Title: Robust clustering based on determinants-and-shape constraints
Authors: Luis Angel Garcia-Escudero - Universidad de Valladolid (Spain) [presenting]
Agustin Mayo-Iscar - Universidad de Valladolid (Spain)
Marco Riani - University of Parma (Italy)
Andrea Cerioli - University of Parma (Italy)
Abstract: Model-based clustering mostly relies on the maximization of classification and mixture likelihoods. Trimming principles can be added to these maximum likelihood maximization in order to robustify them. Trimmed adaptions of traditional (classification) EM can be applied with this aim. However, non-interesting or "spurious" clusters, made of few almost collinear observations, can be easily detected when no proper constraints on the components scatter matrices are considered. Therefore, only trimming is not enough and appropriate constraints are required in order to achieve better robustness performance. Establishing an upper bound on the scatter matrices determinant ratio seems to be a sensible idea for constraining scatter matrices by applying an affine equivariant type of constraints. However, degeneracy issues are not fully solved. On the other hand, we will see how some extra mild constraints on the shape matrices elements can be useful in this framework. A computationally feasible algorithm will be presented and the proposed methodology is illustrated through simulations and real data examples.