{"paper":{"title":"New Coresets for Projective Clustering and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Dan Feldman, Murad Tukan, Samson Zhou, Vladimir Braverman, Xuan Wu","submitted_at":"2022-03-08T19:50:27Z","abstract_excerpt":"$(j,k)$-projective clustering is the natural generalization of the family of $k$-clustering and $j$-subspace clustering problems. Given a set of points $P$ in $\\mathbb{R}^d$, the goal is to find $k$ flats of dimension $j$, i.e., affine subspaces, that best fit $P$ under a given distance measure. In this paper, we propose the first algorithm that returns an $L_\\infty$ coreset of size polynomial in $d$. Moreover, we give the first strong coreset construction for general $M$-estimator regression. Specifically, we show that our construction provides efficient coreset constructions for Cauchy, Wels"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.04370","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/2203.04370/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"}