How does R calculate the PCA ellipses?-CodePudding

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?

CodePudding user response：

If you are talking about the how,

CodePudding user response：

If you trace the code all the way through, you find that the ellipses are simply geom_polygons created with stat = "ellipse", i.e. they are calculated by stat_ellipse in ggplot.

We can show this by recreating the plot using only base R and ggplot. The following is a fully reproducible example:

library(ggplot2)

b <- prcomp(iris[-5], scale. = TRUE, center = TRUE)
df <- as.data.frame(predict(b)[,1:2])
df$Species <- iris$Species


ggplot(df, aes(PC1, PC2, color = Species))   
  geom_point()  
  theme_bw()  
  geom_polygon(stat = "ellipse", aes(fill = Species), alpha = 0.3)

Ultimately, stat_ellipse gets its data from the same method as cars::dataEllipse, so if you want the raw co-ordinates of the ellipses, you can do:

e <- car::dataEllipse(df$PC1, df$PC2, df$Species)

and obtain the 95th centile normal data ellipse co-ordinates like this:

e$setosa$`0.95`
#>               x           y
#>  [1,] -2.167825  2.06328716
#>  [2,] -2.104642  2.04546589
#>  [3,] -2.043166  1.99227221
#>  [4,] -1.984331  1.90451250
#>  [5,] -1.929028  1.78351710
#>  [6,] -1.878095  1.63112017
#>  [7,] -1.832305  1.44963190
#>  [8,] -1.792351  1.24180347
#>  [9,] -1.758839  1.01078534
#> [10,] -1.732278  0.76007952
#> [11,] -1.713069  0.49348644
#> [12,] -1.701504  0.21504739
#> [13,] -1.697759 -0.07101678
#> [14,] -1.701889 -0.36036963
#> [15,] -1.713833 -0.64862486
#> [16,] -1.733410 -0.93141283
#> [17,] -1.760322 -1.20444675
#> [18,] -1.794162 -1.46358770
#> [19,] -1.834417 -1.70490738
#> [20,] -1.880476 -1.92474763
#> [21,] -1.931641 -2.11977588
#> [22,] -1.987137 -2.28703571
#> [23,] -2.046123 -2.42399164
#> [24,] -2.107703 -2.52856754
#> [25,] -2.170946 -2.59917816
#> [26,] -2.234892 -2.63475311
#> [27,] -2.298571 -2.63475311
#> [28,] -2.361018 -2.59917816
#> [29,] -2.421288 -2.52856754
#> [30,] -2.478465 -2.42399164
#> [31,] -2.531684 -2.28703571
#> [32,] -2.580138 -2.11977588
#> [33,] -2.623091 -1.92474763
#> [34,] -2.659894 -1.70490738
#> [35,] -2.689988 -1.46358770
#> [36,] -2.712917 -1.20444675
#> [37,] -2.728333 -0.93141283
#> [38,] -2.736002 -0.64862486
#> [39,] -2.735809 -0.36036963
#> [40,] -2.727757 -0.07101678
#> [41,] -2.711966  0.21504739
#> [42,] -2.688678  0.49348644
#> [43,] -2.658244  0.76007952
#> [44,] -2.621126  1.01078534
#> [45,] -2.577888  1.24180347
#> [46,] -2.529183  1.44963190
#> [47,] -2.475751  1.63112017
#> [48,] -2.418401  1.78351710
#> [49,] -2.358004  1.90451250
#> [50,] -2.295473  1.99227221
#> [51,] -2.231758  2.04546589
#> [52,] -2.167825  2.06328716

^{Created on 2021-11-05 by the reprex package (v2.0.0)}