Nonlinear Eigenproblems in Data Analysis - Balanced Graph Cuts and the RatioDCA-Prox

Leonardo Jost, Simon Setzer, Matthias Hein

It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors which encompasses previous work as special cases. We provide a detailed analysis of the properties and the convergence behavior of these algorithms and then discuss their application in the area of balanced graph cuts.

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