, in $\\tilde O(n \\cdot poly(k/\\epsilon))$ time we output a rank-$k$ matrix $B$, in factored form, for which $\\|A-B\\|_F^2 \\leq (1+\\epsilon)\\|A-A_k\\|_F^2$, where $A_k$ is the best rank-$k$ approximation to $A$. When $k$ and $1/\\epsilon$ are not too large compared to the sparsity of $A$, our algorithm does not need to read all entries of the matrix. Hence, we significantly improve upon previous $nnz(A)$ time algorithms based on oblivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03371","kind":"arxiv","version":3},"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"}