(Probably) Concave Graph Matching

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Haggai Maron, Yaron Lipman


In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of \emph{conditionally concave} and \emph{probably conditionally concave} energies on polytopes and show that they encapsulate many instances of the graph matching problem, including matching Euclidean graphs and graphs on surfaces. We further prove that local minima of probably conditionally concave energies on general matching polytopes (\eg, doubly stochastic) are with high probability extreme points of the matching polytope (\eg, permutations).