{"paper":{"title":"Dynamic Similarity Graph Construction with Kernel Density Estimation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"He Sun, Peter Macgregor, Steinar Laenen","submitted_at":"2025-07-02T13:25:22Z","abstract_excerpt":"In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\\mathbb{R}^d$, a kernel function $k: \\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}$, and a query point $\\mathbf{q} \\in \\mathbb{R}^d$, and the objective is to quickly output an estimate of $\\sum_{\\mathbf{x} \\in X} k(\\mathbf{q}, \\mathbf{x})$. In this paper, we consider $\\textsf{KDE}$ in the dynamic setting, and introduce a data structure that efficiently maintains the estimates for a set of query points as data points are added to $X$ over time. Based on this, we design a dynamic data structure th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01696","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/2507.01696/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"}