{"paper":{"title":"Coresets for Vector Summarization with Applications to Network Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Dan Feldman, Daniela Rus, Sedat Ozer","submitted_at":"2017-06-17T16:00:44Z","abstract_excerpt":"We provide a deterministic data summarization algorithm that approximates the mean $\\bar{p}=\\frac{1}{n}\\sum_{p\\in P} p$ of a set $P$ of $n$ vectors in $\\REAL^d$, by a weighted mean $\\tilde{p}$ of a \\emph{subset} of $O(1/\\eps)$ vectors, i.e., independent of both $n$ and $d$. We prove that the squared Euclidean distance between $\\bar{p}$ and $\\tilde{p}$ is at most $\\eps$ multiplied by the variance of $P$. We use this algorithm to maintain an approximated sum of vectors from an unbounded stream, using memory that is independent of $d$, and logarithmic in the $n$ vectors seen so far. Our main appl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05554","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"}