{"paper":{"title":"Coresets for Data Discretization and Sine Wave Fitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alaa Maalouf, Dan Feldman, Daniel Kane, Eric Price, Murad Tukan","submitted_at":"2022-03-06T17:07:56Z","abstract_excerpt":"In the \\emph{monitoring} problem, the input is an unbounded stream $P={p_1,p_2\\cdots}$ of integers in $[N]:=\\{1,\\cdots,N\\}$, that are obtained from a sensor (such as GPS or heart beats of a human). The goal (e.g., for anomaly detection) is to approximate the $n$ points received so far in $P$ by a single frequency $\\sin$, e.g. $\\min_{c\\in C}cost(P,c)+\\lambda(c)$, where $cost(P,c)=\\sum_{i=1}^n \\sin^2(\\frac{2\\pi}{N} p_ic)$, $C\\subseteq [N]$ is a feasible set of solutions, and $\\lambda$ is a given regularization function. For any approximation error $\\varepsilon>0$, we prove that \\emph{every} set "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03009","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/2203.03009/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"}