Methods for merging Gaussian mixture components

The problem of merging Gaussian mixture components is discussed in situations where a Gaussian mixture is fitted but the mixture components are not separated enough from each other to interpret them as “clusters”. The problem of merging Gaussian mixtures is not statistically identifiable, therefore merging algorithms have to be based on subjective cluster concepts. Cluster concepts based on unimodality and misclassification probabilities (“patterns”) are distinguished. Several different hierarchical merging methods are proposed for different cluster concepts, based on the ridgeline analysis of modality of Gaussian mixtures, the dip test, the Bhattacharyya dissimilarity, a direct estimator of misclassification and the strength of predicting pairwise cluster memberships. The methods are compared by a simulation study and application to two real datasets. A new visualisation method of the separation of Gaussian mixture components, the ordered posterior plot, is also introduced.