如何将散点图中每个点的垂线删除到（Eigen）向量？ [英] How to drop a perpendicular line from each point in a scatterplot to an (Eigen)vector?

问题描述

我正在创建一个可视化文件来说明主成分分析是如何工作的，通过为某些实际数据绘制特征值（为了说明的目的，我是子集到2个维度）。

我想要结合这个奇妙的PCA教程，仅限于我的 real 数据。

$

  Person1 <-c（-3,1， 1，-3,0，-1，-1,0，-1，-1,3,4,5，-2,1,2，-2，-1,1，-2,1，-3， 4，-6,1，-3，-4,3,3，-5,0,3,0，-3,1，-2，-1,0，-3,3，-4，-4， -7，-5，-2，-2，-1,1,1,2,0,0,2，-2,4,2,1,2,2,7,0,3,2,5， 2,6,0,4,0，-2，-1,2,0，-1，-2， -4，-1）
 Person2 <-c（-4，-3,4，-5，-1，-1，-2,2,1,0,3,2,3，-4 ，2，-1,2，-1,4，-2,6，-2，-1，-2，-1，-1，-3,5,2，-1,3,3,1， - 3,1,3，-3,2，-2,4，-4，-6，-4，-7,0，-3,1，-2,0,2，-5,2，-2， -1,4,1,1,0,1,5,1,0,1,1,0,2,0,7，-2,3，-1，-2，-3,0,0,0 ，0）
 df < -  data.frame（cbind（Person1，Person2））
g < -  ggplot（data = df，mapping = aes（x = Person1，y = Person2））
g < -  g + geom_point（alpha = 1/3）＃alpha b / c为
g<  -  g + geom_smooth（method =lm）＃仅用于比较
g<  - g + coord_fixed（）＃否则，向量的角度是off 
 corre< -cor（x = df $ Person1，y = df $ Person2，method =spearman）＃计算相关性，必须是spearman b / c of measurement 
 matrix < -  matrix（c（1，corre，corre，1），nrow = 2）＃将其作为矩阵
 eigen < -  eigen（矩阵）＃计算特征向量和值
 eigen $ vectors.scaled < -  eigen $ vectors％*％diag（sqrt（eigen $ values））
＃根据http缩放特征向量到长度=平方根
＃ ：//stats.sta ckexchange.com/questions/9898/how-to-plot-an-ellipse-from-eigenvalues-and-eigenvectors-in-r 
g < -  g + stat_ellipse（type =norm）
g <  -  g + stat_ellipse（type =t）
＃添加椭圆，但我不确定哪些是适当的类型
＃按照https://github.com/hadley/ggplot2/ blob / master / R / stat-ellipse.R 
g <-g + geom_abline（截距= 0，slope = eigen $ vectors.scaled [1,1]，color =green）＃为pc1添加斜率
g < -  g + geom_abline（截距= 0，slope = eigen $ vectors.scaled [1,2]，color =red）＃为pc2添加斜率
g <-g + geom_segment（ aes（x = 0，y = 0，xend = max（df），yend = eigen $ vectors.scaled [1,1] * max（df）），color =green，arrow = arrow（length = unit （x = 0，y = 0，xend = max（df），yend = eigen $ vectors.scaled [1 ，2] * max（df）），color =red，arrow = arrow（length = unit（0.2，cm）））＃为pc1添加箭头
g 
  

到目前为止这么好（好）。
如何知道如何使用 geom_segment 从每个数据点向例如绿色第一个主要组件删除垂线？ 你可以做

 
 
 code> perp.segment.coord < - 函数（x0，y0，a = 0，b = 1）{
＃查找从点（x0，y0）到直线
＃由lm.mod定义为y = a + b * x 
 x1 < - （x0 + b * y0-a * b）/（1 + b ^ 2）
 y1 <  -  a + b * x1 
 list（x0 = x0，y0 = y0，x1 = x1，y1 = y1）
} 
 
 
 ss < perp.segment.coord（df $ Person1，df $ Person2,0，eigen $ vectors.scaled [1,1]）$ ​​b 
 $ bg + geom_segment（data = as.data.frame（ss），aes （x = x0，y = y0，xend = x1，yend = y1），color =blue）
  

I'm creating a visualization to illustrate how Principal Components Analysis works, by plotting Eigenvalues for some actual data (for the purposes of the illustration, I'm subsetting to 2 dimensions).

