R-square for hierarchical clustering

R.square <- function(x, method="average", k){
  ### R-square for hierarchical clustering given number of cutting groups
  ### x     : original data (col=variables, row=observations)
  ### method: hierarchical clustering linkage method
  ### k     : number of cutting groups

  hc <- hclust(dist(x), method=method)
  group <- as.matrix(cutree(hc,k)) # get the group vectors

  ## sum of squares for all the elements
  ss <- function(x) sum(scale(x, scale = FALSE)^2)

  ## calculate BetweenSS, totalWithinSS, and R-squares
  betweenss <- NULL     # reserve space
  tot.withinss <- NULL
  r.square <- NULL

  for(i in 1:length(k)){
    ## calculate cluster center "fitted" to each obs.:
    fitted.x <- NULL  # reserve space
    for(n in 1:nrow(x)){
      g <- group[n,i]  # get the group for each obs.
      fitted.x <- rbind(fitted.x, colMeans(x[group[,i]==g, , drop = FALSE]))
    }
    resid.x <- x - fitted.x

    betweenss <- rbind(betweenss, ss(fitted.x))
    tot.withinss <- rbind(tot.withinss, ss(resid.x))
    r.square <- rbind(r.square, ss(fitted.x)/ss(x))
  }

  return(data.frame(K.groups = k,
                    betweenss = betweenss, 
                    tot.withinss = tot.withinss,
                    totss = rep(ss(x),length(k)),
                    r.square = r.square))
}

Clustering: Hierarchical Clustering

### Hierarchical Clustering
hc <- hclust(dist(USArrests), method="average", members=NULL)
# Cluster linkage methods:
#  "ward"
#  "single"
#  "complete"
#  "average"
#  "mcquitty"
#  "median"
#  "centroid"
summary(hc)

## plot Cluster Dendrogram
plot(hc, hang=-1, labels=abbreviate(row.names(USArrests),2), cex=0.8) # ?plclust()
rect.hclust(hc, k=5, border="red") # 在圖中框出各群



# Cutting the dendrogram to form k=5 clusters here:
groups <- cutree(hc, k=5) # cut tree into 5 clusters