Construct additional dimensions when the dimension of the canonical space is smaller than the dimension of the biplot

This function is used to add dimensions to the CVA biplot when the dimension of the canonical space \(K\) is smaller than the dimension of the biplot (dim.biplot). This function is already used in the CVA calculations, and will therefore not have to be used in isolation.

Usage

CVAlowdim(bp, G, W, Mmat, low.dim, K, e.vects)

Arguments

bp

an object of class biplot.

G

the indicator matrix defining membership of the classes.

W

the within class sums of squares and cross products matrix.

Mmat

the eigenvector matrix from CVA.

low.dim

a character string indicating which method to use to construct additional dimension(s) if the dimension of the canonical space is smaller than dim.biplot. One of "sample.opt" (default) for maximising the sample predictivity of the individual samples in the biplot or Bhattacharyya.dist which is based on the decomposition of the Bhattacharyya distance into a component for the sample means and a component for the dissimilarity between the sample covariance matrices.

K

the dimension of the canonical space.

e.vects

the vector indicating which canonical variates are plotted in the biplot, with default 1:dim.biplot

Value

A list with three components:

Mr

the first r dimensions of the solution to be plotted.

Mrr

the matrix used for prediction from the canonical space.

Lmat

the matrix for transformation to the canonical space.