{"paper":{"title":"EPTAS for $k$-means Clustering of Affine Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.LG"],"primary_cat":"cs.DS","authors_text":"Eduard Eiben, Fahad Panolan, Fedor V. Fomin, Kirill Simonov, Petr A. Golovach, William Lochet","submitted_at":"2020-10-19T15:04:30Z","abstract_excerpt":"We consider a generalization of the fundamental $k$-means clustering for data with incomplete or corrupted entries. When data objects are represented by points in $\\mathbb{R}^d$, a data point is said to be incomplete when some of its entries are missing or unspecified. An incomplete data point with at most $\\Delta$ unspecified entries corresponds to an axis-parallel affine subspace of dimension at most $\\Delta$, called a $\\Delta$-point. Thus we seek a partition of $n$ input $\\Delta$-points into $k$ clusters minimizing the $k$-means objective. For $\\Delta=0$, when all coordinates of each point "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09580","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/2010.09580/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"}