# Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

## Documentation for package ‘mclust’ version 6.1.2

- DESCRIPTION file
- User guides, package vignettes and other documentation
- Package NEWS

## Help Pages

A B C D E G H I L M N P Q R S T U W

mclust-package | Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

## -- A --

acidity | Acidity data
adjustedRandIndex | Adjusted Rand Index
as.hclust.hc | Model-based Agglomerative Hierarchical Clustering

## -- B --

banknote | Swiss banknotes data
Baudry_etal_2010_JCGS_examples | Simulated Example Datasets From Baudry et al. (2010)
bic | BIC for Parameterized Gaussian Mixture Models
bicEMtrain | Deprecated Functions in mclust package
BrierScore | Brier score to assess the accuracy of probabilistic predictions

## -- C --

cdens | Component Density for Parameterized MVN Mixture Models
cdensE | Component Density for a Parameterized MVN Mixture Model
cdensEEE | Component Density for a Parameterized MVN Mixture Model
cdensEEI | Component Density for a Parameterized MVN Mixture Model
cdensEEV | Component Density for a Parameterized MVN Mixture Model
cdensEII | Component Density for a Parameterized MVN Mixture Model
cdensEVE | Component Density for a Parameterized MVN Mixture Model
cdensEVI | Component Density for a Parameterized MVN Mixture Model
cdensEVV | Component Density for a Parameterized MVN Mixture Model
cdensV | Component Density for a Parameterized MVN Mixture Model
cdensVEE | Component Density for a Parameterized MVN Mixture Model
cdensVEI | Component Density for a Parameterized MVN Mixture Model
cdensVEV | Component Density for a Parameterized MVN Mixture Model
cdensVII | Component Density for a Parameterized MVN Mixture Model
cdensVVE | Component Density for a Parameterized MVN Mixture Model
cdensVVI | Component Density for a Parameterized MVN Mixture Model
cdensVVV | Component Density for a Parameterized MVN Mixture Model
cdensX | Component Density for a Parameterized MVN Mixture Model
cdensXII | Component Density for a Parameterized MVN Mixture Model
cdensXXI | Component Density for a Parameterized MVN Mixture Model
cdensXXX | Component Density for a Parameterized MVN Mixture Model
cdfMclust | Cumulative Distribution and Quantiles for a univariate Gaussian mixture distribution
chevron | Simulated minefield data
classError | Classification error
classPriorProbs | Estimation of class prior probabilities by EM algorithm
clPairs | Pairwise Scatter Plots showing Classification
clPairsLegend | Pairwise Scatter Plots showing Classification
clustCombi | Combining Gaussian Mixture Components for Clustering
clustCombiOptim | Optimal number of clusters obtained by combining mixture components
combiPlot | Plot Classifications Corresponding to Successive Combined Solutions
combiTree | Tree structure obtained from combining mixture components
combMat | Combining Matrix
coordProj | Coordinate projections of multidimensional data modeled by an MVN mixture.
covw | Weighted means, covariance and scattering matrices conditioning on a weighted matrix
crimcoords | Discriminant coordinates data projection
cross | Simulated Cross Data
cv.MclustDA | Deprecated Functions in mclust package
cv1EMtrain | Deprecated Functions in mclust package
cvMclustDA | MclustDA cross-validation

## -- D --

decomp2sigma | Convert mixture component covariances to matrix form
defaultPrior | Default conjugate prior for Gaussian mixtures
dens | Density for Parameterized MVN Mixtures
densityMclust | Density Estimation via Model-Based Clustering
densityMclust.diagnostic | Diagnostic plots for 'mclustDensity' estimation
diabetes | Diabetes Data (flawed)
dmvnorm | Density of multivariate Gaussian distribution
dupPartition | Partition the data by grouping together duplicated data

