Robust low-rank approximation of data matrices with elementwise contamination
We propose a robust method to approximate an n × p data matrix with one of rank q. The method is based on Yohai's regression MM estimates. It is intended to be resistant against the existence of both atypical rows and of scattered atypical cells and also to be able to cope with missing values....
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| Lenguaje: | Inglés |
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2008
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 08179caa a22008177a 4500 | ||
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| 001 | PAPER-22347 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205354.0 | ||
| 008 | 190411s2008 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-55149098958 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a TCMTA | ||
| 100 | 1 | |a Maronna, R. | |
| 245 | 1 | 0 | |a Robust low-rank approximation of data matrices with elementwise contamination |
| 260 | |c 2008 | ||
| 270 | 1 | 0 | |m Maronna, R.; Faculty of Exact Sciences, University of La Plata, CC 172, La Plata 1900, Argentina; email: rmaronna@mail.retina.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Alqallaf, F., Van Aelst, S., Yohai, V. J., and Zamar, R. H. (2007), Propagation of Outliers in Multivariate Data, unpublished manuscript, available at http://mate.dm.uba.ar/vyohai/Alqallaf-VanAelst- Yohai-Zamar.pdf; Bay, S.D., The UCI KDD Archive [http://kdd.ics.uci. edu] (1999) University of California Irvine, Dept, , of Information and Computer Science | ||
| 504 | |a Campbell, N.A., Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation (1980) Applied Statistics, 29, pp. 231-237 | ||
| 504 | |a Croux, C., Haesbroeck, G., Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies (2000) Biometrika, 87, pp. 603-618 | ||
| 504 | |a Croux, C., Ruiz-Gazen, A., A Fast Algorithm for Robust Principal Components Based on Projection Pursuit (1996) Compstat: Proceedings in Computational Statistics, pp. 211-216. , ed. A. Prat, Heidelberg: Physica-Verlag, pp | ||
| 504 | |a Croux, C., Ruiz-Gazen, A., High-Breakdown Estimators for Principal Components: The Projection-Pursuit Approach Revisited (2005) Journal of Multivariate Analysis, 95, pp. 206-226 | ||
| 504 | |a Croux, C., Filzmoser, P., Pison, G., Rousseeuw, P.J., Fitting Multiplicative Models by Robust Alternating Regressions (2003) Statistics and Computing, 13, pp. 23-36 | ||
| 504 | |a De la Torre, F., Black, M.J., Robust Principal Components Analysis for Computer Vision (2001) Proceedings of the International Conference on Computer Vision, , http://citeseer.ist.psu.edu/torre01robust.html, available at | ||
| 504 | |a Devlin, S.J., Gnanadesikan, R., Kettenring, J.R., Robust Estimation of Dispersion Matrices and Principal Components (1981) Journal of the American Statistical Association, 76, pp. 354-362 | ||
| 504 | |a Gabriel, K.R., Zamir, S., Lower-Rank Approximation of Matrices by Least Squares With Any Choice of Weights (1979) Technometrics, 21, pp. 489-498 | ||
| 504 | |a Hubert, M., Rousseeuw, P.J., Vanden Branden, K., ROBPCA: A New Approach to Robust Principal Component Analysis (2005) Technometrics, 47, pp. 64-79 | ||
| 504 | |a Janssens, K., Deraedt, I., Freddy, A., Veekman, J., Composition of 15th-17th Century Archaeological Glass Vessels Excavated in Antwerp, Belgium (1998) Mikrochimica Acta, 15 (SUPPL.), pp. 253-267 | ||
| 504 | |a Li, G., Chen, Z., Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo (1985) Journal of the American Statistical Association, 80, pp. 759-766 | ||
| 504 | |a Liu, L., Hawkins, D.M., Ghosh, S., Young, S.S., Robust Singular Value Decomposition Analysis of Microarray Data (2003) Proceedings of the National Academy of Sciences, 100, pp. 13167-13172 | ||
| 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.A., Principal Components and Orthogonal Regression Based on Robust Scales (2005) Technometrics, 47, pp. 264-273 | ||
