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Another look at principal curves and surfaces
dc.contributor.author | Delicado Useros, Pedro Francisco |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa |
dc.date.accessioned | 2017-07-17T06:46:25Z |
dc.date.available | 2017-07-17T06:46:25Z |
dc.date.issued | 2001-03 |
dc.identifier.citation | Delicado, P. Another look at principal curves and surfaces. "Journal of multivariate analysis", Març 2001, vol. 77, núm. 1, p. 84-116. |
dc.identifier.issn | 0047-259X |
dc.identifier.uri | http://hdl.handle.net/2117/106496 |
dc.description | © <year>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.description.abstract | Principal curves have been defined as smooth curves passing through the “middle” of a multidimensional data set. They are nonlinear generalizations of the first principal component, a characterization of which is the basis of the definition of principal curves. We establish a new characterization of the first principal component and base our new definition of a principal curve on this property. We introduce the notion of principal oriented points and we prove the existence of principal curves passing through these points. We extend the definition of principal curves to multivariate data sets and propose an algorithm to find them. The new notions lead us to generalize the definition of total variance. Successive principal curves are recursively defined from this generalization. The new methods are illustrated on simulated and real data sets. |
dc.format.extent | 33 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.other | fixed points |
dc.subject.other | generalized total variance |
dc.subject.other | nonlinear multivariate analysis |
dc.subject.other | principal components |
dc.subject.other | smoothing techniques |
dc.title | Another look at principal curves and surfaces |
dc.type | Article |
dc.contributor.group | Universitat Politècnica de Catalunya. ADBD - Anàlisi de Dades Complexes per a les Decisions Empresarials |
dc.identifier.doi | 10.1006/jmva.2000.1917 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::46 Associative rings and algebras::46T Nonlinear functional analysis |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0047259X00919171 |
dc.rights.access | Open Access |
local.identifier.drac | 640727 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Delicado, P. |
local.citation.publicationName | Journal of multivariate analysis |
local.citation.volume | 77 |
local.citation.number | 1 |
local.citation.startingPage | 84 |
local.citation.endingPage | 116 |
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