The argument “boundaries” of the function “clover_plot” determines whether the boundary curves should be plotted in appropriate quadrants. The default value is TRUE. The violet curve in quadrant IV determines the set of attainable values of the Mahalanobis depths, see Proposition 1 in the paper. The violet curve in quadrant II (bagdistances) is its symmetric image, useful for detecting possible deviations from the ellipticity of the underlying distributions.
For a visual assessment of the assumption of elliptical symmetry of the two distributions, it is also possible to draw an approximate boundary curve for the illuminations (quadrant III, orange curve). Due to higher computational demands this curve is not computed and plotted by default. Instead one has to call the function “clover_calc” with “boundaryI=TRUE” (defaults to FALSE). Then the orange curve is plotted together with the violet ones by the “clover_plot” function, as shown in the example below.
First we generate data from bivariate normal distributions with different means and the same variance matrices and compute the necessary quantities, also computing the orange boundary curve:
library(mvtnorm)
n1 <- 100
n2 <- 75
set.seed(2020)
X <- rmvnorm(n1, mean=c(0,0), sigma=diag(2)) # Observations of class 1
Y <- rmvnorm(n2, mean=c(2,2), sigma=diag(2)) # Observations of class 2
res <- clover_calc(X, Y, boundaryI=TRUE)The clover plot with boundary curves in quadrants II, III and IV:
clover_plot(res)## Misclassification rate of the QDA classifier: 0.0857
## Non-classification rate of the QDA classifier: 0
##
## Misclassification rate of the DD1 classifier: 0.0914
## Non-classification rate of the DD1 classifier: 0.0686The clover plot without the boundary curves:
clover_plot(res, boundaries=FALSE)## Misclassification rate of the QDA classifier: 0.0857
## Non-classification rate of the QDA classifier: 0
##
## Misclassification rate of the DD1 classifier: 0.0914
## Non-classification rate of the DD1 classifier: 0.0686