I'd like to evaluate my clustering results using only internal indices. For example Silhouette index (S) validates the clustering performance based on the pairwise difference of between- and within-cluster distances. I can't use this metrics on similarity matrix. Another example is Davies–Bouldin index (DB): For each cluster C, the similarities between C and all other clusters are computed, and the highest value is assigned to C as cluster similarity. And I think I can use this metrics. How I can uniforme my data for evaluate all the famous metrics? Like Silhouette, dunn index and so on.
You can adapt the definition of Silhouette for similarity functions.
You can also transform your similarity into a dissimilarity; and since most internal measures do not require the triangle inequality, this should work just fine.
But: every auch "Index" ist just yet another heuristic, and a clustering algorithm (just one where we don't have a fast algorithm). So don't rely on them too much. You just get the same problem again: what is the best index?