Robust nonlinear principal components

Autores
Maronna, Ricardo Antonio; Méndez, Fernanda; Yohai, Victor Jaime
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
All known approaches to nonlinear principal components are based on minimizing a quadratic loss, which makes them sensitive to data contamination. A predictive approach in which a spline curve is fit minimizing a residual M-scale is proposed for this problem. For a p-dimensional random sample xi (i=1,…,n) the method finds a function h:R→Rp and a set {t1,…,tn}⊂R that minimize a joint M-scale of the residuals xi−h(ti), where h ranges on the family of splines with a given number of knots. The computation of the curve then becomes the iterative computing of regression S-estimators. The starting values are obtained from a robust linear principal components estimator. A simulation study and the analysis of a real data set indicate that the proposed approach is almost as good as other proposals for row-wise contamination, and is better for element-wise contamination.
Fil: Maronna, Ricardo Antonio. Universidad Nacional de La Plata; Argentina
Fil: Méndez, Fernanda. Universidad Nacional de Rosario; Argentina
Fil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Materia
PRINCIPAL CURVES
S-ESTIMATORS
SPLINES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/171628
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Robust nonlinear principal componentsMaronna, Ricardo AntonioMéndez, FernandaYohai, Victor JaimePRINCIPAL CURVESS-ESTIMATORSSPLINEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1All known approaches to nonlinear principal components are based on minimizing a quadratic loss, which makes them sensitive to data contamination. A predictive approach in which a spline curve is fit minimizing a residual M-scale is proposed for this problem. For a p-dimensional random sample xi (i=1,…,n) the method finds a function h:R→Rp and a set {t1,…,tn}⊂R that minimize a joint M-scale of the residuals xi−h(ti), where h ranges on the family of splines with a given number of knots. The computation of the curve then becomes the iterative computing of regression S-estimators. The starting values are obtained from a robust linear principal components estimator. A simulation study and the analysis of a real data set indicate that the proposed approach is almost as good as other proposals for row-wise contamination, and is better for element-wise contamination.Fil: Maronna, Ricardo Antonio. Universidad Nacional de La Plata; ArgentinaFil: Méndez, Fernanda. Universidad Nacional de Rosario; ArgentinaFil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaSpringer2015-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/171628Maronna, Ricardo Antonio; Méndez, Fernanda; Yohai, Victor Jaime; Robust nonlinear principal components; Springer; Statistics And Computing; 25; 2; 3-2015; 439-4480960-31741573-1375CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11222-013-9442-0info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11222-013-9442-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:54:34Zoai:ri.conicet.gov.ar:11336/171628instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:54:35.287CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Robust nonlinear principal components
title Robust nonlinear principal components
spellingShingle Robust nonlinear principal components
Maronna, Ricardo Antonio
PRINCIPAL CURVES
S-ESTIMATORS
SPLINES
title_short Robust nonlinear principal components
title_full Robust nonlinear principal components
title_fullStr Robust nonlinear principal components
title_full_unstemmed Robust nonlinear principal components
title_sort Robust nonlinear principal components
dc.creator.none.fl_str_mv Maronna, Ricardo Antonio
Méndez, Fernanda
Yohai, Victor Jaime
author Maronna, Ricardo Antonio
author_facet Maronna, Ricardo Antonio
Méndez, Fernanda
Yohai, Victor Jaime
author_role author
author2 Méndez, Fernanda
Yohai, Victor Jaime
author2_role author
author
dc.subject.none.fl_str_mv PRINCIPAL CURVES
S-ESTIMATORS
SPLINES
topic PRINCIPAL CURVES
S-ESTIMATORS
SPLINES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv All known approaches to nonlinear principal components are based on minimizing a quadratic loss, which makes them sensitive to data contamination. A predictive approach in which a spline curve is fit minimizing a residual M-scale is proposed for this problem. For a p-dimensional random sample xi (i=1,…,n) the method finds a function h:R→Rp and a set {t1,…,tn}⊂R that minimize a joint M-scale of the residuals xi−h(ti), where h ranges on the family of splines with a given number of knots. The computation of the curve then becomes the iterative computing of regression S-estimators. The starting values are obtained from a robust linear principal components estimator. A simulation study and the analysis of a real data set indicate that the proposed approach is almost as good as other proposals for row-wise contamination, and is better for element-wise contamination.
Fil: Maronna, Ricardo Antonio. Universidad Nacional de La Plata; Argentina
Fil: Méndez, Fernanda. Universidad Nacional de Rosario; Argentina
Fil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
description All known approaches to nonlinear principal components are based on minimizing a quadratic loss, which makes them sensitive to data contamination. A predictive approach in which a spline curve is fit minimizing a residual M-scale is proposed for this problem. For a p-dimensional random sample xi (i=1,…,n) the method finds a function h:R→Rp and a set {t1,…,tn}⊂R that minimize a joint M-scale of the residuals xi−h(ti), where h ranges on the family of splines with a given number of knots. The computation of the curve then becomes the iterative computing of regression S-estimators. The starting values are obtained from a robust linear principal components estimator. A simulation study and the analysis of a real data set indicate that the proposed approach is almost as good as other proposals for row-wise contamination, and is better for element-wise contamination.
publishDate 2015
dc.date.none.fl_str_mv 2015-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/171628
Maronna, Ricardo Antonio; Méndez, Fernanda; Yohai, Victor Jaime; Robust nonlinear principal components; Springer; Statistics And Computing; 25; 2; 3-2015; 439-448
0960-3174
1573-1375
CONICET Digital
CONICET
url http://hdl.handle.net/11336/171628
identifier_str_mv Maronna, Ricardo Antonio; Méndez, Fernanda; Yohai, Victor Jaime; Robust nonlinear principal components; Springer; Statistics And Computing; 25; 2; 3-2015; 439-448
0960-3174
1573-1375
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11222-013-9442-0
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11222-013-9442-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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