## -- E --

em | EM algorithm starting with E-step for parameterized Gaussian mixture models
EMclust | BIC for Model-Based Clustering
emControl | Set control values for use with the EM algorithm
emE | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEEE | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEEI | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEEV | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEII | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEVE | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEVI | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emEVV | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emV | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVEE | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVEI | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVEV | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVII | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVVE | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVVI | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emVVV | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emX | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emXII | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emXXI | EM algorithm starting with E-step for a parameterized Gaussian mixture model
emXXX | EM algorithm starting with E-step for a parameterized Gaussian mixture model
entPlot | Plot Entropy Plots
errorBars | Draw error bars on a plot
estep | E-step for parameterized Gaussian mixture models.
estepE | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEEE | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEEI | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEEV | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEII | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEVE | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEVI | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepEVV | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepV | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVEE | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVEI | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVEV | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVII | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVVE | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVVI | E-step in the EM algorithm for a parameterized Gaussian mixture model.
estepVVV | E-step in the EM algorithm for a parameterized Gaussian mixture model.
EuroUnemployment | Unemployment data for European countries in 2014
ex4.1 | Simulated Example Datasets From Baudry et al. (2010)
ex4.2 | Simulated Example Datasets From Baudry et al. (2010)
ex4.3 | Simulated Example Datasets From Baudry et al. (2010)
ex4.4.1 | Simulated Example Datasets From Baudry et al. (2010)
ex4.4.2 | Simulated Example Datasets From Baudry et al. (2010)

## -- G --

gmmhd | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
gmmhdClassify | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
gmmhdClusterCores | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
GvHD | GvHD Dataset
GvHD.control | GvHD Dataset
GvHD.pos | GvHD Dataset

## -- H --

hc | Model-based Agglomerative Hierarchical Clustering
hcE | Model-based Hierarchical Clustering
hcEEE | Model-based Hierarchical Clustering
hcEII | Model-based Hierarchical Clustering
hclass | Classifications from Hierarchical Agglomeration
hcRandomPairs | Random hierarchical structure
hcV | Model-based Hierarchical Clustering
hcVII | Model-based Hierarchical Clustering
hcVVV | Model-based Hierarchical Clustering
hdrlevels | Highest Density Region (HDR) Levels
hypvol | Aproximate Hypervolume for Multivariate Data

## -- I --

icl | ICL for an estimated Gaussian Mixture Model
imputeData | Missing data imputation via the 'mix' package
imputePairs | Pairwise Scatter Plots showing Missing Data Imputations

## -- L --

logLik.Mclust | Log-Likelihood of a 'Mclust' object
logLik.MclustDA | Log-Likelihood of a 'MclustDA' object
logsumexp | Log sum of exponentials

## -- M --

majorityVote | Majority vote
map | Classification given Probabilities
mapClass | Correspondence between classifications
matchCluster | Missing data imputation via the 'mix' package
Mclust | Model-Based Clustering
mclust | Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation
mclust.options | Default values for use with MCLUST package
mclust1Dplot | Plot one-dimensional data modeled by an MVN mixture.
mclust2Dplot | Plot two-dimensional data modelled by an MVN mixture
mclustBIC | BIC for Model-Based Clustering
mclustBICupdate | Update BIC values for parameterized Gaussian mixture models
MclustBootstrap | Resampling-based Inference for Gaussian finite mixture models
mclustBootstrapLRT | Bootstrap Likelihood Ratio Test for the Number of Mixture Components
MclustDA | MclustDA discriminant analysis
MclustDR | Dimension reduction for model-based clustering and classification
MclustDRrecoverdir | Subset selection for GMMDR directions based on BIC
MclustDRsubsel | Subset selection for GMMDR directions based on BIC
MclustDRsubsel1cycle | Subset selection for GMMDR directions based on BIC
MclustDRsubsel_classif | Subset selection for GMMDR directions based on BIC
MclustDRsubsel_cluster | Subset selection for GMMDR directions based on BIC
mclustICL | ICL Criterion for Model-Based Clustering
mclustLoglik | Log-likelihood from a table of BIC values for parameterized Gaussian mixture models
mclustModel | Best model based on BIC
mclustModelNames | MCLUST Model Names
MclustSSC | MclustSSC semi-supervised classification
mclustVariance | Template for variance specification for parameterized Gaussian mixture models
me | EM algorithm starting with M-step for parameterized MVN mixture models
me.weighted | EM algorithm with weights starting with M-step for parameterized Gaussian mixture models
meE | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEEE | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEEI | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEEV | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEII | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEVE | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEVI | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meEVV | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meV | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVEE | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVEI | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVEV | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVII | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVVE | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVVI | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meVVV | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meX | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meXII | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meXXI | EM algorithm starting with M-step for a parameterized Gaussian mixture model
meXXX | EM algorithm starting with M-step for a parameterized Gaussian mixture model
mstep | M-step for parameterized Gaussian mixture models
mstepE | M-step for a parameterized Gaussian mixture model
mstepEEE | M-step for a parameterized Gaussian mixture model
mstepEEI | M-step for a parameterized Gaussian mixture model
mstepEEV | M-step for a parameterized Gaussian mixture model
mstepEII | M-step for a parameterized Gaussian mixture model
mstepEVE | M-step for a parameterized Gaussian mixture model
mstepEVI | M-step for a parameterized Gaussian mixture model
mstepEVV | M-step for a parameterized Gaussian mixture model
mstepV | M-step for a parameterized Gaussian mixture model
mstepVEE | M-step for a parameterized Gaussian mixture model
mstepVEI | M-step for a parameterized Gaussian mixture model
mstepVEV | M-step for a parameterized Gaussian mixture model
mstepVII | M-step for a parameterized Gaussian mixture model
mstepVVE | M-step for a parameterized Gaussian mixture model
mstepVVI | M-step for a parameterized Gaussian mixture model
mstepVVV | M-step for a parameterized Gaussian mixture model
mvn | Univariate or Multivariate Normal Fit
mvnX | Univariate or Multivariate Normal Fit
mvnXII | Univariate or Multivariate Normal Fit
mvnXXI | Univariate or Multivariate Normal Fit
mvnXXX | Univariate or Multivariate Normal Fit

