The Annals of Statistics

A general trimming approach to robust cluster Analysis

Luis A. García-Escudero, Alfonso Gordaliza, Carlos Matrán, and Agustin Mayo-Iscar

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We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion α of contaminating data to guarantee the robustness of the method. As a characteristic feature, restrictions on the ratio between the maximum and the minimum eigenvalues of the groups scatter matrices are introduced. This makes the problem to be well defined and guarantees the consistency of the sample solutions to the population ones.

The method covers a wide range of clustering approaches depending on the strength of the chosen restrictions. Our proposal includes an algorithm for approximately solving the sample problem.

Article information

Ann. Statist., Volume 36, Number 3 (2008), 1324-1345.

First available in Project Euclid: 26 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H3
Secondary: 62H3

Robustness cluster analysis trimming asymptotics trimmed k-means EM-algorithm fast-MCD algorithm Dykstra’s algorithm


García-Escudero, Luis A.; Gordaliza, Alfonso; Matrán, Carlos; Mayo-Iscar, Agustin. A general trimming approach to robust cluster Analysis. Ann. Statist. 36 (2008), no. 3, 1324--1345. doi:10.1214/07-AOS515.

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