R cut dendrogram into groups with minimum size

Question

Is there an easy way to calculate lowest value of h in cut that produces groupings of a given minimum size?

In this example, if I wanted clusters with at least ten members each, I should go with h = 3.80:

# using iris data simply for reproducible example
data(iris)
d <- data.frame(scale(iris[,1:4]))
hc <- hclust(dist(d))
plot(hc)

cut(as.dendrogram(hc), h=3.79) # produces 5 groups; group 4 has 7 members

cut(as.dendrogram(hc), h=3.80) # produces 4 groups; no group has <10 members

Since the heights of the splits are given in hc$height, I could create a set of candidate values using hc$height + 0.00001 and then loop through cuts at each of them. However, I don't see how to parse the cluster size members out of the dendrogram class. For example, cut(as.dendrogram(hc), h=3.80)$lower[[1]]$members returns NULL, not 66 as desired.

Please note that this is a simpler question than Cutting dendrogram into n trees with minimum cluster size in R which uses the package dynamicTreeCut; here I am not specifying number of trees, just minimum cluster size. TYVM.

Answer 1

Thanks to @Vlo and @lukeA I'm able to implement a loop. However, I am just posting this for a starting point and certainly open to a more elegant solution.

unnest <- function(x) { # from Vlo's answer
  if(is.null(names(x))) x
  else c(list(all=unname(unlist(x))), do.call(c, lapply(x, unnest)))
}

cuts <- hc$height + 1e-9

min_size <- 10
smallest <- 0
i <- 0

while(smallest < min_size & i <= length(cuts)){
  h_i <- cuts[i <- i+1]
  if(i > length(cuts)){
    warning("Couldn't find a cluster big enough.")
  }
  else  smallest <- 
           Reduce(min, 
                  lapply(X = unnest(cut(as.dendrogram(hc), h=h_i)$lower), 
                         FUN = attr, which = "members") ) # from lukeA's comment
}
h_i # returns desired output: [1] 3.79211

Answer 2

This feature is available in the dendextend package with the heights_per_k.dendrogram function (which also has a faster C++ implementation when loading the dendextendRcpp function).

## Not run: 
hc <- hclust(dist(USArrests[1:4,]), "ave")
dend <- as.dendrogram(hc)
heights_per_k.dendrogram(dend)
##       1        2        3        4
##86.47086 68.84745 45.98871 28.36531

As a sidenote, the dendextend package has a cutree.dendrogram S3 method for dendrograms (which works very similarly to cutree for hclust objects).