mclust

mclust is an R package for model-based clustering, classification, and density estimation based on finite Gaussian mixture models. Developed by Fraley and Raftery, it provides a principled approach to uncover structure in multivariate data by assuming that observations come from a mixture of Gaussian distributions with distinct parameters.

A core feature of mclust is its use of the Expectation-Maximization algorithm to fit Gaussian mixture models and to select among models using the Bayesian Information Criterion (BIC). The package offers a family of models that differ in how they constrain covariance matrices, spanning from simple spherical clusters to more flexible ellipsoidal shapes with varying volume, shape, and orientation. These covariance structures are commonly labeled by model names such as EII, VII, EEE, VVV, and related variants, representing different parameter restrictions.

The primary function, Mclust, fits models across a range of cluster numbers and parameterizations, returning the best model with estimated parameters, cluster assignments, posterior probabilities, and BIC values. For supervised analysis, MclustDA performs discriminant analysis using a model-based framework. In addition to clustering and classification, mclust provides density estimation from the fitted mixture model and visualization tools, including plots of BIC curves, classification assignments, and uncertainty in cluster membership.

mclust is available on CRAN and is widely cited in statistical and data-analytic workflows for tasks such as exploratory clustering, density estimation, and predictive classification. It is implemented in R and commonly used in applications requiring probabilistic clustering with explicit model interpretation.