Handling missing data in complex phenomena: an ultrametric model-based approach for clustering

In the model-based clustering literature, we find several methodologies to study latent structures underlying the data, among which mixtures of factor analyzers. However, none of them can detect hierarchical relationships among latent variables. The Ultrametric Gaussian Mixture Model (UGMM) is intended to reach this goal by identifying a hierarchy of variables, starting by partitioning the variables into a reduced number of groups per mixture component. Nonetheless, up to now, it requires complete observations, which is often not the case in real data collections. In this paper, we propose the extension of UGMM in the missing data framework. The proposal is applied to a real data set for inspecting the relationships among features of songs of different genres.