Robust nonlinear principal components
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=...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09603174_v25_n2_p439_Maronna |
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todo:paper_09603174_v25_n2_p439_Maronna2023-10-03T15:53:47Z Robust nonlinear principal components Maronna, R.A. Méndez, F. Yohai, V.J. Principal curves S-estimators Splines 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. © 2013, Springer Science+Business Media New York. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09603174_v25_n2_p439_Maronna |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Principal curves S-estimators Splines |
| spellingShingle |
Principal curves S-estimators Splines Maronna, R.A. Méndez, F. Yohai, V.J. Robust nonlinear principal components |
| topic_facet |
Principal curves S-estimators Splines |
| 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. © 2013, Springer Science+Business Media New York. |
| format |
JOUR |
| author |
Maronna, R.A. Méndez, F. Yohai, V.J. |
| author_facet |
Maronna, R.A. Méndez, F. Yohai, V.J. |
| author_sort |
Maronna, R.A. |
| title |
Robust nonlinear principal components |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_09603174_v25_n2_p439_Maronna |
| work_keys_str_mv |
AT maronnara robustnonlinearprincipalcomponents AT mendezf robustnonlinearprincipalcomponents AT yohaivj robustnonlinearprincipalcomponents |
| _version_ |
1807322890134093824 |