The breakdown bahavior of the TCLUST procedure

The TCLUST procedure is a new robust clustering method introduced by García-Escudero et al. (2008). It performs clustering with the aim of finding 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. This trimming level has to be chosen by the practitioner, as well as the number of clusters. Suitable values for these parameters can be obtained throughout the careful examination of some classification trimmed likelihood curves (García-Escudero et al., 2010). The first part of this talk will consist of a brief presentation of this clustering procedure and the related R package (tclust).
In the second part of the talk, the robustness of the TCLUST procedure, and more precisely its breakdown behavior, will be studied. In the context of cluster analysis, Hennig (2004, 2008) has defined some useful concepts to characterize the breakdown of a procedure; the r-components breakdown point, the dissolution point and the isolation robustness. These tools will be applied to the TCLUST procedure and some examples will be presented.