mvdcoord {fpc}

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.

...

no effect

Value

List with the following components

ev

eigenvalues in descending order.

units

columns are coordinates of projection basis vectors. New points x can be projected onto the projection basis vectors by x %*% units

proj

projections of xd onto units.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

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

  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.