| dc.contributor.advisor | Schuhmacher, Dominic Prof. Dr. | |
| dc.contributor.author | Schrieber, Jörn | |
| dc.date.accessioned | 2019-02-28T09:54:27Z | |
| dc.date.available | 2019-02-28T09:54:27Z | |
| dc.date.issued | 2019-02-28 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E5B2-B | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-7314 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Algorithms for Optimal Transport and Wasserstein Distances | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Schuhmacher, Dominic Prof. Dr. | |
| dc.date.examination | 2019-02-14 | |
| dc.description.abstracteng | Optimal Transport and Wasserstein Distance are closely related terms that
do not only have a long history in the mathematical literature, but also
have seen a resurgence in recent years, particularly in the context of the
many applications they are used in, which span a variety of scientific fields
including - but not limited to - imaging, statistics and machine learning.
Due to drastic increases in data volume and a high demand for Wasserstein
distance computation, the development of more efficient algorithms in the
domain of optimal transport increased in priority and the advancement picked
up pace quickly. This thesis is dedicated to algorithms for solving the optimal transport
problem and computing Wasserstein distances. After an introduction to the
field of optimal transport, there will be an overview of the application areas
as well as a summary of the most important methods for computation with
a focus on the discrete optimal transport problem. This is followed by a
presentation of a benchmark for discrete optimal transport together with a
performance test of a selection of algorithms on this data set. Afterwards,
two new approaches are introduced: a probabilistic approximation method
for Wasserstein distances using subsampling and a clustering method, which
aims to generalize multiscale methods to discrete optimal transport problems,
including instances with a non-metric cost function. | de |
| dc.contributor.coReferee | Schöbel, Anita Prof. Dr. | |
| dc.subject.eng | Optimal transport | de |
| dc.subject.eng | Wasserstein metric | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E5B2-B-4 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematik (PPN61756535X) | de |
| dc.identifier.ppn | 1067351973 | |