How does R calculate the PCA ellipses?

Question

How does R know where to place the confidence ellipse for a PCA plot? I have a minimal code using the iris dataset:

library(factoextra)
a<-data.matrix(iris[-5])
b<-prcomp(a, scale. = TRUE, center = TRUE)
fviz_pca_ind(b,
             col.ind = iris$Species,
             addEllipses = TRUE)

I know that I can find the plot coordinate with b$x. I also know that I can find the cluster centers with b$center. How do I re-derive the ellipses from the data?

Answer 1

If you are talking about the how, it eventually calls ggplot2::stat_ellipse.

If you want the coordinates, like with other ggplot objects, you can extract the data with ggplot_build

library(factoextra)
a<-data.matrix(iris[-5])
b<-prcomp(a, scale. = TRUE, center = TRUE)
p <- fviz_pca_ind(b,
             col.ind = iris$Species,
             addEllipses = TRUE)

ell <- ggplot2::ggplot_build(p)$data[[2]]

head(ell)
#    colour    fill         x           y group PANEL size linetype alpha
# 1 #F8766D #F8766D -1.697756 -0.06395559     1     1  0.5        1   0.1
# 2 #F8766D #F8766D -1.701694  0.22197334     1     1  0.5        1   0.1
# 3 #F8766D #F8766D -1.713449  0.50017215     1     1  0.5        1   0.1
# 4 #F8766D #F8766D -1.732842  0.76642364     1     1  0.5        1   0.1
# 5 #F8766D #F8766D -1.759579  1.01669171     1     1  0.5        1   0.1
# 6 #F8766D #F8766D -1.793255  1.24718254     1     1  0.5        1   0.1

p + geom_point(aes(x, y, color = factor(group)), data = ell, size = 4)