{"paper":{"title":"Relative Error Tensor Low Rank Approximation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.LG"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Peilin Zhong, Zhao Song","submitted_at":"2017-04-26T17:59:11Z","abstract_excerpt":"We consider relative error low rank approximation of $tensors$ with respect to the Frobenius norm: given an order-$q$ tensor $A \\in \\mathbb{R}^{\\prod_{i=1}^q n_i}$, output a rank-$k$ tensor $B$ for which $\\|A-B\\|_F^2 \\leq (1+\\epsilon)$OPT, where OPT $= \\inf_{\\textrm{rank-}k~A'} \\|A-A'\\|_F^2$. Despite the success on obtaining relative error low rank approximations for matrices, no such results were known for tensors. One structural issue is that there may be no rank-$k$ tensor $A_k$ achieving the above infinum. Another, computational issue, is that an efficient relative error low rank approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08246","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"}