I want to experiment with different clustering methods and parameters. Especially, with different distance functions (euclid, cityblock, ...). But how can I compare the use of different distance functions by measures like the silhouette coefficient? I have to apply a distance function again, to calculate this coefficient. It seems non-consistent to me, to use distance function A to cluster and distance function B to evaluate. But on the other hand, I am not sure if it makes any sense to compare coefficients that are based on different distance functions as I noticed that for example the cityblock-silhouette coefficient tends to be lower then the euclid-silhouette coefficient.
I think I should use the same distance function when evaluating the cluster results. Maybe a complete new one that I didn't use for the clustering method itself?
How can I overcome these problems? Have you any ideas and advices?