Mode merging for the finite mixture of t‐distributions

Abstract

Finite mixture models can be interpreted as a model representing heterogeneous subpopulations within the whole population. However, more care is needed when associating a mixture component with a cluster, because a mixture model may fit more components than the number of clusters. Modal merging via the mean shift algorithm can help identify such multicomponent clusters. So far, most of the related works are focused on the Gaussian finite mixture. As the non‐Gaussian finite mixture models are gaining attention, the need to address the component‐cluster correspondence issue in these mixture models grows. Thus, we introduce a mode merging method via the mean shift for the finite mixture of t‐distributions and its parsimonious variants. It can be framed as an expectation–maximization algorithm and enjoys similar theoretical properties as the mean shift for the Gaussian finite mixture. The performance of our method is demonstrated via simulated and real data experiments, where it shows a competitive performance against some of the existing methods.