Model-Based Clustering with Nested Gaussian Clusters

Jason Hou-Liu () and Ryan P. Browne ()
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Jason Hou-Liu: 200 University Avenue West
Ryan P. Browne: 200 University Avenue West

Journal of Classification, 2024, vol. 41, issue 1, No 4, 39-64

Abstract: Abstract 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.

Keywords: Intercluster structure; Model-based clustering; Hierarchical structure; Gaussian mixture model (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00357-023-09453-z

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