{"paper":{"title":"Consistency of modularity clustering on random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Erik Davis, Sunder Sethuraman","submitted_at":"2016-04-13T22:52:05Z","abstract_excerpt":"We consider a large class of random geometric graphs constructed from samples $\\mathcal{X}_n = \\{X_1,X_2,\\ldots,X_n\\}$ of independent, identically distributed observations of an underlying probability measure $\\nu$ on a bounded domain $D\\subset \\mathbb{R}^d$. The popular `modularity' clustering method specifies a partition $\\mathcal{U}_n$ of the set $\\mathcal{X}_n$ as the solution of an optimization problem. In this paper, under conditions on $\\nu$ and $D$, we derive scaling limits of the modularity clustering on random geometric graphs. Among other results, we show a geometric form of consist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03993","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"}