{"paper":{"title":"Pointed subspace approach to incomplete data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jacek Tabor, {\\L}ukasz Struski, Marek \\'Smieja","submitted_at":"2017-05-02T07:59:01Z","abstract_excerpt":"Incomplete data are often represented as vectors with filled missing attributes joined with flag vectors indicating missing components. In this paper we generalize this approach and represent incomplete data as pointed affine subspaces. This allows to perform various affine transformations of data, as whitening or dimensionality reduction. We embed such generalized missing data into a vector space by mapping pointed affine subspace (generalized missing data point) to a vector containing imputed values joined with a corresponding projection matrix. Such an operation preserves the scalar product"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00840","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":""},"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"}