An adaptation of K-means-type algorithms to the Grassmann manifold
| dc.contributor.author | Stiverson, Shannon J., author | |
| dc.contributor.author | Kirby, Michael, advisor | |
| dc.contributor.author | Adams, Henry, committee member | |
| dc.contributor.author | Ben-Hur, Asa, committee member | |
| dc.date.accessioned | 2019-06-14T17:06:49Z | |
| dc.date.available | 2019-06-14T17:06:49Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | The Grassmann manifold provides a robust framework for analysis of high-dimensional data through the use of subspaces. Treating data as subspaces allows for separability between data classes that is not otherwise achieved in Euclidean space, particularly with the use of the smallest principal angle pseudometric. Clustering algorithms focus on identifying similarities within data and highlighting the underlying structure. To exploit the properties of the Grassmannian for unsupervised data analysis, two variations of the popular K-means algorithm are adapted to perform clustering directly on the manifold. We provide the theoretical foundations needed for computations on the Grassmann manifold and detailed derivations of the key equations. Both algorithms are then thoroughly tested on toy data and two benchmark data sets from machine learning: the MNIST handwritten digit database and the AVIRIS Indian Pines hyperspectral data. Performance of algorithms is tested on manifolds of varying dimension. Unsupervised classification results on the benchmark data are compared to those currently found in the literature. | |
| dc.format.medium | born digital | |
| dc.format.medium | masters theses | |
| dc.identifier | Stiverson_colostate_0053N_15444.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/195396 | |
| 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.subject | Grassmannian | |
| dc.subject | LBG | |
| dc.subject | clustering | |
| dc.subject | subspaces | |
| dc.subject | K-means | |
| dc.title | An adaptation of K-means-type algorithms to the Grassmann manifold | |
| 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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