# Clustering multivariate data using factor analytic Bayesian mixtures with an unknown number of components

@article{Papastamoulis2020ClusteringMD, title={Clustering multivariate data using factor analytic Bayesian mixtures with an unknown number of components}, author={Panagiotis Papastamoulis}, journal={Statistics and Computing}, year={2020}, volume={30}, pages={485-506} }

Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting mixture models yields a simple and efficient way in order to estimate the unknown number of clusters and model parameters by Markov chain Monte Carlo sampling. The present study extends this approach by considering a set of eight parameterizations, giving rise to… Expand

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#### References

SHOWING 1-10 OF 83 REFERENCES

Overfitting Bayesian mixtures of factor analyzers with an unknown number of components

- Computer Science, Mathematics
- Comput. Stat. Data Anal.
- 2018

The applicability of an overfitting mixture of factor analyzers in clustering correlated high dimensional data is demonstrated and the method is benchmarked against state-of-the-art software for maximum likelihood estimation of mixtures of factor Analyzers using an extensive simulation study. Expand

Overfitting Bayesian Mixture Models with an Unknown Number of Components

- Mathematics, Medicine
- PloS one
- 2015

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of… Expand

Model-based clustering based on sparse finite Gaussian mixtures

- Computer Science, Medicine
- Stat. Comput.
- 2016

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… Expand

Identifying Mixtures of Mixtures Using Bayesian Estimation

- Mathematics, Medicine
- Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
- 2017

This work proposes a different approach based on sparse finite mixtures to achieve identifiability within the Bayesian framework, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. Expand

Sparse Bayesian infinite factor models.

- Mathematics, Medicine
- Biometrika
- 2011

This work proposes a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases, and develops an efficient Gibbs sampler that scales well as data dimensionality increases. Expand

Infinite Mixtures of Infinite Factor Analysers

- Mathematics
- 2017

Factor-analytic Gaussian mixture models are often employed as a model-based approach to clustering high-dimensional data. Typically, the numbers of clusters and latent factors must be specified in… Expand

Mixtures of Factor Analysers. Bayesian Estimation and Inference by Stochastic Simulation

- Mathematics, Computer Science
- Machine Learning
- 2004

A Bayesian approach toFactor Analysis is adopted, and more specifically a treatment that bases estimation and inference on the stochastic simulation of the posterior distributions of interest, and can be envisaged as an alternative to the other approaches used for this model. Expand

BayesBinMix: an R Package for Model Based Clustering of Multivariate Binary Data

- Computer Science, Mathematics
- R J.
- 2017

The BayesBinMix package offers a Bayesian framework for clustering binary data with or without missing values by fitting mixtures of multivariate Bernoulli distributions with an unknown number of components using Markov chain Monte Carlo sampling. Expand

Bayesian Modelling and Inference on Mixtures of Distributions

- Computer Science
- 2005

This chapter aims to introduce the prior modeling, estimation, and evaluation of mixture distributions in a Bayesian paradigm, and shows that mixture distributions provide a flexible, parametric framework for statistical modeling and analysis. Expand

Model-based clustering of microarray expression data via latent Gaussian mixture models

- Mathematics, Computer Science
- Bioinform.
- 2010

This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models, which gives very good performance, relative to existing popular clustering techniques, when applied to real gene expression microarray data. Expand