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Mixtures of Gaussian wells: Theory, computation, and application

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  • Manolopoulou, Ioanna
  • Kepler, Thomas B.
  • Merl, Daniel M.

Abstract

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.

Suggested Citation

  • Manolopoulou, Ioanna & Kepler, Thomas B. & Merl, Daniel M., 2012. "Mixtures of Gaussian wells: Theory, computation, and application," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3809-3820.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:3809-3820
    DOI: 10.1016/j.csda.2012.03.027
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    References listed on IDEAS

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    1. Kanatani, Kenichi & Rangarajan, Prasanna, 2011. "Hyper least squares fitting of circles and ellipses," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2197-2208, June.
    2. Shogo Kato, 2010. "A Markov process for circular data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 655-672, November.
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    Cited by:

    1. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.

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