pmln {leptokurticMixture}

Parsimonious model-based clustering with the multivariate elliptical leptokurtic-normal

Description

Performs parsimonious clustering with the multivariate elliptical leptokurtic-normal (MLN). There are 14 possible scale matrix structure and 2 for the kurtosis parameter for a total of 28 models.

Usage

pmln(
  data = NULL,
  G = 1:3,
  covModels = NULL,
  betaModels = "B",
  kml = c(1, 0, 1),
  label = NULL,
  scale.data = TRUE,
  veo = FALSE,
  iterMax = 1000,
  tol = 1e-08,
  pprogress = FALSE,
  method = "FP"
)

Arguments

data

A n x p matrix of observations.

G

A integer determine the number of components of the mixture model.

covModels

if NULL fit 14 possible scale matrix structures. Otherwise a character vector where each element has length 3. e.g. c("VVV", "EEE") A character of length 4 such as "VVVV", indicating the model; the covariance and beta parameters. The 1st position controls, lambda, the volume; "V" varying across components or "E" equal across components. The 2nd position controls the eigenvalues; V" varying across components, "E" equal across components or "I" the identity matrix. The 3rd position controls the orientation; "V" varying across components, "E" equal across components or "I" the identity matrix.

betaModels

set to "V", "E", "B", "F". "V" varying across components, "E" equal across components, "B" consider both "V" & "E", "F" fixed at the maximum value.

kml

a vector of length 3 indicating, the number of k-means starts, number of random starts and the number of EM iterations used for each start

label

If NULL then the data has no known groups. If is.integer then some of the observations have known groups. If label[i]=k then observation belongs to group k. If label[i]=0 then observation has no known group.

scale.data

Should the data be scaled before clustering. The default is TRUE.

veo

"Variables exceed observations". If TRUE, fit the model even though the number variables in the model exceeds the number of observations.

iterMax

The maximum number of EM iterations for each model fitted.

tol

The tol for the stopping rule; lack of progress. The default is 1e-6 but it depends on the data set.

pprogress

If TRUE print the progress of the function.

method

If FP use the fixed point iteration method otherwise if MM use the MM method.

Value

A list of

• startobject - A statement on how the models were initialized

• gpar - A list of parameter values for the model choosen by the BIC

• loglik - A vector of the log-likelihoods values

• z - A n x G matrix of the posterior probabilities from the model choosen by the BIC

• map - A vector the maximum a posteriori derived from z

• BIC - An array with dimensions (G, number of fitted models, 3). The last dimension indices the loglik, number of free parameters and BIC for each fitted model.

• bicModel - Information as list on the model choosen by the BIC.

Examples

x1 = rmln(n=100, d=4, mu=rep(5,4), diag(4), beta=2)
x2 = rmln(n=100, d=4, mu=rep(-5,4), diag(4), beta=2)
x = rbind( x1,x2)
mlnFit = pmln(data=x, G=2, covModels=c("VVV", "EEE"), betaModels="B")