Model-Based Clustering with Nested Gaussian Clusters

• Published in: Journal of classification Vol. 41; no. 1; pp. 39 - 64
• Main Authors: Hou-Liu, Jason, Browne, Ryan P.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-03-2024; Springer Nature B.V
• Subjects: Algorithms; Bioinformatics; Clustering; Datasets; Labels; Marketing; Mathematics and Statistics; Original Research; Pattern Recognition; Psychometrics; Signal,Image and Speech Processing; Statistical Theory and Methods; Statistics; Subspaces; Intercluster structure; Gaussian mixture model; Model-based clustering; Hierarchical structure
• ISSN: 0176-4268; 1432-1343
• DOI: 10.1007/s00357-023-09453-z

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.