.BG
.FN meVEV
.TL
EM for constant shape, varying volume MVN mixture models
.SH 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.
.CS
meVEV(data, z, eps, tol, itmax, equal = F, noise = F, Vinv)
.PP
.RA
.AG data
matrix of observations.
.AG z
matrix of conditional probabilities. `z' should have a row for each observation
in `data', and a column for each component of the mixture.
.OA
.AG eps
a 2-vector giving lower bounds on reciprocal condition estimates for cholesky
factors of covariances, and on the volume scale factor for covariances.
 Default : `c(sqrt(.Machine$double.eps), .Machine$double.eps)'.
If only one value is given only the first default is overridden.
.AG 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 terminated if the relative error in both the estimate
of the pth root of the volume and the shape estimate falls below `tol[2]'.
Default: `c(sqrt(.Machine$double.eps), sqrt(.Machine$double.eps))'.
If only one value is given it is assumed to override only the first
default.
.AG 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.
.AG equal
Logical variable indicating whether or not to assume equal proportions in the
mixture. Default : `F'.
.AG noise
Logical variable indicating whether or not to include a Poisson noise term in
the model. Default : `F'.
.AG Vinv
An estimate of the inverse hypervolume of the data region (needed only if
`noise = T'). Default : determined by function `hypvol'
.RT
the conditional probablilities at the final iteration (information about the
iteration is included as attributes).
.SH 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.
.SH REFERENCES
G. Celeux and G. Govaert, Gaussian parsimonious clustering models,
\fIPattern Recognition, \fR28:781-793 (1995).

A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood from
Incomplete Data via the EM Algorithm, \fIJournal of the Royal Statistical
Society, Series B, \fR39:1-22 (1977).

C. Fraley and A. E. Raftery, How many clusters? Which clustering method?
Answers via model-based cluster analysis. \fIComputer Journal,
\fR41:578-588 (1998).

C. Fraley and A. E. Raftery, \fIMCLUST:Software for model-based cluster
and discriminant analysis. \fRTechnical Report No. 342, Department of
Statistics, University of Washington (1998).

G. J. MacLachlan and T. Krishnan, The EM Algorithm and Extensions, Wiley,
(1997).
.SA
`me', `mstepVEV', `estepVVV'
.EX
> data <- matrix(aperm(iris, c(1,3,2)), 150, 4)
> cl <- mhclass(mhtree(data, modelid = 4),3)
> meVEV( data, ctoz(cl))

.KW clustering
.WR