| 504 | |a Maronna, R. A., and Yohai, V. J. (2007), Robust Lower-Rank Approximation of Data Matrices With Elementwise Contamination, unpublished manuscript, available at http://mate.dm.uba.ar/̃vyohai/LowRankFull. pdf; Maronna, R.A., Zamar, R.H., Robust Estimation of Location and Dispersion for High-Dimensional Data Sets (2002) Technometrics, 44, pp. 307-317 | ||
| 504 | |a Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust Statistics: Theory and Methods, , New York: Wiley | ||
| 504 | |a Naga, R., Antille, G., Stability of Robust and Non-Robust Principal Component Analysis (1990) Computational Statistics & Data Analysis, 10, pp. 169-174 | ||
| 504 | |a Rey, W. (2007), Total Singular Value Decomposition: Robust SVD, Regression and Location-Scale, unpublished manuscript, available at http://arxiv.org/abs/0706.0096; Serneels, S., Verdonck, T., Principal Component Analysis for Data Containing Outliers and Missing Elements (2008) Computational Statistics and Data Analysis, 52, pp. 1712-1727 | ||
| 504 | |a Sigillito, V.G., Wing, S.P., Hutton, L.V., Baker, K.B., Classification of Radar Returns From the Ionosphere Using Neural Networks (1989) Johns Hopkins APL Technical Digest, 10, pp. 262-266 | ||
| 504 | |a Verboon, P., Heiser, W.J., Resistant Lower-Rank Approximation of Matrices by Iterative Majorization (1994) Computational Statistics and Data Analysis, 18, pp. 457-467 | ||
| 504 | |a Yohai, V.J., High-Breakdown Point and High-Efficiency Estimates for Regression (1987) The Annals of Statistics, 15, pp. 642-656 | ||
| 504 | |a Yohai, V.J., Zamar, R.H., High-Breakdown Estimates of Regression by Means of the Minimization of an Efficient Scale (1988) Journal of the American Statistical Association, 83, pp. 406-413 | ||
| 520 | 3 | |a We propose a robust method to approximate an n × p data matrix with one of rank q. The method is based on Yohai's regression MM estimates. It is intended to be resistant against the existence of both atypical rows and of scattered atypical cells and also to be able to cope with missing values. We propose an algorithm based on alternating M-regressions and a starting estimate based on successive rank-one fits, which involves O(npq) operations. Simulations show that our estimate outperforms competing estimates in terms of both efficiency and resistance. Three high-dimensional real data sets are analyzed. The running time of our estimate for large data sets is shown to be less than that of its competitors. © 2008 American Statistical Association and the American Society for Quality. |l eng | |
| 536 | |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, PAV 120, PICT 21407 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PIP 5505 | ||
| 536 | |a Detalles de la financiación: This research was supported in part by CONICET (grant PIP 5505), ANPCyT, Argentina (grants PICT 21407 and PAV 120). | ||
| 593 | |a Faculty of Exact Sciences, University of La Plata, CC 172, La Plata 1900, Argentina | ||
| 593 | |a CICPBA | ||
| 593 | |a Faculty of Exact Sciences, University of Buenos Aires, Ciudad Universitaria, Buenos Aires 1428, Argentina | ||
| 593 | |a CONICET | ||
| 690 | 1 | 0 | |a ALTERNATING REGRESSIONS |
| 690 | 1 | 0 | |a MM ESTIMATE |
| 690 | 1 | 0 | |a MULTIVARIATE OUTLIERS |
| 690 | 1 | 0 | |a PRINCIPAL COMPONENTS |
| 690 | 1 | 0 | |a RAR ESTIMATE. |
| 690 | 1 | 0 | |a COMPETITION |
| 690 | 1 | 0 | |a KETONES |
| 690 | 1 | 0 | |a METHOD OF MOMENTS |
| 690 | 1 | 0 | |a ALTERNATING REGRESSIONS |
| 690 | 1 | 0 | |a MM ESTIMATE |
| 690 | 1 | 0 | |a MULTIVARIATE OUTLIERS |
| 690 | 1 | 0 | |a PRINCIPAL COMPONENTS |
| 690 | 1 | 0 | |a RAR ESTIMATE. |
| 690 | 1 | 0 | |a REGRESSION ANALYSIS |
| 700 | 1 | |a Yohai, V. | |
| 773 | 0 | |d 2008 |g v. 50 |h pp. 295-304 |k n. 3 |p Technometrics |x 00401706 |t Technometrics | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-55149098958&doi=10.1198%2f004017008000000190&partnerID=40&md5=42c00ccbbab54939bb55e7ac301ac236 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1198/004017008000000190 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00401706_v50_n3_p295_Maronna |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00401706_v50_n3_p295_Maronna |y Registro en la Biblioteca Digital |
| 961 | |a paper_00401706_v50_n3_p295_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 83300 | ||