Model-Based Clustering with Nested Gaussian Clusters

A dataset may exhibit multiple class labels for each observation; sometimes, these class labels manifest in a hierarchical structure. A textbook analogy would be that a book can be labelled as statistics as well as the encompassing label of non-fiction. To capture this behaviour in a model-based clustering context, we describe a model formulation and estimation procedure for performing clustering with nested Gaussian clusters in orthogonal intrinsic variable subspaces. We elucidate a two-stage clustering model, whereby the observed manifest variables are assumed to be a rotation of intrinsic primary and secondary clustering subspaces with additional noise subspaces. In a hierarchical sense, secondary clusters are presumed to be subclusters of primary clusters and so share Gaussian cluster parameters in the primary cluster subspace. An estimation procedure using the expectation-maximization algorithm is provided, with model selection via Bayesian information criterion. Real-world datasets are evaluated under the proposed model.

Automated summary

In this paper, a model formulation and estimation procedure for clustering with nested Gaussian clusters in orthogonal intrinsic variable subspaces are described. The model considers observed variables to be rotations of intrinsic primary and secondary clustering subspaces with additional noise subspaces. An estimation procedure using the expectation-maximization algorithm is provided with model selection via Bayesian information criterion.