I'm want a combination of these two plots from this fantastic PCA tutorial, only for my real data.

I can plot the vectors and all ok:

Person1 <- c(-3,1,1,-3,0,-1,-1,0,-1,-1,3,4,5,-2,1,2,-2,-1,1,-2,1,-3,4,-6,1,-3,-4,3,3,-5,0,3,0,-3,1,-2,-1,0,-3,3,-4,-4,-7,-5,-2,-2,-1,1,1,2,0,0,2,-2,4,2,1,2,2,7,0,3,2,5,2,6,0,4,0,-2,-1,2,0,-1,-2,-4,-1)
Person2 <- c(-4,-3,4,-5,-1,-1,-2,2,1,0,3,2,3,-4,2,-1,2,-1,4,-2,6,-2,-1,-2,-1,-1,-3,5,2,-1,3,3,1,-3,1,3,-3,2,-2,4,-4,-6,-4,-7,0,-3,1,-2,0,2,-5,2,-2,-1,4,1,1,0,1,5,1,0,1,1,0,2,0,7,-2,3,-1,-2,-3,0,0,0,0)
df <- data.frame(cbind(Person1, Person2))
g <- ggplot(data = df, mapping = aes(x = Person1, y = Person2))
g <- g + geom_point(alpha = 1/3)  # alpha b/c of overplotting
g <- g + geom_smooth(method = "lm")  # just for comparsion
g <- g + coord_fixed()  # otherwise, the angles of vectors are off
corre <- cor(x = df$Person1, y = df$Person2, method = "spearman")  # calculate correlation, must be spearman b/c of measurement
matrix <- matrix(c(1, corre, corre, 1), nrow = 2)  # make this into a matrix
eigen <- eigen(matrix)  # calculate eigenvectors and values
eigen$vectors.scaled <- eigen$vectors %*% diag(sqrt(eigen$values))  
  # scale eigenvectors to length = square-root
  # as per http://stats.stackexchange.com/questions/9898/how-to-plot-an-ellipse-from-eigenvalues-and-eigenvectors-in-r
g <- g + stat_ellipse(type = "norm")
g <- g + stat_ellipse(type = "t")
  # add ellipse, though I am not sure which is the adequate type
  # as per https://github.com/hadley/ggplot2/blob/master/R/stat-ellipse.R
g <- g + geom_abline(intercept = 0, slope = eigen$vectors.scaled[1,1], colour = "green")  # add slope for pc1
g <- g + geom_abline(intercept = 0, slope = eigen$vectors.scaled[1,2], colour = "red")  # add slope for pc2
g <- g + geom_segment(aes(x = 0, y = 0, xend = max(df), yend = eigen$vectors.scaled[1,1] * max(df)), colour = "green", arrow = arrow(length = unit(0.2, "cm")))  # add arrow for pc1
g <- g + geom_segment(aes(x = 0, y = 0, xend = max(df), yend = eigen$vectors.scaled[1,2] * max(df)), colour = "red", arrow = arrow(length = unit(0.2, "cm")))  # add arrow for pc1
g

So far so good (well). How do I know use geom_segment to drop a perpendicular from every datapoint to, say, the green first principal component?

解决方案

Adapting a previous answer, you can do

perp.segment.coord <- function(x0, y0, a=0,b=1){
 #finds endpoint for a perpendicular segment from the point (x0,y0) to the line
 # defined by lm.mod as y=a+b*x
  x1 <- (x0+b*y0-a*b)/(1+b^2)
  y1 <- a + b*x1
  list(x0=x0, y0=y0, x1=x1, y1=y1)
}


ss<-perp.segment.coord(df$Person1, df$Person2,0,eigen$vectors.scaled[1,1])

g + geom_segment(data=as.data.frame(ss), aes(x = x0, y = y0, xend = x1, yend = y1), colour = "blue")

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