# mvdcoord: Mean/variance differences discriminant coordinates

## Description

Discriminant projections as defined in Young, Marco and Odell (1987).
The principle is to maximize the projection of a matrix consisting of
the differences between the means of all classes and the first mean
and the differences between the covariance matrices of all classes and
the forst covariance matrix.

## Usage

mvdcoord(xd, clvecd, clnum=1, sphere="mcd", ...)

## Arguments

xd

the data matrix; a numerical object which can be coerced
to a matrix.

clvecd

integer vector of class numbers; length must equal
`nrow(xd)`

.

clnum

integer. Number of the class to which all differences are
computed.

sphere

a covariance matrix or one of
"mve", "mcd", "classical", "none". The matrix used for sphering the
data. "mcd" and "mve" are robust covariance matrices as implemented
in `cov.rob`

. "classical" refers to the classical
covariance matrix. "none" means no sphering and use of the raw
data.

## Value

List with the following components

eveigenvalues in descending order.

unitscolumns are coordinates of projection basis vectors.
New points `x`

can be projected onto the projection basis vectors
by `x %*% units`

projprojections of `xd`

onto `units`

.

## References

Young, D. M., Marco, V. R. and Odell, P. L. (1987). Quadratic
discrimination: some results on optimal low-dimensional
representation, *Journal of Statistical Planning and Inference*,
17, 307-319.

## See Also

`plotcluster`

for straight forward discriminant plots.
`discrproj`

for alternatives.
`rFace`

for generation of the example data used below.

## Examples

# NOT RUN {
set.seed(4634)
face <- rFace(300,dMoNo=2,dNoEy=0,p=3)
grface <- as.integer(attr(face,"grouping"))
mcf <- mvdcoord(face,grface)
plot(mcf$proj,col=grface)
# ...done in one step by function plotcluster.
# }