k-simplex volume optimizing projection algorithms for high-dimensional data sets
| dc.contributor.author | Stiverson, Shannon J., author | |
| dc.contributor.author | Kirby, Michael, advisor | |
| dc.contributor.author | Peterson, Chris, advisor | |
| dc.contributor.author | Adams, Henry, committee member | |
| dc.contributor.author | Hess, Ann, committee member | |
| dc.date.accessioned | 2021-06-07T10:21:30Z | |
| dc.date.available | 2021-06-07T10:21:30Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | Many applications produce data sets that contain hundreds or thousands of features, and consequently sit in very high dimensional space. It is desirable for purposes of analysis to reduce the dimension in a way that preserves certain important properties. Previous work has established conditions necessary for projecting data into lower dimensions while preserving pairwise distances up to some tolerance threshold, and algorithms have been developed to do so optimally. However, although similar criteria for projecting data into lower dimensions while preserving k-simplex volumes has been established, there are currently no algorithms seeking to optimally preserve such embedded volumes. In this work, two new algorithms are developed and tested: one which seeks to optimize the smallest projected k-simplex volume, and another which optimizes the average projected k-simplex volume. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Stiverson_colostate_0053A_16564.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/232627 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2020- | |
| 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 | k-simplex volume optimizing projection algorithms for high-dimensional data sets | |
| 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 | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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