{"paper":{"title":"Approximation and Streaming Algorithms for Projective Clustering via Random Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Michael Kerber, Sharath Raghvendra","submitted_at":"2014-07-08T12:34:11Z","abstract_excerpt":"Let $P$ be a set of $n$ points in $\\mathbb{R}^d$. In the projective clustering problem, given $k, q$ and norm $\\rho \\in [1,\\infty]$, we have to compute a set $\\mathcal{F}$ of $k$ $q$-dimensional flats such that $(\\sum_{p\\in P}d(p, \\mathcal{F})^\\rho)^{1/\\rho}$ is minimized; here $d(p, \\mathcal{F})$ represents the (Euclidean) distance of $p$ to the closest flat in $\\mathcal{F}$. We let $f_k^q(P,\\rho)$ denote the minimal value and interpret $f_k^q(P,\\infty)$ to be $\\max_{r\\in P}d(r, \\mathcal{F})$. When $\\rho=1,2$ and $\\infty$ and $q=0$, the problem corresponds to the $k$-median, $k$-mean and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2063","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"}