The TCLUST Approach to Robust Cluster Analysis

A new method for performing robust clustering is proposed. The method is designed with the aim of fitting clusters with different scatters and weights. A proportion α of contaminating data points is also allowed. Restrictions on the ratio between the maximum and the minimum eigenvalues of the groups scatter matrices are introduced. These restrictions make the problem to be well-defined guaranteeing the existence and the consistency of the sample estimators to the population parameters. ∗Research partially supported by Ministerio de Ciencia y Tecnoloǵıa and FEDER grant MTM2005-08519C02-01 and by Consejeŕıa de Educación y Cultura de la Junta de Castilla y León grant PAPIJCL VA102A06. †Departamento de Estad́ıstica e Investigación Operativa. Facultad de Ciencias. Universidad de Valladolid. 47002, Valladolid. Spain. 1 The method covers a wide range of clustering approaches, which arise depending on the strength of the chosen restrictions. Our proposal includes an algorithm for approximately solving the sample problem which takes advantage of the Dykstra’s algorithm.

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