Total variation, Cheeger ratio cuts, and graph clustering

I will discuss a continuous relaxation of the Cheeger cut problem on a weighted graph, and show how the relaxation is actually equivalent to the original problem.  Then I will introduce an algorithm which experimentally is very efficient at approximating the solution to this problem on some clustering benchmarks.  I will also give a heuristic variant of the algorithm which is faster but often gives just as accurate clustering results.  This is joint work with Xavier Bresson, inspired by recent papers of Buhler and Hein, and Goldstein and Osher, and by an older paper of Strang.

http://www.math.yale.edu/~tl292/seminar/appliedanalysis