# Average distance within/average distance between ratio, in hierarchical clustering

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.

• average distance within/average distance between ratio This is entirely not clear. – ttnphns Oct 30 '15 at 9:11
• It's the average of the distances within each cluster to the average of the distances between two clusters (as defined by complete method from hclust in R). It is a good way to check your clustering results. – Kwnwps Oct 30 '15 at 16:46
• You might be mixing up things... Complete linkage method has nothing to do with averages or ratios. – ttnphns Oct 30 '15 at 18:01
• Please read it again. An average can be an average of distances. Also a ratio can be a ratio of average values. – Kwnwps Oct 30 '15 at 23:30