Annals of Statistics

Trimmed $k$-means: an attempt to robustify quantizers

J. A. Cuesta-Albertos, A. Gordaliza, and C. Matrán

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Abstract

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.

Article information

Source
Ann. Statist., Volume 25, Number 2 (1997), 553-576.

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031833664

Digital Object Identifier
doi:10.1214/aos/1031833664

Mathematical Reviews number (MathSciNet)
MR1439314

Zentralblatt MATH identifier
0878.62045

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 60F15: Strong theorems
Secondary: 62F35: Robustness and adaptive procedures

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

Citation

Cuesta-Albertos, J. A.; Gordaliza, A.; Matrán, C. Trimmed $k$-means: an attempt to robustify quantizers. Ann. Statist. 25 (1997), no. 2, 553--576. doi:10.1214/aos/1031833664. https://projecteuclid.org/euclid.aos/1031833664


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References

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