Wie wird eine senkrechte Linie von jedem Punkt in einem Streudiagramm auf einen (Eigen) Vektor gelegt?

Question

Ich erstelle eine Visualisierung zu illustriere, wie Principal Components-Analyse funktioniert, indem Eigenwerte für einige tatsächlichen Daten (für die Zwecke der Illustration, ich bin subsetting zu 2 Dimensionen).

Ich möchte eine Kombination dieser beiden Plots von this fantastic PCA tutorial, nur für meine echte Daten.

ich die Vektoren und alle ok plotten können:

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 weit, so gut (gut). Wie kann ich verwenden geom_segment, um eine Senkrechte von jedem Datenpunkt auf, sagen wir, die grüne erste Hauptkomponente fallen lassen?

Answer 1

Anpassung einer previous answer, können Sie

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")