## -- N --

nMclustParams | Number of Estimated Parameters in Gaussian Mixture Models
nVarParams | Number of Variance Parameters in Gaussian Mixture Models

## -- P --

partconv | Numeric Encoding of a Partitioning
partuniq | Classifies Data According to Unique Observations
plot.clustCombi | Plot Combined Clusterings Results
plot.crimcoords | Discriminant coordinates data projection
plot.densityMclust | Plots for Mixture-Based Density Estimate
plot.gmmhd | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
plot.hc | Dendrograms for Model-based Agglomerative Hierarchical Clustering
plot.Mclust | Plotting method for Mclust model-based clustering
plot.mclustBIC | BIC Plot for Model-Based Clustering
plot.MclustBootstrap | Plot of bootstrap distributions for mixture model parameters
plot.mclustBootstrapLRT | Bootstrap Likelihood Ratio Test for the Number of Mixture Components
plot.MclustDA | Plotting method for MclustDA discriminant analysis
plot.MclustDR | Plotting method for dimension reduction for model-based clustering and classification
plot.mclustICL | ICL Plot for Model-Based Clustering
plot.MclustSSC | Plotting method for MclustSSC semi-supervised classification
plotDensityMclust1 | Plots for Mixture-Based Density Estimate
plotDensityMclust2 | Plots for Mixture-Based Density Estimate
plotDensityMclustd | Plots for Mixture-Based Density Estimate
plotEvalues.MclustDR | Plotting method for dimension reduction for model-based clustering and classification
predict.densityMclust | Density estimate of multivariate observations by Gaussian finite mixture modeling
predict.Mclust | Cluster multivariate observations by Gaussian finite mixture modeling
predict.MclustDA | Classify multivariate observations by Gaussian finite mixture modeling
predict.MclustDR | Classify multivariate observations on a dimension reduced subspace by Gaussian finite mixture modeling
predict.MclustSSC | Classification of multivariate observations by semi-supervised Gaussian finite mixtures
predict2D.MclustDR | Classify multivariate observations on a dimension reduced subspace by Gaussian finite mixture modeling
print.clustCombi | Combining Gaussian Mixture Components for Clustering
print.crimcoords | Discriminant coordinates data projection
print.gmmhd | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
print.hc | Model-based Agglomerative Hierarchical Clustering
print.Mclust | Model-Based Clustering
print.mclustBIC | BIC for Model-Based Clustering
print.MclustBootstrap | Resampling-based Inference for Gaussian finite mixture models
print.mclustBootstrapLRT | Bootstrap Likelihood Ratio Test for the Number of Mixture Components
print.MclustDA | MclustDA discriminant analysis
print.MclustDR | Dimension reduction for model-based clustering and classification
print.MclustDRsubsel | Subset selection for GMMDR directions based on BIC
print.mclustICL | ICL Criterion for Model-Based Clustering
print.mclustLoglik | Log-likelihood from a table of BIC values for parameterized Gaussian mixture models
print.MclustSSC | MclustSSC semi-supervised classification
print.summary.clustCombi | Combining Gaussian Mixture Components for Clustering
print.summary.crimcoords | Discriminant coordinates data projection
print.summary.gmmhd | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
print.summary.Mclust | Summarizing Gaussian Finite Mixture Model Fits
print.summary.mclustBIC | Summary function for model-based clustering via BIC
print.summary.MclustBootstrap | Summary Function for Bootstrap Inference for Gaussian Finite Mixture Models
print.summary.MclustDA | Summarizing discriminant analysis based on Gaussian finite mixture modeling
print.summary.MclustDR | Summarizing dimension reduction method for model-based clustering and classification
print.summary.mclustICL | ICL Criterion for Model-Based Clustering
print.summary.MclustSSC | Summarizing semi-supervised classification model based on Gaussian finite mixtures
printSummaryMclustBIC | Summary function for model-based clustering via BIC
printSummaryMclustBICn | Summary function for model-based clustering via BIC
priorControl | Conjugate Prior for Gaussian Mixtures.

