mclust (version 1.1-7)

me.VEV: EM for constant shape, varying volume MVN mixture models

Description

EM iteration (M-step followed by E-step) for estimating parameters in an MVN mixture model having constant shape, varying volume and possibly one Poisson noise term.

Usage

me.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(.Mach

tol

A 2 vector giving the tolerances for the outer (EM) and inner (volume and shape estimating) iterations. The outer iteration is terminated if the relative error in the loglikelihood value falls below tol[1]. The inner iteration is terminate

itmax

A 2-vector giving an upper limit on the number of outer and inner iterations. Default : c(Inf,Inf) - no upper limit for outer or inner iterations. If only one value is given it is assumed to override only the first default.

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

• the conditional probablilities at the final iteration (information about the iteration is included as attributes).

NOTE

The default for inner iterations are set up so as to compute the true M-step parameters at each iteration. However if you plan to run me.VEV to convergence, then it is usually safe to set the number of inner iterations to 0, 1, or some small number.

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

me, mstep.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)