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Identifying Mixtures of Mixtures Using Bayesian Estimation.

Gertraud Malsiner-Walli1, Sylvia Frühwirth-Schnatter2, Bettina Grün1

  • 1Department of Applied Statistics, Johannes Kepler University, Linz, Austria.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|June 20, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Bayesian approach using sparse finite mixtures for robust cluster analysis. It effectively identifies non-Gaussian clusters and determines the number of clusters without model constraints.

Keywords:
Bayesian nonparametric mixture modelDirichlet priorFinite mixture modelModel-based clusteringNormal gamma priorNumber of components

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Mining

Background:

  • Model-based clustering with finite normal mixtures can capture complex data structures.
  • Identifying clusters and their parameters from normal components is often challenging, requiring constraints or post-processing.
  • Existing methods struggle with simultaneous cluster number determination, flexible distribution approximation, and parameter identification.

Purpose of the Study:

  • To propose a Bayesian framework for identifiable cluster analysis using sparse finite mixtures.
  • To develop a method that simultaneously determines the number of clusters, approximates cluster distributions, and identifies cluster-specific parameters.
  • To enable flexible semiparametric approximation of cluster distributions using finite mixtures of normals.

Main Methods:

  • Utilizing a Bayesian framework with sparse finite mixtures for inherent identifiability.
  • Specifying a hierarchical prior with carefully selected hyperparameters to reflect cluster structure.
  • Employing standard Markov Chain Monte Carlo (MCMC) sampling methods for model estimation.
  • Integrating a post-processing step to resolve label switching and ensure model identification.

Main Results:

  • The proposed sparse finite mixture model achieves identifiability without imposing constraints on model parameters.
  • The approach successfully determines the number of clusters, approximates distributions semiparametrically, and identifies cluster-specific parameters.
  • Demonstrated effectiveness through simulation studies and on benchmark datasets, validating the method's performance.

Conclusions:

  • The Bayesian sparse finite mixture approach offers a robust and identifiable solution for model-based clustering.
  • This method provides a flexible and simultaneous approach to cluster number determination, distribution approximation, and parameter estimation.
  • The proposed technique enhances cluster analysis by addressing identifiability and label switching issues effectively.