Stable and visualizable Gaussian parsimonious clustering models

Gaussian mixture model-based clustering is now a standard tool to determine a hypothetical underlying structure in continuous data. However, many usual parsimonious models, despite either their appealing geometrical interpretation or their ability to deal with high dimensional data, suffer from major drawbacks due to scale dependence or unsustainability of the constraints after projection. In this work we present a new family of parsimonious Gaussian models based on a variance-correlation decomposition of the covariance matrices. These new models are stable when projected into the canonical planes and, so, faithfully representable in low dimension. They are also stable by modification of the measurement units of the data and such a modification does not change the model selection based on likelihood criteria. We highlight all these stability properties by a specific graphical representation of each model. A detailed Generalized EM (GEM) algorithm is also provided for every model inference. Then, on biological and geological data, we compare our stable models to standard ones (geometrical models and factor analyzer models), which underlines all the profit to obtain unit-free models.