Modern Preconditioned Eigensolvers for Spectral Image Segmentation and Graph Bisection Workshop on Clustering Large Data Sets Third IEEE International Conference on Data Mining (ICDM 2003)

Known spectral methods for graph bipartition and image segmentation require numerical solution of eigenvalue problems with the graph Laplacian. We discuss several modern preconditioned eigenvalue solvers for computing the Fiedler vectors of large scale eigenvalue problems. The ultimate goal is to find a method with a linear complexity, i.e. a method with computational costs that scale linearly with the problem size. A locally optimal block preconditioned conjugate gradient method,be a promising candidate (if matched with a high quality preconditioner), compared against the Lanczos method. This material is based upon work supported by the National Science Foundation and the Intelligence Technology Innovation Center through the joint ”Approaches to Combat Terrorism” Program Solicitation NSF 03-569.