如何计算ggplot2绘制的椭圆的面积？

Question

在ggplot2中，我用stat_ellipse绘制椭圆图后，有什么方法可以计算这个椭圆的面积吗？这是代码和情节：

library(ggplot2)
set.seed(1234)
x <- rnorm (1:1000)
y <- rnorm (1:1000)
data <- cbind(x, y)
data <- as.data.frame(data)
ggplot (data, aes (x = x, y = y))+
  geom_point()+
  stat_ellipse()

Answer 1

你可以通过求椭圆的半长轴和半短轴来计算椭圆的面积（如this SO answer所示）：

# Plot object
p = ggplot (data, aes (x = x, y = y))+
  geom_point()+
  stat_ellipse(segments=201) # Default is 51. We use a finer grid for more accurate area.

# Get ellipse coordinates from plot
pb = ggplot_build(p)
el = pb$data[[2]][c("x","y")]

# Center of ellipse
ctr = MASS::cov.trob(el)$center  # Per @Roland's comment

# Calculate distance to center from each point on the ellipse
dist2center <- sqrt(rowSums((t(t(el)-ctr))^2))

# Calculate area of ellipse from semi-major and semi-minor axes. 
# These are, respectively, the largest and smallest values of dist2center. 
pi*min(dist2center)*max(dist2center)

[1] 13.82067

Answer 2

通过先计算特征值，可以直接从协方差矩阵计算出面积。

您需要根据您想要获得的置信度来缩放方差/特征值。

This thread is very helpful

set.seed(1234)
dat <- data.frame(x = rnorm(1:1000), y = rnorm(1:1000))

cov_dat <- cov(dat) # covariance matrix

eig_dat <- eigen(cov(dat))$values #eigenvalues of covariance matrix

vec <- sqrt(5.991* eig_dat) # half the length of major and minor axis for the 95% confidence ellipse

pi * vec[1] * vec[2]  
#> [1] 18.38858

^{由 reprex package (v0.3.0)}

于 2020-02-27 创建

在这种特殊情况下，协方差为零，特征值或多或少是变量的方差。因此，您可以仅使用方差进行计算。 - 假设两者都是正态分布的。

set.seed(1234)
data <- data.frame(x = rnorm(1:1000), y = rnorm(1:1000))

pi * 5.991 * sd(data$x) * sd(data$y) # factor for 95% confidence = 5.991
#> [1] 18.41814

^{由 reprex package (v0.3.0)}

于 2020-02-27 创建

计算出的值不同. This is likely due to the different calculation under the hood, with different assumptions on the underlying distribution. see this thread。

如何计算ggplot2绘制的椭圆的面积？

How to calculate the area of ellipse drawn by ggplot2?

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