A robust method for cluster analysis

Details A robust method for cluster analysis A robust method for cluster analysis

2005-04-25

arxiv.org/abs/math/0504513v1

Annals of Statistics 2005, Vol. 33, No. 1, 347-380

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000940 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000940

Let there be given a contaminated list of n R^d-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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