Principal points, principal curves and principal surfaces

dc.contributor.advisorLubbe, Sugneten_ZA
dc.contributor.authorGaney, Raeesaen_ZA
dc.date.accessioned2015-12-02T12:04:56Z
dc.date.available2015-12-02T12:04:56Z
dc.date.issued2015en_ZA
dc.description.abstractThe 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.en_ZA
dc.identifier.apacitationGaney, R. (2015). <i>Principal points, principal curves and principal surfaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Statistical Sciences. Retrieved from http://hdl.handle.net/11427/15515en_ZA
dc.identifier.chicagocitationGaney, Raeesa. <i>"Principal points, principal curves and principal surfaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2015. http://hdl.handle.net/11427/15515en_ZA
dc.identifier.citationGaney, R. 2015. Principal points, principal curves and principal surfaces. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ganey, Raeesa AB - 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. DA - 2015 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - Principal points, principal curves and principal surfaces TI - Principal points, principal curves and principal surfaces UR - http://hdl.handle.net/11427/15515 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/15515
dc.identifier.vancouvercitationGaney R. Principal points, principal curves and principal surfaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15515en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Statistical Sciencesen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherStatistical Sciencesen_ZA
dc.subject.otherPrincipal pointsen_ZA
dc.subject.otherk-means algorithmen_ZA
dc.subject.othercomputational methodsen_ZA
dc.subject.othermachine learningen_ZA
dc.titlePrincipal points, principal curves and principal surfacesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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