In case you haven't come across it already, here is a very exhaustive list of distance measures for dealing with problems of this kind - http://www.iiisci.org/journal/CV$/sci/pdfs/GS315JG.pdf

I fooled around a bit with lastfm data for band recommendation and found this sheet quite helpful.

If you are interested in learning more about asymmetrical similarity, here is a great primer by Tversky - http://www.cogsci.ucsd.edu/~coulson/203/tversky-features.pdf