{"paper":{"title":"Manifold learning in Wasserstein space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.DG"],"primary_cat":"stat.ML","authors_text":"Bernhard Schmitzer, Caroline Moosm\\\"uller, Keaton Hamm, Matthew Thorpe","submitted_at":"2023-11-14T21:21:35Z","abstract_excerpt":"This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures $\\mathcal{P}_{\\mathrm{a.c.}}(\\Omega)$ with $\\Omega$ a compact and convex subset of $\\mathbb{R}^d$, metrized with the Wasserstein-2 distance $\\mathbb{W}$. We begin by introducing a construction of submanifolds $\\Lambda$ in $\\mathcal{P}_{\\mathrm{a.c.}}(\\Omega)$ equipped with metric $\\mathbb{W}_\\Lambda$, the geodesic restriction of $\\mathbb{W}$ to $\\Lambda$. In contrast to other constructions, these submanifolds are not necessarily flat, but still all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.08549","kind":"arxiv","version":3},"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/2311.08549/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"}