Aggregating Gaussian mixture components

The finite mixture of Gaussians is a well-known model frequently used to classify a sample of observations. It considers the sample as drawn from a heterogeneous population where each subpopulation, cluster, is Gaussian and corresponds to one component of the mixture. Whenever such assumption is false, the model may use two or more Gaussians to describe a single cluster. In this case, the researcher has the problem of how to identify the clusters starting from the estimated components. This work proposes to solve this problem by aggregating the components in clusters by optimizing an appropriate criterion based on their posterior probabilities.