I don't know if I have formulated this problem right:
I have tons of items and the distances between each pair of them. Feeding this data into some visualization tool, I am able to create a nice image of network with arbitrarily defined center of the coordinate. (Since I only have distances, which do not imply any coordinate) I can eye-ball some clusters in the graph.
Now I want to show with high confidence that there exists some valid classification of the items.
Let's not ask from where the number of clusters comes. The worst case is I have to search for it exhaustively within a reasonable interval.
I have the distances in a matrix form, where the (row, column) = (i, j) entry is the distance from point i to point j. Distances are normalized by the largest, therefore they range from 0 to 1.
Is there a good way to extract the clusters out of this?