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April 1997 Trimmed $k$-means: an attempt to robustify quantizers
J. A. Cuesta-Albertos, A. Gordaliza, C. Matrán
Ann. Statist. 25(2): 553-576 (April 1997). DOI: 10.1214/aos/1031833664


A class of procedures based on "impartial trimming" (self-determined by the data) is introduced with the aim of robustifying k-means, hence the associated clustering analysis. We include a detailed study of optimal regions, showing that only nonpathological regions can arise from impartial trimming procedures. The asymptotic results provided in the paper focus on strong consistency of the suggested methods under widely general conditions. A section is devoted to exploring the performance of the procedure to detect anomalous data in simulated data sets.


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J. A. Cuesta-Albertos. A. Gordaliza. C. Matrán. "Trimmed $k$-means: an attempt to robustify quantizers." Ann. Statist. 25 (2) 553 - 576, April 1997.


Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0878.62045
MathSciNet: MR1439314
Digital Object Identifier: 10.1214/aos/1031833664

Primary: 60F15 , 62H30
Secondary: 62F35

Keywords: $k$-means , clustering methods , consistency , robustness , trimmed $k$-means

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 1997
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