I am using agglomerative hierarchical clustering to cluster 200 variables based on their Manhattan distances. When calculating the average distance within/average distance between ratio, I was expecting declining values as the number of clusters is increasing, for the reason that (as far as I now) the algorithm tries to optimise these values (well, ok, maybe not exactly this specific ratio but..).
My question is: is it possible that this ratio is not declining while k is increasing (where k is the number of clusters)? Increasing the number of clusters does not always decreasing this ratio? (by reducing the distance within or/and increasing the distance between)?
ps. the method for the distance calculation is the "complete" method from
hclust in R.