mclust (version 5.0.2)

Mclust: Model-Based Clustering

Description

The optimal model according to BIC for EM initialized by hierarchical clustering for parameterized Gaussian mixture models.

Usage

Mclust(data, G = NULL, modelNames = NULL, 
       prior = NULL, 
       control = emControl(), 
       initialization = NULL, 
       warn = mclust.options("warn"), ...)

Arguments

data

A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables.

G

An integer vector specifying the numbers of mixture components (clusters) for which the BIC is to be calculated. The default is G=1:9.

modelNames

A vector of character strings indicating the models to be fitted in the EM phase of clustering. The default is: ll{ for univariate data c("E", "V") for multivariate data ($n > d$) mclust.options("emMod

prior

The default assumes no prior, but this argument allows specification of a conjugate prior on the means and variances through the function priorControl.

control

A list of control parameters for EM. The defaults are set by the call emControl().

initialization

A list containing zero or more of the following components: [object Object],[object Object],[object Object]

warn

A logical value indicating whether or not certain warnings (usually related to singularity) should be issued. The default is controlled by mclust.options.

...

Catches unused arguments in indirect or list calls via do.call.

Value

• An object of class 'Mclust' providing the optimal (according to BIC) mixture model estimation. The details of the output components are as follows:
• call
  The matched call
• data
  The input data matrix.
• modelName
  A character string denoting the model at which the optimal BIC occurs.
• n
  The number of observations in the data.
• d
  The dimension of the data.
• G
  The optimal number of mixture components.
• BIC
  All BIC values.
• bic
  Optimal BIC value.
• loglik
  The loglikelihood corresponding to the optimal BIC.
• df
  The number of estimated parameters.
• hypvol
  The hypervolume parameter for the noise component if required, otherwise set to NULL (see hypvol).
• parameters
  A list with the following components: [object Object],[object Object],[object Object]
• z
  A matrix whose [i,k]th entry is the probability that observation i in the test data belongs to the kth class.
• classification
  The classification corresponding to z, i.e. map(z).
• uncertainty
  The uncertainty associated with the classification.

References

C. Fraley, A. E. Raftery, T. B. Murphy and L. Scrucca (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington. C. Fraley and A. E. Raftery (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611:631.

C. Fraley and A. E. Raftery (2005, revised 2009). Bayesian regularization for normal mixture estimation and model-based clustering. Technical Report, Department of Statistics, University of Washington.

C. Fraley and A. E. Raftery (2007). Bayesian regularization for normal mixture estimation and model-based clustering. Journal of Classification 24:155-181.

See Also

summary.Mclust, plot.Mclust, priorControl, emControl, hc, mclustBIC, mclustModelNames, mclust.options

Examples

mod1 = Mclust(iris[,1:4])
summary(mod1)

mod2 = Mclust(iris[,1:4], G = 3)
summary(mod2, parameters = TRUE)

# Using prior
mod3 = Mclust(iris[,1:4], prior = priorControl())
summary(mod3)

mod4 = Mclust(iris[,1:4], prior = priorControl(functionName="defaultPrior", shrinkage=0.1))
summary(mod4)

# Clustering of faithful data with some artificial noise added 
nNoise = 100
set.seed(0) # to make it reproducible
Noise = apply(faithful, 2, function(x) 
                           runif(nNoise, min = min(x)-.1, max = max(x)+.1))
data = rbind(faithful, Noise)
plot(faithful)
points(Noise, pch = 20, cex = 0.5, col = "lightgrey")
set.seed(0)
NoiseInit = sample(c(TRUE,FALSE), size = nrow(faithful)+nNoise, 
                   replace = TRUE, prob = c(3,1)/4)
mod5 = Mclust(data, initialization = list(noise = NoiseInit))
summary(mod5, parameter = TRUE)
plot(mod5, what = "classification")