## -- Q --

quantileMclust | Cumulative Distribution and Quantiles for a univariate Gaussian mixture distribution

## -- R --

randomOrthogonalMatrix | Random orthogonal matrix
randomPairs | Random hierarchical structure
randProj | Random projections of multidimensional data modeled by an MVN mixture

## -- S --

sigma2decomp | Convert mixture component covariances to decomposition form.
sim | Simulate from Parameterized MVN Mixture Models
simE | Simulate from a Parameterized MVN Mixture Model
simEEE | Simulate from a Parameterized MVN Mixture Model
simEEI | Simulate from a Parameterized MVN Mixture Model
simEEV | Simulate from a Parameterized MVN Mixture Model
simEII | Simulate from a Parameterized MVN Mixture Model
simEVE | Simulate from a Parameterized MVN Mixture Model
simEVI | Simulate from a Parameterized MVN Mixture Model
simEVV | Simulate from a Parameterized MVN Mixture Model
simV | Simulate from a Parameterized MVN Mixture Model
simVEE | Simulate from a Parameterized MVN Mixture Model
simVEI | Simulate from a Parameterized MVN Mixture Model
simVEV | Simulate from a Parameterized MVN Mixture Model
simVII | Simulate from a Parameterized MVN Mixture Model
simVVE | Simulate from a Parameterized MVN Mixture Model
simVVI | Simulate from a Parameterized MVN Mixture Model
simVVV | Simulate from a Parameterized MVN Mixture Model
softmax | Softmax function
summary.clustCombi | Combining Gaussian Mixture Components for Clustering
summary.crimcoords | Discriminant coordinates data projection
summary.gmmhd | Identifying Connected Components in Gaussian Finite Mixture Models for Clustering
summary.Mclust | Summarizing Gaussian Finite Mixture Model Fits
summary.mclustBIC | Summary function for model-based clustering via BIC
summary.MclustBootstrap | Summary Function for Bootstrap Inference for Gaussian Finite Mixture Models
summary.MclustDA | Summarizing discriminant analysis based on Gaussian finite mixture modeling
summary.MclustDR | Summarizing dimension reduction method for model-based clustering and classification
summary.MclustDRsubsel | Subset selection for GMMDR directions based on BIC
summary.mclustICL | ICL Criterion for Model-Based Clustering
summary.MclustSSC | Summarizing semi-supervised classification model based on Gaussian finite mixtures
summaryMclustBIC | Summary function for model-based clustering via BIC
summaryMclustBICn | Summary function for model-based clustering via BIC
surfacePlot | Density or uncertainty surface for bivariate mixtures

## -- T --

Test1D | Simulated Example Datasets From Baudry et al. (2010)
thyroid | UCI Thyroid Gland Data

## -- U --

uncerPlot | Uncertainty Plot for Model-Based Clustering
unmap | Indicator Variables given Classification

## -- W --

wdbc | UCI Wisconsin Diagnostic Breast Cancer Data
wreath | Data Simulated from a 14-Component Mixture