Robustness properties of the TCLUST procedure

The TCLUST procedure is a robust clustering procedure introduced by García-Escudero et al. (2008). It performs clustering with the aim of fitting clusters with different scatters and weights. As the corresponding objective function can be unbounded, a restriction is added on the eigenvalues-ratio of the scatter matrices. The robustness of the method is guaranteed by allowing the trimming of a given proportion of observations. As García-Escudero and Gordaliza (1999) have done for the k-means and trimmed k-means methodologies, the robustness properties of the TCLUST procedure are studied by means of the influence function and the breakdown point. In order to be able to compare the robustness of TCLUST with other clustering methods, dissolution point and isolation robustness (Hennig, 2008) are also considered. It turns out that the TCLUST procedure has a behavior close to that of the trimmed k-means.