Exploratory
tools in model-based clustering

Augustin Mayo-Iscar

Universidad de Valladolid, Spain

How to adequately choose the number of groups and how to measure the
strength of group-assignments are two frequent requirements in Cluster
Analysis. The answer to these two important questions is clearly
dependent on the assumed formal "cluster-structure". For instance, we
should specify in advance which is the type of different group scatters
that we are allowing for. Moreover, a clear distinction should be made
between what it is understood by a "proper" group compared to what it
may be understood by a (small) fraction of outlying data.
Some methods have been recently introduced which are able to handle
different types of constraints in the group scatter matrices and to
deal with the presence of contaminating data. For instance, with these
ideas in mind, the so-called TCLUST method has been proposed.
This general framework for doing robust model-based clustering can be
applied here to design some exploratory tools that turn out to be very
useful when trying to provide appropriate answers to the previously
stated key questions.
Two graphical exploratory displays will be presented together with some
justifications for their practical use. The monitoring of optimal
values of the target functions defining the robust clustering problem
together with the use of some Bayes factors will be the keystone of
these graphical approaches.