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Principal points, principal curves and principal surfaces
The idea of approximating a distribution is a prominent problem in statistics. This dissertation explores the theory of principal points and principal curves as approximation methods to a distribution. Principal points of a distribution have been initially introduced by Flury (1990) who tackled the...
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| Format: | Thesis |
| Language: | English |
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Department of Statistical Sciences
2015
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| _version_ | 1867614354539544576 |
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| access_status_str | Open Access |
| author | Ganey, Raeesa |
| author2 | Lubbe, Sugnet |
| author_browse | Ganey, Raeesa Lubbe, Sugnet |
| author_facet | Lubbe, Sugnet Ganey, Raeesa |
| author_sort | Ganey, Raeesa |
| collection | Thesis |
| description | The idea of approximating a distribution is a prominent problem in statistics. This dissertation explores the theory of principal points and principal curves as approximation methods to a distribution. Principal points of a distribution have been initially introduced by Flury (1990) who tackled the problem of optimal grouping in multivariate data. In essence, principal points are the theoretical counterparts of cluster means obtained by the k-means algorithm. Principal curves defined by Hastie (1984), are smooth one-dimensional curves that pass through the middle of a p-dimensional data set, providing a nonlinear summary of the data. In this dissertation, details on the usefulness of principal points and principal curves are reviewed. The application of principal points and principal curves are then extended beyond its original purpose to well-known computational methods like Support Vector Machines in machine learning. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15515 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:50:42.876Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Statistical Sciences |
| publisherStr | Department of Statistical Sciences |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15515 Principal points, principal curves and principal surfaces Ganey, Raeesa Lubbe, Sugnet Statistical Sciences Principal points k-means algorithm computational methods machine learning The idea of approximating a distribution is a prominent problem in statistics. This dissertation explores the theory of principal points and principal curves as approximation methods to a distribution. Principal points of a distribution have been initially introduced by Flury (1990) who tackled the problem of optimal grouping in multivariate data. In essence, principal points are the theoretical counterparts of cluster means obtained by the k-means algorithm. Principal curves defined by Hastie (1984), are smooth one-dimensional curves that pass through the middle of a p-dimensional data set, providing a nonlinear summary of the data. In this dissertation, details on the usefulness of principal points and principal curves are reviewed. The application of principal points and principal curves are then extended beyond its original purpose to well-known computational methods like Support Vector Machines in machine learning. 2015-12-02T12:04:56Z 2015-12-02T12:04:56Z 2015 Master Thesis Masters MSc http://hdl.handle.net/11427/15515 eng application/pdf Department of Statistical Sciences Faculty of Science University of Cape Town |
| spellingShingle | Statistical Sciences Principal points k-means algorithm computational methods machine learning Ganey, Raeesa Principal points, principal curves and principal surfaces |
| thesis_degree_str | Master's |
| title | Principal points, principal curves and principal surfaces |
| title_full | Principal points, principal curves and principal surfaces |
| title_fullStr | Principal points, principal curves and principal surfaces |
| title_full_unstemmed | Principal points, principal curves and principal surfaces |
| title_short | Principal points, principal curves and principal surfaces |
| title_sort | principal points principal curves and principal surfaces |
| topic | Statistical Sciences Principal points k-means algorithm computational methods machine learning |
| url | http://hdl.handle.net/11427/15515 |
| work_keys_str_mv | AT ganeyraeesa principalpointsprincipalcurvesandprincipalsurfaces |