I have a test data set comprising a list of people and their preferred subjects.

{{"john" -> "physics"}, {"john" -> "chemistry"}, {"jane" -> 
   "physics"}, {"jane" -> "biology"}, {"peter" -> 
   "biology"}, {"peter" -> "chemistry"}, {"peter" -> 
   "mathematics"}, {"david" -> "mathematics"}, {"paul" -> 
   "chemistry"}, {"liz" -> "chemistry"}, {"liz" -> 
   "mathematics"}, {"liz" -> "physics"}}

I would like to process the data such that I can produce a limited number of groups, which contain participants with the 'best' collection of overlapping interests.

There seem to be a number of ways that one might do this, and I have been experimenting with Graph functions, as well as Cluster functions. However, none of them produce quite what I need. For instance FindClusters[testSet] produces

{{"physics", "chemistry"}, {"physics", "biology", "mathematics", 
  "chemistry", "chemistry", "mathematics", "physics"}, {"biology", 
  "chemistry", "mathematics"}}

I need it to a) show the people rather than the subjects, and b) not repeat them, i.e. John can only be in one group.

I am more than happy to reorganize the data if that would make it easier, i.e. have John ->{physics, chemistry}. I am just a bit stuck on how to tackle this problem.

All suggestions gratefully received :-)