A hierarchical Bayesian language model based on Pitman-Yor processes
ACL-44 Proceedings of the 21st International Conference on Computational Linguistics and the 44th annual meeting of the Association for Computational Linguistics
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
Model-based clustering of high-dimensional data: A review
Computational Statistics & Data Analysis
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A primary challenge in unsupervised clustering using mixture models is the selection of a family of basis distributions flexible enough to succinctly represent the distributions of the target subpopulations. In this paper we introduce a new family of Gaussian well distributions (GWDs) for clustering applications where the target subpopulations are characterized by hollow (hyper-)elliptical structures. We develop the primary theory pertaining to the GWD, including mixtures of GWDs, selection of prior distributions, and computationally efficient inference strategies using Markov chain Monte Carlo. We demonstrate the utility of our approach, as compared to standard Gaussian mixture methods on a synthetic dataset, and exemplify its applicability on an example from immunofluorescence imaging, emphasizing the improved interpretability and parsimony of the GWD-based model.