Issues in robust clustering

It is now widely recognized that the presence of outliers can affect the results of any statistical analysis. This is also the case of cluster analysis methods. Recently, special attention in the robust clustering literature has been devoted to classification methods based on trimming which try to discard most outlying ob- servations when carrying out the clustering process. The idea of trimming, together with the need of considering groups of different sizes and orientation, has led to the suggestion of maximization of very complicated functions with many parameters and a very high computational complexity due to the “combinatorial” nature of the problem and constraints in order to avoid spurious solutions. In this paper we give a general overview about the computational/theoretical problems that recent robust cluster analysis methods necessarily imply and we concentrate on the graphical tools which have been proposed in order to select the optimal trimming proportion and the optimal number of groups.