我想知道如何计算两个椭圆之间的交集，例如在此图表中所示的versicolor和virginca之间的交集的体积：
该图表是基于这个教程的以下mwe绘制的：
data(iris)
log.ir <- log(iris[, 1:4])
ir.species <- iris[, 5]
ir.pca <- prcomp(log.ir, center = TRUE, scale. = TRUE)
library(ggbiplot)
g <- ggbiplot(ir.pca, obs.scale = 1, var.scale = 1,
groups = ir.species, ellipse = TRUE,
circle = TRUE)
g <- g + scale_color_discrete(name = '')
g <- g + theme(legend.direction = 'horizontal',
legend.position = 'top')
print(g)
我将按照以下方式获取椭圆的协方差和中心点：
我获取椭圆的协方差和中心点如下：
setosa.cov <- cov(ir.pca$x[ir.species=="setosa",])
versicolor.cov <- cov(ir.pca$x[ir.species=="versicolor",])
virginica.cov <- cov(ir.pca$x[ir.species=="virginica",])
setosa.centre <- colMeans(ir.pca$x[ir.species=="setosa",])
versicolor.centre <- colMeans(ir.pca$x[ir.species=="versicolor",])
virginica.centre <- colMeans(ir.pca$x[ir.species=="virginica",])
但是我已经无计可施了 :-|
编辑： 根据下面@carl-witthoft的指示，这里有一个使用siar::overlap的例子：
library(siar)
setosa <- ir.pca$x[ir.species=="setosa",]
versicolor <- ir.pca$x[ir.species=="versicolor",]
virginica <- ir.pca$x[ir.species=="virginica",]
overlap.fun <- function(data.1, data.2){
dimensions <- ncol(data.1)
for(i in 1:(dimensions-1)){
overlap.out <- overlap(data.1[,i], data.1[,i+1], data.2[,i], data.2[,i+1], steps = 5)
out$overlap[i] <- overlap.out$overlap
out$area1[i] <- overlap.out$area1
out$area2[i] <- overlap.out$area2
}
return(out)
}
overlap.fun(versicolor, virginica)
返回值：
$overlap
[1] 0.01587977 0.48477088 0.08375927
$area1
[1]1.020596 1.04614461 0.08758691
$area2
[1] 1.028594 1.1535106 0.1208483
奇怪的是，当我进行百分比计算时，结果并不真正对应于ggbiplot PCA中的椭球体：
tmp <- overlap(versicolor[,1], versicolor[,2], virginica[,1], virginica[,2], steps = 5)
virginica.percentage <- round(x=(tmp$overlap/tmp$area2*100), digits = 2)
versicolor.percentage <- round(x=(tmp$overlap/tmp$area1*100), digits = 2)
> virginica.percentage [1] 1.54
> versicolor.percentage[1] 1.56