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How can we separate distinct regions in an image quickly and accurately? One effective method is Normalized Cuts, a graph-based method which is NP-hard but may be relaxed and then dualized to obtain an approximate solution in O(n^2) operations. The resulting problem (our working example for the talk) is an eigenvalue optimization problem. These problems cover a wide range of optimization territory and have efficient, easily implemented methods for large-scale problems. In this talk, we will discuss the Normalized Cuts model, introduce the basics of eigenvalue optimization, and outline our current research goals (e.g., exploring necessary and sufficient conditions for solvability, generalizing the well-established conic duality theory to fit this nonconvex primal-dual pair).

Register for pita here.