Model-based clustering based on sparse finite Gaussian mixtures View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-01

AUTHORS

Gertraud Malsiner-Walli, Sylvia Frühwirth-Schnatter, Bettina 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 it to benchmark data sets. More... »

PAGES

303-324

References to SciGraph publications

  • 2010-02. Latent class analysis variable selection in ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
  • 2010-04. Methods for merging Gaussian mixture components in ADVANCES IN DATA ANALYSIS AND CLASSIFICATION
  • 2002. Modern Applied Statistics with S in NONE
  • 2006-01. Multivariate mixtures of normals with unknown number of components in STATISTICS AND COMPUTING
  • 1998. Bayesian Inference for Mixture: The Label Switching Problem in COMPSTAT
  • 2010-07. Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models in STATISTICS AND COMPUTING
  • 1997-03. Inference in model-based cluster analysis in STATISTICS AND COMPUTING
  • 2011-12. Panel data analysis: a survey on model-based clustering of time series in ADVANCES IN DATA ANALYSIS AND CLASSIFICATION
  • 2014-03. Finite mixtures of multivariate skew t-distributions: some recent and new results in STATISTICS AND COMPUTING
  • 2008-09. Parsimonious Gaussian mixture models in STATISTICS AND COMPUTING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11222-014-9500-2

    DOI

    http://dx.doi.org/10.1007/s11222-014-9500-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1003696325

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/26900266


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