Abstract
This paper deals with the problem of identifying multiple outliers in multivariate data. Detection of anomalous values is achieved by looking at the variations in the convex hull of the data set as block of observations are deleted.
Work supported by ex-40% MURST Research Project “Nuovi Metodi di Classificazione e Analisi dei Dati”. M. R. D’Esposito wrote sections 1, 2 and 6. G. Ragozini sections 3, 4 and 5. Computations are due to G. Ragozini and were made by S-Plus code.
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References
Atkinson, A.C. (1994), “Fast Very Robust Methods for the Detection of Multiple Outliers”, Journal of the American Statistical Association, 89, pp. 1329–1339.
Barber, C. B., Dobkin, D. P. and Huhdanpaa, H. (1996), “The Quickhull Algorithm for Convex Hulls”, ACM Trans. on Math. Softw., 22, pp. 469–483
Barnett, V. and Lewis, T. (1994), Outliers in Statistical Data, John Wiley, New York
Chand, D. and Kapur, S. (1970), “An Algorithm for Convex Polytopes”, Journal of ACM, 7, 78–86
Clarkson, K. and Shor, P. (1989), “Applications of Random Sampling in Computational Geometry”, ii. Discrete Computational Geom., 4, pp. 387–421
Eddy, W. (1977), “A New Convex Hull Algorithm for Planar Sets”, ACM Transaction on Mathematical Software, 3, pp. 398–403
Edelsbrunner, H. (1987) Algorithms in Combinatorial Geometry,Springer-Verlag.
Gnanadesikan, R. and Kettering, J.R. (1972), “Robust Estimates, Residuals, and Outlier Detection with Multiresponse Data”, Biometrics, 28, pp. 81–124.
Grunbaum, B. (1967). Convex Polytopes, John Wiley, New York.
Hadi, Ali S. (1992), “Identifying Multiple Outliers in Multivariate Data”, Journal of Royal Statistical Society, B, 54, pp. 761–771
Preparata, F. P. and Hong, S. J. (1977), “Convex Hulls of Finite Sets of Points in Two and Three Dimensions”, Communications of ACM, 20, pp. 87–93
Rousseeuw, P.J. and Leroy, A.M. (1987), Robust Regression and Outlier Detection, John Wiley, New York
Rousseeuw, P.J. and van Zomeren, B.C. (1990), “Unmasking Multivariate Outliers and Leverage Points”, Journal of the American Statistical Association, 85, pp. 633–651.
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© 1999 Springer-Verlag Berlin · Heidelberg
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D’Esposito, M.R., Ragozini, G. (1999). Detection of Multivariate Outliers by Convex Hulls. In: Vichi, M., Opitz, O. (eds) Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60126-2_35
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DOI: https://doi.org/10.1007/978-3-642-60126-2_35
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Print ISBN: 978-3-540-65633-3
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