An Efficient Model Selection for Gaussian Mixture Model in a Bayesian Framework

TL;DR

This paper introduces a fast Bayesian model selection algorithm for Gaussian Mixture Models that effectively estimates the number of components, overcoming limitations of traditional criteria like AIC and BIC.

Contribution

It proposes a novel algorithm that accurately reconstructs the model order density in a Bayesian framework, outperforming existing methods in speed and reliability.

Findings

Reconstructs model order density where AIC and BIC fail.

Faster than Monte Carlo simulation for model selection.

Effective in determining the number of Gaussian components.

Abstract

In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of $\hat{K}$ Gaussian component densities. However, model selection to find underlying $\hat{K}$ is one of the key concerns in GMM clustering, since we can obtain the desired clusters only when $\hat{K}$ is known. In this paper, we propose a new model selection algorithm to explore $\hat{K}$ in a Bayesian framework. The proposed algorithm builds the density of the model order which any information criterions such as AIC and BIC basically fail to reconstruct. In addition, this algorithm reconstructs the density quickly as compared to the time-consuming Monte Carlo simulation.