The moduli space of senators and the moduli space of movies

Last week I blogged about Dmitri Tymoczko’s lecture and the moduli space of chords; since then I remembered some more nice examples of “moduli spaces” in the loose sense described in that post. One comes from the work of Keith Poole and Howard Rosenthal, who attempt to answer the question: what is the best way of “mapping” the members of a legislature in two-dimensional space so that two legislators are close together precisely when their voting records are very closely aligned? In other words, what is the moduli space of senators? Go to Poole’s VoteView page and scroll to the bottom to see the last 100 years of the House and Senate as an animated .gif. Or just read what I wrote about their research on Slate. (Article from 2001, so some links may be dead.)

Votes in the Senate make up a complicated dataset, which people like Poole and Rosenthal like to make more accessible by means of two-dimensional charts. An even more complicated dataset is the set of 100,000,000 Netflix ratings of 18,000 movies which the strivers for the Netflix Prize have to wrestle with. But this too can be nicely mapped into two-dimensional space (or any-dimensional space, but two-dimensional pictures are the easiest to look at!) yielding a “moduli space of movies” in which two movies are close together just when they tend to be liked by the same set of users. Todd Holloway, a CS grad student at Indiana,has made some beautiful examples:

Go to his blog to see the interactive version, or his visualization of the power struggle in Wikipedia.