A robust method for cluster analysis
María Teresa Gallegos and Gunter Ritter
Source: Ann. Statist. Volume 33, Number 1
(2005), 347-380.
Abstract
Let there be given a contaminated list of n ℝd-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 n−r 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.
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Keywords: Cluster analysis; multivariate data; outliers; robustness; breakdown point; determinant criterion; minimal distance partition
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1112967709
Digital Object Identifier: doi:10.1214/009053604000000940
Zentralblatt MATH identifier: 02182566
Mathematical Reviews number (MathSciNet): MR2157806
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