主成分分析雙標圖與凸多邊形

Question

我已經使用以下代碼生成附雙標圖：

dd = data.frame(x = runif(10), y=runif(10)) 
pcr = prcomp(~x + y, data=dd) 
biplot(pcr) 

這產生表示X和Y與各10個數據點的軸線的雙標圖。可以說10個數據點由2個不同的組（5個在一個組中，5個在另一個組中）組成。我怎樣才能在每個組周圍生成一個帶有最小凸多邊形的雙標圖，以顯示兩組的分割？

Answer 1

我看着統計::: biplot.default和統計::: biplot.prcomp，我接近你想要什麼。您可以修改此代碼以滿足您的需求。 （我使用了虹膜數據集）

require(plyr) 

data(iris) 

pcr <- prcomp(~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data = iris) 

indiv <- data.frame(pcr$x[,1:2]) 

indiv$species <- iris$Species 

column <- data.frame(pcr$rotation[ ,1:2]) 

n <- nrow(indiv) 

eigenval <- pcr$sdev[1:2] 

eigenval <- eigenval * sqrt(n) 

indiv <- transform(indiv, pc1 = PC1/eigenval[1], pc2 = PC2/eigenval[2]) 

column <- transform(column, pc1 = PC1 * eigenval[1], pc2 = PC2 * eigenval[2]) 

### based on stats:::biplot.default 

unsigned.range <- function(x) c(-abs(min(x, na.rm = TRUE)), abs(max(x, na.rm = TRUE))) 

rangx1 <- unsigned.range(indiv[, 4]) 
rangx2 <- unsigned.range(indiv[, 5]) 
rangy1 <- unsigned.range(column[, 3]) 
rangy2 <- unsigned.range(column[, 4]) 

mylim <- range(rangx1, rangx2) 
ratio <- max(rangy1/rangx1, rangy2/rangx2) 

nspecies <- table(iris$Species) 

# compute the convex hull for each species 
hull <- dlply(indiv[,1:3], .(species), chull) 

# get points connected 
hull <- llply(hull, function(x) c(x, x[1])) 


plot(pc2 ~ pc1, data = indiv, cex = 0.5, col = c("blue", "yellow", "green")[iris$Species], xlim = mylim, ylim = mylim) 

lines(indiv$pc1[hull$setosa], indiv$pc2[hull$setosa] , col = "blue") 

lines(indiv$pc1[cumsum(nspecies)[1] + hull$versicolor], indiv$pc2[cumsum(nspecies)[1] + hull$versicolor], col = "yellow") 

lines(indiv$pc1[cumsum(nspecies)[2] + hull$virginica], indiv$pc2[cumsum(nspecies)[2] + hull$virginica], col = "green") 

par(new = TRUE) 

plot(pc1 ~ pc2, data = column, axes = FALSE, type = "n", xlim = mylim * ratio, ylim = mylim * ratio, xlab = "", ylab = "") 

text(column$pc1, column$pc2, labels = rownames(column), cex = 0.5, col = "red") 

arrows(0, 0, column$pc1 * 0.8, column$pc2 * 0.8, col = "red", length = 0.2) 

axis(3, col = "red") 

axis(4, col = "red")