Title: A computationally feasible algorithm for robust clustering under determinant-and-shape constraints
Authors: Luis Angel Garcia-Escudero - Universidad de Valladolid (Spain) [presenting]
Andrea Cerioli - University of Parma (Italy)
Agustin Mayo-Iscar - Universidad de Valladolid (Spain)
Marco Riani - University of Parma (Italy)
Abstract: The most widely applied approaches in model-based clustering are based on the maximization of classification and mixture likelihoods. Under standard normal assumptions, these likelihood maximizations are mathematically ill-posed problems without appropriate constraints on the components' scatter matrices. Moreover, non-interesting or ``spurious'' solutions are often detected by traditional CEM and EM algorithms designed for them. This is also the case when robustifying them through the use of trimmed likelihoods. An upper bound on the ratio between the largest and smallest determinants for the components' scatter matrices is apparently a sensible way to overcome those degeneracy troubles. Unfortunately, this type of constraints, although affine equivariant, does not always avoid spurious solutions and, consequently, robustness cannot be guaranteed. On the other hand, we will see how some additionally added constraints on the components shape elements actually serve to cope with those degeneracy issues. The combination of trimming and this new type of constraints results in an (almost) affine equivariant robust model-based clustering approach. A computationally feasible algorithm is proposed for this new approach.