Applied Math And Analysis Seminar
Monday, April 18, 2016, 4:30pm, 119 Physics
Braxton Osting (University of Utah)
Dirichlet Graph Partitions
Abstract:
I’ll discuss a geometric approach to graph partitioning where the optimality criterion is given by the sum of the first Laplace-Dirichlet eigenvalues of the partition components. This eigenvalue optimization problem can be solved by a rearrangement algorithm, which we show to converge in a finite number of iterations to a local minimum of a relaxed objective. This partitioning method compares well to state-of-the-art approaches on a variety of graphs constructed from manifold discretizations, synthetic data, the MNIST handwritten digit dataset, and images. I'll present a consistency result for geometric graphs, stating convergence of graph partitions to an appropriate continuum partition. [video]

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