{"paper":{"title":"Uniform spaces and the Newtonian structure of (big)data affinity kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.GN","authors_text":"Hugo Aimar, Ivana G\\'omez","submitted_at":"2017-01-13T17:35:03Z","abstract_excerpt":"Let $X$ be a (data) set. Let $K(x,y)>0$ be a measure of the affinity between the data points $x$ and $y$. We prove that $K$ has the structure of a Newtonian potential $K(x,y)=\\varphi(d(x,y))$ with $\\varphi$ decreasing and $d$ a quasi-metric on $X$ under two mild conditions on $K$. The first is that the affinity of each $x$ to itself is infinite and that for $x\\neq y$ the affinity is positive and finite. The second is a quantitative transitivity; if the affinity between $x$ and $y$ is larger than $\\lambda>0$ and the affinity of $y$ and $z$ is also larger than $\\lambda$, then the affinity betwee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03746","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"}