The Annals of Statistics

A robust method for cluster analysis

María Teresa Gallegos and Gunter Ritter

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Let there be given a contaminated list of nd-valued observations coming from g different, normally distributed populations with a common covariance matrix. We compute the ML-estimator with respect to a certain statistical model with nr outliers for the parameters of the g populations; it detects outliers and simultaneously partitions their complement into g clusters. It turns out that the estimator unites both the minimum-covariance-determinant rejection method and the well-known pooled determinant criterion of cluster analysis. We also propose an efficient algorithm for approximating this estimator and study its breakdown points for mean values and pooled SSP matrix.

Article information

Ann. Statist., Volume 33, Number 1 (2005), 347-380.

First available in Project Euclid: 8 April 2005

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Cluster analysis multivariate data outliers robustness breakdown point determinant criterion minimal distance partition


Gallegos, María Teresa; Ritter, Gunter. A robust method for cluster analysis. Ann. Statist. 33 (2005), no. 1, 347--380. doi:10.1214/009053604000000940.

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