College Football Conferences
There are about 120 Division IA college football teams in the USA. They are divided in groups called conferences. Each year, each teams play teams both within their conferences and outside their conferences. Roughly speaking, they play 7 teams within their conferences and 4 teams outside. Many conferences have more than 8 teams, so teams in the same conference may not play each other in a year.
ProblemYou know which teams played which teams in a particular year (here, 2000 - thanks to Mark Newman for supplying this data). Try to find out which teams are in the same conference.
Laplacian Eigenmaps, by Belkin and Niyogi, 2003.
The first dimension is somehow thrown off by Brigham Young (!), the next three are more interesting, and seem to do quite well. But to really see how well (or badly) it does, download the whole visual and play with it yourself.
This visual was produced in May 2004 and documented in July 2004.