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=...
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Kluwer Academic Publishers
2013
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 05916caa a22006137a 4500 | ||
|---|---|---|---|
| 001 | PAPER-24359 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205612.0 | ||
| 008 | 190411s2013 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84889255680 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Maronna, R.A. | |
| 245 | 1 | 0 | |a Robust nonlinear principal components |
| 260 | |b Kluwer Academic Publishers |c 2013 | ||
| 270 | 1 | 0 | |m Maronna, R.A.; University of La Plata, C.C. 172, Argentina |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Alqallaf, F., Van Aelst, S., Yohai, V.J., Zamar, R.H., Propagation of outliers in multivariate data (2009) Ann. Stat, 37, pp. 311-331 | ||
| 504 | |a Bolton, R.J., Hand, D.J., Webb, A.R., Projection techniques for nonlinear principal components analysis (2003) Stat. Comput, 13, pp. 267-276 | ||
| 504 | |a Candès, E., Li, X., Ma, Y., Wright, J., Robust principal component analysis (2011) J. ACM, 58 (3) | ||
| 504 | |a Cleveland, W., Robust locally weighted regression and smoothing scatterplots (1979) J. Am. Stat. Assoc, 74, pp. 829-836 | ||
| 504 | |a Croux, C., Filzmoser, P., Pison, G., Rousseeuw, P.J., Fitting multiplicative models by robust alternating regressions (2003) Stat. Comput, 13, pp. 23-36 | ||
| 504 | |a Delicado, P., Another look at principal curves and surfaces (2001) J. Multivar. Anal, 77, pp. 84-116 | ||
| 504 | |a Ein-Dor, P., Feldmesser, J., Attributes of the performance of central processing units: a relative performance prediction model (1987) Commun. ACM, 30, pp. 308-317 | ||
| 504 | |a Gerber, S., Whitaker, R., Regularization free principal curve estimation (2013) J. Mach. Learn. Res, 14, pp. 1285-1302 | ||
| 504 | |a Hastie, T., Stuetzle, W., Principal curves (1989) J. Am. Stat. Assoc, 84, pp. 502-516 | ||
| 504 | |a Hubert, M., Rousseeuw, P.J., Verboven, S., Robust PCA for high-dimensional data (2003) Developments in Robust Statistics, pp. 169-179. , Dutter R., Filzmoser P., Gather U., Rousseeuw P.J., (eds), Physika Verlag, Heidelberg: | ||
| 504 | |a Locantore, N., Marron, J.S., Simpson, D.G., Tripoli, N., Zhang, J.T., Cohen, K.L., Robust principal components for functional data (1999) Test, 8, pp. 1-28 | ||
| 504 | |a Maronna, R., Principal components and orthogonal regression based on robust scales (2005) Technometrics, 47, pp. 264-273 | ||
| 504 | |a Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust Statistics: Theory and Methods, , Wiley, New York: | ||
| 504 | |a Maronna, R.A., Yohai, V.J., Robust lower-rank approximation of data matrices with element-wise contamination (2008) Technometrics, 50, pp. 295-304 | ||
| 504 | |a Rousseeuw, P.J., Yohai, V.J., Robust regression by means of S estimators (1984) Robust and Nonlinear Time Series Analysis, pp. 256-272. , Franke J., Härdle W., Martin D., (eds), Lecture Notes in Statistics, 26, Springer, New York: | ||
| 504 | |a Tharmaratnam, K., Claeskens, G., Croux, C., Salibian-Barrera, M., S-estimation for penalized regression splines (2010) J. Comput. Graph. Stat, 19, pp. 609-625 | ||
| 504 | |a Tibshirani, R., Principal curves revisited (1992) Stat. Comput, 2, pp. 183-190 | ||
| 504 | |a Verbeek, J.J., Vlassis, N., Kröse, B., A k-segments algorithm for finding principal curves (2002) Pattern Recognit. Lett, 23, pp. 1009-1017 | ||
| 504 | |a Yohai, V.J., High breakdown-point and high efficiency estimates for regression (1987) Ann. Stat, 15, pp. 642-665 | ||
| 504 | |a Yohai, V.J., Ackerman, W., Haigh, C., Nonlinear principal components (1985) Qual. Quant, 19, pp. 53-71 | ||
| 504 | |a Yohai, V.J., Zamar, R., High breakdown point estimates of regression by means of the minimization of an efficient scale (1988) J. Am. Stat. Assoc, 86, pp. 403-413 | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a University of La Plata, C.C. 172, La Plata, 1900, Argentina | ||
| 593 | |a University of Rosario, Bv. Oroño 1261, Rosario, 2000, Argentina | ||
| 593 | |a Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon 1, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a PRINCIPAL CURVES |
| 690 | 1 | 0 | |a S-ESTIMATORS |
| 690 | 1 | 0 | |a SPLINES |
| 700 | 1 | |a Méndez, F. | |
| 700 | 1 | |a Yohai, V.J. | |
| 773 | 0 | |d Kluwer Academic Publishers, 2013 |g v. 25 |h pp. 439-448 |k n. 2 |p Stat. Comput. |x 09603174 |t Statistics and Computing | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-84889255680&doi=10.1007%2fs11222-013-9442-0&partnerID=40&md5=3f95334241d73c08e3ec1e9fce7fdf42 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s11222-013-9442-0 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_09603174_v25_n2_p439_Maronna |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09603174_v25_n2_p439_Maronna |y Registro en la Biblioteca Digital |
| 961 | |a paper_09603174_v25_n2_p439_Maronna |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 85312 | ||