Model-based clustering based on sparse finite Gaussian mixtures

Statistics and Computing
Gertraud Malsiner-WalliBettina Grün

Abstract

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using [Formula: see text]-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying i...Continue Reading

References

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Citations

Jan 12, 2020·Annals of Neurology·Rick van der VlietGert Kwakkel
Sep 22, 2020·Journal of the American Statistical Association·Briana J K StephensonAndrew Olshan
Jun 20, 2017·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Gertraud Malsiner-WalliBettina Grün
Apr 23, 2019·Advances in Data Analysis and Classification·Sylvia Frühwirth-Schnatter, Gertraud Malsiner-Walli
Feb 5, 2021·Daru : Journal of Faculty of Pharmacy, Tehran University of Medical Sciences·Silvijus AbramavičiusEdgaras Stankevičius
Oct 16, 2021·Psychometrika·Minjung KyungJi Yeh Choi

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Software Mentioned

R package
RJMCMC
R package PReMiuM
PReMiuM

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