Calculate elements for the CVA biplot

This function performs calculations for the construction of a CVA biplot.

# S3 method for biplot
CVA(
  bp,
  classes = bp$classes,
  dim.biplot = c(2, 1, 3),
  e.vects = 1:ncol(bp$X),
  weightedCVA = "weighted",
  show.class.means = TRUE,
  low.dim = "sample.opt"
)

Arguments

bp

an object of class biplot obtained from preceding function biplot().

classes

a vector of the same length as the number of rows in the data matrix with the class indicator for the samples.

dim.biplot

the dimension of the biplot. Only values 1, 2 and 3 are accepted, with default 2.

e.vects

the vector indicating which eigenvectors (canonical variates) should be plotted in the biplot, with default 1:dim.biplot.

weightedCVA

a character string indicating which type of CVA to perform. One of "weighted" (default) for a weighted CVA to be performed (The centring matrix will be a diagonal matrix with the class sizes (\(\mathbf{C} = \mathbf{N}\)), "unweightedCent" for unweighted CVA to be performed (The centring matrix is the usual centring matrix (\(\mathbf{C} = \mathbf{I}_{G} - G^{-1}\mathbf{1}_{G}\mathbf{1}_{G}'\))) or "unweightedI" for unweighted CVA to be performed while retaining the weighted centroid (The centring matrix is an indicator matrix (\(\mathbf{C} = \mathbf{I}_{G}\))).

show.class.means

a logical value indicating whether to plot the class means on the biplot.

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.

Value

an object of class CVA, inherits from class biplot.

Examples

biplot(iris[,1:4]) |> CVA(classes=iris[,5])
#> Object of class biplot, based on 150 samples and 4 variables.
#> 4 numeric variables.
#> 3 classes: setosa versicolor virginica