How to transfer a perpendicular line from each point in the scattering diagram to a (eigenvector) vector?

Question

I am creating a visualization to illustrate how basic component analysis works by plotting eigenvalues ​​for some actual data (for purposes of illustration, I am a subset of two dimensions).

I need a combination of these two graphs from this fantastic PCA training course , only for my real data.

I can build vectors and everything is fine:

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 (good). How can I use geom_segment to remove a perpendicular from each datapoint to, say, the green first main component?

Answer 1

Adapting the 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")