mstep.VEV(mclust)R Documentation

M-step for constant shape, constant volume MVN mixture models

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(.Machine$double.eps, .Machine$double.eps)
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.

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.

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)


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