  Motivated by a geometric problem, we introduce a new non-convex graph
partitioning objective where the optimality criterion is given by the sum of
the Dirichlet eigenvalues of the partition components. A relaxed formulation is
identified and a novel rearrangement algorithm is proposed, which we show is
strictly decreasing and converges in a finite number of iterations to a local
minimum of the relaxed objective function. Our method is applied to several
clustering problems on graphs constructed from synthetic data, MNIST
handwritten digits, and manifold discretizations. The model has a
semi-supervised extension and provides a natural representative for the
clusters as well.
