Identifying Mixtures of Mixtures Using Bayesian Estimation

TL;DR

This paper introduces a Bayesian method using sparse finite mixtures and hierarchical priors to identify and classify clusters in non-Gaussian data, overcoming traditional challenges in mixture model identifiability.

Contribution

It proposes a novel Bayesian approach with hierarchical priors and post-processing to simultaneously determine the number of clusters and identify cluster-specific parameters.

Findings

Successfully determines the number of clusters in simulations and benchmark data

Accurately estimates cluster-specific parameters and classifications

Outperforms traditional methods in cluster identifiability

Abstract

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition this prior allows to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semi-parametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark data sets.