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Voronoi Cells of Varieties with respect to Wasserstein Distances
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2021 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Voronoiceller för Varieteter med avseende på Wasserstein Avstånd (Swedish)
Abstract [en]

Voronoi diagrams are partitions of a metric space into Voronoi cells according to distance from points on some set w.r.t. some distance. In this thesis we examine Voronoi diagrams of manifolds and varieties w.r.t. the Wasserstein distance from probability theory. We give some upper and lower bounds on the dimension of Voronoi cells based on the geometry of the manifolds and Wasserstein distance balls. We provide an upper bound on the number of full-dimensional Voronoi cells of algebraic varieties and show examples of the bound being tight.

Abstract [sv]

Voronoi diagram är partitioner av ett metriskt rum i Voronoiceller enligt avstånd från punkter på någon mängd med avseende på ett visst mått.

I den här avhandlingen undersöker vi Voronoidiagram för mångfald och varieteter med avseende på Wasserstein avstånd från sannolikhetsteori

Vi ger några över och nedre gränser för dimensionen på Voronoiceller baserat på geometrin hos mångfalden och avståndsklot med Wasserstein mått. Vi presenterar en övre gräns för antalet fulldimensionella Voronoiceller för algebraiska varieteter och visar exempel på när gränsen är strikt.

Place, publisher, year, edition, pages
2021. , p. 30
Series
TRITA-SCI-GRU ; 2021:214
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-319199OAI: oai:DiVA.org:kth-319199DiVA, id: diva2:1699449
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2022-09-29 Created: 2022-09-28 Last updated: 2022-09-29Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • de-DE
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Output format
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