Model-based clustering based on sparse finite Gaussian mixtures.

Area of Science:

• Statistics
• Machine Learning
• Computational Statistics

Background:

• Finite mixture models are widely used for clustering.
• Determining the optimal number of components and relevant variables remains challenging.
• Existing methods often require separate steps for component estimation and variable selection.

Purpose of the Study:

• To develop a unified Bayesian approach for simultaneous estimation of mixture components and cluster-relevant variables.
• To obtain an identified model for Gaussian mixture clustering.
• To improve parameter estimation and variable selection accuracy.

Main Methods:

• Utilizing sparse hierarchical priors on mixture weights and component means.
• Employing Markov Chain Monte Carlo (MCMC) methods with data augmentation and Gibbs sampling.
• Applying k-centroids cluster analysis with Mahalanobis distance for model identification.

Main Results:

• Sparse priors effectively remove superfluous components during MCMC sampling.
• The normal gamma prior enhances parameter estimates and identifies cluster-relevant variables.
• A straightforward estimator for the number of components is derived from MCMC sampling frequencies.

Conclusions:

• The proposed joint Bayesian approach offers a robust framework for Gaussian mixture model-based clustering.
• Simultaneous estimation of components and variables leads to more accurate and interpretable results.
• The method demonstrates effectiveness in simulation studies and on benchmark datasets.