ABSTRACT
A new methodology for constrained parsimonious model-based clustering is introduced, where some tuning parameter allows to control the strength of these constraints. The methodology includes the 14 parsimonious models that are often applied in model-based clustering when assuming normal components as limit cases. This is done in a natural way by filling the gap among models and providing a smooth transition among them. The methodology provides mathematically well-defined problems and is also useful to prevent us from obtaining spurious solutions. Novel information criteria are proposed to help the user in choosing parameters. The interest of the proposed methodology is illustrated through simulation studies and a real-data application on COVID data.