EM {leptokurticMixture}

EM for the finite mixtures of MLN

Description

Performs a number of iterations of the EM for the multivariate elliptical leptokurtic-normal (MLN) distribution until the tolerance for the lack progress or the maximum number of iterations is reached. An implementation of parsimonious clustering models via the eigen-decomposition of the scatter matrix and allowing the concentration parameter to be varying, equal or fixed across components.

Usage

EM(
  data = NULL,
  G = 2,
  model = NULL,
  kml = c(1, 0, 1),
  n = 10,
  epsilon = 0.01,
  gpar0 = NULL,
  estimation = 1,
  label = NULL
)

Arguments

data

A n x p matrix of observations.

G

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

model

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. The 4th position controls the concentration, beta; "V" varying across components, "E" equal across components, "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

n

The maximum number of EM iterations.

epsilon

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

gpar0

A list of model parameters .

estimation

If 1 (default) use the fixed point iterations and if 2 the MM algorithm.

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.

Value

A list with following items

• loglik - A vector of the loglikelihood values

• gpar - A list containing the parameters values

• z - A n x G matrix of the posterior probabilities

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

• label - The input provided.

• numpar - The number of free parameters in the fitted model.

• maxLoglik - The largest value from loglik.

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 = EM(data=x, G=2, model="VVVF")