{"paper":{"title":"Efficient Frequent Directions Algorithm for Sparse Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Edo Liberty, Jeff M. Phillips, Mina Ghashami","submitted_at":"2016-02-01T07:33:02Z","abstract_excerpt":"This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \\times d}$ one by one in the streaming setting and compute a small sketch $B \\in R^{\\ell \\times d}$. Both share the same strong (provably optimal) asymptotic guarantees with respect to the space-accuracy tradeoff in the streaming setting. However, unlike Frequent Directions which runs in $O(nd\\ell)$ time regardless of the sparsity of the input matrix $A$, Sparse Frequent Directions runs "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00412","kind":"arxiv","version":2},"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"}