mclust (version 1.1-7)

mstep.VEV: M-step for constant shape, constant volume MVN mixture models

Description

M-step for estimating parameters given conditional probabilities in an MVN mixture model having constant shape, constant volume and possibly one Poisson noise term.

Usage

mstep.VEV(data, z, eps, tol, itmax, equal = F, noise = F, Vinv)

Arguments

data

matrix of observations.

z

matrix of conditional probabilities. z should have a row for each observation in data, and a column for each component of the mixture.

eps

A 2-vector specifying lower bounds on the pth root of the volume of the ellipsoids defining the clusters, where p is the data dimension, and on the reciprocal condition number for the estimated shape of the covariance estimates. Default: c(.Machi

tol

The iteration for volume/shape estimates is terminated if their relative error is less than tol.

itmax

The iteration for volume/shape estimates is terminated if the number of iterations exceeds itmax. Default: Inf (termination is determined by tol).

equal

Logical variable indicating whether or not to assume equal proportions in the mixture. Default : F.

noise

Logical variable indicating whether or not to include a Poisson noise term in the model. Default : F.

Vinv

An estimate of the inverse hypervolume of the data region (needed only if noise = T). Default : determined by function hypvol

Value

• A list whose components are the parameter estimates corresponding to z:
• mu
  matrix whose columns are the Gaussian group means.
• sigma
  group variance matrix.
• prob
  probabilities (mixing proportions) for each group (present only when equal = T). The loglikelihood and reciprocal condition estimate are returned as attributes.

References

G. Celeux and G. Govaert, Gaussian parsimonious clustering models, Pattern Recognition,28:781-793 (1995).

A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society, Series B,39:1-22 (1977).

G. J. MacLachlan and K. E. Basford, The EM Algorithm and Extensions, Wiley, (1997).

See Also

mstep, me.VEV, estep.XEV

Examples

data(iris)
cl <- mhclass(mhtree(iris[,1:4]),3)
z <- me.VEV( iris[,1:4], ctoz(cl))
mstep.VEV(iris[,1:4], z)