{"paper":{"title":"Dimension Reduction for Curves: Simplified and Generalized","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Alexander Munteanu, Jie Lu, Matthijs Ebbens","submitted_at":"2026-07-03T08:48:35Z","abstract_excerpt":"We revisit random projections for reducing the dimension of high-dimensional polygonal curves. Drawing from the toolbox of randomized linear algebra, we give a considerably simplified proof of the known $O(\\varepsilon^{-2}\\log(nm))$ bound on the target dimension of a random projection that preserves the continuous Fr\\'echet distance of polygonal curves up to a factor $(1\\pm\\varepsilon)$. Our proof is based on the concept of sparse oblivious subspace embeddings. While previous techniques were limited to the case of the Fr\\'echet distance, our techniques are fairly general and extend to all poss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03112","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03112/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}