A general trimming approach to robust Cluster Analysis

Details A general trimming approach to robust Cluster Analysis A general trimming approach to robust Cluster Analysis

2008-06-18

arxiv.org/abs/0806.2976v1

Annals of Statistics 2008, Vol. 36, No. 3, 1324-1345

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS515 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS515

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 $\alpha$ 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.

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