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Title: Robust parsimonious approach for model based clustering Authors:  Agustin Mayo-Iscar - Universidad de Valladolid (Spain) [presenting]
Luis Angel Garcia-Escudero - Universidad de Valladolid (Spain)
Marco Riani - University of Parma (Italy)
Andrea Cerioli - University of Parma (Italy)
Abstract: Trimmed k-means were introduced 20 years ago for robustifying the well-known k-means. The base of the success of this simple procedure was the joint application of impartial trimming and constraints. Later, TCLUST approaches extended this procedure by reducing the strength of the constraints, implicit in the application of that procedure, in order to fit better the existing patterns in data sets from mixtures of normal multivariate distributions. Impartial trimming application allows us to avoid the undesired effect that deviations from the assumed model produce in maximum likelihood based estimators. Constraints are useful for getting a well posed estimation problem and for reducing the prevalence of spurious local maximizers. Trimming and constraints based procedures were also designed for robustifying the estimation of clusters around linear subspaces and the estimation of the mixture of factor analyzers model. TCLUST methodologies are available in the TCLUST package in CRAN and in the FSDA library in MATLAB. Now we are developing robust estimators for a parsimonious collection of models for being incorporated in these packages. As usual, a BIC application allows to select the model. It will allow the users to get adaptive robust estimations for their data sets.