Correlation-based distance can be computed using the as.dist() function, which converts an arbitrary square symmetric matrix into a form that the hclust() function recognizes as a distance matrix. However, this only makes sense for data with at least three features since the absolute correlation between any two observations with measurements on two features is always 1. Hence, we will cluster a three-dimensional data set.

x <- matrix(rnorm(30 * 3), ncol = 3)
dd <- as.dist(1 - cor(t(x)))
plot(hclust(dd, method = "complete"), main = "Complete Linkage with Correlation-Based Distance", xlab = "", sub = "")

Questions

• Calculate the absolute correlation between the data x and store the distance matrix in dd.
• Apply hierarchical clustering using average linkage on the distance matrix and store the result in hc.average.