# Model-based clustering based on sparse finite Gaussian mixtures

arXiv: https://arxiv.org/abs/1606.06828 · HTML: https://mlsanity.com/paper/1606.06828/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2016.

## Built on by (most cited first, 11 of 11)

- [On the intrinsic dimensionality of Covid-19 data: a global perspective](https://mlsanity.com/paper/2203.04165/) (2022)
- [VICatMix: variational Bayesian clustering and variable selection for discrete biomedical data](https://mlsanity.com/paper/2406.16227/) (2024)
- [Federated Variational Inference for Bayesian Mixture Models](https://mlsanity.com/paper/2502.12684/) (2025)
- [Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles](https://mlsanity.com/paper/2507.01542/) (2025)
- [Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport](https://mlsanity.com/paper/2609.16622/) (2026)
- [Clustering of longitudinal data: A tutorial on a variety of approaches](https://mlsanity.com/paper/2111.05469/) (2021)
- [Modeling Random Networks with Heterogeneous Reciprocity](https://mlsanity.com/paper/2308.10113/) (2023)
- [Variational Markov chain mixtures with automatic component selection](https://mlsanity.com/paper/2406.04653/) (2024)
- [Bayesian temporal biclustering with applications to multi-subject neuroscience studies](https://mlsanity.com/paper/2406.17131/) (2024)
- [DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting](https://mlsanity.com/paper/2607.10912/) (2026)
- [Amortized Bandwidth Learning for Kernel Density Estimation under Logarithmic Score](https://mlsanity.com/paper/2608.20445/) (2026)

## Abstract (arXiv)

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 K-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.