I think this is a very neat idea - using an existing technique with a new distance measure. It seems to get very good results (once I was able to make sense of the organization of the figures - their organizational scheme is still unknown to me). Its application does however seem fairly limited in that the data must lend itself to description by geodesic distances, though that may not really differ much from data that is well suited to dimensionality reduction.

I wonder how well this does in the situation where the data is a set of clusters that may have reasonable distances within them but are widely separated in space.