My question is triggered by a question that was asked on stackoverflow: https://stackoverflow.com/questions/12198115/using-different-metric-for-hclust-linkage.
The thing is this:
I can formulate an algorithm for hierarchical clustering with some kind of distance between original objects, and I'll also need a distance between objects and clusters of objects (linkage).
Let's say the linkage attaches a "handle" to the cluster which is a (hypothetic) object that can be used with the distance function to calculate the distance from another object (or cluster, if it has such a "handle").
For consistency, I'd use the same distance function for the initial calculation of distance between single objects and later for distance between objects or "cluster handles".
So far, so good.
What I'm wondering about is: what happens if the cluster algorithm is fed with a distance matrix instead of the data matrix (as it is e.g. the case with R's
- How do I know which distance function on the distance matrix agrees with what distance function on the data matrix? Examples?
- The more basic maths/statistics question underlying this is: please explain to me (chemist, no mathematician/statistician) what the meaning of e.g. Euclidean distance between rows of a distance matrix is?