Multidimensional scaling: infinite metric measure spaces
| dc.contributor.author | Kassab, Lara, author | |
| dc.contributor.author | Adams, Henry, advisor | |
| dc.contributor.author | Kirby, Michael, committee member | |
| dc.contributor.author | Fosdick, Bailey, committee member | |
| dc.date.accessioned | 2019-06-14T17:05:49Z | |
| dc.date.available | 2019-06-14T17:05:49Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces, along with its optimality properties and goodness of fit. This allows us to study the MDS embeddings of the geodesic circle S1 into Rm for all m, and to ask questions about the MDS embeddings of the geodesic n-spheres Sn into Rm. Furthermore, we address questions on convergence of MDS. For instance, if a sequence of metric measure spaces converges to a fixed metric measure space X, then in what sense do the MDS embeddings of these spaces converge to the MDS embedding of X? Convergence is understood when each metric space in the sequence has the same finite number of points, or when each metric space has a finite number of points tending to infinity. We are also interested in notions of convergence when each metric space in the sequence has an arbitrary (possibly infinite) number of points. | |
| dc.format.medium | born digital | |
| dc.format.medium | masters theses | |
| dc.identifier | Kassab_colostate_0053N_15327.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/195291 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.title | Multidimensional scaling: infinite metric measure spaces | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.S.) |
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